Struct Matrix

#[repr(C)]
pub struct Matrix<T, R, C, S> {
    pub data: S,
    /* private fields */
}

The most generic column-major matrix (and vector) type.

Methods summary

Because Matrix is the most generic types used as a common representation of all matrices and vectors of nalgebra this documentation page contains every single matrix/vector-related method. In order to make browsing this page simpler, the next subsections contain direct links to groups of methods related to a specific topic.

Vector and matrix construction

• Constructors of statically-sized vectors or statically-sized matrices (Vector3, Matrix3x6…)
• Constructors of fully dynamic matrices (DMatrix)
• Constructors of dynamic vectors and matrices with a dynamic number of rows (DVector, MatrixXx3…)
• Constructors of matrices with a dynamic number of columns (Matrix2xX…)
• Generic constructors (For code generic wrt. the vectors or matrices dimensions.)

Computer graphics utilities for transformations

• 2D transformations as a Matrix3 new_rotation…
• 3D transformations as a Matrix4 new_rotation, new_perspective, look_at_rh…
• Translation and scaling in any dimension new_scaling, new_translation…
• Append/prepend translation and scaling append_scaling, prepend_translation_mut…
• Transformation of vectors and points transform_vector, transform_point…

Common math operations

• Componentwise operations component_mul, component_div, inf…
• Special multiplications tr_mul, ad_mul, kronecker…
• Dot/scalar product dot, dotc, tr_dot…
• Cross product cross, perp…
• Magnitude and norms norm, normalize, metric_distance…
• In-place normalization normalize_mut, try_normalize_mut…
• Interpolation lerp, slerp…
• BLAS functions gemv, gemm, syger…
• Swizzling xx, yxz…
• Triangular matrix extraction upper_triangle, lower_triangle

Statistics

• Common operations row_sum, column_mean, variance…
• Find the min and max components min, max, amin, amax, camin, cmax…
• Find the min and max components (vector-specific methods) argmin, argmax, icamin, icamax…

Iteration, map, and fold

• Iteration on components, rows, and columns iter, column_iter…
• Parallel iterators using rayon par_column_iter, par_column_iter_mut…
• Elementwise mapping and folding map, fold, zip_map…
• Folding or columns and rows compress_rows, compress_columns…

Vector and matrix views

• Creating matrix views from &[T] from_slice, from_slice_with_strides…
• Creating mutable matrix views from &mut [T] from_slice_mut, from_slice_with_strides_mut…
• Views based on index and length row, columns, view…
• Mutable views based on index and length row_mut, columns_mut, view_mut…
• Views based on ranges rows_range, columns_range…
• Mutable views based on ranges rows_range_mut, columns_range_mut…

In-place modification of a single matrix or vector

• In-place filling fill, fill_diagonal, fill_with_identity…
• In-place swapping swap, swap_columns…
• Set rows, columns, and diagonal set_column, set_diagonal…

Vector and matrix size modification

• Rows and columns insertion insert_row, insert_column…
• Rows and columns removal remove_row, remove column…
• Rows and columns extraction select_rows, select_columns…
• Resizing and reshaping resize, reshape_generic…
• In-place resizing resize_mut, resize_vertically_mut…

Matrix decomposition

• Rectangular matrix decomposition qr, lu, svd…
• Square matrix decomposition cholesky, symmetric_eigen…

Vector basis computation

• Basis and orthogonalization orthonormal_subspace_basis, orthonormalize…

Type parameters

The generic Matrix type has four type parameters:

• T: for the matrix components scalar type.
• R: for the matrix number of rows.
• C: for the matrix number of columns.
• S: for the matrix data storage, i.e., the buffer that actually contains the matrix components.

The matrix dimensions parameters R and C can either be:

• type-level unsigned integer constants (e.g. U1, U124) from the nalgebra:: root module. All numbers from 0 to 127 are defined that way.
• type-level unsigned integer constants (e.g. U1024, U10000) from the typenum:: crate. Using those, you will not get error messages as nice as for numbers smaller than 128 defined on the nalgebra:: module.
• the special value Dyn from the nalgebra:: root module. This indicates that the specified dimension is not known at compile-time. Note that this will generally imply that the matrix data storage S performs a dynamic allocation and contains extra metadata for the matrix shape.

Note that mixing Dyn with type-level unsigned integers is allowed. Actually, a dynamically-sized column vector should be represented as a Matrix<T, Dyn, U1, S> (given some concrete types for T and a compatible data storage type S).

Fields

data: S

The data storage that contains all the matrix components. Disappointed?

Well, if you came here to see how you can access the matrix components, you may be in luck: you can access the individual components of all vectors with compile-time dimensions <= 6 using field notation like this: vec.x, vec.y, vec.z, vec.w, vec.a, vec.b. Reference and assignation work too:

let mut vec = Vector3::new(1.0, 2.0, 3.0);
vec.x = 10.0;
vec.y += 30.0;
assert_eq!(vec.x, 10.0);
assert_eq!(vec.y + 100.0, 132.0);

Similarly, for matrices with compile-time dimensions <= 6, you can use field notation like this: mat.m11, mat.m42, etc. The first digit identifies the row to address and the second digit identifies the column to address. So mat.m13 identifies the component at the first row and third column (note that the count of rows and columns start at 1 instead of 0 here. This is so we match the mathematical notation).

For all matrices and vectors, independently from their size, individual components can be accessed and modified using indexing: vec[20], mat[(20, 19)]. Here the indexing starts at 0 as you would expect.

Implementations

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

where T: Scalar + Zero + ClosedAddAssign + ClosedMulAssign,

Dot/scalar product

pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> T

where SB: RawStorage<T, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

The dot product between two vectors or matrices (seen as vectors).

This is equal to self.transpose() * rhs. For the sesquilinear complex dot product, use self.dotc(rhs).

Note that this is not the matrix multiplication as in, e.g., numpy. For matrix multiplication, use one of: .gemm, .mul_to, .mul, the * operator.

Example

let vec1 = Vector3::new(1.0, 2.0, 3.0);
let vec2 = Vector3::new(0.1, 0.2, 0.3);
assert_eq!(vec1.dot(&vec2), 1.4);

let mat1 = Matrix2x3::new(1.0, 2.0, 3.0,
                          4.0, 5.0, 6.0);
let mat2 = Matrix2x3::new(0.1, 0.2, 0.3,
                          0.4, 0.5, 0.6);
assert_eq!(mat1.dot(&mat2), 9.1);

pub fn dotc<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> T

where T: SimdComplexField, SB: RawStorage<T, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

The conjugate-linear dot product between two vectors or matrices (seen as vectors).

This is equal to self.adjoint() * rhs. For real vectors, this is identical to self.dot(&rhs). Note that this is not the matrix multiplication as in, e.g., numpy. For matrix multiplication, use one of: .gemm, .mul_to, .mul, the * operator.

Example

let vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
let vec2 = Vector2::new(Complex::new(0.4, 0.3), Complex::new(0.2, 0.1));
assert_eq!(vec1.dotc(&vec2), Complex::new(2.0, -1.0));

// Note that for complex vectors, we generally have:
// vec1.dotc(&vec2) != vec2.dot(&vec2)
assert_ne!(vec1.dotc(&vec2), vec1.dot(&vec2));

pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> T

where SB: RawStorage<T, R2, C2>, ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>,

The dot product between the transpose of self and rhs.

Example

let vec1 = Vector3::new(1.0, 2.0, 3.0);
let vec2 = RowVector3::new(0.1, 0.2, 0.3);
assert_eq!(vec1.tr_dot(&vec2), 1.4);

let mat1 = Matrix2x3::new(1.0, 2.0, 3.0,
                          4.0, 5.0, 6.0);
let mat2 = Matrix3x2::new(0.1, 0.4,
                          0.2, 0.5,
                          0.3, 0.6);
assert_eq!(mat1.tr_dot(&mat2), 9.1);

impl<T, D: Dim, S> Matrix<T, D, Const<1>, S>

where T: Scalar + Zero + ClosedAddAssign + ClosedMulAssign, S: StorageMut<T, D>,

BLAS functions

pub fn axcpy<D2: Dim, SB>(&mut self, a: T, x: &Vector<T, D2, SB>, c: T, b: T)

where SB: Storage<T, D2>, ShapeConstraint: DimEq<D, D2>,

Computes self = a * x * c + b * self.

If b is zero, self is never read from.

Example

let mut vec1 = Vector3::new(1.0, 2.0, 3.0);
let vec2 = Vector3::new(0.1, 0.2, 0.3);
vec1.axcpy(5.0, &vec2, 2.0, 5.0);
assert_eq!(vec1, Vector3::new(6.0, 12.0, 18.0));

pub fn axpy<D2: Dim, SB>(&mut self, a: T, x: &Vector<T, D2, SB>, b: T)

where T: One, SB: Storage<T, D2>, ShapeConstraint: DimEq<D, D2>,

Computes self = a * x + b * self.

If b is zero, self is never read from.

Example

let mut vec1 = Vector3::new(1.0, 2.0, 3.0);
let vec2 = Vector3::new(0.1, 0.2, 0.3);
vec1.axpy(10.0, &vec2, 5.0);
assert_eq!(vec1, Vector3::new(6.0, 12.0, 18.0));

pub fn gemv<R2: Dim, C2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, x: &Vector<T, D3, SC>, beta: T, )

where T: One, SB: Storage<T, R2, C2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<D, R2> + AreMultipliable<R2, C2, D3, U1>,

Computes self = alpha * a * x + beta * self, where a is a matrix, x a vector, and alpha, beta two scalars.

If beta is zero, self is never read.

Example

let mut vec1 = Vector2::new(1.0, 2.0);
let vec2 = Vector2::new(0.1, 0.2);
let mat = Matrix2::new(1.0, 2.0,
                       3.0, 4.0);
vec1.gemv(10.0, &mat, &vec2, 5.0);
assert_eq!(vec1, Vector2::new(10.0, 21.0));

pub fn sygemv<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, a: &SquareMatrix<T, D2, SB>, x: &Vector<T, D3, SC>, beta: T, )

where T: One, SB: Storage<T, D2, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,

Computes self = alpha * a * x + beta * self, where a is a symmetric matrix, x a vector, and alpha, beta two scalars.

For hermitian matrices, use .hegemv instead. If beta is zero, self is never read. If self is read, only its lower-triangular part (including the diagonal) is actually read.

Examples

let mat = Matrix2::new(1.0, 2.0,
                       2.0, 4.0);
let mut vec1 = Vector2::new(1.0, 2.0);
let vec2 = Vector2::new(0.1, 0.2);
vec1.sygemv(10.0, &mat, &vec2, 5.0);
assert_eq!(vec1, Vector2::new(10.0, 20.0));


// The matrix upper-triangular elements can be garbage because it is never
// read by this method. Therefore, it is not necessary for the caller to
// fill the matrix struct upper-triangle.
let mat = Matrix2::new(1.0, 9999999.9999999,
                       2.0, 4.0);
let mut vec1 = Vector2::new(1.0, 2.0);
vec1.sygemv(10.0, &mat, &vec2, 5.0);
assert_eq!(vec1, Vector2::new(10.0, 20.0));

pub fn hegemv<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, a: &SquareMatrix<T, D2, SB>, x: &Vector<T, D3, SC>, beta: T, )

where T: SimdComplexField, SB: Storage<T, D2, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,

Computes self = alpha * a * x + beta * self, where a is an hermitian matrix, x a vector, and alpha, beta two scalars.

If beta is zero, self is never read. If self is read, only its lower-triangular part (including the diagonal) is actually read.

Examples

let mat = Matrix2::new(Complex::new(1.0, 0.0), Complex::new(2.0, -0.1),
                       Complex::new(2.0, 1.0), Complex::new(4.0, 0.0));
let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
vec1.sygemv(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
assert_eq!(vec1, Vector2::new(Complex::new(-48.0, 44.0), Complex::new(-75.0, 110.0)));


// The matrix upper-triangular elements can be garbage because it is never
// read by this method. Therefore, it is not necessary for the caller to
// fill the matrix struct upper-triangle.

let mat = Matrix2::new(Complex::new(1.0, 0.0), Complex::new(99999999.9, 999999999.9),
                       Complex::new(2.0, 1.0), Complex::new(4.0, 0.0));
let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
vec1.sygemv(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
assert_eq!(vec1, Vector2::new(Complex::new(-48.0, 44.0), Complex::new(-75.0, 110.0)));

pub fn gemv_tr<R2: Dim, C2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, x: &Vector<T, D3, SC>, beta: T, )

where T: One, SB: Storage<T, R2, C2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,

Computes self = alpha * a.transpose() * x + beta * self, where a is a matrix, x a vector, and alpha, beta two scalars.

If beta is zero, self is never read.

Example

let mat = Matrix2::new(1.0, 3.0,
                       2.0, 4.0);
let mut vec1 = Vector2::new(1.0, 2.0);
let vec2 = Vector2::new(0.1, 0.2);
let expected = mat.transpose() * vec2 * 10.0 + vec1 * 5.0;

vec1.gemv_tr(10.0, &mat, &vec2, 5.0);
assert_eq!(vec1, expected);

pub fn gemv_ad<R2: Dim, C2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, x: &Vector<T, D3, SC>, beta: T, )

where T: SimdComplexField, SB: Storage<T, R2, C2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,

Computes self = alpha * a.adjoint() * x + beta * self, where a is a matrix, x a vector, and alpha, beta two scalars.

For real matrices, this is the same as .gemv_tr. If beta is zero, self is never read.

Example

let mat = Matrix2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0),
                       Complex::new(5.0, 6.0), Complex::new(7.0, 8.0));
let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
let expected = mat.adjoint() * vec2 * Complex::new(10.0, 20.0) + vec1 * Complex::new(5.0, 15.0);

vec1.gemv_ad(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
assert_eq!(vec1, expected);

impl<T, R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>> Matrix<T, R1, C1, S>

where T: Scalar + Zero + ClosedAddAssign + ClosedMulAssign,

pub fn ger<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, x: &Vector<T, D2, SB>, y: &Vector<T, D3, SC>, beta: T, )

where T: One, SB: Storage<T, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,

Computes self = alpha * x * y.transpose() + beta * self.

If beta is zero, self is never read.

Example

let mut mat = Matrix2x3::repeat(4.0);
let vec1 = Vector2::new(1.0, 2.0);
let vec2 = Vector3::new(0.1, 0.2, 0.3);
let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;

mat.ger(10.0, &vec1, &vec2, 5.0);
assert_eq!(mat, expected);

pub fn gerc<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, x: &Vector<T, D2, SB>, y: &Vector<T, D3, SC>, beta: T, )

where T: SimdComplexField, SB: Storage<T, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,

Computes self = alpha * x * y.adjoint() + beta * self.

If beta is zero, self is never read.

Example

let mut mat = Matrix2x3::repeat(Complex::new(4.0, 5.0));
let vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
let vec2 = Vector3::new(Complex::new(0.6, 0.5), Complex::new(0.4, 0.5), Complex::new(0.2, 0.1));
let expected = vec1 * vec2.adjoint() * Complex::new(10.0, 20.0) + mat * Complex::new(5.0, 15.0);

mat.gerc(Complex::new(10.0, 20.0), &vec1, &vec2, Complex::new(5.0, 15.0));
assert_eq!(mat, expected);

pub fn gemm<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T, )

where T: One, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C3> + AreMultipliable<R2, C2, R3, C3>,

Computes self = alpha * a * b + beta * self, where a, b, self are matrices. alpha and beta are scalar.

If beta is zero, self is never read.

Example

let mut mat1 = Matrix2x4::identity();
let mat2 = Matrix2x3::new(1.0, 2.0, 3.0,
                          4.0, 5.0, 6.0);
let mat3 = Matrix3x4::new(0.1, 0.2, 0.3, 0.4,
                          0.5, 0.6, 0.7, 0.8,
                          0.9, 1.0, 1.1, 1.2);
let expected = mat2 * mat3 * 10.0 + mat1 * 5.0;

mat1.gemm(10.0, &mat2, &mat3, 5.0);
assert_relative_eq!(mat1, expected);

pub fn gemm_tr<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T, )

where T: One, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, C2> + SameNumberOfColumns<C1, C3> + AreMultipliable<C2, R2, R3, C3>,

Computes self = alpha * a.transpose() * b + beta * self, where a, b, self are matrices. alpha and beta are scalar.

If beta is zero, self is never read.

Example

let mut mat1 = Matrix2x4::identity();
let mat2 = Matrix3x2::new(1.0, 4.0,
                          2.0, 5.0,
                          3.0, 6.0);
let mat3 = Matrix3x4::new(0.1, 0.2, 0.3, 0.4,
                          0.5, 0.6, 0.7, 0.8,
                          0.9, 1.0, 1.1, 1.2);
let expected = mat2.transpose() * mat3 * 10.0 + mat1 * 5.0;

mat1.gemm_tr(10.0, &mat2, &mat3, 5.0);
assert_eq!(mat1, expected);

pub fn gemm_ad<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T, )

where T: SimdComplexField, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, C2> + SameNumberOfColumns<C1, C3> + AreMultipliable<C2, R2, R3, C3>,

Computes self = alpha * a.adjoint() * b + beta * self, where a, b, self are matrices. alpha and beta are scalar.

If beta is zero, self is never read.

Example

let mut mat1 = Matrix2x4::identity();
let mat2 = Matrix3x2::new(Complex::new(1.0, 4.0), Complex::new(7.0, 8.0),
                          Complex::new(2.0, 5.0), Complex::new(9.0, 10.0),
                          Complex::new(3.0, 6.0), Complex::new(11.0, 12.0));
let mat3 = Matrix3x4::new(Complex::new(0.1, 1.3), Complex::new(0.2, 1.4), Complex::new(0.3, 1.5), Complex::new(0.4, 1.6),
                          Complex::new(0.5, 1.7), Complex::new(0.6, 1.8), Complex::new(0.7, 1.9), Complex::new(0.8, 2.0),
                          Complex::new(0.9, 2.1), Complex::new(1.0, 2.2), Complex::new(1.1, 2.3), Complex::new(1.2, 2.4));
let expected = mat2.adjoint() * mat3 * Complex::new(10.0, 20.0) + mat1 * Complex::new(5.0, 15.0);

mat1.gemm_ad(Complex::new(10.0, 20.0), &mat2, &mat3, Complex::new(5.0, 15.0));
assert_eq!(mat1, expected);

impl<T, R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>> Matrix<T, R1, C1, S>

where T: Scalar + Zero + ClosedAddAssign + ClosedMulAssign,

pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, x: &Vector<T, D2, SB>, y: &Vector<T, D3, SC>, beta: T, )

where T: One, SB: Storage<T, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,

👎Deprecated: This is renamed syger to match the original BLAS terminology.

Computes self = alpha * x * y.transpose() + beta * self, where self is a symmetric matrix.

If beta is zero, self is never read. The result is symmetric. Only the lower-triangular (including the diagonal) part of self is read/written.

Example

let mut mat = Matrix2::identity();
let vec1 = Vector2::new(1.0, 2.0);
let vec2 = Vector2::new(0.1, 0.2);
let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
mat.m12 = 99999.99999; // This component is on the upper-triangular part and will not be read/written.

mat.ger_symm(10.0, &vec1, &vec2, 5.0);
assert_eq!(mat.lower_triangle(), expected.lower_triangle());
assert_eq!(mat.m12, 99999.99999); // This was untouched.

pub fn syger<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, x: &Vector<T, D2, SB>, y: &Vector<T, D3, SC>, beta: T, )

where T: One, SB: Storage<T, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,

Computes self = alpha * x * y.transpose() + beta * self, where self is a symmetric matrix.

For hermitian complex matrices, use .hegerc instead. If beta is zero, self is never read. The result is symmetric. Only the lower-triangular (including the diagonal) part of self is read/written.

Example

let mut mat = Matrix2::identity();
let vec1 = Vector2::new(1.0, 2.0);
let vec2 = Vector2::new(0.1, 0.2);
let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
mat.m12 = 99999.99999; // This component is on the upper-triangular part and will not be read/written.

mat.syger(10.0, &vec1, &vec2, 5.0);
assert_eq!(mat.lower_triangle(), expected.lower_triangle());
assert_eq!(mat.m12, 99999.99999); // This was untouched.

pub fn hegerc<D2: Dim, D3: Dim, SB, SC>( &mut self, alpha: T, x: &Vector<T, D2, SB>, y: &Vector<T, D3, SC>, beta: T, )

where T: SimdComplexField, SB: Storage<T, D2>, SC: Storage<T, D3>, ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,

Computes self = alpha * x * y.adjoint() + beta * self, where self is an hermitian matrix.

If beta is zero, self is never read. The result is symmetric. Only the lower-triangular (including the diagonal) part of self is read/written.

Example

let mut mat = Matrix2::identity();
let vec1 = Vector2::new(Complex::new(1.0, 3.0), Complex::new(2.0, 4.0));
let vec2 = Vector2::new(Complex::new(0.2, 0.4), Complex::new(0.1, 0.3));
let expected = vec1 * vec2.adjoint() * Complex::new(10.0, 20.0) + mat * Complex::new(5.0, 15.0);
mat.m12 = Complex::new(99999.99999, 88888.88888); // This component is on the upper-triangular part and will not be read/written.

mat.hegerc(Complex::new(10.0, 20.0), &vec1, &vec2, Complex::new(5.0, 15.0));
assert_eq!(mat.lower_triangle(), expected.lower_triangle());
assert_eq!(mat.m12, Complex::new(99999.99999, 88888.88888)); // This was untouched.

impl<T, D1: Dim, S: StorageMut<T, D1, D1>> Matrix<T, D1, D1, S>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign,

pub fn quadform_tr_with_workspace<D2, S2, R3, C3, S3, D4, S4>( &mut self, work: &mut Vector<T, D2, S2>, alpha: T, lhs: &Matrix<T, R3, C3, S3>, mid: &SquareMatrix<T, D4, S4>, beta: T, )

where D2: Dim, R3: Dim, C3: Dim, D4: Dim, S2: StorageMut<T, D2>, S3: Storage<T, R3, C3>, S4: Storage<T, D4, D4>, ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,

Computes the quadratic form self = alpha * lhs * mid * lhs.transpose() + beta * self.

This uses the provided workspace work to avoid allocations for intermediate results.

Example

// Note that all those would also work with statically-sized matrices.
// We use DMatrix/DVector since that's the only case where pre-allocating the
// workspace is actually useful (assuming the same workspace is re-used for
// several computations) because it avoids repeated dynamic allocations.
let mut mat = DMatrix::identity(2, 2);
let lhs = DMatrix::from_row_slice(2, 3, &[1.0, 2.0, 3.0,
                                          4.0, 5.0, 6.0]);
let mid = DMatrix::from_row_slice(3, 3, &[0.1, 0.2, 0.3,
                                          0.5, 0.6, 0.7,
                                          0.9, 1.0, 1.1]);
// The random shows that values on the workspace do not
// matter as they will be overwritten.
let mut workspace = DVector::new_random(2);
let expected = &lhs * &mid * lhs.transpose() * 10.0 + &mat * 5.0;

mat.quadform_tr_with_workspace(&mut workspace, 10.0, &lhs, &mid, 5.0);
assert_relative_eq!(mat, expected);

pub fn quadform_tr<R3, C3, S3, D4, S4>( &mut self, alpha: T, lhs: &Matrix<T, R3, C3, S3>, mid: &SquareMatrix<T, D4, S4>, beta: T, )

where R3: Dim, C3: Dim, D4: Dim, S3: Storage<T, R3, C3>, S4: Storage<T, D4, D4>, ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>, DefaultAllocator: Allocator<D1>,

Computes the quadratic form self = alpha * lhs * mid * lhs.transpose() + beta * self.

This allocates a workspace vector of dimension D1 for intermediate results. If D1 is a type-level integer, then the allocation is performed on the stack. Use .quadform_tr_with_workspace(...) instead to avoid allocations.

Example

let mut mat = Matrix2::identity();
let lhs = Matrix2x3::new(1.0, 2.0, 3.0,
                         4.0, 5.0, 6.0);
let mid = Matrix3::new(0.1, 0.2, 0.3,
                       0.5, 0.6, 0.7,
                       0.9, 1.0, 1.1);
let expected = lhs * mid * lhs.transpose() * 10.0 + mat * 5.0;

mat.quadform_tr(10.0, &lhs, &mid, 5.0);
assert_relative_eq!(mat, expected);

pub fn quadform_with_workspace<D2, S2, D3, S3, R4, C4, S4>( &mut self, work: &mut Vector<T, D2, S2>, alpha: T, mid: &SquareMatrix<T, D3, S3>, rhs: &Matrix<T, R4, C4, S4>, beta: T, )

where D2: Dim, D3: Dim, R4: Dim, C4: Dim, S2: StorageMut<T, D2>, S3: Storage<T, D3, D3>, S4: Storage<T, R4, C4>, ShapeConstraint: DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,

Computes the quadratic form self = alpha * rhs.transpose() * mid * rhs + beta * self.

This uses the provided workspace work to avoid allocations for intermediate results.

Example

// Note that all those would also work with statically-sized matrices.
// We use DMatrix/DVector since that's the only case where pre-allocating the
// workspace is actually useful (assuming the same workspace is re-used for
// several computations) because it avoids repeated dynamic allocations.
let mut mat = DMatrix::identity(2, 2);
let rhs = DMatrix::from_row_slice(3, 2, &[1.0, 2.0,
                                          3.0, 4.0,
                                          5.0, 6.0]);
let mid = DMatrix::from_row_slice(3, 3, &[0.1, 0.2, 0.3,
                                          0.5, 0.6, 0.7,
                                          0.9, 1.0, 1.1]);
// The random shows that values on the workspace do not
// matter as they will be overwritten.
let mut workspace = DVector::new_random(3);
let expected = rhs.transpose() * &mid * &rhs * 10.0 + &mat * 5.0;

mat.quadform_with_workspace(&mut workspace, 10.0, &mid, &rhs, 5.0);
assert_relative_eq!(mat, expected);

pub fn quadform<D2, S2, R3, C3, S3>( &mut self, alpha: T, mid: &SquareMatrix<T, D2, S2>, rhs: &Matrix<T, R3, C3, S3>, beta: T, )

where D2: Dim, R3: Dim, C3: Dim, S2: Storage<T, D2, D2>, S3: Storage<T, R3, C3>, ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, U1>, DefaultAllocator: Allocator<D2>,

Computes the quadratic form self = alpha * rhs.transpose() * mid * rhs + beta * self.

This allocates a workspace vector of dimension D2 for intermediate results. If D2 is a type-level integer, then the allocation is performed on the stack. Use .quadform_with_workspace(...) instead to avoid allocations.

Example

let mut mat = Matrix2::identity();
let rhs = Matrix3x2::new(1.0, 2.0,
                         3.0, 4.0,
                         5.0, 6.0);
let mid = Matrix3::new(0.1, 0.2, 0.3,
                       0.5, 0.6, 0.7,
                       0.9, 1.0, 1.1);
let expected = rhs.transpose() * mid * rhs * 10.0 + mat * 5.0;

mat.quadform(10.0, &mid, &rhs, 5.0);
assert_relative_eq!(mat, expected);

impl<T, R: Dim, C: Dim, S> Matrix<T, R, C, S>

where T: Scalar + ClosedNeg, S: StorageMut<T, R, C>,

pub fn neg_mut(&mut self)

Negates self in-place.

impl<T, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>> Matrix<T, R1, C1, SA>

where T: Scalar + ClosedAddAssign,

pub fn add_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>( &self, rhs: &Matrix<T, R2, C2, SB>, out: &mut Matrix<T, R3, C3, SC>, )

where SB: Storage<T, R2, C2>, SC: StorageMut<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>,

Equivalent to self + rhs but stores the result into out to avoid allocations.

impl<T, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>> Matrix<T, R1, C1, SA>

where T: Scalar + ClosedSubAssign,

pub fn sub_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>( &self, rhs: &Matrix<T, R2, C2, SB>, out: &mut Matrix<T, R3, C3, SC>, )

where SB: Storage<T, R2, C2>, SC: StorageMut<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>,

Equivalent to self + rhs but stores the result into out to avoid allocations.

impl<T, R1: Dim, C1: Dim, SA> Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SA: Storage<T, R1, C1>,

Special multiplications.

pub fn tr_mul<R2: Dim, C2: Dim, SB>( &self, rhs: &Matrix<T, R2, C2, SB>, ) -> OMatrix<T, C1, C2>

where SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,

Equivalent to self.transpose() * rhs.

pub fn ad_mul<R2: Dim, C2: Dim, SB>( &self, rhs: &Matrix<T, R2, C2, SB>, ) -> OMatrix<T, C1, C2>

where T: SimdComplexField, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,

Equivalent to self.adjoint() * rhs.

pub fn tr_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>( &self, rhs: &Matrix<T, R2, C2, SB>, out: &mut Matrix<T, R3, C3, SC>, )

where SB: Storage<T, R2, C2>, SC: StorageMut<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>,

Equivalent to self.transpose() * rhs but stores the result into out to avoid allocations.

pub fn ad_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>( &self, rhs: &Matrix<T, R2, C2, SB>, out: &mut Matrix<T, R3, C3, SC>, )

where T: SimdComplexField, SB: Storage<T, R2, C2>, SC: StorageMut<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>,

Equivalent to self.adjoint() * rhs but stores the result into out to avoid allocations.

pub fn mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>( &self, rhs: &Matrix<T, R2, C2, SB>, out: &mut Matrix<T, R3, C3, SC>, )

where SB: Storage<T, R2, C2>, SC: StorageMut<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R3, R1> + SameNumberOfColumns<C3, C2> + AreMultipliable<R1, C1, R2, C2>,

Equivalent to self * rhs but stores the result into out to avoid allocations.

pub fn kronecker<R2: Dim, C2: Dim, SB>( &self, rhs: &Matrix<T, R2, C2, SB>, ) -> OMatrix<T, DimProd<R1, R2>, DimProd<C1, C2>>

where T: ClosedMulAssign, R1: DimMul<R2>, C1: DimMul<C2>, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<DimProd<R1, R2>, DimProd<C1, C2>>,

The kronecker product of two matrices (aka. tensor product of the corresponding linear maps).

impl<T, D: DimName> Matrix<T, D, D, <DefaultAllocator as Allocator<D, D>>::Buffer<T>>

where T: Scalar + Zero + One, DefaultAllocator: Allocator<D, D>,

Translation and scaling in any dimension

pub fn new_scaling(scaling: T) -> Self

Creates a new homogeneous matrix that applies the same scaling factor on each dimension.

pub fn new_nonuniform_scaling<SB>( scaling: &Vector<T, DimNameDiff<D, U1>, SB>, ) -> Self

where D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>,

Creates a new homogeneous matrix that applies a distinct scaling factor for each dimension.

pub fn new_translation<SB>( translation: &Vector<T, DimNameDiff<D, U1>, SB>, ) -> Self

where D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>,

Creates a new homogeneous matrix that applies a pure translation.

impl<T: RealField> Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>

2D transformations as a Matrix3

pub fn new_rotation(angle: T) -> Self

Builds a 2 dimensional homogeneous rotation matrix from an angle in radian.

pub fn new_nonuniform_scaling_wrt_point( scaling: &Vector2<T>, pt: &Point2<T>, ) -> Self

Creates a new homogeneous matrix that applies a scaling factor for each dimension with respect to point.

Can be used to implement zoom_to functionality.

impl<T: RealField> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>

3D transformations as a Matrix4

pub fn new_rotation(axisangle: Vector3<T>) -> Self

Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).

Returns the identity matrix if the given argument is zero.

pub fn new_rotation_wrt_point(axisangle: Vector3<T>, pt: Point3<T>) -> Self

Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).

Returns the identity matrix if the given argument is zero.

pub fn new_nonuniform_scaling_wrt_point( scaling: &Vector3<T>, pt: &Point3<T>, ) -> Self

Creates a new homogeneous matrix that applies a scaling factor for each dimension with respect to point.

Can be used to implement zoom_to functionality.

pub fn from_scaled_axis(axisangle: Vector3<T>) -> Self

Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).

Returns the identity matrix if the given argument is zero. This is identical to Self::new_rotation.

pub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Self

Creates a new rotation from Euler angles.

The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.

pub fn from_axis_angle(axis: &Unit<Vector3<T>>, angle: T) -> Self

Builds a 3D homogeneous rotation matrix from an axis and a rotation angle.

pub fn new_orthographic( left: T, right: T, bottom: T, top: T, znear: T, zfar: T, ) -> Self

Creates a new homogeneous matrix for an orthographic projection.

pub fn new_perspective(aspect: T, fovy: T, znear: T, zfar: T) -> Self

Creates a new homogeneous matrix for a perspective projection.

pub fn face_towards( eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>, ) -> Self

Creates an isometry that corresponds to the local frame of an observer standing at the point eye and looking toward target.

It maps the view direction target - eye to the positive z axis and the origin to the eye.

pub fn new_observer_frame( eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>, ) -> Self

👎Deprecated: renamed to face_towards

Deprecated: Use Matrix4::face_towards instead.

pub fn look_at_rh(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> Self

Builds a right-handed look-at view matrix.

pub fn look_at_lh(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> Self

Builds a left-handed look-at view matrix.

impl<T: Scalar + Zero + One + ClosedMulAssign + ClosedAddAssign, D: DimName, S: Storage<T, D, D>> Matrix<T, D, D, S>

Append/prepend translation and scaling

pub fn append_scaling(&self, scaling: T) -> OMatrix<T, D, D>

where D: DimNameSub<U1>, DefaultAllocator: Allocator<D, D>,

Computes the transformation equal to self followed by an uniform scaling factor.

pub fn prepend_scaling(&self, scaling: T) -> OMatrix<T, D, D>

where D: DimNameSub<U1>, DefaultAllocator: Allocator<D, D>,

Computes the transformation equal to an uniform scaling factor followed by self.

pub fn append_nonuniform_scaling<SB>( &self, scaling: &Vector<T, DimNameDiff<D, U1>, SB>, ) -> OMatrix<T, D, D>

where D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>, DefaultAllocator: Allocator<D, D>,

Computes the transformation equal to self followed by a non-uniform scaling factor.

pub fn prepend_nonuniform_scaling<SB>( &self, scaling: &Vector<T, DimNameDiff<D, U1>, SB>, ) -> OMatrix<T, D, D>

where D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>, DefaultAllocator: Allocator<D, D>,

Computes the transformation equal to a non-uniform scaling factor followed by self.

pub fn append_translation<SB>( &self, shift: &Vector<T, DimNameDiff<D, U1>, SB>, ) -> OMatrix<T, D, D>

where D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>, DefaultAllocator: Allocator<D, D>,

Computes the transformation equal to self followed by a translation.

pub fn prepend_translation<SB>( &self, shift: &Vector<T, DimNameDiff<D, U1>, SB>, ) -> OMatrix<T, D, D>

where D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>, DefaultAllocator: Allocator<D, D> + Allocator<DimNameDiff<D, U1>>,

Computes the transformation equal to a translation followed by self.

pub fn append_scaling_mut(&mut self, scaling: T)

where S: StorageMut<T, D, D>, D: DimNameSub<U1>,

Computes in-place the transformation equal to self followed by an uniform scaling factor.

pub fn prepend_scaling_mut(&mut self, scaling: T)

where S: StorageMut<T, D, D>, D: DimNameSub<U1>,

Computes in-place the transformation equal to an uniform scaling factor followed by self.

pub fn append_nonuniform_scaling_mut<SB>( &mut self, scaling: &Vector<T, DimNameDiff<D, U1>, SB>, )

where S: StorageMut<T, D, D>, D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>,

Computes in-place the transformation equal to self followed by a non-uniform scaling factor.

pub fn prepend_nonuniform_scaling_mut<SB>( &mut self, scaling: &Vector<T, DimNameDiff<D, U1>, SB>, )

where S: StorageMut<T, D, D>, D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>,

Computes in-place the transformation equal to a non-uniform scaling factor followed by self.

pub fn append_translation_mut<SB>( &mut self, shift: &Vector<T, DimNameDiff<D, U1>, SB>, )

where S: StorageMut<T, D, D>, D: DimNameSub<U1>, SB: Storage<T, DimNameDiff<D, U1>>,

Computes the transformation equal to self followed by a translation.

pub fn prepend_translation_mut<SB>( &mut self, shift: &Vector<T, DimNameDiff<D, U1>, SB>, )

where D: DimNameSub<U1>, S: StorageMut<T, D, D>, SB: Storage<T, DimNameDiff<D, U1>>, DefaultAllocator: Allocator<DimNameDiff<D, U1>>,

Computes the transformation equal to a translation followed by self.

impl<T: RealField, D: DimNameSub<U1>, S: Storage<T, D, D>> Matrix<T, D, D, S>

where DefaultAllocator: Allocator<D, D> + Allocator<DimNameDiff<D, U1>> + Allocator<DimNameDiff<D, U1>, DimNameDiff<D, U1>>,

Transformation of vectors and points

pub fn transform_vector( &self, v: &OVector<T, DimNameDiff<D, U1>>, ) -> OVector<T, DimNameDiff<D, U1>>

Transforms the given vector, assuming the matrix self uses homogeneous coordinates.

impl<T: RealField, S: Storage<T, Const<3>, Const<3>>> Matrix<T, Const<3>, Const<3>, S>

pub fn transform_point(&self, pt: &Point<T, 2>) -> Point<T, 2>

Transforms the given point, assuming the matrix self uses homogeneous coordinates.

impl<T: RealField, S: Storage<T, Const<4>, Const<4>>> Matrix<T, Const<4>, Const<4>, S>

pub fn transform_point(&self, pt: &Point<T, 3>) -> Point<T, 3>

Transforms the given point, assuming the matrix self uses homogeneous coordinates.

impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

pub fn abs(&self) -> OMatrix<T, R, C>

where T: Signed, DefaultAllocator: Allocator<R, C>,

Computes the component-wise absolute value.

Example

let a = Matrix2::new(0.0, 1.0,
                     -2.0, -3.0);
assert_eq!(a.abs(), Matrix2::new(0.0, 1.0, 2.0, 3.0))

impl<T: Scalar, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>> Matrix<T, R1, C1, SA>

Componentwise operations

pub fn component_mul<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB>, ) -> MatrixSum<T, R1, C1, R2, C2>

where T: ClosedMulAssign, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Componentwise matrix or vector multiplication.

Example

let a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = Matrix2::new(0.0, 5.0, 12.0, 21.0);

assert_eq!(a.component_mul(&b), expected);

pub fn cmpy<R2, C2, SB, R3, C3, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T, )

where T: ClosedMulAssign + Zero + Mul<T, Output = T> + Add<T, Output = T>, R2: Dim, C2: Dim, R3: Dim, C3: Dim, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>,

Computes componentwise self[i] = alpha * a[i] * b[i] + beta * self[i].

Example

let mut m = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = (a.component_mul(&b) * 5.0) + m * 10.0;

m.cmpy(5.0, &a, &b, 10.0);
assert_eq!(m, expected);

pub fn component_mul_assign<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)

where T: ClosedMulAssign, R2: Dim, C2: Dim, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Inplace componentwise matrix or vector multiplication.

Example

let mut a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = Matrix2::new(0.0, 5.0, 12.0, 21.0);

a.component_mul_assign(&b);

assert_eq!(a, expected);

pub fn component_mul_mut<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)

where T: ClosedMulAssign, R2: Dim, C2: Dim, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

👎Deprecated: This is renamed using the _assign suffix instead of the _mut suffix.

Inplace componentwise matrix or vector multiplication.

Example

let mut a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = Matrix2::new(0.0, 5.0, 12.0, 21.0);

a.component_mul_assign(&b);

assert_eq!(a, expected);

pub fn component_div<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB>, ) -> MatrixSum<T, R1, C1, R2, C2>

where T: ClosedDivAssign, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Componentwise matrix or vector division.

Example

let a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = Matrix2::new(0.0, 1.0 / 5.0, 2.0 / 6.0, 3.0 / 7.0);

assert_eq!(a.component_div(&b), expected);

pub fn cdpy<R2, C2, SB, R3, C3, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T, )

where T: ClosedDivAssign + Zero + Mul<T, Output = T> + Add<T, Output = T>, R2: Dim, C2: Dim, R3: Dim, C3: Dim, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>,

Computes componentwise self[i] = alpha * a[i] / b[i] + beta * self[i].

Example

let mut m = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let a = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = (a.component_div(&b) * 5.0) + m * 10.0;

m.cdpy(5.0, &a, &b, 10.0);
assert_eq!(m, expected);

pub fn component_div_assign<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)

where T: ClosedDivAssign, R2: Dim, C2: Dim, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Inplace componentwise matrix or vector division.

Example

let mut a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = Matrix2::new(0.0, 1.0 / 5.0, 2.0 / 6.0, 3.0 / 7.0);

a.component_div_assign(&b);

assert_eq!(a, expected);

pub fn component_div_mut<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)

where T: ClosedDivAssign, R2: Dim, C2: Dim, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

👎Deprecated: This is renamed using the _assign suffix instead of the _mut suffix.

Inplace componentwise matrix or vector division.

Example

let mut a = Matrix2::new(0.0, 1.0, 2.0, 3.0);
let b = Matrix2::new(4.0, 5.0, 6.0, 7.0);
let expected = Matrix2::new(0.0, 1.0 / 5.0, 2.0 / 6.0, 3.0 / 7.0);

a.component_div_assign(&b);

assert_eq!(a, expected);

pub fn inf(&self, other: &Self) -> OMatrix<T, R1, C1>

where T: SimdPartialOrd, DefaultAllocator: Allocator<R1, C1>,

Computes the infimum (aka. componentwise min) of two matrices/vectors.

Example

let u = Matrix2::new(4.0, 2.0, 1.0, -2.0);
let v = Matrix2::new(2.0, 4.0, -2.0, 1.0);
let expected = Matrix2::new(2.0, 2.0, -2.0, -2.0);
assert_eq!(u.inf(&v), expected)

pub fn sup(&self, other: &Self) -> OMatrix<T, R1, C1>

where T: SimdPartialOrd, DefaultAllocator: Allocator<R1, C1>,

Computes the supremum (aka. componentwise max) of two matrices/vectors.

Example

let u = Matrix2::new(4.0, 2.0, 1.0, -2.0);
let v = Matrix2::new(2.0, 4.0, -2.0, 1.0);
let expected = Matrix2::new(4.0, 4.0, 1.0, 1.0);
assert_eq!(u.sup(&v), expected)

pub fn inf_sup(&self, other: &Self) -> (OMatrix<T, R1, C1>, OMatrix<T, R1, C1>)

where T: SimdPartialOrd, DefaultAllocator: Allocator<R1, C1>,

Computes the (infimum, supremum) of two matrices/vectors.

Example

let u = Matrix2::new(4.0, 2.0, 1.0, -2.0);
let v = Matrix2::new(2.0, 4.0, -2.0, 1.0);
let expected = (Matrix2::new(2.0, 2.0, -2.0, -2.0), Matrix2::new(4.0, 4.0, 1.0, 1.0));
assert_eq!(u.inf_sup(&v), expected)

pub fn add_scalar(&self, rhs: T) -> OMatrix<T, R1, C1>

where T: ClosedAddAssign, DefaultAllocator: Allocator<R1, C1>,

Adds a scalar to self.

Example

let u = Matrix2::new(1.0, 2.0, 3.0, 4.0);
let s = 10.0;
let expected = Matrix2::new(11.0, 12.0, 13.0, 14.0);
assert_eq!(u.add_scalar(s), expected)

pub fn add_scalar_mut(&mut self, rhs: T)

where T: ClosedAddAssign, SA: StorageMut<T, R1, C1>,

Adds a scalar to self in-place.

Example

let mut u = Matrix2::new(1.0, 2.0, 3.0, 4.0);
let s = 10.0;
u.add_scalar_mut(s);
let expected = Matrix2::new(11.0, 12.0, 13.0, 14.0);
assert_eq!(u, expected)

impl<T: Scalar, R: Dim, C: Dim> Matrix<MaybeUninit<T>, R, C, <DefaultAllocator as Allocator<R, C>>::BufferUninit<T>>

where DefaultAllocator: Allocator<R, C>,

pub fn uninit(nrows: R, ncols: C) -> Self

Builds a matrix with uninitialized elements of type MaybeUninit<T>.

impl<T: Scalar, R: Dim, C: Dim> Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

where DefaultAllocator: Allocator<R, C>,

Generic constructors

This set of matrix and vector construction functions are all generic with-regard to the matrix dimensions. They all expect to be given the dimension as inputs.

These functions should only be used when working on dimension-generic code.

pub fn from_element_generic(nrows: R, ncols: C, elem: T) -> Self

Creates a matrix with all its elements set to elem.

pub fn repeat_generic(nrows: R, ncols: C, elem: T) -> Self

Creates a matrix with all its elements set to elem.

Same as from_element_generic.

pub fn zeros_generic(nrows: R, ncols: C) -> Self

where T: Zero,

Creates a matrix with all its elements set to 0.

pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix with all its elements filled by an iterator.

pub fn from_row_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix with all its elements filled by an row-major order iterator.

pub fn from_row_slice_generic(nrows: R, ncols: C, slice: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in row-major order.

The order of elements in the slice must follow the usual mathematic writing, i.e., row-by-row.

pub fn from_column_slice_generic(nrows: R, ncols: C, slice: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice. The components must have the same layout as the matrix data storage (i.e. column-major).

pub fn from_fn_generic<F>(nrows: R, ncols: C, f: F) -> Self

where F: FnMut(usize, usize) -> T,

Creates a matrix filled with the results of a function applied to each of its component coordinates.

pub fn identity_generic(nrows: R, ncols: C) -> Self

where T: Zero + One,

Creates a new identity matrix.

If the matrix is not square, the largest square submatrix starting at index (0, 0) is set to the identity matrix. All other entries are set to zero.

pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: T) -> Self

where T: Zero + One,

Creates a new matrix with its diagonal filled with copies of elt.

If the matrix is not square, the largest square submatrix starting at index (0, 0) is set to the identity matrix. All other entries are set to zero.

pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[T]) -> Self

where T: Zero,

Creates a new matrix that may be rectangular. The first elts.len() diagonal elements are filled with the content of elts. Others are set to 0.

Panics if elts.len() is larger than the minimum among nrows and ncols.

pub fn from_rows<SB>(rows: &[Matrix<T, Const<1>, C, SB>]) -> Self

where SB: RawStorage<T, Const<1>, C>,

Builds a new matrix from its rows.

Panics if not enough rows are provided (for statically-sized matrices), or if all rows do not have the same dimensions.

Example

let m = Matrix3::from_rows(&[ RowVector3::new(1.0, 2.0, 3.0),  RowVector3::new(4.0, 5.0, 6.0),  RowVector3::new(7.0, 8.0, 9.0) ]);

assert!(m.m11 == 1.0 && m.m12 == 2.0 && m.m13 == 3.0 &&
        m.m21 == 4.0 && m.m22 == 5.0 && m.m23 == 6.0 &&
        m.m31 == 7.0 && m.m32 == 8.0 && m.m33 == 9.0);

pub fn from_columns<SB>(columns: &[Vector<T, R, SB>]) -> Self

where SB: RawStorage<T, R>,

Builds a new matrix from its columns.

Panics if not enough columns are provided (for statically-sized matrices), or if all columns do not have the same dimensions.

Example

let m = Matrix3::from_columns(&[ Vector3::new(1.0, 2.0, 3.0),  Vector3::new(4.0, 5.0, 6.0),  Vector3::new(7.0, 8.0, 9.0) ]);

assert!(m.m11 == 1.0 && m.m12 == 4.0 && m.m13 == 7.0 &&
        m.m21 == 2.0 && m.m22 == 5.0 && m.m23 == 8.0 &&
        m.m31 == 3.0 && m.m32 == 6.0 && m.m33 == 9.0);

impl<T, D: Dim> Matrix<T, D, D, <DefaultAllocator as Allocator<D, D>>::Buffer<T>>

where T: Scalar, DefaultAllocator: Allocator<D, D>,

pub fn from_diagonal<SB: RawStorage<T, D>>(diag: &Vector<T, D, SB>) -> Self

where T: Zero,

Creates a square matrix with its diagonal set to diag and all other entries set to 0.

Example

let m = Matrix3::from_diagonal(&Vector3::new(1.0, 2.0, 3.0));
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_diagonal(&DVector::from_row_slice(&[1.0, 2.0, 3.0]));

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
        m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 3.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
        dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 3.0);

impl<T: Scalar, R: DimName, C: DimName> Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

where DefaultAllocator: Allocator<R, C>,

Constructors of statically-sized vectors or statically-sized matrices

pub fn from_element(elem: T) -> Self

Creates a matrix or vector with all its elements set to elem.

Example

let v = Vector3::from_element(2.0);
// The additional argument represents the vector dimension.
let dv = DVector::from_element(3, 2.0);
let m = Matrix2x3::from_element(2.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_element(2, 3, 2.0);

assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
        m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
        dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);

pub fn repeat(elem: T) -> Self

Creates a matrix or vector with all its elements set to elem.

Same as .from_element.

Example

let v = Vector3::repeat(2.0);
// The additional argument represents the vector dimension.
let dv = DVector::repeat(3, 2.0);
let m = Matrix2x3::repeat(2.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::repeat(2, 3, 2.0);

assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
        m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
        dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);

pub fn zeros() -> Self

where T: Zero,

Creates a matrix or vector with all its elements set to 0.

Example

let v = Vector3::<f32>::zeros();
// The argument represents the vector dimension.
let dv = DVector::<f32>::zeros(3);
let m = Matrix2x3::<f32>::zeros();
// The two arguments represent the matrix dimensions.
let dm = DMatrix::<f32>::zeros(2, 3);

assert!(v.x == 0.0 && v.y == 0.0 && v.z == 0.0);
assert!(dv[0] == 0.0 && dv[1] == 0.0 && dv[2] == 0.0);
assert!(m.m11 == 0.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 0.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 0.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 0.0 && dm[(1, 2)] == 0.0);

pub fn from_iterator<I>(iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix or vector with all its elements filled by an iterator.

The output matrix is filled column-by-column.

Example

let v = Vector3::from_iterator((0..3).into_iter());
// The additional argument represents the vector dimension.
let dv = DVector::from_iterator(3, (0..3).into_iter());
let m = Matrix2x3::from_iterator((0..6).into_iter());
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_iterator(2, 3, (0..6).into_iter());

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

pub fn from_row_iterator<I>(iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix or vector with all its elements filled by a row-major iterator.

The output matrix is filled row-by-row.

Example

let v = Vector3::from_row_iterator((0..3).into_iter());
// The additional argument represents the vector dimension.
let dv = DVector::from_row_iterator(3, (0..3).into_iter());
let m = Matrix2x3::from_row_iterator((0..6).into_iter());
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_row_iterator(2, 3, (0..6).into_iter());

// For Vectors from_row_iterator is identical to from_iterator
assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn from_fn<F>(f: F) -> Self

where F: FnMut(usize, usize) -> T,

Creates a matrix or vector filled with the results of a function applied to each of its component coordinates.

Example

let v = Vector3::from_fn(|i, _| i);
// The additional argument represents the vector dimension.
let dv = DVector::from_fn(3, |i, _| i);
let m = Matrix2x3::from_fn(|i, j| i * 3 + j);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_fn(2, 3, |i, j| i * 3 + j);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn identity() -> Self

where T: Zero + One,

Creates an identity matrix. If the matrix is not square, the largest square submatrix (starting at the first row and column) is set to the identity while all other entries are set to zero.

Example

let m = Matrix2x3::<f32>::identity();
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::<f32>::identity(2, 3);

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 1.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 1.0 && dm[(1, 2)] == 0.0);

pub fn from_diagonal_element(elt: T) -> Self

where T: Zero + One,

Creates a matrix filled with its diagonal filled with elt and all other components set to zero.

Example

let m = Matrix2x3::from_diagonal_element(5.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_diagonal_element(2, 3, 5.0);

assert!(m.m11 == 5.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 5.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 5.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 5.0 && dm[(1, 2)] == 0.0);

pub fn from_partial_diagonal(elts: &[T]) -> Self

where T: Zero,

Creates a new matrix that may be rectangular. The first elts.len() diagonal elements are filled with the content of elts. Others are set to 0.

Panics if elts.len() is larger than the minimum among nrows and ncols.

Example

let m = Matrix3::from_partial_diagonal(&[1.0, 2.0]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_partial_diagonal(3, 3, &[1.0, 2.0]);

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
        m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 0.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
        dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 0.0);

impl<T: Scalar, R: DimName> Matrix<T, R, Dyn, <DefaultAllocator as Allocator<R, Dyn>>::Buffer<T>>

where DefaultAllocator: Allocator<R, Dyn>,

Constructors of matrices with a dynamic number of columns

pub fn from_element(ncols: usize, elem: T) -> Self

Creates a matrix or vector with all its elements set to elem.

Example

let v = Vector3::from_element(2.0);
// The additional argument represents the vector dimension.
let dv = DVector::from_element(3, 2.0);
let m = Matrix2x3::from_element(2.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_element(2, 3, 2.0);

assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
        m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
        dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);

pub fn repeat(ncols: usize, elem: T) -> Self

Creates a matrix or vector with all its elements set to elem.

Same as .from_element.

Example

let v = Vector3::repeat(2.0);
// The additional argument represents the vector dimension.
let dv = DVector::repeat(3, 2.0);
let m = Matrix2x3::repeat(2.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::repeat(2, 3, 2.0);

assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
        m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
        dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);

pub fn zeros(ncols: usize) -> Self

where T: Zero,

Creates a matrix or vector with all its elements set to 0.

Example

let v = Vector3::<f32>::zeros();
// The argument represents the vector dimension.
let dv = DVector::<f32>::zeros(3);
let m = Matrix2x3::<f32>::zeros();
// The two arguments represent the matrix dimensions.
let dm = DMatrix::<f32>::zeros(2, 3);

assert!(v.x == 0.0 && v.y == 0.0 && v.z == 0.0);
assert!(dv[0] == 0.0 && dv[1] == 0.0 && dv[2] == 0.0);
assert!(m.m11 == 0.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 0.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 0.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 0.0 && dm[(1, 2)] == 0.0);

pub fn from_iterator<I>(ncols: usize, iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix or vector with all its elements filled by an iterator.

The output matrix is filled column-by-column.

Example

let v = Vector3::from_iterator((0..3).into_iter());
// The additional argument represents the vector dimension.
let dv = DVector::from_iterator(3, (0..3).into_iter());
let m = Matrix2x3::from_iterator((0..6).into_iter());
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_iterator(2, 3, (0..6).into_iter());

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

pub fn from_row_iterator<I>(ncols: usize, iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix or vector with all its elements filled by a row-major iterator.

The output matrix is filled row-by-row.

Example

let v = Vector3::from_row_iterator((0..3).into_iter());
// The additional argument represents the vector dimension.
let dv = DVector::from_row_iterator(3, (0..3).into_iter());
let m = Matrix2x3::from_row_iterator((0..6).into_iter());
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_row_iterator(2, 3, (0..6).into_iter());

// For Vectors from_row_iterator is identical to from_iterator
assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn from_fn<F>(ncols: usize, f: F) -> Self

where F: FnMut(usize, usize) -> T,

Creates a matrix or vector filled with the results of a function applied to each of its component coordinates.

Example

let v = Vector3::from_fn(|i, _| i);
// The additional argument represents the vector dimension.
let dv = DVector::from_fn(3, |i, _| i);
let m = Matrix2x3::from_fn(|i, j| i * 3 + j);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_fn(2, 3, |i, j| i * 3 + j);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn identity(ncols: usize) -> Self

where T: Zero + One,

Creates an identity matrix. If the matrix is not square, the largest square submatrix (starting at the first row and column) is set to the identity while all other entries are set to zero.

Example

let m = Matrix2x3::<f32>::identity();
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::<f32>::identity(2, 3);

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 1.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 1.0 && dm[(1, 2)] == 0.0);

pub fn from_diagonal_element(ncols: usize, elt: T) -> Self

where T: Zero + One,

Creates a matrix filled with its diagonal filled with elt and all other components set to zero.

Example

let m = Matrix2x3::from_diagonal_element(5.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_diagonal_element(2, 3, 5.0);

assert!(m.m11 == 5.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 5.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 5.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 5.0 && dm[(1, 2)] == 0.0);

pub fn from_partial_diagonal(ncols: usize, elts: &[T]) -> Self

where T: Zero,

Creates a new matrix that may be rectangular. The first elts.len() diagonal elements are filled with the content of elts. Others are set to 0.

Panics if elts.len() is larger than the minimum among nrows and ncols.

Example

let m = Matrix3::from_partial_diagonal(&[1.0, 2.0]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_partial_diagonal(3, 3, &[1.0, 2.0]);

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
        m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 0.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
        dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 0.0);

impl<T: Scalar, C: DimName> Matrix<T, Dyn, C, <DefaultAllocator as Allocator<Dyn, C>>::Buffer<T>>

where DefaultAllocator: Allocator<Dyn, C>,

Constructors of dynamic vectors and matrices with a dynamic number of rows

pub fn from_element(nrows: usize, elem: T) -> Self

Creates a matrix or vector with all its elements set to elem.

Example

let v = Vector3::from_element(2.0);
// The additional argument represents the vector dimension.
let dv = DVector::from_element(3, 2.0);
let m = Matrix2x3::from_element(2.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_element(2, 3, 2.0);

assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
        m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
        dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);

pub fn repeat(nrows: usize, elem: T) -> Self

Creates a matrix or vector with all its elements set to elem.

Same as .from_element.

Example

let v = Vector3::repeat(2.0);
// The additional argument represents the vector dimension.
let dv = DVector::repeat(3, 2.0);
let m = Matrix2x3::repeat(2.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::repeat(2, 3, 2.0);

assert!(v.x == 2.0 && v.y == 2.0 && v.z == 2.0);
assert!(dv[0] == 2.0 && dv[1] == 2.0 && dv[2] == 2.0);
assert!(m.m11 == 2.0 && m.m12 == 2.0 && m.m13 == 2.0 &&
        m.m21 == 2.0 && m.m22 == 2.0 && m.m23 == 2.0);
assert!(dm[(0, 0)] == 2.0 && dm[(0, 1)] == 2.0 && dm[(0, 2)] == 2.0 &&
        dm[(1, 0)] == 2.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 2.0);

pub fn zeros(nrows: usize) -> Self

where T: Zero,

Creates a matrix or vector with all its elements set to 0.

Example

let v = Vector3::<f32>::zeros();
// The argument represents the vector dimension.
let dv = DVector::<f32>::zeros(3);
let m = Matrix2x3::<f32>::zeros();
// The two arguments represent the matrix dimensions.
let dm = DMatrix::<f32>::zeros(2, 3);

assert!(v.x == 0.0 && v.y == 0.0 && v.z == 0.0);
assert!(dv[0] == 0.0 && dv[1] == 0.0 && dv[2] == 0.0);
assert!(m.m11 == 0.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 0.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 0.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 0.0 && dm[(1, 2)] == 0.0);

pub fn from_iterator<I>(nrows: usize, iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix or vector with all its elements filled by an iterator.

The output matrix is filled column-by-column.

Example

let v = Vector3::from_iterator((0..3).into_iter());
// The additional argument represents the vector dimension.
let dv = DVector::from_iterator(3, (0..3).into_iter());
let m = Matrix2x3::from_iterator((0..6).into_iter());
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_iterator(2, 3, (0..6).into_iter());

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

pub fn from_row_iterator<I>(nrows: usize, iter: I) -> Self

where I: IntoIterator<Item = T>,

Creates a matrix or vector with all its elements filled by a row-major iterator.

The output matrix is filled row-by-row.

Example

let v = Vector3::from_row_iterator((0..3).into_iter());
// The additional argument represents the vector dimension.
let dv = DVector::from_row_iterator(3, (0..3).into_iter());
let m = Matrix2x3::from_row_iterator((0..6).into_iter());
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_row_iterator(2, 3, (0..6).into_iter());

// For Vectors from_row_iterator is identical to from_iterator
assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn from_fn<F>(nrows: usize, f: F) -> Self

where F: FnMut(usize, usize) -> T,

Creates a matrix or vector filled with the results of a function applied to each of its component coordinates.

Example

let v = Vector3::from_fn(|i, _| i);
// The additional argument represents the vector dimension.
let dv = DVector::from_fn(3, |i, _| i);
let m = Matrix2x3::from_fn(|i, j| i * 3 + j);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_fn(2, 3, |i, j| i * 3 + j);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn identity(nrows: usize) -> Self

where T: Zero + One,

Creates an identity matrix. If the matrix is not square, the largest square submatrix (starting at the first row and column) is set to the identity while all other entries are set to zero.

Example

let m = Matrix2x3::<f32>::identity();
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::<f32>::identity(2, 3);

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 1.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 1.0 && dm[(1, 2)] == 0.0);

pub fn from_diagonal_element(nrows: usize, elt: T) -> Self

where T: Zero + One,

Creates a matrix filled with its diagonal filled with elt and all other components set to zero.

Example

let m = Matrix2x3::from_diagonal_element(5.0);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_diagonal_element(2, 3, 5.0);

assert!(m.m11 == 5.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 5.0 && m.m23 == 0.0);
assert!(dm[(0, 0)] == 5.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 5.0 && dm[(1, 2)] == 0.0);

pub fn from_partial_diagonal(nrows: usize, elts: &[T]) -> Self

where T: Zero,

Creates a new matrix that may be rectangular. The first elts.len() diagonal elements are filled with the content of elts. Others are set to 0.

Panics if elts.len() is larger than the minimum among nrows and ncols.

Example

let m = Matrix3::from_partial_diagonal(&[1.0, 2.0]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_partial_diagonal(3, 3, &[1.0, 2.0]);

assert!(m.m11 == 1.0 && m.m12 == 0.0 && m.m13 == 0.0 &&
        m.m21 == 0.0 && m.m22 == 2.0 && m.m23 == 0.0 &&
        m.m31 == 0.0 && m.m32 == 0.0 && m.m33 == 0.0);
assert!(dm[(0, 0)] == 1.0 && dm[(0, 1)] == 0.0 && dm[(0, 2)] == 0.0 &&
        dm[(1, 0)] == 0.0 && dm[(1, 1)] == 2.0 && dm[(1, 2)] == 0.0 &&
        dm[(2, 0)] == 0.0 && dm[(2, 1)] == 0.0 && dm[(2, 2)] == 0.0);

impl<T: Scalar, R: DimName, C: DimName> Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

where DefaultAllocator: Allocator<R, C>,

pub fn from_row_slice(data: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in row-major order.

The order of elements in the slice must follow the usual mathematic writing, i.e., row-by-row.

Example

let v = Vector3::from_row_slice(&[0, 1, 2]);
// The additional argument represents the vector dimension.
let dv = DVector::from_row_slice(&[0, 1, 2]);
let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn from_column_slice(data: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in column-major order.

Example

let v = Vector3::from_column_slice(&[0, 1, 2]);
// The additional argument represents the vector dimension.
let dv = DVector::from_column_slice(&[0, 1, 2]);
let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

impl<T: Scalar, R: DimName> Matrix<T, R, Dyn, <DefaultAllocator as Allocator<R, Dyn>>::Buffer<T>>

where DefaultAllocator: Allocator<R, Dyn>,

pub fn from_row_slice(data: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in row-major order.

The order of elements in the slice must follow the usual mathematic writing, i.e., row-by-row.

Example

let v = Vector3::from_row_slice(&[0, 1, 2]);
// The additional argument represents the vector dimension.
let dv = DVector::from_row_slice(&[0, 1, 2]);
let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn from_column_slice(data: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in column-major order.

Example

let v = Vector3::from_column_slice(&[0, 1, 2]);
// The additional argument represents the vector dimension.
let dv = DVector::from_column_slice(&[0, 1, 2]);
let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

impl<T: Scalar, C: DimName> Matrix<T, Dyn, C, <DefaultAllocator as Allocator<Dyn, C>>::Buffer<T>>

where DefaultAllocator: Allocator<Dyn, C>,

pub fn from_row_slice(data: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in row-major order.

The order of elements in the slice must follow the usual mathematic writing, i.e., row-by-row.

Example

let v = Vector3::from_row_slice(&[0, 1, 2]);
// The additional argument represents the vector dimension.
let dv = DVector::from_row_slice(&[0, 1, 2]);
let m = Matrix2x3::from_row_slice(&[0, 1, 2, 3, 4, 5]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_row_slice(2, 3, &[0, 1, 2, 3, 4, 5]);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 1 && m.m13 == 2 &&
        m.m21 == 3 && m.m22 == 4 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 1 && dm[(0, 2)] == 2 &&
        dm[(1, 0)] == 3 && dm[(1, 1)] == 4 && dm[(1, 2)] == 5);

pub fn from_column_slice(data: &[T]) -> Self

Creates a matrix with its elements filled with the components provided by a slice in column-major order.

Example

let v = Vector3::from_column_slice(&[0, 1, 2]);
// The additional argument represents the vector dimension.
let dv = DVector::from_column_slice(&[0, 1, 2]);
let m = Matrix2x3::from_column_slice(&[0, 1, 2, 3, 4, 5]);
// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_column_slice(2, 3, &[0, 1, 2, 3, 4, 5]);

assert!(v.x == 0 && v.y == 1 && v.z == 2);
assert!(dv[0] == 0 && dv[1] == 1 && dv[2] == 2);
assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);
assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

impl<T> Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>

pub const fn new(m11: T, m12: T, m21: T, m22: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<3>, Const<3>, ArrayStorage<T, 3, 3>>

pub const fn new( m11: T, m12: T, m13: T, m21: T, m22: T, m23: T, m31: T, m32: T, m33: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<4>, Const<4>, ArrayStorage<T, 4, 4>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m21: T, m22: T, m23: T, m24: T, m31: T, m32: T, m33: T, m34: T, m41: T, m42: T, m43: T, m44: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<5>, Const<5>, ArrayStorage<T, 5, 5>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m21: T, m22: T, m23: T, m24: T, m25: T, m31: T, m32: T, m33: T, m34: T, m35: T, m41: T, m42: T, m43: T, m44: T, m45: T, m51: T, m52: T, m53: T, m54: T, m55: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<6>, Const<6>, ArrayStorage<T, 6, 6>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m16: T, m21: T, m22: T, m23: T, m24: T, m25: T, m26: T, m31: T, m32: T, m33: T, m34: T, m35: T, m36: T, m41: T, m42: T, m43: T, m44: T, m45: T, m46: T, m51: T, m52: T, m53: T, m54: T, m55: T, m56: T, m61: T, m62: T, m63: T, m64: T, m65: T, m66: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<2>, Const<3>, ArrayStorage<T, 2, 3>>

pub const fn new(m11: T, m12: T, m13: T, m21: T, m22: T, m23: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<2>, Const<4>, ArrayStorage<T, 2, 4>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m21: T, m22: T, m23: T, m24: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<2>, Const<5>, ArrayStorage<T, 2, 5>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m21: T, m22: T, m23: T, m24: T, m25: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<2>, Const<6>, ArrayStorage<T, 2, 6>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m16: T, m21: T, m22: T, m23: T, m24: T, m25: T, m26: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<3>, Const<2>, ArrayStorage<T, 3, 2>>

pub const fn new(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<3>, Const<4>, ArrayStorage<T, 3, 4>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m21: T, m22: T, m23: T, m24: T, m31: T, m32: T, m33: T, m34: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<3>, Const<5>, ArrayStorage<T, 3, 5>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m21: T, m22: T, m23: T, m24: T, m25: T, m31: T, m32: T, m33: T, m34: T, m35: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<3>, Const<6>, ArrayStorage<T, 3, 6>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m16: T, m21: T, m22: T, m23: T, m24: T, m25: T, m26: T, m31: T, m32: T, m33: T, m34: T, m35: T, m36: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<4>, Const<2>, ArrayStorage<T, 4, 2>>

pub const fn new( m11: T, m12: T, m21: T, m22: T, m31: T, m32: T, m41: T, m42: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<4>, Const<3>, ArrayStorage<T, 4, 3>>

pub const fn new( m11: T, m12: T, m13: T, m21: T, m22: T, m23: T, m31: T, m32: T, m33: T, m41: T, m42: T, m43: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<4>, Const<5>, ArrayStorage<T, 4, 5>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m21: T, m22: T, m23: T, m24: T, m25: T, m31: T, m32: T, m33: T, m34: T, m35: T, m41: T, m42: T, m43: T, m44: T, m45: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<4>, Const<6>, ArrayStorage<T, 4, 6>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m16: T, m21: T, m22: T, m23: T, m24: T, m25: T, m26: T, m31: T, m32: T, m33: T, m34: T, m35: T, m36: T, m41: T, m42: T, m43: T, m44: T, m45: T, m46: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<5>, Const<2>, ArrayStorage<T, 5, 2>>

pub const fn new( m11: T, m12: T, m21: T, m22: T, m31: T, m32: T, m41: T, m42: T, m51: T, m52: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<5>, Const<3>, ArrayStorage<T, 5, 3>>

pub const fn new( m11: T, m12: T, m13: T, m21: T, m22: T, m23: T, m31: T, m32: T, m33: T, m41: T, m42: T, m43: T, m51: T, m52: T, m53: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<5>, Const<4>, ArrayStorage<T, 5, 4>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m21: T, m22: T, m23: T, m24: T, m31: T, m32: T, m33: T, m34: T, m41: T, m42: T, m43: T, m44: T, m51: T, m52: T, m53: T, m54: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<5>, Const<6>, ArrayStorage<T, 5, 6>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m16: T, m21: T, m22: T, m23: T, m24: T, m25: T, m26: T, m31: T, m32: T, m33: T, m34: T, m35: T, m36: T, m41: T, m42: T, m43: T, m44: T, m45: T, m46: T, m51: T, m52: T, m53: T, m54: T, m55: T, m56: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<6>, Const<2>, ArrayStorage<T, 6, 2>>

pub const fn new( m11: T, m12: T, m21: T, m22: T, m31: T, m32: T, m41: T, m42: T, m51: T, m52: T, m61: T, m62: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<6>, Const<3>, ArrayStorage<T, 6, 3>>

pub const fn new( m11: T, m12: T, m13: T, m21: T, m22: T, m23: T, m31: T, m32: T, m33: T, m41: T, m42: T, m43: T, m51: T, m52: T, m53: T, m61: T, m62: T, m63: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<6>, Const<4>, ArrayStorage<T, 6, 4>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m21: T, m22: T, m23: T, m24: T, m31: T, m32: T, m33: T, m34: T, m41: T, m42: T, m43: T, m44: T, m51: T, m52: T, m53: T, m54: T, m61: T, m62: T, m63: T, m64: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<6>, Const<5>, ArrayStorage<T, 6, 5>>

pub const fn new( m11: T, m12: T, m13: T, m14: T, m15: T, m21: T, m22: T, m23: T, m24: T, m25: T, m31: T, m32: T, m33: T, m34: T, m35: T, m41: T, m42: T, m43: T, m44: T, m45: T, m51: T, m52: T, m53: T, m54: T, m55: T, m61: T, m62: T, m63: T, m64: T, m65: T, ) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>

pub const fn new(x: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<1>, Const<2>, ArrayStorage<T, 1, 2>>

pub const fn new(x: T, y: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<1>, Const<3>, ArrayStorage<T, 1, 3>>

pub const fn new(x: T, y: T, z: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<1>, Const<4>, ArrayStorage<T, 1, 4>>

pub const fn new(x: T, y: T, z: T, w: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<1>, Const<5>, ArrayStorage<T, 1, 5>>

pub const fn new(x: T, y: T, z: T, w: T, a: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<1>, Const<6>, ArrayStorage<T, 1, 6>>

pub const fn new(x: T, y: T, z: T, w: T, a: T, b: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

pub const fn new(x: T, y: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

pub const fn new(x: T, y: T, z: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>

pub const fn new(x: T, y: T, z: T, w: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<5>, Const<1>, ArrayStorage<T, 5, 1>>

pub const fn new(x: T, y: T, z: T, w: T, a: T) -> Self

Initializes this matrix from its components.

impl<T> Matrix<T, Const<6>, Const<1>, ArrayStorage<T, 6, 1>>

pub const fn new(x: T, y: T, z: T, w: T, a: T, b: T) -> Self

Initializes this matrix from its components.

impl<T, R> Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<R>>::Buffer<T>>

where R: ToTypenum + DimName, T: Scalar + Zero + One, DefaultAllocator: Allocator<R>,

pub fn ith(i: usize, val: T) -> Self

The column vector with val as its i-th component.

pub fn ith_axis(i: usize) -> Unit<Self>

The column unit vector with T::one() as its i-th component.

pub fn x() -> Self

where R::Typenum: Cmp<U0, Output = Greater>,

The column vector with a 1 as its first component, and zero elsewhere.

pub fn y() -> Self

where R::Typenum: Cmp<U1, Output = Greater>,

The column vector with a 1 as its second component, and zero elsewhere.

pub fn z() -> Self

where R::Typenum: Cmp<U2, Output = Greater>,

The column vector with a 1 as its third component, and zero elsewhere.

pub fn w() -> Self

where R::Typenum: Cmp<U3, Output = Greater>,

The column vector with a 1 as its fourth component, and zero elsewhere.

pub fn a() -> Self

where R::Typenum: Cmp<U4, Output = Greater>,

The column vector with a 1 as its fifth component, and zero elsewhere.

pub fn b() -> Self

where R::Typenum: Cmp<U5, Output = Greater>,

The column vector with a 1 as its sixth component, and zero elsewhere.

pub fn x_axis() -> Unit<Self>

where R::Typenum: Cmp<U0, Output = Greater>,

The unit column vector with a 1 as its first component, and zero elsewhere.

pub fn y_axis() -> Unit<Self>

where R::Typenum: Cmp<U1, Output = Greater>,

The unit column vector with a 1 as its second component, and zero elsewhere.

pub fn z_axis() -> Unit<Self>

where R::Typenum: Cmp<U2, Output = Greater>,

The unit column vector with a 1 as its third component, and zero elsewhere.

pub fn w_axis() -> Unit<Self>

where R::Typenum: Cmp<U3, Output = Greater>,

The unit column vector with a 1 as its fourth component, and zero elsewhere.

pub fn a_axis() -> Unit<Self>

where R::Typenum: Cmp<U4, Output = Greater>,

The unit column vector with a 1 as its fifth component, and zero elsewhere.

pub fn b_axis() -> Unit<Self>

where R::Typenum: Cmp<U5, Output = Greater>,

The unit column vector with a 1 as its sixth component, and zero elsewhere.

impl<'a, T: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Matrix<T, R, C, ViewStorage<'a, T, R, C, RStride, CStride>>

Creating matrix views from &[T]

pub unsafe fn from_slice_with_strides_generic_unchecked( data: &'a [T], start: usize, nrows: R, ncols: C, rstride: RStride, cstride: CStride, ) -> Self

Creates, without bounds checking, a matrix view from an array and with dimensions and strides specified by generic types instances.

Safety

This method is unsafe because the input data array is not checked to contain enough elements. The generic types R, C, RStride, CStride can either be type-level integers or integers wrapped with Dyn().

pub fn from_slice_with_strides_generic( data: &'a [T], nrows: R, ncols: C, rstride: RStride, cstride: CStride, ) -> Self

Creates a matrix view from an array and with dimensions and strides specified by generic types instances.

Panics if the input data array dose not contain enough elements. The generic types R, C, RStride, CStride can either be type-level integers or integers wrapped with Dyn().

impl<'a, T: Scalar, R: Dim, C: Dim> Matrix<T, R, C, ViewStorage<'a, T, R, C, Const<1>, R>>

pub unsafe fn from_slice_generic_unchecked( data: &'a [T], start: usize, nrows: R, ncols: C, ) -> Self

Creates, without bound-checking, a matrix view from an array and with dimensions specified by generic types instances.

Safety

This method is unsafe because the input data array is not checked to contain enough elements. The generic types R and C can either be type-level integers or integers wrapped with Dyn().

pub fn from_slice_generic(data: &'a [T], nrows: R, ncols: C) -> Self

Creates a matrix view from an array and with dimensions and strides specified by generic types instances.

Panics if the input data array dose not contain enough elements. The generic types R and C can either be type-level integers or integers wrapped with Dyn().

impl<'a, T: Scalar, R: DimName, C: DimName> Matrix<T, R, C, ViewStorage<'a, T, R, C, Const<1>, R>>

pub fn from_slice(data: &'a [T]) -> Self

Creates a new matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked(data: &'a [T], start: usize) -> Self

Creates, without bound checking, a new matrix view from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar, R: DimName, C: DimName> Matrix<T, R, C, ViewStorage<'a, T, R, C, Dyn, Dyn>>

pub fn from_slice_with_strides( data: &'a [T], rstride: usize, cstride: usize, ) -> Self

Creates a new matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a [T], start: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new matrix view with the specified strides from the given data array.

Safety

start, rstride, and cstride, with the given matrix size will not index outside of data.

impl<'a, T: Scalar, R: DimName> Matrix<T, R, Dyn, ViewStorage<'a, T, R, Dyn, Const<1>, R>>

pub fn from_slice(data: &'a [T], ncols: usize) -> Self

Creates a new matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a [T], start: usize, ncols: usize, ) -> Self

Creates, without bound checking, a new matrix view from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar, R: DimName> Matrix<T, R, Dyn, ViewStorage<'a, T, R, Dyn, Dyn, Dyn>>

pub fn from_slice_with_strides( data: &'a [T], ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates a new matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a [T], start: usize, ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new matrix view with the specified strides from the given data array.

Safety

start, rstride, and cstride, with the given matrix size will not index outside of data.

impl<'a, T: Scalar, C: DimName> Matrix<T, Dyn, C, ViewStorage<'a, T, Dyn, C, Const<1>, Dyn>>

pub fn from_slice(data: &'a [T], nrows: usize) -> Self

Creates a new matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a [T], start: usize, nrows: usize, ) -> Self

Creates, without bound checking, a new matrix view from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar, C: DimName> Matrix<T, Dyn, C, ViewStorage<'a, T, Dyn, C, Dyn, Dyn>>

pub fn from_slice_with_strides( data: &'a [T], nrows: usize, rstride: usize, cstride: usize, ) -> Self

Creates a new matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a [T], start: usize, nrows: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new matrix view with the specified strides from the given data array.

Safety

start, rstride, and cstride, with the given matrix size will not index outside of data.

impl<'a, T: Scalar> Matrix<T, Dyn, Dyn, ViewStorage<'a, T, Dyn, Dyn, Const<1>, Dyn>>

pub fn from_slice(data: &'a [T], nrows: usize, ncols: usize) -> Self

Creates a new matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a [T], start: usize, nrows: usize, ncols: usize, ) -> Self

Creates, without bound checking, a new matrix view from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar> Matrix<T, Dyn, Dyn, ViewStorage<'a, T, Dyn, Dyn, Dyn, Dyn>>

pub fn from_slice_with_strides( data: &'a [T], nrows: usize, ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates a new matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a [T], start: usize, nrows: usize, ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new matrix view with the specified strides from the given data array.

Safety

start, rstride, and cstride, with the given matrix size will not index outside of data.

impl<'a, T: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> Matrix<T, R, C, ViewStorageMut<'a, T, R, C, RStride, CStride>>

Creating mutable matrix views from &mut [T]

pub unsafe fn from_slice_with_strides_generic_unchecked( data: &'a mut [T], start: usize, nrows: R, ncols: C, rstride: RStride, cstride: CStride, ) -> Self

Creates, without bound-checking, a mutable matrix view from an array and with dimensions and strides specified by generic types instances.

Safety

This method is unsafe because the input data array is not checked to contain enough elements. The generic types R, C, RStride, CStride can either be type-level integers or integers wrapped with Dyn().

pub fn from_slice_with_strides_generic( data: &'a mut [T], nrows: R, ncols: C, rstride: RStride, cstride: CStride, ) -> Self

Creates a mutable matrix view from an array and with dimensions and strides specified by generic types instances.

Panics if the input data array dose not contain enough elements. The generic types R, C, RStride, CStride can either be type-level integers or integers wrapped with Dyn().

impl<'a, T: Scalar, R: Dim, C: Dim> Matrix<T, R, C, ViewStorageMut<'a, T, R, C, Const<1>, R>>

pub unsafe fn from_slice_generic_unchecked( data: &'a mut [T], start: usize, nrows: R, ncols: C, ) -> Self

Creates, without bound-checking, a mutable matrix view from an array and with dimensions specified by generic types instances.

Safety

This method is unsafe because the input data array is not checked to contain enough elements. The generic types R and C can either be type-level integers or integers wrapped with Dyn().

pub fn from_slice_generic(data: &'a mut [T], nrows: R, ncols: C) -> Self

Creates a mutable matrix view from an array and with dimensions and strides specified by generic types instances.

Panics if the input data array dose not contain enough elements. The generic types R and C can either be type-level integers or integers wrapped with Dyn().

impl<'a, T: Scalar, R: DimName, C: DimName> Matrix<T, R, C, ViewStorageMut<'a, T, R, C, Const<1>, R>>

pub fn from_slice(data: &'a mut [T]) -> Self

Creates a new mutable matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked(data: &'a mut [T], start: usize) -> Self

Creates, without bound checking, a new mutable matrix view from the given data array.

Safety

data[start..start+(R * C)] must be within bounds.

impl<'a, T: Scalar, R: DimName, C: DimName> Matrix<T, R, C, ViewStorageMut<'a, T, R, C, Dyn, Dyn>>

pub fn from_slice_with_strides_mut( data: &'a mut [T], rstride: usize, cstride: usize, ) -> Self

Creates a new mutable matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a mut [T], start: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view with the specified strides from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar, R: DimName> Matrix<T, R, Dyn, ViewStorageMut<'a, T, R, Dyn, Const<1>, R>>

pub fn from_slice(data: &'a mut [T], ncols: usize) -> Self

Creates a new mutable matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a mut [T], start: usize, ncols: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view from the given data array.

Safety

data[start..start+(R * C)] must be within bounds.

impl<'a, T: Scalar, R: DimName> Matrix<T, R, Dyn, ViewStorageMut<'a, T, R, Dyn, Dyn, Dyn>>

pub fn from_slice_with_strides_mut( data: &'a mut [T], ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates a new mutable matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a mut [T], start: usize, ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view with the specified strides from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar, C: DimName> Matrix<T, Dyn, C, ViewStorageMut<'a, T, Dyn, C, Const<1>, Dyn>>

pub fn from_slice(data: &'a mut [T], nrows: usize) -> Self

Creates a new mutable matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a mut [T], start: usize, nrows: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view from the given data array.

Safety

data[start..start+(R * C)] must be within bounds.

impl<'a, T: Scalar, C: DimName> Matrix<T, Dyn, C, ViewStorageMut<'a, T, Dyn, C, Dyn, Dyn>>

pub fn from_slice_with_strides_mut( data: &'a mut [T], nrows: usize, rstride: usize, cstride: usize, ) -> Self

Creates a new mutable matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a mut [T], start: usize, nrows: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view with the specified strides from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<'a, T: Scalar> Matrix<T, Dyn, Dyn, ViewStorageMut<'a, T, Dyn, Dyn, Const<1>, Dyn>>

pub fn from_slice(data: &'a mut [T], nrows: usize, ncols: usize) -> Self

Creates a new mutable matrix view from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a mut [T], start: usize, nrows: usize, ncols: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view from the given data array.

Safety

data[start..start+(R * C)] must be within bounds.

impl<'a, T: Scalar> Matrix<T, Dyn, Dyn, ViewStorageMut<'a, T, Dyn, Dyn, Dyn, Dyn>>

pub fn from_slice_with_strides_mut( data: &'a mut [T], nrows: usize, ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates a new mutable matrix view with the specified strides from the given data array.

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a mut [T], start: usize, nrows: usize, ncols: usize, rstride: usize, cstride: usize, ) -> Self

Creates, without bound checking, a new mutable matrix view with the specified strides from the given data array.

Safety

data[start..start+rstride * cstride] must be within bounds.

impl<T: Scalar + Zero, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

Triangular matrix extraction

pub fn upper_triangle(&self) -> OMatrix<T, R, C>

where DefaultAllocator: Allocator<R, C>,

Extracts the upper triangular part of this matrix (including the diagonal).

pub fn lower_triangle(&self) -> OMatrix<T, R, C>

where DefaultAllocator: Allocator<R, C>,

Extracts the lower triangular part of this matrix (including the diagonal).

impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

This impl block contains no items.

Rows and columns extraction

impl<T: Scalar, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

Set rows, columns, and diagonal

pub fn set_diagonal<R2: Dim, S2>(&mut self, diag: &Vector<T, R2, S2>)

where R: DimMin<C>, S2: RawStorage<T, R2>, ShapeConstraint: DimEq<DimMinimum<R, C>, R2>,

Fills the diagonal of this matrix with the content of the given vector.

pub fn set_partial_diagonal(&mut self, diag: impl Iterator<Item = T>)

Fills the diagonal of this matrix with the content of the given iterator.

This will fill as many diagonal elements as the iterator yields, up to the minimum of the number of rows and columns of self, and starting with the diagonal element at index (0, 0).

pub fn set_row<C2: Dim, S2>(&mut self, i: usize, row: &RowVector<T, C2, S2>)

where S2: RawStorage<T, U1, C2>, ShapeConstraint: SameNumberOfColumns<C, C2>,

Fills the selected row of this matrix with the content of the given vector.

pub fn set_column<R2: Dim, S2>(&mut self, i: usize, column: &Vector<T, R2, S2>)

where S2: RawStorage<T, R2, U1>, ShapeConstraint: SameNumberOfRows<R, R2>,

Fills the selected column of this matrix with the content of the given vector.

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

In-place filling

pub fn fill_with(&mut self, val: impl Fn() -> T)

Sets all the elements of this matrix to the value returned by the closure.

pub fn fill(&mut self, val: T)

where T: Scalar,

Sets all the elements of this matrix to val.

pub fn fill_with_identity(&mut self)

where T: Scalar + Zero + One,

Fills self with the identity matrix.

pub fn fill_diagonal(&mut self, val: T)

where T: Scalar,

Sets all the diagonal elements of this matrix to val.

pub fn fill_row(&mut self, i: usize, val: T)

where T: Scalar,

Sets all the elements of the selected row to val.

pub fn fill_column(&mut self, j: usize, val: T)

where T: Scalar,

Sets all the elements of the selected column to val.

pub fn fill_lower_triangle(&mut self, val: T, shift: usize)

where T: Scalar,

Sets all the elements of the lower-triangular part of this matrix to val.

The parameter shift allows some subdiagonals to be left untouched:

• If shift = 0 then the diagonal is overwritten as well.
• If shift = 1 then the diagonal is left untouched.
• If shift > 1, then the diagonal and the first shift - 1 subdiagonals are left untouched.

pub fn fill_upper_triangle(&mut self, val: T, shift: usize)

where T: Scalar,

Sets all the elements of the lower-triangular part of this matrix to val.

The parameter shift allows some superdiagonals to be left untouched:

• If shift = 0 then the diagonal is overwritten as well.
• If shift = 1 then the diagonal is left untouched.
• If shift > 1, then the diagonal and the first shift - 1 superdiagonals are left untouched.

impl<T: Scalar, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S>

pub fn fill_lower_triangle_with_upper_triangle(&mut self)

Copies the upper-triangle of this matrix to its lower-triangular part.

This makes the matrix symmetric. Panics if the matrix is not square.

pub fn fill_upper_triangle_with_lower_triangle(&mut self)

Copies the upper-triangle of this matrix to its upper-triangular part.

This makes the matrix symmetric. Panics if the matrix is not square.

impl<T: Scalar, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

In-place swapping

pub fn swap_rows(&mut self, irow1: usize, irow2: usize)

Swaps two rows in-place.

pub fn swap_columns(&mut self, icol1: usize, icol2: usize)

Swaps two columns in-place.

impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

Rows and columns removal

pub fn remove_column(self, i: usize) -> OMatrix<T, R, DimDiff<C, U1>>

where C: DimSub<U1>, DefaultAllocator: Reallocator<T, R, C, R, DimDiff<C, U1>>,

Removes the i-th column from this matrix.

pub fn remove_fixed_columns<const D: usize>( self, i: usize, ) -> OMatrix<T, R, DimDiff<C, Const<D>>>

where C: DimSub<Const<D>>, DefaultAllocator: Reallocator<T, R, C, R, DimDiff<C, Const<D>>>,

Removes D::dim() consecutive columns from this matrix, starting with the i-th (included).

pub fn remove_columns_generic<D>( self, i: usize, nremove: D, ) -> OMatrix<T, R, DimDiff<C, D>>

where D: Dim, C: DimSub<D>, DefaultAllocator: Reallocator<T, R, C, R, DimDiff<C, D>>,

Removes nremove.value() columns from this matrix, starting with the i-th (included).

This is the generic implementation of .remove_columns(...) and .remove_fixed_columns(...) which have nicer API interfaces.

pub fn remove_row(self, i: usize) -> OMatrix<T, DimDiff<R, U1>, C>

where R: DimSub<U1>, DefaultAllocator: Reallocator<T, R, C, DimDiff<R, U1>, C>,

Removes the i-th row from this matrix.

pub fn remove_fixed_rows<const D: usize>( self, i: usize, ) -> OMatrix<T, DimDiff<R, Const<D>>, C>

where R: DimSub<Const<D>>, DefaultAllocator: Reallocator<T, R, C, DimDiff<R, Const<D>>, C>,

Removes D::dim() consecutive rows from this matrix, starting with the i-th (included).

pub fn remove_rows_generic<D>( self, i: usize, nremove: D, ) -> OMatrix<T, DimDiff<R, D>, C>

where D: Dim, R: DimSub<D>, DefaultAllocator: Reallocator<T, R, C, DimDiff<R, D>, C>,

Removes nremove.value() rows from this matrix, starting with the i-th (included).

This is the generic implementation of .remove_rows(...) and .remove_fixed_rows(...) which have nicer API interfaces.

impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

Rows and columns insertion

pub fn insert_column(self, i: usize, val: T) -> OMatrix<T, R, DimSum<C, U1>>

where C: DimAdd<U1>, DefaultAllocator: Reallocator<T, R, C, R, DimSum<C, U1>>,

Inserts a column filled with val at the i-th position.

pub fn insert_fixed_columns<const D: usize>( self, i: usize, val: T, ) -> OMatrix<T, R, DimSum<C, Const<D>>>

where C: DimAdd<Const<D>>, DefaultAllocator: Reallocator<T, R, C, R, DimSum<C, Const<D>>>,

Inserts D columns filled with val starting at the i-th position.

pub unsafe fn insert_columns_generic_uninitialized<D>( self, i: usize, ninsert: D, ) -> UninitMatrix<T, R, DimSum<C, D>>

where D: Dim, C: DimAdd<D>, DefaultAllocator: Reallocator<T, R, C, R, DimSum<C, D>>,

Inserts ninsert.value() columns starting at the i-th place of this matrix.

Safety

The output matrix has all its elements initialized except for the the components of the added columns.

pub fn insert_row(self, i: usize, val: T) -> OMatrix<T, DimSum<R, U1>, C>

where R: DimAdd<U1>, DefaultAllocator: Reallocator<T, R, C, DimSum<R, U1>, C>,

Inserts a row filled with val at the i-th position.

pub fn insert_fixed_rows<const D: usize>( self, i: usize, val: T, ) -> OMatrix<T, DimSum<R, Const<D>>, C>

where R: DimAdd<Const<D>>, DefaultAllocator: Reallocator<T, R, C, DimSum<R, Const<D>>, C>,

Inserts D::dim() rows filled with val starting at the i-th position.

pub unsafe fn insert_rows_generic_uninitialized<D>( self, i: usize, ninsert: D, ) -> UninitMatrix<T, DimSum<R, D>, C>

where D: Dim, R: DimAdd<D>, DefaultAllocator: Reallocator<T, R, C, DimSum<R, D>, C>,

Inserts ninsert.value() rows at the i-th place of this matrix.

Safety

The added rows values are not initialized. This is the generic implementation of .insert_rows(...) and .insert_fixed_rows(...) which have nicer API interfaces.

impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

Resizing and reshaping

pub fn fixed_resize<const R2: usize, const C2: usize>( self, val: T, ) -> OMatrix<T, Const<R2>, Const<C2>>

where DefaultAllocator: Reallocator<T, R, C, Const<R2>, Const<C2>>,

Resizes this matrix so that it contains R2::value() rows and C2::value() columns.

The values are copied such that self[(i, j)] == result[(i, j)]. If the result has more rows and/or columns than self, then the extra rows or columns are filled with val.

pub fn resize_generic<R2: Dim, C2: Dim>( self, new_nrows: R2, new_ncols: C2, val: T, ) -> OMatrix<T, R2, C2>

where DefaultAllocator: Reallocator<T, R, C, R2, C2>,

Resizes self such that it has dimensions new_nrows × new_ncols.

The values are copied such that self[(i, j)] == result[(i, j)]. If the result has more rows and/or columns than self, then the extra rows or columns are filled with val.

pub fn reshape_generic<R2, C2>( self, new_nrows: R2, new_ncols: C2, ) -> Matrix<T, R2, C2, S::Output>

where R2: Dim, C2: Dim, S: ReshapableStorage<T, R, C, R2, C2>,

Reshapes self such that it has dimensions new_nrows × new_ncols.

This will reinterpret self as if it is a matrix with new_nrows rows and new_ncols columns. The arrangements of the component in the output matrix are the same as what would be obtained by Matrix::from_slice_generic(self.as_slice(), new_nrows, new_ncols).

If self is a dynamically-sized matrix, then its components are neither copied nor moved. If self is staticyll-sized, then a copy may happen in some situations. This function will panic if the given dimensions are such that the number of elements of the input matrix are not equal to the number of elements of the output matrix.

Examples

let m1 = Matrix2x3::new(
    1.1, 1.2, 1.3,
    2.1, 2.2, 2.3
);
let m2 = Matrix3x2::new(
    1.1, 2.2,
    2.1, 1.3,
    1.2, 2.3
);
let reshaped = m1.reshape_generic(Const::<3>, Const::<2>);
assert_eq!(reshaped, m2);

let dm1 = DMatrix::from_row_slice(
    4,
    3,
    &[
        1.0, 0.0, 0.0,
        0.0, 0.0, 1.0,
        0.0, 0.0, 0.0,
        0.0, 1.0, 0.0
    ],
);
let dm2 = DMatrix::from_row_slice(
    6,
    2,
    &[
        1.0, 0.0,
        0.0, 1.0,
        0.0, 0.0,
        0.0, 1.0,
        0.0, 0.0,
        0.0, 0.0,
    ],
);
let reshaped = dm1.reshape_generic(Dyn(6), Dyn(2));
assert_eq!(reshaped, dm2);

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Views based on ranges

Indices to Individual Elements

Two-Dimensional Indices

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert_eq!(matrix.index((0, 0)), &0);
assert_eq!(matrix.index((1, 0)), &1);
assert_eq!(matrix.index((0, 1)), &2);
assert_eq!(matrix.index((1, 1)), &3);

Linear Address Indexing

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert_eq!(matrix.get(0), Some(&0));
assert_eq!(matrix.get(1), Some(&1));
assert_eq!(matrix.get(2), Some(&2));
assert_eq!(matrix.get(3), Some(&3));

Indices to Individual Rows and Columns

Index to a Row

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert!(matrix.index((0, ..))
    .eq(&Matrix1x2::new(0, 2)));

Index to a Column

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert!(matrix.index((.., 0))
    .eq(&Matrix2x1::new(0,
                        1)));

Indices to Parts of Individual Rows and Columns

Index to a Partial Row

let matrix = Matrix3::new(0, 3, 6,
                          1, 4, 7,
                          2, 5, 8);

assert!(matrix.index((0, ..2))
    .eq(&Matrix1x2::new(0, 3)));

Index to a Partial Column

let matrix = Matrix3::new(0, 3, 6,
                          1, 4, 7,
                          2, 5, 8);

assert!(matrix.index((..2, 0))
    .eq(&Matrix2x1::new(0,
                        1)));

assert!(matrix.index((Const::<1>.., 0))
    .eq(&Matrix2x1::new(1,
                        2)));

Indices to Ranges of Rows and Columns

Index to a Range of Rows

let matrix = Matrix3::new(0, 3, 6,
                          1, 4, 7,
                          2, 5, 8);

assert!(matrix.index((1..3, ..))
    .eq(&Matrix2x3::new(1, 4, 7,
                        2, 5, 8)));

Index to a Range of Columns

let matrix = Matrix3::new(0, 3, 6,
                          1, 4, 7,
                          2, 5, 8);

assert!(matrix.index((.., 1..3))
    .eq(&Matrix3x2::new(3, 6,
                        4, 7,
                        5, 8)));

pub fn get<'a, I>(&'a self, index: I) -> Option<I::Output>

where I: MatrixIndex<'a, T, R, C, S>,

Produces a view of the data at the given index, or None if the index is out of bounds.

pub fn get_mut<'a, I>(&'a mut self, index: I) -> Option<I::OutputMut>

where S: RawStorageMut<T, R, C>, I: MatrixIndexMut<'a, T, R, C, S>,

Produces a mutable view of the data at the given index, or None if the index is out of bounds.

pub fn index<'a, I>(&'a self, index: I) -> I::Output

where I: MatrixIndex<'a, T, R, C, S>,

Produces a view of the data at the given index, or panics if the index is out of bounds.

pub fn index_mut<'a, I>(&'a mut self, index: I) -> I::OutputMut

where S: RawStorageMut<T, R, C>, I: MatrixIndexMut<'a, T, R, C, S>,

Produces a mutable view of the data at the given index, or panics if the index is out of bounds.

pub unsafe fn get_unchecked<'a, I>(&'a self, index: I) -> I::Output

where I: MatrixIndex<'a, T, R, C, S>,

Produces a view of the data at the given index, without doing any bounds checking.

Safety

index must within bounds of the array.

pub unsafe fn get_unchecked_mut<'a, I>(&'a mut self, index: I) -> I::OutputMut

where S: RawStorageMut<T, R, C>, I: MatrixIndexMut<'a, T, R, C, S>,

Returns a mutable view of the data at the given index, without doing any bounds checking.

Safety

index must within bounds of the array.

impl<T, R, C, S> Matrix<T, R, C, S>

pub const unsafe fn from_data_statically_unchecked( data: S, ) -> Matrix<T, R, C, S>

Creates a new matrix with the given data without statically checking that the matrix dimension matches the storage dimension.

Safety

The storage dimension must match the given dimensions.

impl<T, const R: usize, const C: usize> Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>

pub const fn from_array_storage(storage: ArrayStorage<T, R, C>) -> Self

Creates a new statically-allocated matrix from the given ArrayStorage.

This method exists primarily as a workaround for the fact that from_data can not work in const fn contexts.

impl<T: Scalar, R: Dim, C: Dim> Matrix<MaybeUninit<T>, R, C, <DefaultAllocator as Allocator<R, C>>::BufferUninit<T>>

where DefaultAllocator: Allocator<R, C>,

pub unsafe fn assume_init(self) -> OMatrix<T, R, C>

Assumes a matrix’s entries to be initialized. This operation should be near zero-cost.

Safety

The user must make sure that every single entry of the buffer has been initialized, or Undefined Behavior will immediately occur.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

pub fn from_data(data: S) -> Self

Creates a new matrix with the given data.

pub fn shape(&self) -> (usize, usize)

The shape of this matrix returned as the tuple (number of rows, number of columns).

Example

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.shape(), (3, 4));

pub fn shape_generic(&self) -> (R, C)

The shape of this matrix wrapped into their representative types (Const or Dyn).

pub fn nrows(&self) -> usize

The number of rows of this matrix.

Example

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.nrows(), 3);

pub fn ncols(&self) -> usize

The number of columns of this matrix.

Example

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.ncols(), 4);

pub fn strides(&self) -> (usize, usize)

The strides (row stride, column stride) of this matrix.

Example

let mat = DMatrix::<f32>::zeros(10, 10);
let view = mat.view_with_steps((0, 0), (5, 3), (1, 2));
// The column strides is the number of steps (here 2) multiplied by the corresponding dimension.
assert_eq!(mat.strides(), (1, 10));

pub fn vector_to_matrix_index(&self, i: usize) -> (usize, usize)

Computes the row and column coordinates of the i-th element of this matrix seen as a vector.

Example

let m = Matrix2::new(1, 2,
                     3, 4);
let i = m.vector_to_matrix_index(3);
assert_eq!(i, (1, 1));
assert_eq!(m[i], m[3]);

pub fn as_ptr(&self) -> *const T

Returns a pointer to the start of the matrix.

If the matrix is not empty, this pointer is guaranteed to be aligned and non-null.

Example

let m = Matrix2::new(1, 2,
                     3, 4);
let ptr = m.as_ptr();
assert_eq!(unsafe { *ptr }, m[0]);

pub fn relative_eq<R2, C2, SB>( &self, other: &Matrix<T, R2, C2, SB>, eps: T::Epsilon, max_relative: T::Epsilon, ) -> bool

where T: RelativeEq + Scalar, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, T::Epsilon: Clone, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Tests whether self and rhs are equal up to a given epsilon.

See relative_eq from the RelativeEq trait for more details.

pub fn eq<R2, C2, SB>(&self, other: &Matrix<T, R2, C2, SB>) -> bool

where T: PartialEq, R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Tests whether self and rhs are exactly equal.

pub fn into_owned(self) -> OMatrix<T, R, C>

where T: Scalar, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

Moves this matrix into one that owns its data.

pub fn into_owned_sum<R2, C2>(self) -> MatrixSum<T, R, C, R2, C2>

where T: Scalar, S: Storage<T, R, C>, R2: Dim, C2: Dim, DefaultAllocator: SameShapeAllocator<R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Moves this matrix into one that owns its data. The actual type of the result depends on matrix storage combination rules for addition.

pub fn clone_owned(&self) -> OMatrix<T, R, C>

where T: Scalar, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

Clones this matrix to one that owns its data.

pub fn clone_owned_sum<R2, C2>(&self) -> MatrixSum<T, R, C, R2, C2>

where T: Scalar, S: Storage<T, R, C>, R2: Dim, C2: Dim, DefaultAllocator: SameShapeAllocator<R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Clones this matrix into one that owns its data. The actual type of the result depends on matrix storage combination rules for addition.

pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<T, R2, C2, SB>)

where T: Scalar, R2: Dim, C2: Dim, SB: RawStorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,

Transposes self and store the result into out.

pub fn transpose(&self) -> OMatrix<T, C, R>

where T: Scalar, DefaultAllocator: Allocator<C, R>,

Transposes self.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Elementwise mapping and folding

pub fn map<T2: Scalar, F: FnMut(T) -> T2>(&self, f: F) -> OMatrix<T2, R, C>

where T: Scalar, DefaultAllocator: Allocator<R, C>,

Returns a matrix containing the result of f applied to each of its entries.

pub fn cast<T2: Scalar>(self) -> OMatrix<T2, R, C>

where T: Scalar, OMatrix<T2, R, C>: SupersetOf<Self>, DefaultAllocator: Allocator<R, C>,

Cast the components of self to another type.

Example

let q = Vector3::new(1.0f64, 2.0, 3.0);
let q2 = q.cast::<f32>();
assert_eq!(q2, Vector3::new(1.0f32, 2.0, 3.0));

pub fn try_cast<T2: Scalar>(self) -> Option<OMatrix<T2, R, C>>

where T: Scalar, Self: SupersetOf<OMatrix<T2, R, C>>, DefaultAllocator: Allocator<R, C>,

Attempts to cast the components of self to another type.

Example

let q = Vector3::new(1.0f64, 2.0, 3.0);
let q2 = q.try_cast::<i32>();
assert_eq!(q2, Some(Vector3::new(1, 2, 3)));

pub fn fold_with<T2>( &self, init_f: impl FnOnce(Option<&T>) -> T2, f: impl FnMut(T2, &T) -> T2, ) -> T2

where T: Scalar,

Similar to self.iter().fold(init, f) except that init is replaced by a closure.

The initialization closure is given the first component of this matrix:

• If the matrix has no component (0 rows or 0 columns) then init_f is called with None and its return value is the value returned by this method.
• If the matrix has has least one component, then init_f is called with the first component to compute the initial value. Folding then continues on all the remaining components of the matrix.

pub fn map_with_location<T2: Scalar, F: FnMut(usize, usize, T) -> T2>( &self, f: F, ) -> OMatrix<T2, R, C>

where T: Scalar, DefaultAllocator: Allocator<R, C>,

Returns a matrix containing the result of f applied to each of its entries. Unlike map, f also gets passed the row and column index, i.e. f(row, col, value).

pub fn zip_map<T2, N3, S2, F>( &self, rhs: &Matrix<T2, R, C, S2>, f: F, ) -> OMatrix<N3, R, C>

where T: Scalar, T2: Scalar, N3: Scalar, S2: RawStorage<T2, R, C>, F: FnMut(T, T2) -> N3, DefaultAllocator: Allocator<R, C>,

Returns a matrix containing the result of f applied to each entries of self and rhs.

pub fn zip_zip_map<T2, N3, N4, S2, S3, F>( &self, b: &Matrix<T2, R, C, S2>, c: &Matrix<N3, R, C, S3>, f: F, ) -> OMatrix<N4, R, C>

where T: Scalar, T2: Scalar, N3: Scalar, N4: Scalar, S2: RawStorage<T2, R, C>, S3: RawStorage<N3, R, C>, F: FnMut(T, T2, N3) -> N4, DefaultAllocator: Allocator<R, C>,

Returns a matrix containing the result of f applied to each entries of self and b, and c.

pub fn fold<Acc>(&self, init: Acc, f: impl FnMut(Acc, T) -> Acc) -> Acc

where T: Scalar,

Folds a function f on each entry of self.

pub fn zip_fold<T2, R2, C2, S2, Acc>( &self, rhs: &Matrix<T2, R2, C2, S2>, init: Acc, f: impl FnMut(Acc, T, T2) -> Acc, ) -> Acc

where T: Scalar, T2: Scalar, R2: Dim, C2: Dim, S2: RawStorage<T2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Folds a function f on each pairs of entries from self and rhs.

pub fn apply<F: FnMut(&mut T)>(&mut self, f: F)

where S: RawStorageMut<T, R, C>,

Applies a closure f to modify each component of self.

pub fn zip_apply<T2, R2, C2, S2>( &mut self, rhs: &Matrix<T2, R2, C2, S2>, f: impl FnMut(&mut T, T2), )

where S: RawStorageMut<T, R, C>, T2: Scalar, R2: Dim, C2: Dim, S2: RawStorage<T2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Replaces each component of self by the result of a closure f applied on its components joined with the components from rhs.

pub fn zip_zip_apply<T2, R2, C2, S2, N3, R3, C3, S3>( &mut self, b: &Matrix<T2, R2, C2, S2>, c: &Matrix<N3, R3, C3, S3>, f: impl FnMut(&mut T, T2, N3), )

where S: RawStorageMut<T, R, C>, T2: Scalar, R2: Dim, C2: Dim, S2: RawStorage<T2, R2, C2>, N3: Scalar, R3: Dim, C3: Dim, S3: RawStorage<N3, R3, C3>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Replaces each component of self by the result of a closure f applied on its components joined with the components from b and c.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Iteration on components, rows, and columns

pub fn iter(&self) -> MatrixIter<'_, T, R, C, S>

Iterates through this matrix coordinates in column-major order.

Example

let mat = Matrix2x3::new(11, 12, 13,
                         21, 22, 23);
let mut it = mat.iter();
assert_eq!(*it.next().unwrap(), 11);
assert_eq!(*it.next().unwrap(), 21);
assert_eq!(*it.next().unwrap(), 12);
assert_eq!(*it.next().unwrap(), 22);
assert_eq!(*it.next().unwrap(), 13);
assert_eq!(*it.next().unwrap(), 23);
assert!(it.next().is_none());

pub fn row_iter(&self) -> RowIter<'_, T, R, C, S>

Iterate through the rows of this matrix.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, row) in a.row_iter().enumerate() {
    assert_eq!(row, a.row(i))
}

pub fn column_iter(&self) -> ColumnIter<'_, T, R, C, S>

Iterate through the columns of this matrix.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, column) in a.column_iter().enumerate() {
    assert_eq!(column, a.column(i))
}

pub fn iter_mut(&mut self) -> MatrixIterMut<'_, T, R, C, S>

where S: RawStorageMut<T, R, C>,

Mutably iterates through this matrix coordinates.

pub fn row_iter_mut(&mut self) -> RowIterMut<'_, T, R, C, S>

where S: RawStorageMut<T, R, C>,

Mutably iterates through this matrix rows.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, mut row) in a.row_iter_mut().enumerate() {
    row *= (i + 1) * 10;
}

let expected = Matrix2x3::new(10, 20, 30,
                              80, 100, 120);
assert_eq!(a, expected);

pub fn column_iter_mut(&mut self) -> ColumnIterMut<'_, T, R, C, S>

where S: RawStorageMut<T, R, C>,

Mutably iterates through this matrix columns.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, mut col) in a.column_iter_mut().enumerate() {
    col *= (i + 1) * 10;
}

let expected = Matrix2x3::new(10, 40, 90,
                              40, 100, 180);
assert_eq!(a, expected);

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

pub fn as_mut_ptr(&mut self) -> *mut T

Returns a mutable pointer to the start of the matrix.

If the matrix is not empty, this pointer is guaranteed to be aligned and non-null.

pub unsafe fn swap_unchecked( &mut self, row_cols1: (usize, usize), row_cols2: (usize, usize), )

Swaps two entries without bound-checking.

Safety

Both (r, c) must have r < nrows(), c < ncols().

pub fn swap(&mut self, row_cols1: (usize, usize), row_cols2: (usize, usize))

Swaps two entries.

pub fn copy_from_slice(&mut self, slice: &[T])

where T: Scalar,

Fills this matrix with the content of a slice. Both must hold the same number of elements.

The components of the slice are assumed to be ordered in column-major order.

pub fn copy_from<R2, C2, SB>(&mut self, other: &Matrix<T, R2, C2, SB>)

where T: Scalar, R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Fills this matrix with the content of another one. Both must have the same shape.

pub fn tr_copy_from<R2, C2, SB>(&mut self, other: &Matrix<T, R2, C2, SB>)

where T: Scalar, R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: DimEq<R, C2> + SameNumberOfColumns<C, R2>,

Fills this matrix with the content of the transpose another one.

pub fn apply_into<F: FnMut(&mut T)>(self, f: F) -> Self

Returns self with each of its components replaced by the result of a closure f applied on it.

impl<T, D: Dim, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

pub unsafe fn vget_unchecked(&self, i: usize) -> &T

Gets a reference to the i-th element of this column vector without bound checking.

Safety

i must be less than D.

impl<T, D: Dim, S: RawStorageMut<T, D>> Matrix<T, D, Const<1>, S>

pub unsafe fn vget_unchecked_mut(&mut self, i: usize) -> &mut T

Gets a mutable reference to the i-th element of this column vector without bound checking.

Safety

i must be less than D.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C> + IsContiguous> Matrix<T, R, C, S>

pub fn as_slice(&self) -> &[T]

Extracts a slice containing the entire matrix entries ordered column-by-columns.

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C> + IsContiguous> Matrix<T, R, C, S>

pub fn as_mut_slice(&mut self) -> &mut [T]

Extracts a mutable slice containing the entire matrix entries ordered column-by-columns.

impl<T: Scalar, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S>

pub fn transpose_mut(&mut self)

Transposes the square matrix self in-place.

impl<T: SimdComplexField, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

pub fn adjoint_to<R2, C2, SB>(&self, out: &mut Matrix<T, R2, C2, SB>)

where R2: Dim, C2: Dim, SB: RawStorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,

Takes the adjoint (aka. conjugate-transpose) of self and store the result into out.

pub fn adjoint(&self) -> OMatrix<T, C, R>

where DefaultAllocator: Allocator<C, R>,

The adjoint (aka. conjugate-transpose) of self.

pub fn conjugate_transpose_to<R2, C2, SB>( &self, out: &mut Matrix<T, R2, C2, SB>, )

where R2: Dim, C2: Dim, SB: RawStorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,

👎Deprecated: Renamed self.adjoint_to(out).

Takes the conjugate and transposes self and store the result into out.

pub fn conjugate_transpose(&self) -> OMatrix<T, C, R>

where DefaultAllocator: Allocator<C, R>,

👎Deprecated: Renamed self.adjoint().

The conjugate transposition of self.

pub fn conjugate(&self) -> OMatrix<T, R, C>

where DefaultAllocator: Allocator<R, C>,

The conjugate of self.

pub fn unscale(&self, real: T::SimdRealField) -> OMatrix<T, R, C>

where DefaultAllocator: Allocator<R, C>,

Divides each component of the complex matrix self by the given real.

pub fn scale(&self, real: T::SimdRealField) -> OMatrix<T, R, C>

where DefaultAllocator: Allocator<R, C>,

Multiplies each component of the complex matrix self by the given real.

impl<T: SimdComplexField, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

pub fn conjugate_mut(&mut self)

The conjugate of the complex matrix self computed in-place.

pub fn unscale_mut(&mut self, real: T::SimdRealField)

Divides each component of the complex matrix self by the given real.

pub fn scale_mut(&mut self, real: T::SimdRealField)

Multiplies each component of the complex matrix self by the given real.

impl<T: SimdComplexField, D: Dim, S: RawStorageMut<T, D, D>> Matrix<T, D, D, S>

pub fn conjugate_transform_mut(&mut self)

👎Deprecated: Renamed to self.adjoint_mut().

Sets self to its adjoint.

pub fn adjoint_mut(&mut self)

Sets self to its adjoint (aka. conjugate-transpose).

impl<T: Scalar, D: Dim, S: RawStorage<T, D, D>> Matrix<T, D, D, S>

pub fn diagonal(&self) -> OVector<T, D>

where DefaultAllocator: Allocator<D>,

The diagonal of this matrix.

pub fn map_diagonal<T2: Scalar>(&self, f: impl FnMut(T) -> T2) -> OVector<T2, D>

where DefaultAllocator: Allocator<D>,

Apply the given function to this matrix’s diagonal and returns it.

This is a more efficient version of self.diagonal().map(f) since this allocates only once.

pub fn trace(&self) -> T

where T: Scalar + Zero + ClosedAddAssign,

Computes a trace of a square matrix, i.e., the sum of its diagonal elements.

impl<T: SimdComplexField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

pub fn symmetric_part(&self) -> OMatrix<T, D, D>

where DefaultAllocator: Allocator<D, D>,

The symmetric part of self, i.e., 0.5 * (self + self.transpose()).

pub fn hermitian_part(&self) -> OMatrix<T, D, D>

where DefaultAllocator: Allocator<D, D>,

The hermitian part of self, i.e., 0.5 * (self + self.adjoint()).

impl<T: Scalar + Zero + One, D: DimAdd<U1> + IsNotStaticOne, S: RawStorage<T, D, D>> Matrix<T, D, D, S>

pub fn to_homogeneous(&self) -> OMatrix<T, DimSum<D, U1>, DimSum<D, U1>>

where DefaultAllocator: Allocator<DimSum<D, U1>, DimSum<D, U1>>,

Yields the homogeneous matrix for this matrix, i.e., appending an additional dimension and and setting the diagonal element to 1.

impl<T: Scalar + Zero, D: DimAdd<U1>, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

pub fn to_homogeneous(&self) -> OVector<T, DimSum<D, U1>>

where DefaultAllocator: Allocator<DimSum<D, U1>>,

Computes the coordinates in projective space of this vector, i.e., appends a 0 to its coordinates.

pub fn from_homogeneous<SB>( v: Vector<T, DimSum<D, U1>, SB>, ) -> Option<OVector<T, D>>

where SB: RawStorage<T, DimSum<D, U1>>, DefaultAllocator: Allocator<D>,

Constructs a vector from coordinates in projective space, i.e., removes a 0 at the end of self. Returns None if this last component is not zero.

impl<T: Scalar, D: DimAdd<U1>, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

pub fn push(&self, element: T) -> OVector<T, DimSum<D, U1>>

where DefaultAllocator: Allocator<DimSum<D, U1>>,

Constructs a new vector of higher dimension by appending element to the end of self.

impl<T: Scalar + ClosedAddAssign + ClosedSubAssign + ClosedMulAssign, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Cross product

pub fn perp<R2, C2, SB>(&self, b: &Matrix<T, R2, C2, SB>) -> T

where R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, U2> + SameNumberOfColumns<C, U1> + SameNumberOfRows<R2, U2> + SameNumberOfColumns<C2, U1>,

The perpendicular product between two 2D column vectors, i.e. a.x * b.y - a.y * b.x.

pub fn cross<R2, C2, SB>( &self, b: &Matrix<T, R2, C2, SB>, ) -> MatrixCross<T, R, C, R2, C2>

where R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

The 3D cross product between two vectors.

Panics if the shape is not 3D vector. In the future, this will be implemented only for dynamically-sized matrices and statically-sized 3D matrices.

impl<T: Scalar + Field, S: RawStorage<T, U3>> Matrix<T, Const<3>, Const<1>, S>

pub fn cross_matrix(&self) -> OMatrix<T, U3, U3>

Computes the matrix M such that for all vector v we have M * v == self.cross(&v).

impl<T: SimdComplexField, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

pub fn angle<R2: Dim, C2: Dim, SB>( &self, other: &Matrix<T, R2, C2, SB>, ) -> T::SimdRealField

where SB: Storage<T, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

The smallest angle between two vectors.

impl<T, S> Matrix<T, U1, U1, S>

where S: RawStorage<T, U1, U1>,

pub fn as_scalar(&self) -> &T

Returns a reference to the single element in this matrix.

As opposed to indexing, using this provides type-safety when flattening dimensions.

Example

let v = Vector3::new(0., 0., 1.);
let inner_product: f32 = *(v.transpose() * v).as_scalar();

 let v = Vector3::new(0., 0., 1.);
 let inner_product = (v * v.transpose()).item(); // Typo, does not compile.

pub fn as_scalar_mut(&mut self) -> &mut T

where S: RawStorageMut<T, U1>,

Get a mutable reference to the single element in this matrix

As opposed to indexing, using this provides type-safety when flattening dimensions.

Example

let v = Vector3::new(0., 0., 1.);
let mut inner_product = (v.transpose() * v);
*inner_product.as_scalar_mut() = 3.;

 let v = Vector3::new(0., 0., 1.);
 let mut inner_product = (v * v.transpose());
 *inner_product.as_scalar_mut() = 3.;

pub fn to_scalar(&self) -> T

where T: Clone,

Convert this 1x1 matrix by reference into a scalar.

As opposed to indexing, using this provides type-safety when flattening dimensions.

Example

let v = Vector3::new(0., 0., 1.);
let mut inner_product: f32 = (v.transpose() * v).to_scalar();

 let v = Vector3::new(0., 0., 1.);
 let mut inner_product: f32 = (v * v.transpose()).to_scalar();

impl<T> Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>

pub fn into_scalar(self) -> T

Convert this 1x1 matrix into a scalar.

As opposed to indexing, using this provides type-safety when flattening dimensions.

Example

let v = Vector3::new(0., 0., 1.);
let inner_product: f32 = (v.transpose() * v).into_scalar();
assert_eq!(inner_product, 1.);

 let v = Vector3::new(0., 0., 1.);
 let mut inner_product: f32 = (v * v.transpose()).into_scalar();

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Views based on index and length

pub fn row(&self, i: usize) -> MatrixView<'_, T, U1, C, S::RStride, S::CStride>

Returns a view containing the i-th row of this matrix.

pub fn row_part( &self, i: usize, n: usize, ) -> MatrixView<'_, T, U1, Dyn, S::RStride, S::CStride>

Returns a view containing the n first elements of the i-th row of this matrix.

pub fn rows( &self, first_row: usize, nrows: usize, ) -> MatrixView<'_, T, Dyn, C, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive rows.

pub fn rows_with_step( &self, first_row: usize, nrows: usize, step: usize, ) -> MatrixView<'_, T, Dyn, C, Dyn, S::CStride>

Extracts from this matrix a set of consecutive rows regularly skipping step rows.

pub fn fixed_rows<const RVIEW: usize>( &self, first_row: usize, ) -> MatrixView<'_, T, Const<RVIEW>, C, S::RStride, S::CStride>

Extracts a compile-time number of consecutive rows from this matrix.

pub fn fixed_rows_with_step<const RVIEW: usize>( &self, first_row: usize, step: usize, ) -> MatrixView<'_, T, Const<RVIEW>, C, Dyn, S::CStride>

Extracts from this matrix a compile-time number of rows regularly skipping step rows.

pub fn rows_generic<RView: Dim>( &self, row_start: usize, nrows: RView, ) -> MatrixView<'_, T, RView, C, S::RStride, S::CStride>

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn rows_generic_with_step<RView>( &self, row_start: usize, nrows: RView, step: usize, ) -> MatrixView<'_, T, RView, C, Dyn, S::CStride>

where RView: Dim,

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn column( &self, i: usize, ) -> MatrixView<'_, T, R, U1, S::RStride, S::CStride>

Returns a view containing the i-th column of this matrix.

pub fn column_part( &self, i: usize, n: usize, ) -> MatrixView<'_, T, Dyn, U1, S::RStride, S::CStride>

Returns a view containing the n first elements of the i-th column of this matrix.

pub fn columns( &self, first_col: usize, ncols: usize, ) -> MatrixView<'_, T, R, Dyn, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive columns.

pub fn columns_with_step( &self, first_col: usize, ncols: usize, step: usize, ) -> MatrixView<'_, T, R, Dyn, S::RStride, Dyn>

Extracts from this matrix a set of consecutive columns regularly skipping step columns.

pub fn fixed_columns<const CVIEW: usize>( &self, first_col: usize, ) -> MatrixView<'_, T, R, Const<CVIEW>, S::RStride, S::CStride>

Extracts a compile-time number of consecutive columns from this matrix.

pub fn fixed_columns_with_step<const CVIEW: usize>( &self, first_col: usize, step: usize, ) -> MatrixView<'_, T, R, Const<CVIEW>, S::RStride, Dyn>

Extracts from this matrix a compile-time number of columns regularly skipping step columns.

pub fn columns_generic<CView: Dim>( &self, first_col: usize, ncols: CView, ) -> MatrixView<'_, T, R, CView, S::RStride, S::CStride>

Extracts from this matrix ncols columns. The number of columns may or may not be known at compile-time.

pub fn columns_generic_with_step<CView: Dim>( &self, first_col: usize, ncols: CView, step: usize, ) -> MatrixView<'_, T, R, CView, S::RStride, Dyn>

Extracts from this matrix ncols columns skipping step columns. Both argument may or may not be values known at compile-time.

pub fn slice( &self, start: (usize, usize), shape: (usize, usize), ) -> MatrixView<'_, T, Dyn, Dyn, S::RStride, S::CStride>

👎Deprecated: Use view instead. See issue #1076 for more information.

Slices this matrix starting at its component (irow, icol) and with (nrows, ncols) consecutive elements.

pub fn view( &self, start: (usize, usize), shape: (usize, usize), ) -> MatrixView<'_, T, Dyn, Dyn, S::RStride, S::CStride>

Return a view of this matrix starting at its component (irow, icol) and with (nrows, ncols) consecutive elements.

pub fn slice_with_steps( &self, start: (usize, usize), shape: (usize, usize), steps: (usize, usize), ) -> MatrixView<'_, T, Dyn, Dyn, Dyn, Dyn>

👎Deprecated: Use view_with_steps instead. See issue #1076 for more information.

Slices this matrix starting at its component (start.0, start.1) and with (shape.0, shape.1) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn view_with_steps( &self, start: (usize, usize), shape: (usize, usize), steps: (usize, usize), ) -> MatrixView<'_, T, Dyn, Dyn, Dyn, Dyn>

Return a view of this matrix starting at its component (start.0, start.1) and with (shape.0, shape.1) components. Each row (resp. column) of the matrix view is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn fixed_slice<const RVIEW: usize, const CVIEW: usize>( &self, irow: usize, icol: usize, ) -> MatrixView<'_, T, Const<RVIEW>, Const<CVIEW>, S::RStride, S::CStride>

👎Deprecated: Use fixed_view instead. See issue #1076 for more information.

Slices this matrix starting at its component (irow, icol) and with (RVIEW, CVIEW) consecutive components.

pub fn fixed_view<const RVIEW: usize, const CVIEW: usize>( &self, irow: usize, icol: usize, ) -> MatrixView<'_, T, Const<RVIEW>, Const<CVIEW>, S::RStride, S::CStride>

Return a view of this matrix starting at its component (irow, icol) and with (RVIEW, CVIEW) consecutive components.

pub fn fixed_slice_with_steps<const RVIEW: usize, const CVIEW: usize>( &self, start: (usize, usize), steps: (usize, usize), ) -> MatrixView<'_, T, Const<RVIEW>, Const<CVIEW>, Dyn, Dyn>

👎Deprecated: Use fixed_view_with_steps instead. See issue #1076 for more information.

Slices this matrix starting at its component (start.0, start.1) and with (RVIEW, CVIEW) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn fixed_view_with_steps<const RVIEW: usize, const CVIEW: usize>( &self, start: (usize, usize), steps: (usize, usize), ) -> MatrixView<'_, T, Const<RVIEW>, Const<CVIEW>, Dyn, Dyn>

Returns a view of this matrix starting at its component (start.0, start.1) and with (RVIEW, CVIEW) components. Each row (resp. column) of the matrix view is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn generic_slice<RView, CView>( &self, start: (usize, usize), shape: (RView, CView), ) -> MatrixView<'_, T, RView, CView, S::RStride, S::CStride>

where RView: Dim, CView: Dim,

👎Deprecated: Use generic_view instead. See issue #1076 for more information.

Creates a slice that may or may not have a fixed size and stride.

pub fn generic_view<RView, CView>( &self, start: (usize, usize), shape: (RView, CView), ) -> MatrixView<'_, T, RView, CView, S::RStride, S::CStride>

where RView: Dim, CView: Dim,

Creates a matrix view that may or may not have a fixed size and stride.

pub fn generic_slice_with_steps<RView, CView>( &self, start: (usize, usize), shape: (RView, CView), steps: (usize, usize), ) -> MatrixView<'_, T, RView, CView, Dyn, Dyn>

where RView: Dim, CView: Dim,

👎Deprecated: Use generic_view_with_steps instead. See issue #1076 for more information.

Creates a slice that may or may not have a fixed size and stride.

pub fn generic_view_with_steps<RView, CView>( &self, start: (usize, usize), shape: (RView, CView), steps: (usize, usize), ) -> MatrixView<'_, T, RView, CView, Dyn, Dyn>

where RView: Dim, CView: Dim,

Creates a matrix view that may or may not have a fixed size and stride.

pub fn rows_range_pair<Range1: DimRange<R>, Range2: DimRange<R>>( &self, r1: Range1, r2: Range2, ) -> (MatrixView<'_, T, Range1::Size, C, S::RStride, S::CStride>, MatrixView<'_, T, Range2::Size, C, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

pub fn columns_range_pair<Range1: DimRange<C>, Range2: DimRange<C>>( &self, r1: Range1, r2: Range2, ) -> (MatrixView<'_, T, R, Range1::Size, S::RStride, S::CStride>, MatrixView<'_, T, R, Range2::Size, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

Mutable views based on index and length

pub fn row_mut( &mut self, i: usize, ) -> MatrixViewMut<'_, T, U1, C, S::RStride, S::CStride>

Returns a view containing the i-th row of this matrix.

pub fn row_part_mut( &mut self, i: usize, n: usize, ) -> MatrixViewMut<'_, T, U1, Dyn, S::RStride, S::CStride>

Returns a view containing the n first elements of the i-th row of this matrix.

pub fn rows_mut( &mut self, first_row: usize, nrows: usize, ) -> MatrixViewMut<'_, T, Dyn, C, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive rows.

pub fn rows_with_step_mut( &mut self, first_row: usize, nrows: usize, step: usize, ) -> MatrixViewMut<'_, T, Dyn, C, Dyn, S::CStride>

Extracts from this matrix a set of consecutive rows regularly skipping step rows.

pub fn fixed_rows_mut<const RVIEW: usize>( &mut self, first_row: usize, ) -> MatrixViewMut<'_, T, Const<RVIEW>, C, S::RStride, S::CStride>

Extracts a compile-time number of consecutive rows from this matrix.

pub fn fixed_rows_with_step_mut<const RVIEW: usize>( &mut self, first_row: usize, step: usize, ) -> MatrixViewMut<'_, T, Const<RVIEW>, C, Dyn, S::CStride>

Extracts from this matrix a compile-time number of rows regularly skipping step rows.

pub fn rows_generic_mut<RView: Dim>( &mut self, row_start: usize, nrows: RView, ) -> MatrixViewMut<'_, T, RView, C, S::RStride, S::CStride>

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn rows_generic_with_step_mut<RView>( &mut self, row_start: usize, nrows: RView, step: usize, ) -> MatrixViewMut<'_, T, RView, C, Dyn, S::CStride>

where RView: Dim,

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn column_mut( &mut self, i: usize, ) -> MatrixViewMut<'_, T, R, U1, S::RStride, S::CStride>

Returns a view containing the i-th column of this matrix.

pub fn column_part_mut( &mut self, i: usize, n: usize, ) -> MatrixViewMut<'_, T, Dyn, U1, S::RStride, S::CStride>

Returns a view containing the n first elements of the i-th column of this matrix.

pub fn columns_mut( &mut self, first_col: usize, ncols: usize, ) -> MatrixViewMut<'_, T, R, Dyn, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive columns.

pub fn columns_with_step_mut( &mut self, first_col: usize, ncols: usize, step: usize, ) -> MatrixViewMut<'_, T, R, Dyn, S::RStride, Dyn>

Extracts from this matrix a set of consecutive columns regularly skipping step columns.

pub fn fixed_columns_mut<const CVIEW: usize>( &mut self, first_col: usize, ) -> MatrixViewMut<'_, T, R, Const<CVIEW>, S::RStride, S::CStride>

Extracts a compile-time number of consecutive columns from this matrix.

pub fn fixed_columns_with_step_mut<const CVIEW: usize>( &mut self, first_col: usize, step: usize, ) -> MatrixViewMut<'_, T, R, Const<CVIEW>, S::RStride, Dyn>

Extracts from this matrix a compile-time number of columns regularly skipping step columns.

pub fn columns_generic_mut<CView: Dim>( &mut self, first_col: usize, ncols: CView, ) -> MatrixViewMut<'_, T, R, CView, S::RStride, S::CStride>

Extracts from this matrix ncols columns. The number of columns may or may not be known at compile-time.

pub fn columns_generic_with_step_mut<CView: Dim>( &mut self, first_col: usize, ncols: CView, step: usize, ) -> MatrixViewMut<'_, T, R, CView, S::RStride, Dyn>

Extracts from this matrix ncols columns skipping step columns. Both argument may or may not be values known at compile-time.

pub fn slice_mut( &mut self, start: (usize, usize), shape: (usize, usize), ) -> MatrixViewMut<'_, T, Dyn, Dyn, S::RStride, S::CStride>

👎Deprecated: Use view_mut instead. See issue #1076 for more information.

Slices this matrix starting at its component (irow, icol) and with (nrows, ncols) consecutive elements.

pub fn view_mut( &mut self, start: (usize, usize), shape: (usize, usize), ) -> MatrixViewMut<'_, T, Dyn, Dyn, S::RStride, S::CStride>

Return a view of this matrix starting at its component (irow, icol) and with (nrows, ncols) consecutive elements.

pub fn slice_with_steps_mut( &mut self, start: (usize, usize), shape: (usize, usize), steps: (usize, usize), ) -> MatrixViewMut<'_, T, Dyn, Dyn, Dyn, Dyn>

👎Deprecated: Use view_with_steps_mut instead. See issue #1076 for more information.

Slices this matrix starting at its component (start.0, start.1) and with (shape.0, shape.1) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn view_with_steps_mut( &mut self, start: (usize, usize), shape: (usize, usize), steps: (usize, usize), ) -> MatrixViewMut<'_, T, Dyn, Dyn, Dyn, Dyn>

Return a view of this matrix starting at its component (start.0, start.1) and with (shape.0, shape.1) components. Each row (resp. column) of the matrix view is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn fixed_slice_mut<const RVIEW: usize, const CVIEW: usize>( &mut self, irow: usize, icol: usize, ) -> MatrixViewMut<'_, T, Const<RVIEW>, Const<CVIEW>, S::RStride, S::CStride>

👎Deprecated: Use fixed_view_mut instead. See issue #1076 for more information.

Slices this matrix starting at its component (irow, icol) and with (RVIEW, CVIEW) consecutive components.

pub fn fixed_view_mut<const RVIEW: usize, const CVIEW: usize>( &mut self, irow: usize, icol: usize, ) -> MatrixViewMut<'_, T, Const<RVIEW>, Const<CVIEW>, S::RStride, S::CStride>

Return a view of this matrix starting at its component (irow, icol) and with (RVIEW, CVIEW) consecutive components.

pub fn fixed_slice_with_steps_mut<const RVIEW: usize, const CVIEW: usize>( &mut self, start: (usize, usize), steps: (usize, usize), ) -> MatrixViewMut<'_, T, Const<RVIEW>, Const<CVIEW>, Dyn, Dyn>

👎Deprecated: Use fixed_view_with_steps_mut instead. See issue #1076 for more information.

Slices this matrix starting at its component (start.0, start.1) and with (RVIEW, CVIEW) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn fixed_view_with_steps_mut<const RVIEW: usize, const CVIEW: usize>( &mut self, start: (usize, usize), steps: (usize, usize), ) -> MatrixViewMut<'_, T, Const<RVIEW>, Const<CVIEW>, Dyn, Dyn>

Returns a view of this matrix starting at its component (start.0, start.1) and with (RVIEW, CVIEW) components. Each row (resp. column) of the matrix view is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn generic_slice_mut<RView, CView>( &mut self, start: (usize, usize), shape: (RView, CView), ) -> MatrixViewMut<'_, T, RView, CView, S::RStride, S::CStride>

where RView: Dim, CView: Dim,

👎Deprecated: Use generic_view_mut instead. See issue #1076 for more information.

Creates a slice that may or may not have a fixed size and stride.

pub fn generic_view_mut<RView, CView>( &mut self, start: (usize, usize), shape: (RView, CView), ) -> MatrixViewMut<'_, T, RView, CView, S::RStride, S::CStride>

where RView: Dim, CView: Dim,

Creates a matrix view that may or may not have a fixed size and stride.

pub fn generic_slice_with_steps_mut<RView, CView>( &mut self, start: (usize, usize), shape: (RView, CView), steps: (usize, usize), ) -> MatrixViewMut<'_, T, RView, CView, Dyn, Dyn>

where RView: Dim, CView: Dim,

👎Deprecated: Use generic_view_with_steps_mut instead. See issue #1076 for more information.

Creates a slice that may or may not have a fixed size and stride.

pub fn generic_view_with_steps_mut<RView, CView>( &mut self, start: (usize, usize), shape: (RView, CView), steps: (usize, usize), ) -> MatrixViewMut<'_, T, RView, CView, Dyn, Dyn>

where RView: Dim, CView: Dim,

Creates a matrix view that may or may not have a fixed size and stride.

pub fn rows_range_pair_mut<Range1: DimRange<R>, Range2: DimRange<R>>( &mut self, r1: Range1, r2: Range2, ) -> (MatrixViewMut<'_, T, Range1::Size, C, S::RStride, S::CStride>, MatrixViewMut<'_, T, Range2::Size, C, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

pub fn columns_range_pair_mut<Range1: DimRange<C>, Range2: DimRange<C>>( &mut self, r1: Range1, r2: Range2, ) -> (MatrixViewMut<'_, T, R, Range1::Size, S::RStride, S::CStride>, MatrixViewMut<'_, T, R, Range2::Size, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

pub fn slice_range<RowRange, ColRange>( &self, rows: RowRange, cols: ColRange, ) -> MatrixView<'_, T, RowRange::Size, ColRange::Size, S::RStride, S::CStride>

where RowRange: DimRange<R>, ColRange: DimRange<C>,

👎Deprecated: Use view_range instead. See issue #1076 for more information.

Slices a sub-matrix containing the rows indexed by the range rows and the columns indexed by the range cols.

pub fn view_range<RowRange, ColRange>( &self, rows: RowRange, cols: ColRange, ) -> MatrixView<'_, T, RowRange::Size, ColRange::Size, S::RStride, S::CStride>

where RowRange: DimRange<R>, ColRange: DimRange<C>,

Returns a view containing the rows indexed by the range rows and the columns indexed by the range cols.

pub fn rows_range<RowRange: DimRange<R>>( &self, rows: RowRange, ) -> MatrixView<'_, T, RowRange::Size, C, S::RStride, S::CStride>

View containing all the rows indexed by the range rows.

pub fn columns_range<ColRange: DimRange<C>>( &self, cols: ColRange, ) -> MatrixView<'_, T, R, ColRange::Size, S::RStride, S::CStride>

View containing all the columns indexed by the range rows.

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> Matrix<T, R, C, S>

pub fn slice_range_mut<RowRange, ColRange>( &mut self, rows: RowRange, cols: ColRange, ) -> MatrixViewMut<'_, T, RowRange::Size, ColRange::Size, S::RStride, S::CStride>

where RowRange: DimRange<R>, ColRange: DimRange<C>,

👎Deprecated: Use view_range_mut instead. See issue #1076 for more information.

Slices a mutable sub-matrix containing the rows indexed by the range rows and the columns indexed by the range cols.

pub fn view_range_mut<RowRange, ColRange>( &mut self, rows: RowRange, cols: ColRange, ) -> MatrixViewMut<'_, T, RowRange::Size, ColRange::Size, S::RStride, S::CStride>

where RowRange: DimRange<R>, ColRange: DimRange<C>,

Return a mutable view containing the rows indexed by the range rows and the columns indexed by the range cols.

pub fn rows_range_mut<RowRange: DimRange<R>>( &mut self, rows: RowRange, ) -> MatrixViewMut<'_, T, RowRange::Size, C, S::RStride, S::CStride>

Mutable view containing all the rows indexed by the range rows.

pub fn columns_range_mut<ColRange: DimRange<C>>( &mut self, cols: ColRange, ) -> MatrixViewMut<'_, T, R, ColRange::Size, S::RStride, S::CStride>

Mutable view containing all the columns indexed by the range cols.

impl<T, R, C, S> Matrix<T, R, C, S>

where R: Dim, C: Dim, S: RawStorage<T, R, C>,

pub fn as_view<RView, CView, RViewStride, CViewStride>( &self, ) -> MatrixView<'_, T, RView, CView, RViewStride, CViewStride>

where RView: Dim, CView: Dim, RViewStride: Dim, CViewStride: Dim, ShapeConstraint: DimEq<R, RView> + DimEq<C, CView> + DimEq<RViewStride, S::RStride> + DimEq<CViewStride, S::CStride>,

Returns this matrix as a view.

The returned view type is generally ambiguous unless specified. This is particularly useful when working with functions or methods that take matrix views as input.

Panics

Panics if the dimensions of the view and the matrix are not compatible and this cannot be proven at compile-time. This might happen, for example, when constructing a static view of size 3x3 from a dynamically sized matrix of dimension 5x5.

Examples

use nalgebra::{DMatrixSlice, SMatrixView};

fn consume_view(_: DMatrixSlice<f64>) {}

let matrix = nalgebra::Matrix3::zeros();
consume_view(matrix.as_view());

let dynamic_view: DMatrixSlice<f64> = matrix.as_view();
let static_view_from_dyn: SMatrixView<f64, 3, 3> = dynamic_view.as_view();

impl<T, R, C, S> Matrix<T, R, C, S>

where R: Dim, C: Dim, S: RawStorageMut<T, R, C>,

pub fn as_view_mut<RView, CView, RViewStride, CViewStride>( &mut self, ) -> MatrixViewMut<'_, T, RView, CView, RViewStride, CViewStride>

where RView: Dim, CView: Dim, RViewStride: Dim, CViewStride: Dim, ShapeConstraint: DimEq<R, RView> + DimEq<C, CView> + DimEq<RViewStride, S::RStride> + DimEq<CViewStride, S::CStride>,

Returns this matrix as a mutable view.

The returned view type is generally ambiguous unless specified. This is particularly useful when working with functions or methods that take matrix views as input.

Panics

Panics if the dimensions of the view and the matrix are not compatible and this cannot be proven at compile-time. This might happen, for example, when constructing a static view of size 3x3 from a dynamically sized matrix of dimension 5x5.

Examples

use nalgebra::{DMatrixViewMut, SMatrixViewMut};

fn consume_view(_: DMatrixViewMut<f64>) {}

let mut matrix = nalgebra::Matrix3::zeros();
consume_view(matrix.as_view_mut());

let mut dynamic_view: DMatrixViewMut<f64> = matrix.as_view_mut();
let static_view_from_dyn: SMatrixViewMut<f64, 3, 3> = dynamic_view.as_view_mut();

impl<T: Scalar, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

Magnitude and norms

pub fn norm_squared(&self) -> T::SimdRealField

where T: SimdComplexField,

The squared L2 norm of this vector.

pub fn norm(&self) -> T::SimdRealField

where T: SimdComplexField,

The L2 norm of this matrix.

Use .apply_norm to apply a custom norm.

pub fn metric_distance<R2, C2, S2>( &self, rhs: &Matrix<T, R2, C2, S2>, ) -> T::SimdRealField

where T: SimdComplexField, R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Compute the distance between self and rhs using the metric induced by the euclidean norm.

Use .apply_metric_distance to apply a custom norm.

pub fn apply_norm(&self, norm: &impl Norm<T>) -> T::SimdRealField

where T: SimdComplexField,

Uses the given norm to compute the norm of self.

Example

let v = Vector3::new(1.0, 2.0, 3.0);
assert_eq!(v.apply_norm(&UniformNorm), 3.0);
assert_eq!(v.apply_norm(&LpNorm(1)), 6.0);
assert_eq!(v.apply_norm(&EuclideanNorm), v.norm());

pub fn apply_metric_distance<R2, C2, S2>( &self, rhs: &Matrix<T, R2, C2, S2>, norm: &impl Norm<T>, ) -> T::SimdRealField

where T: SimdComplexField, R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Uses the metric induced by the given norm to compute the metric distance between self and rhs.

Example

let v1 = Vector3::new(1.0, 2.0, 3.0);
let v2 = Vector3::new(10.0, 20.0, 30.0);

assert_eq!(v1.apply_metric_distance(&v2, &UniformNorm), 27.0);
assert_eq!(v1.apply_metric_distance(&v2, &LpNorm(1)), 27.0 + 18.0 + 9.0);
assert_eq!(v1.apply_metric_distance(&v2, &EuclideanNorm), (v1 - v2).norm());

pub fn magnitude(&self) -> T::SimdRealField

where T: SimdComplexField,

A synonym for the norm of this matrix.

Aka the length.

This function is simply implemented as a call to norm()

pub fn magnitude_squared(&self) -> T::SimdRealField

where T: SimdComplexField,

A synonym for the squared norm of this matrix.

Aka the squared length.

This function is simply implemented as a call to norm_squared()

pub fn set_magnitude(&mut self, magnitude: T::SimdRealField)

where T: SimdComplexField, S: StorageMut<T, R, C>,

Sets the magnitude of this vector.

pub fn normalize(&self) -> OMatrix<T, R, C>

where T: SimdComplexField, DefaultAllocator: Allocator<R, C>,

Returns a normalized version of this matrix.

pub fn lp_norm(&self, p: i32) -> T::SimdRealField

where T: SimdComplexField,

The Lp norm of this matrix.

pub fn simd_try_normalize( &self, min_norm: T::SimdRealField, ) -> SimdOption<OMatrix<T, R, C>>

where T: SimdComplexField, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

Attempts to normalize self.

The components of this matrix can be SIMD types.

pub fn try_set_magnitude( &mut self, magnitude: T::RealField, min_magnitude: T::RealField, )

where T: ComplexField, S: StorageMut<T, R, C>,

Sets the magnitude of this vector unless it is smaller than min_magnitude.

If self.magnitude() is smaller than min_magnitude, it will be left unchanged. Otherwise this is equivalent to: *self = self.normalize() * magnitude.

pub fn cap_magnitude(&self, max: T::RealField) -> OMatrix<T, R, C>

where T: ComplexField, DefaultAllocator: Allocator<R, C>,

Returns a new vector with the same magnitude as self clamped between 0.0 and max.

pub fn simd_cap_magnitude(&self, max: T::SimdRealField) -> OMatrix<T, R, C>

where T: SimdComplexField, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

Returns a new vector with the same magnitude as self clamped between 0.0 and max.

pub fn try_normalize(&self, min_norm: T::RealField) -> Option<OMatrix<T, R, C>>

where T: ComplexField, DefaultAllocator: Allocator<R, C>,

Returns a normalized version of this matrix unless its norm as smaller or equal to eps.

The components of this matrix cannot be SIMD types (see simd_try_normalize) instead.

impl<T: Scalar, R: Dim, C: Dim, S: StorageMut<T, R, C>> Matrix<T, R, C, S>

In-place normalization

pub fn normalize_mut(&mut self) -> T::SimdRealField

where T: SimdComplexField,

Normalizes this matrix in-place and returns its norm.

The components of the matrix cannot be SIMD types (see simd_try_normalize_mut instead).

pub fn simd_try_normalize_mut( &mut self, min_norm: T::SimdRealField, ) -> SimdOption<T::SimdRealField>

where T: SimdComplexField, T::Element: Scalar, DefaultAllocator: Allocator<R, C>,

Normalizes this matrix in-place and return its norm.

The components of the matrix can be SIMD types.

pub fn try_normalize_mut( &mut self, min_norm: T::RealField, ) -> Option<T::RealField>

where T: ComplexField,

Normalizes this matrix in-place or does nothing if its norm is smaller or equal to eps.

If the normalization succeeded, returns the old norm of this matrix.

impl<T: ComplexField, D: DimName> Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<T>>

where DefaultAllocator: Allocator<D>,

Basis and orthogonalization

pub fn orthonormalize(vs: &mut [Self]) -> usize

Orthonormalizes the given family of vectors. The largest free family of vectors is moved at the beginning of the array and its size is returned. Vectors at an indices larger or equal to this length can be modified to an arbitrary value.

pub fn orthonormal_subspace_basis<F>(vs: &[Self], f: F)

where F: FnMut(&Self) -> bool,

Applies the given closure to each element of the orthonormal basis of the subspace orthogonal to free family of vectors vs. If vs is not a free family, the result is unspecified.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

pub fn len(&self) -> usize

The total number of elements of this matrix.

Examples:

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.len(), 12);

pub fn is_empty(&self) -> bool

Returns true if the matrix contains no elements.

Examples:

let mat = Matrix3x4::<f32>::zeros();
assert!(!mat.is_empty());

pub fn is_square(&self) -> bool

Indicates if this is a square matrix.

pub fn is_identity(&self, eps: T::Epsilon) -> bool

where T: Zero + One + RelativeEq, T::Epsilon: Clone,

Indicated if this is the identity matrix within a relative error of eps.

If the matrix is diagonal, this checks that diagonal elements (i.e. at coordinates (i, i) for i from 0 to min(R, C)) are equal one; and that all other elements are zero.

impl<T: ComplexField, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

pub fn is_orthogonal(&self, eps: T::Epsilon) -> bool

where T: Zero + One + ClosedAddAssign + ClosedMulAssign + RelativeEq, S: Storage<T, R, C>, T::Epsilon: Clone, DefaultAllocator: Allocator<R, C> + Allocator<C, C>,

Checks that Mᵀ × M = Id.

In this definition Id is approximately equal to the identity matrix with a relative error equal to eps.

impl<T: RealField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

where DefaultAllocator: Allocator<D, D>,

pub fn is_special_orthogonal(&self, eps: T) -> bool

where D: DimMin<D, Output = D>, DefaultAllocator: Allocator<D>,

Checks that this matrix is orthogonal and has a determinant equal to 1.

pub fn is_invertible(&self) -> bool

Returns true if this matrix is invertible.

impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Folding on columns and rows

pub fn compress_rows( &self, f: impl Fn(VectorView<'_, T, R, S::RStride, S::CStride>) -> T, ) -> RowOVector<T, C>

where DefaultAllocator: Allocator<U1, C>,

Returns a row vector where each element is the result of the application of f on the corresponding column of the original matrix.

pub fn compress_rows_tr( &self, f: impl Fn(VectorView<'_, T, R, S::RStride, S::CStride>) -> T, ) -> OVector<T, C>

where DefaultAllocator: Allocator<C>,

Returns a column vector where each element is the result of the application of f on the corresponding column of the original matrix.

This is the same as self.compress_rows(f).transpose().

pub fn compress_columns( &self, init: OVector<T, R>, f: impl Fn(&mut OVector<T, R>, VectorView<'_, T, R, S::RStride, S::CStride>), ) -> OVector<T, R>

where DefaultAllocator: Allocator<R>,

Returns a column vector resulting from the folding of f on each column of this matrix.

impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Common statistics operations

pub fn sum(&self) -> T

where T: ClosedAddAssign + Zero,

The sum of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.sum(), 21.0);

pub fn row_sum(&self) -> RowOVector<T, C>

where T: ClosedAddAssign + Zero, DefaultAllocator: Allocator<U1, C>,

The sum of all the rows of this matrix.

Use .row_sum_tr if you need the result in a column vector instead.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_sum(), RowVector3::new(5.0, 7.0, 9.0));

let mint = Matrix3x2::new(1, 2,
                          3, 4,
                          5, 6);
assert_eq!(mint.row_sum(), RowVector2::new(9,12));

pub fn row_sum_tr(&self) -> OVector<T, C>

where T: ClosedAddAssign + Zero, DefaultAllocator: Allocator<C>,

The sum of all the rows of this matrix. The result is transposed and returned as a column vector.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_sum_tr(), Vector3::new(5.0, 7.0, 9.0));

let mint = Matrix3x2::new(1, 2,
                          3, 4,
                          5, 6);
assert_eq!(mint.row_sum_tr(), Vector2::new(9, 12));

pub fn column_sum(&self) -> OVector<T, R>

where T: ClosedAddAssign + Zero, DefaultAllocator: Allocator<R>,

The sum of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.column_sum(), Vector2::new(6.0, 15.0));

let mint = Matrix3x2::new(1, 2,
                          3, 4,
                          5, 6);
assert_eq!(mint.column_sum(), Vector3::new(3, 7, 11));

pub fn product(&self) -> T

where T: ClosedMulAssign + One,

The product of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.product(), 720.0);

pub fn row_product(&self) -> RowOVector<T, C>

where T: ClosedMulAssign + One, DefaultAllocator: Allocator<U1, C>,

The product of all the rows of this matrix.

Use .row_sum_tr if you need the result in a column vector instead.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_product(), RowVector3::new(4.0, 10.0, 18.0));

let mint = Matrix3x2::new(1, 2,
                          3, 4,
                          5, 6);
assert_eq!(mint.row_product(), RowVector2::new(15, 48));

pub fn row_product_tr(&self) -> OVector<T, C>

where T: ClosedMulAssign + One, DefaultAllocator: Allocator<C>,

The product of all the rows of this matrix. The result is transposed and returned as a column vector.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_product_tr(), Vector3::new(4.0, 10.0, 18.0));

let mint = Matrix3x2::new(1, 2,
                          3, 4,
                          5, 6);
assert_eq!(mint.row_product_tr(), Vector2::new(15, 48));

pub fn column_product(&self) -> OVector<T, R>

where T: ClosedMulAssign + One, DefaultAllocator: Allocator<R>,

The product of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.column_product(), Vector2::new(6.0, 120.0));

let mint = Matrix3x2::new(1, 2,
                          3, 4,
                          5, 6);
assert_eq!(mint.column_product(), Vector3::new(2, 12, 30));

pub fn variance(&self) -> T

where T: Field + SupersetOf<f64>,

The variance of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_relative_eq!(m.variance(), 35.0 / 12.0, epsilon = 1.0e-8);

pub fn row_variance(&self) -> RowOVector<T, C>

where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<U1, C>,

The variance of all the rows of this matrix.

Use .row_variance_tr if you need the result in a column vector instead.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_variance(), RowVector3::new(2.25, 2.25, 2.25));

pub fn row_variance_tr(&self) -> OVector<T, C>

where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<C>,

The variance of all the rows of this matrix. The result is transposed and returned as a column vector.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_variance_tr(), Vector3::new(2.25, 2.25, 2.25));

pub fn column_variance(&self) -> OVector<T, R>

where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<R>,

The variance of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_relative_eq!(m.column_variance(), Vector2::new(2.0 / 3.0, 2.0 / 3.0), epsilon = 1.0e-8);

pub fn mean(&self) -> T

where T: Field + SupersetOf<f64>,

The mean of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.mean(), 3.5);

pub fn row_mean(&self) -> RowOVector<T, C>

where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<U1, C>,

The mean of all the rows of this matrix.

Use .row_mean_tr if you need the result in a column vector instead.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_mean(), RowVector3::new(2.5, 3.5, 4.5));

pub fn row_mean_tr(&self) -> OVector<T, C>

where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<C>,

The mean of all the rows of this matrix. The result is transposed and returned as a column vector.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_mean_tr(), Vector3::new(2.5, 3.5, 4.5));

pub fn column_mean(&self) -> OVector<T, R>

where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<R>,

The mean of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.column_mean(), Vector2::new(2.0, 5.0));

impl<T: Scalar, D, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

where D: DimName + ToTypenum,

Swizzling

pub fn xx(&self) -> Vector2<T>

where D::Typenum: Cmp<U0, Output = Greater>,

Builds a new vector from components of self.

pub fn xxx(&self) -> Vector3<T>

where D::Typenum: Cmp<U0, Output = Greater>,

Builds a new vector from components of self.

pub fn xy(&self) -> Vector2<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yx(&self) -> Vector2<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yy(&self) -> Vector2<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xxy(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xyx(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xyy(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yxx(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yxy(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yyx(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yyy(&self) -> Vector3<T>

where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xz(&self) -> Vector2<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yz(&self) -> Vector2<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zx(&self) -> Vector2<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zy(&self) -> Vector2<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zz(&self) -> Vector2<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xxz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xyz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xzx(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xzy(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xzz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yxz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yyz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yzx(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yzy(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yzz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zxx(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zxy(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zxz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zyx(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zyy(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zyz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zzx(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zzy(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zzz(&self) -> Vector3<T>

where D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

impl<T: Scalar + Zero + One + ClosedAddAssign + ClosedSubAssign + ClosedMulAssign, D: Dim, S: Storage<T, D>> Matrix<T, D, Const<1>, S>

Interpolation

pub fn lerp<S2: Storage<T, D>>( &self, rhs: &Vector<T, D, S2>, t: T, ) -> OVector<T, D>

where DefaultAllocator: Allocator<D>,

Returns self * (1.0 - t) + rhs * t, i.e., the linear blend of the vectors x and y using the scalar value a.

The value for a is not restricted to the range [0, 1].

Examples:

let x = Vector3::new(1.0, 2.0, 3.0);
let y = Vector3::new(10.0, 20.0, 30.0);
assert_eq!(x.lerp(&y, 0.1), Vector3::new(1.9, 3.8, 5.7));

pub fn slerp<S2: Storage<T, D>>( &self, rhs: &Vector<T, D, S2>, t: T, ) -> OVector<T, D>

where T: RealField, DefaultAllocator: Allocator<D>,

Computes the spherical linear interpolation between two non-zero vectors.

The result is a unit vector.

Examples:

let v1 =Vector2::new(1.0, 2.0);
let v2 = Vector2::new(2.0, -3.0);

let v = v1.slerp(&v2, 1.0);

assert_eq!(v, v2.normalize());

impl<T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

Find the min and max components

pub fn amax(&self) -> T

where T: Zero + SimdSigned + SimdPartialOrd,

Returns the absolute value of the component with the largest absolute value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).amax(), 3.0);
assert_eq!(Vector3::new(-1.0, -2.0, -3.0).amax(), 3.0);

pub fn camax(&self) -> T::SimdRealField

where T: SimdComplexField,

Returns the the 1-norm of the complex component with the largest 1-norm.

Example

assert_eq!(Vector3::new(
    Complex::new(-3.0, -2.0),
    Complex::new(1.0, 2.0),
    Complex::new(1.0, 3.0)).camax(), 5.0);

pub fn max(&self) -> T

where T: SimdPartialOrd + Zero,

Returns the component with the largest value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).max(), 3.0);
assert_eq!(Vector3::new(-1.0, -2.0, -3.0).max(), -1.0);
assert_eq!(Vector3::new(5u32, 2, 3).max(), 5);

pub fn amin(&self) -> T

where T: Zero + SimdPartialOrd + SimdSigned,

Returns the absolute value of the component with the smallest absolute value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, -3.0).amin(), 1.0);
assert_eq!(Vector3::new(10.0, 2.0, 30.0).amin(), 2.0);

pub fn camin(&self) -> T::SimdRealField

where T: SimdComplexField,

Returns the the 1-norm of the complex component with the smallest 1-norm.

Example

assert_eq!(Vector3::new(
    Complex::new(-3.0, -2.0),
    Complex::new(1.0, 2.0),
    Complex::new(1.0, 3.0)).camin(), 3.0);

pub fn min(&self) -> T

where T: SimdPartialOrd + Zero,

Returns the component with the smallest value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).min(), -1.0);
assert_eq!(Vector3::new(1.0, 2.0, 3.0).min(), 1.0);
assert_eq!(Vector3::new(5u32, 2, 3).min(), 2);

pub fn icamax_full(&self) -> (usize, usize)

where T: ComplexField,

Computes the index of the matrix component with the largest absolute value.

Examples:

let mat = Matrix2x3::new(Complex::new(11.0, 1.0), Complex::new(-12.0, 2.0), Complex::new(13.0, 3.0),
                         Complex::new(21.0, 43.0), Complex::new(22.0, 5.0), Complex::new(-23.0, 0.0));
assert_eq!(mat.icamax_full(), (1, 0));

impl<T: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

pub fn iamax_full(&self) -> (usize, usize)

Computes the index of the matrix component with the largest absolute value.

Examples:

let mat = Matrix2x3::new(11, -12, 13,
                         21, 22, -23);
assert_eq!(mat.iamax_full(), (1, 2));

impl<T: Scalar, D: Dim, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

Find the min and max components (vector-specific methods)

pub fn icamax(&self) -> usize

where T: ComplexField,

Computes the index of the vector component with the largest complex or real absolute value.

Examples:

let vec = Vector3::new(Complex::new(11.0, 3.0), Complex::new(-15.0, 0.0), Complex::new(13.0, 5.0));
assert_eq!(vec.icamax(), 2);

pub fn argmax(&self) -> (usize, T)

where T: PartialOrd,

Computes the index and value of the vector component with the largest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.argmax(), (2, 13));

pub fn imax(&self) -> usize

where T: PartialOrd,

Computes the index of the vector component with the largest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.imax(), 2);

pub fn iamax(&self) -> usize

where T: PartialOrd + Signed,

Computes the index of the vector component with the largest absolute value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.iamax(), 1);

pub fn argmin(&self) -> (usize, T)

where T: PartialOrd,

Computes the index and value of the vector component with the smallest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.argmin(), (1, -15));

pub fn imin(&self) -> usize

where T: PartialOrd,

Computes the index of the vector component with the smallest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.imin(), 1);

pub fn iamin(&self) -> usize

where T: PartialOrd + Signed,

Computes the index of the vector component with the smallest absolute value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.iamin(), 0);

impl<T: RealField, D1: Dim, S1: Storage<T, D1>> Matrix<T, D1, Const<1>, S1>

pub fn convolve_full<D2, S2>( &self, kernel: Vector<T, D2, S2>, ) -> OVector<T, DimDiff<DimSum<D1, D2>, U1>>

where D1: DimAdd<D2>, D2: DimAdd<D1, Output = DimSum<D1, D2>>, DimSum<D1, D2>: DimSub<U1>, S2: Storage<T, D2>, DefaultAllocator: Allocator<DimDiff<DimSum<D1, D2>, U1>>,

Returns the convolution of the target vector and a kernel.

Arguments

• kernel - A Vector with size > 0

Errors

Inputs must satisfy vector.len() >= kernel.len() > 0.

pub fn convolve_valid<D2, S2>( &self, kernel: Vector<T, D2, S2>, ) -> OVector<T, DimDiff<DimSum<D1, U1>, D2>>

where D1: DimAdd<U1>, D2: Dim, DimSum<D1, U1>: DimSub<D2>, S2: Storage<T, D2>, DefaultAllocator: Allocator<DimDiff<DimSum<D1, U1>, D2>>,

Returns the convolution of the target vector and a kernel.

The output convolution consists only of those elements that do not rely on the zero-padding.

Arguments

• kernel - A Vector with size > 0

Errors

Inputs must satisfy self.len() >= kernel.len() > 0.

pub fn convolve_same<D2, S2>(&self, kernel: Vector<T, D2, S2>) -> OVector<T, D1>

where D2: Dim, S2: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

Returns the convolution of the target vector and a kernel.

The output convolution is the same size as vector, centered with respect to the ‘full’ output.

Arguments

• kernel - A Vector with size > 0

Errors

Inputs must satisfy self.len() >= kernel.len() > 0.

impl<T: ComplexField, D: DimMin<D, Output = D>, S: Storage<T, D, D>> Matrix<T, D, D, S>

pub fn determinant(&self) -> T

where DefaultAllocator: Allocator<D, D> + Allocator<D>,

Computes the matrix determinant.

If the matrix has a dimension larger than 3, an LU decomposition is used.

impl<T: ComplexField, R: Dim, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

Rectangular matrix decomposition

This section contains the methods for computing some common decompositions of rectangular matrices with real or complex components. The following are currently supported:

Decomposition	Factors	Details
QR	Q * R	Q is an unitary matrix, and R is upper-triangular.
QR with column pivoting	Q * R * P⁻¹	Q is an unitary matrix, and R is upper-triangular. P is a permutation matrix.
LU with partial pivoting	P⁻¹ * L * U	L is lower-triangular with a diagonal filled with 1 and U is upper-triangular. P is a permutation matrix.
LU with full pivoting	P⁻¹ * L * U * Q⁻¹	L is lower-triangular with a diagonal filled with 1 and U is upper-triangular. P and Q are permutation matrices.
SVD	U * Σ * Vᵀ	U and V are two orthogonal matrices and Σ is a diagonal matrix containing the singular values.
Polar (Left Polar)	P' * U	U is semi-unitary/unitary and P' is a positive semi-definite Hermitian Matrix

pub fn bidiagonalize(self) -> Bidiagonal<T, R, C>

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimMinimum<R, C>> + Allocator<DimDiff<DimMinimum<R, C>, U1>>,

Computes the bidiagonalization using householder reflections.

pub fn full_piv_lu(self) -> FullPivLU<T, R, C>

where R: DimMin<C>, DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>,

Computes the LU decomposition with full pivoting of matrix.

This effectively computes P, L, U, Q such that P * matrix * Q = LU.

pub fn lu(self) -> LU<T, R, C>

where R: DimMin<C>, DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>>,

Computes the LU decomposition with partial (row) pivoting of matrix.

pub fn qr(self) -> QR<T, R, C>

where R: DimMin<C>, DefaultAllocator: Allocator<R, C> + Allocator<R> + Allocator<DimMinimum<R, C>>,

Computes the QR decomposition of this matrix.

pub fn col_piv_qr(self) -> ColPivQR<T, R, C>

where R: DimMin<C>, DefaultAllocator: Allocator<R, C> + Allocator<R> + Allocator<DimMinimum<R, C>>,

Computes the QR decomposition (with column pivoting) of this matrix.

pub fn svd(self, compute_u: bool, compute_v: bool) -> SVD<T, R, C>

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>>,

Computes the Singular Value Decomposition using implicit shift. The singular values are guaranteed to be sorted in descending order. If this order is not required consider using svd_unordered.

pub fn svd_unordered(self, compute_u: bool, compute_v: bool) -> SVD<T, R, C>

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>>,

Computes the Singular Value Decomposition using implicit shift. The singular values are not guaranteed to be sorted in any particular order. If a descending order is required, consider using svd instead.

pub fn try_svd( self, compute_u: bool, compute_v: bool, eps: T::RealField, max_niter: usize, ) -> Option<SVD<T, R, C>>

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>>,

Attempts to compute the Singular Value Decomposition of matrix using implicit shift. The singular values are guaranteed to be sorted in descending order. If this order is not required consider using try_svd_unordered.

Arguments

• compute_u − set this to true to enable the computation of left-singular vectors.
• compute_v − set this to true to enable the computation of right-singular vectors.
• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn try_svd_unordered( self, compute_u: bool, compute_v: bool, eps: T::RealField, max_niter: usize, ) -> Option<SVD<T, R, C>>

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>>,

Attempts to compute the Singular Value Decomposition of matrix using implicit shift. The singular values are not guaranteed to be sorted in any particular order. If a descending order is required, consider using try_svd instead.

Arguments

• compute_u − set this to true to enable the computation of left-singular vectors.
• compute_v − set this to true to enable the computation of right-singular vectors.
• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn polar(self) -> (OMatrix<T, R, R>, OMatrix<T, R, C>)

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>, R> + Allocator<DimMinimum<R, C>> + Allocator<R, R> + Allocator<DimMinimum<R, C>, DimMinimum<R, C>> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>>,

Computes the Polar Decomposition of a matrix (indirectly uses SVD).

pub fn try_polar( self, eps: T::RealField, max_niter: usize, ) -> Option<(OMatrix<T, R, R>, OMatrix<T, R, C>)>

where R: DimMin<C>, DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<DimMinimum<R, C>, R> + Allocator<DimMinimum<R, C>> + Allocator<R, R> + Allocator<DimMinimum<R, C>, DimMinimum<R, C>> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>>,

Attempts to compute the Polar Decomposition of a matrix (indirectly uses SVD).

Arguments

• eps − tolerance used to determine when a value converged to 0 when computing the SVD.
• max_niter − maximum total number of iterations performed by the SVD computation algorithm.

impl<T: ComplexField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

Square matrix decomposition

This section contains the methods for computing some common decompositions of square matrices with real or complex components. The following are currently supported:

Decomposition	Factors	Details
Hessenberg	Q * H * Qᵀ	Q is a unitary matrix and H an upper-Hessenberg matrix.
Cholesky	L * Lᵀ	L is a lower-triangular matrix.
UDU	U * D * Uᵀ	U is a upper-triangular matrix, and D a diagonal matrix.
Schur decomposition	Q * T * Qᵀ	Q is an unitary matrix and T a quasi-upper-triangular matrix.
Symmetric eigendecomposition	Q ~ Λ ~ Qᵀ	Q is an unitary matrix, and Λ is a real diagonal matrix.
Symmetric tridiagonalization	Q ~ T ~ Qᵀ	Q is an unitary matrix, and T is a tridiagonal matrix.

pub fn cholesky(self) -> Option<Cholesky<T, D>>

where DefaultAllocator: Allocator<D, D>,

Attempts to compute the Cholesky decomposition of this matrix.

Returns None if the input matrix is not definite-positive. The input matrix is assumed to be symmetric and only the lower-triangular part is read.

pub fn udu(self) -> Option<UDU<T, D>>

where T: RealField, DefaultAllocator: Allocator<D> + Allocator<D, D>,

Attempts to compute the UDU decomposition of this matrix.

The input matrix self is assumed to be symmetric and this decomposition will only read the upper-triangular part of self.

pub fn hessenberg(self) -> Hessenberg<T, D>

where D: DimSub<U1>, DefaultAllocator: Allocator<D, D> + Allocator<D> + Allocator<DimDiff<D, U1>>,

Computes the Hessenberg decomposition of this matrix using householder reflections.

pub fn schur(self) -> Schur<T, D>

where D: DimSub<U1>, DefaultAllocator: Allocator<D, DimDiff<D, U1>> + Allocator<DimDiff<D, U1>> + Allocator<D, D> + Allocator<D>,

Computes the Schur decomposition of a square matrix.

pub fn try_schur( self, eps: T::RealField, max_niter: usize, ) -> Option<Schur<T, D>>

where D: DimSub<U1>, DefaultAllocator: Allocator<D, DimDiff<D, U1>> + Allocator<DimDiff<D, U1>> + Allocator<D, D> + Allocator<D>,

Attempts to compute the Schur decomposition of a square matrix.

If only eigenvalues are needed, it is more efficient to call the matrix method .eigenvalues() instead.

Arguments

• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn symmetric_eigen(self) -> SymmetricEigen<T, D>

where D: DimSub<U1>, DefaultAllocator: Allocator<D, D> + Allocator<DimDiff<D, U1>> + Allocator<D>,

Computes the eigendecomposition of this symmetric matrix.

Only the lower-triangular part (including the diagonal) of m is read.

pub fn try_symmetric_eigen( self, eps: T::RealField, max_niter: usize, ) -> Option<SymmetricEigen<T, D>>

where D: DimSub<U1>, DefaultAllocator: Allocator<D, D> + Allocator<DimDiff<D, U1>> + Allocator<D>,

Computes the eigendecomposition of the given symmetric matrix with user-specified convergence parameters.

Only the lower-triangular part (including the diagonal) of m is read.

Arguments

• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn symmetric_tridiagonalize(self) -> SymmetricTridiagonal<T, D>

where D: DimSub<U1>, DefaultAllocator: Allocator<D, D> + Allocator<DimDiff<D, U1>>,

Computes the tridiagonalization of this symmetric matrix.

Only the lower-triangular part (including the diagonal) of m is read.

impl<T: ComplexField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

pub fn try_inverse(self) -> Option<OMatrix<T, D, D>>

where DefaultAllocator: Allocator<D, D>,

Attempts to invert this square matrix.

Panics

Panics if self isn’t a square matrix.

impl<T: ComplexField, D: Dim, S: StorageMut<T, D, D>> Matrix<T, D, D, S>

pub fn try_inverse_mut(&mut self) -> bool

where DefaultAllocator: Allocator<D, D>,

Attempts to invert this square matrix in-place. Returns false and leaves self untouched if inversion fails.

Panics

Panics if self isn’t a square matrix.

impl<T, D, S> Matrix<T, D, D, S>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, D: DimMin<D, Output = D>, S: StorageMut<T, D, D>, DefaultAllocator: Allocator<D, D> + Allocator<D>,

pub fn pow_mut(&mut self, exp: u32)

Raises this matrix to an integral power exp in-place.

impl<T, D, S> Matrix<T, D, D, S>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, D: DimMin<D, Output = D>, S: StorageMut<T, D, D> + Storage<T, D, D>, DefaultAllocator: Allocator<D, D> + Allocator<D>,

pub fn pow(&self, exp: u32) -> OMatrix<T, D, D>

Raise this matrix to an integral power exp.

impl<T: ComplexField, D, S: Storage<T, D, D>> Matrix<T, D, D, S>

where D: DimSub<U1> + Dim, DefaultAllocator: Allocator<D, DimDiff<D, U1>> + Allocator<DimDiff<D, U1>> + Allocator<D, D> + Allocator<D>,

pub fn eigenvalues(&self) -> Option<OVector<T, D>>

Computes the eigenvalues of this matrix.

pub fn complex_eigenvalues(&self) -> OVector<NumComplex<T>, D>

where T: RealField, DefaultAllocator: Allocator<D>,

Computes the eigenvalues of this matrix.

impl<T: ComplexField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

pub fn solve_lower_triangular<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<OMatrix<T, R2, C2>>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_upper_triangular<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<OMatrix<T, R2, C2>>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_with_diag_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, diag: T, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self is considered not-zero. The diagonal is never read as it is assumed to be equal to diag. Returns false and does not modify its inputs if diag is zero.

pub fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<OMatrix<T, R2, C2>>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<OMatrix<T, R2, C2>>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<OMatrix<T, R2, C2>>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> Option<OMatrix<T, R2, C2>>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, ) -> bool

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

impl<T: SimdComplexField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

pub fn solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> OMatrix<T, R2, C2>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> OMatrix<T, R2, C2>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_with_diag_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, diag: T, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self is considered not-zero. The diagonal is never read as it is assumed to be equal to diag. Returns false and does not modify its inputs if diag is zero.

pub fn solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> OMatrix<T, R2, C2>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> OMatrix<T, R2, C2>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular_unchecked<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> OMatrix<T, R2, C2>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular_unchecked<R2: Dim, C2: Dim, S2>( &self, b: &Matrix<T, R2, C2, S2>, ) -> OMatrix<T, R2, C2>

where S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular_unchecked_mut<R2: Dim, C2: Dim, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, )

where S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

impl<T: ComplexField, R: DimMin<C>, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

where DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>>,

pub fn singular_values_unordered( &self, ) -> OVector<T::RealField, DimMinimum<R, C>>

Computes the singular values of this matrix. The singular values are not guaranteed to be sorted in any particular order. If a descending order is required, consider using singular_values instead.

pub fn rank(&self, eps: T::RealField) -> usize

Computes the rank of this matrix.

All singular values below eps are considered equal to 0.

pub fn pseudo_inverse( self, eps: T::RealField, ) -> Result<OMatrix<T, C, R>, &'static str>

where DefaultAllocator: Allocator<C, R>,

Computes the pseudo-inverse of this matrix.

All singular values below eps are considered equal to 0.

impl<T: ComplexField, R: DimMin<C>, C: Dim, S: Storage<T, R, C>> Matrix<T, R, C, S>

where DimMinimum<R, C>: DimSub<U1>, DefaultAllocator: Allocator<R, C> + Allocator<C> + Allocator<R> + Allocator<DimDiff<DimMinimum<R, C>, U1>> + Allocator<DimMinimum<R, C>, C> + Allocator<R, DimMinimum<R, C>> + Allocator<DimMinimum<R, C>>,

pub fn singular_values(&self) -> OVector<T::RealField, DimMinimum<R, C>>

Computes the singular values of this matrix. The singular values are guaranteed to be sorted in descending order. If this order is not required consider using singular_values_unordered.

impl<T: ComplexField, D: DimSub<U1>, S: Storage<T, D, D>> Matrix<T, D, D, S>

where DefaultAllocator: Allocator<D, D> + Allocator<DimDiff<D, U1>> + Allocator<D>,

pub fn symmetric_eigenvalues(&self) -> OVector<T::RealField, D>

Computes the eigenvalues of this symmetric matrix.

Only the lower-triangular part of the matrix is read.

Trait Implementations

impl<T, R: Dim, C: Dim, S> AbsDiffEq for Matrix<T, R, C, S>

where T: Scalar + AbsDiffEq, S: RawStorage<T, R, C>, T::Epsilon: Clone,

type Epsilon = <T as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<'a, 'b, T, D1, D2, SB> Add<&'b Matrix<T, D2, Const<1>, SB>> for &'a OPoint<T, D1>

where T: Scalar + ClosedAddAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the + operator.

fn add(self, right: &'b Vector<T, D2, SB>) -> Self::Output

Performs the + operation.

impl<'b, T, D1, D2, SB> Add<&'b Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedAddAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the + operator.

fn add(self, right: &'b Vector<T, D2, SB>) -> Self::Output

Performs the + operation.

impl<'a, 'b, T, R1, C1, R2, C2, SA, SB> Add<&'b Matrix<T, R2, C2, SB>> for &'a Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAddAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer<T>>

The resulting type after applying the + operator.

fn add(self, rhs: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<'b, T, R1, C1, R2, C2, SA, SB> Add<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAddAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer<T>>

The resulting type after applying the + operator.

fn add(self, rhs: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<'a, T, D1, D2, SB> Add<Matrix<T, D2, Const<1>, SB>> for &'a OPoint<T, D1>

where T: Scalar + ClosedAddAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the + operator.

fn add(self, right: Vector<T, D2, SB>) -> Self::Output

Performs the + operation.

impl<T, D1, D2, SB> Add<Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedAddAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the + operator.

fn add(self, right: Vector<T, D2, SB>) -> Self::Output

Performs the + operation.

impl<'a, T, R1, C1, R2, C2, SA, SB> Add<Matrix<T, R2, C2, SB>> for &'a Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAddAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R2, C2, R1, C1>, ShapeConstraint: SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R2, R1>>::Representative, <ShapeConstraint as SameNumberOfColumns<C2, C1>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R2, R1>>::Representative, <ShapeConstraint as SameNumberOfColumns<C2, C1>>::Representative>>::Buffer<T>>

The resulting type after applying the + operator.

fn add(self, rhs: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<T, R1, C1, R2, C2, SA, SB> Add<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAddAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer<T>>

The resulting type after applying the + operator.

fn add(self, rhs: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<'b, T, D1: DimName, D2: Dim, SB> AddAssign<&'b Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedAddAssign, SB: Storage<T, D2>, ShapeConstraint: SameNumberOfRows<D1, D2>, DefaultAllocator: Allocator<D1>,

fn add_assign(&mut self, right: &'b Vector<T, D2, SB>)

Performs the += operation.

impl<'b, T, R1, C1, R2, C2, SA, SB> AddAssign<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAddAssign, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn add_assign(&mut self, rhs: &'b Matrix<T, R2, C2, SB>)

Performs the += operation.

impl<T, D1: DimName, D2: Dim, SB> AddAssign<Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedAddAssign, SB: Storage<T, D2>, ShapeConstraint: SameNumberOfRows<D1, D2>, DefaultAllocator: Allocator<D1>,

fn add_assign(&mut self, right: Vector<T, D2, SB>)

Performs the += operation.

impl<T, R1, C1, R2, C2, SA, SB> AddAssign<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAddAssign, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn add_assign(&mut self, rhs: Matrix<T, R2, C2, SB>)

Performs the += operation.

impl<T: Scalar, S> AsMut<[[T; 2]; 2]> for Matrix<T, U2, U2, S>

where S: RawStorageMut<T, U2, U2> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 2]; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 2]; 3]> for Matrix<T, U2, U3, S>

where S: RawStorageMut<T, U2, U3> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 2]; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 2]; 4]> for Matrix<T, U2, U4, S>

where S: RawStorageMut<T, U2, U4> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 2]; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 2]; 5]> for Matrix<T, U2, U5, S>

where S: RawStorageMut<T, U2, U5> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 2]; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 2]; 6]> for Matrix<T, U2, U6, S>

where S: RawStorageMut<T, U2, U6> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 2]; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 3]; 2]> for Matrix<T, U3, U2, S>

where S: RawStorageMut<T, U3, U2> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 3]; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 3]; 3]> for Matrix<T, U3, U3, S>

where S: RawStorageMut<T, U3, U3> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 3]; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 3]; 4]> for Matrix<T, U3, U4, S>

where S: RawStorageMut<T, U3, U4> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 3]; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 3]; 5]> for Matrix<T, U3, U5, S>

where S: RawStorageMut<T, U3, U5> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 3]; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 3]; 6]> for Matrix<T, U3, U6, S>

where S: RawStorageMut<T, U3, U6> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 3]; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 4]; 2]> for Matrix<T, U4, U2, S>

where S: RawStorageMut<T, U4, U2> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 4]; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 4]; 3]> for Matrix<T, U4, U3, S>

where S: RawStorageMut<T, U4, U3> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 4]; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 4]; 4]> for Matrix<T, U4, U4, S>

where S: RawStorageMut<T, U4, U4> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 4]; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 4]; 5]> for Matrix<T, U4, U5, S>

where S: RawStorageMut<T, U4, U5> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 4]; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 4]; 6]> for Matrix<T, U4, U6, S>

where S: RawStorageMut<T, U4, U6> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 4]; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 5]; 2]> for Matrix<T, U5, U2, S>

where S: RawStorageMut<T, U5, U2> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 5]; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 5]; 3]> for Matrix<T, U5, U3, S>

where S: RawStorageMut<T, U5, U3> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 5]; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 5]; 4]> for Matrix<T, U5, U4, S>

where S: RawStorageMut<T, U5, U4> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 5]; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 5]; 5]> for Matrix<T, U5, U5, S>

where S: RawStorageMut<T, U5, U5> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 5]; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 5]; 6]> for Matrix<T, U5, U6, S>

where S: RawStorageMut<T, U5, U6> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 5]; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 6]; 2]> for Matrix<T, U6, U2, S>

where S: RawStorageMut<T, U6, U2> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 6]; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 6]; 3]> for Matrix<T, U6, U3, S>

where S: RawStorageMut<T, U6, U3> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 6]; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 6]; 4]> for Matrix<T, U6, U4, S>

where S: RawStorageMut<T, U6, U4> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 6]; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 6]; 5]> for Matrix<T, U6, U5, S>

where S: RawStorageMut<T, U6, U5> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 6]; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsMut<[[T; 6]; 6]> for Matrix<T, U6, U6, S>

where S: RawStorageMut<T, U6, U6> + IsContiguous,

fn as_mut(&mut self) -> &mut [[T; 6]; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 1]> for Matrix<T, U1, U1, S>

where T: Scalar, S: RawStorageMut<T, U1, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 1]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 10]> for Matrix<T, U1, U10, S>

where T: Scalar, S: RawStorageMut<T, U1, U10> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 10]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 10]> for Matrix<T, U10, U1, S>

where T: Scalar, S: RawStorageMut<T, U10, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 10]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 11]> for Matrix<T, U1, U11, S>

where T: Scalar, S: RawStorageMut<T, U1, U11> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 11]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 11]> for Matrix<T, U11, U1, S>

where T: Scalar, S: RawStorageMut<T, U11, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 11]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 12]> for Matrix<T, U1, U12, S>

where T: Scalar, S: RawStorageMut<T, U1, U12> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 12]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 12]> for Matrix<T, U12, U1, S>

where T: Scalar, S: RawStorageMut<T, U12, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 12]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 13]> for Matrix<T, U1, U13, S>

where T: Scalar, S: RawStorageMut<T, U1, U13> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 13]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 13]> for Matrix<T, U13, U1, S>

where T: Scalar, S: RawStorageMut<T, U13, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 13]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 14]> for Matrix<T, U1, U14, S>

where T: Scalar, S: RawStorageMut<T, U1, U14> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 14]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 14]> for Matrix<T, U14, U1, S>

where T: Scalar, S: RawStorageMut<T, U14, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 14]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 15]> for Matrix<T, U1, U15, S>

where T: Scalar, S: RawStorageMut<T, U1, U15> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 15]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 15]> for Matrix<T, U15, U1, S>

where T: Scalar, S: RawStorageMut<T, U15, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 15]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 16]> for Matrix<T, U1, U16, S>

where T: Scalar, S: RawStorageMut<T, U1, U16> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 16]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 16]> for Matrix<T, U16, U1, S>

where T: Scalar, S: RawStorageMut<T, U16, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 16]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 2]> for Matrix<T, U1, U2, S>

where T: Scalar, S: RawStorageMut<T, U1, U2> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 2]> for Matrix<T, U2, U1, S>

where T: Scalar, S: RawStorageMut<T, U2, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 2]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 3]> for Matrix<T, U1, U3, S>

where T: Scalar, S: RawStorageMut<T, U1, U3> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 3]> for Matrix<T, U3, U1, S>

where T: Scalar, S: RawStorageMut<T, U3, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 3]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 4]> for Matrix<T, U1, U4, S>

where T: Scalar, S: RawStorageMut<T, U1, U4> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 4]> for Matrix<T, U4, U1, S>

where T: Scalar, S: RawStorageMut<T, U4, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 5]> for Matrix<T, U1, U5, S>

where T: Scalar, S: RawStorageMut<T, U1, U5> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 5]> for Matrix<T, U5, U1, S>

where T: Scalar, S: RawStorageMut<T, U5, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 5]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 6]> for Matrix<T, U1, U6, S>

where T: Scalar, S: RawStorageMut<T, U1, U6> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 6]> for Matrix<T, U6, U1, S>

where T: Scalar, S: RawStorageMut<T, U6, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 6]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 7]> for Matrix<T, U1, U7, S>

where T: Scalar, S: RawStorageMut<T, U1, U7> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 7]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 7]> for Matrix<T, U7, U1, S>

where T: Scalar, S: RawStorageMut<T, U7, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 7]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 8]> for Matrix<T, U1, U8, S>

where T: Scalar, S: RawStorageMut<T, U1, U8> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 8]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 8]> for Matrix<T, U8, U1, S>

where T: Scalar, S: RawStorageMut<T, U8, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 8]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 9]> for Matrix<T, U1, U9, S>

where T: Scalar, S: RawStorageMut<T, U1, U9> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 9]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T, S> AsMut<[T; 9]> for Matrix<T, U9, U1, S>

where T: Scalar, S: RawStorageMut<T, U9, U1> + IsContiguous,

fn as_mut(&mut self) -> &mut [T; 9]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 2]; 2]> for Matrix<T, U2, U2, S>

where S: RawStorage<T, U2, U2> + IsContiguous,

fn as_ref(&self) -> &[[T; 2]; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 2]; 3]> for Matrix<T, U2, U3, S>

where S: RawStorage<T, U2, U3> + IsContiguous,

fn as_ref(&self) -> &[[T; 2]; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 2]; 4]> for Matrix<T, U2, U4, S>

where S: RawStorage<T, U2, U4> + IsContiguous,

fn as_ref(&self) -> &[[T; 2]; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 2]; 5]> for Matrix<T, U2, U5, S>

where S: RawStorage<T, U2, U5> + IsContiguous,

fn as_ref(&self) -> &[[T; 2]; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 2]; 6]> for Matrix<T, U2, U6, S>

where S: RawStorage<T, U2, U6> + IsContiguous,

fn as_ref(&self) -> &[[T; 2]; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 3]; 2]> for Matrix<T, U3, U2, S>

where S: RawStorage<T, U3, U2> + IsContiguous,

fn as_ref(&self) -> &[[T; 3]; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 3]; 3]> for Matrix<T, U3, U3, S>

where S: RawStorage<T, U3, U3> + IsContiguous,

fn as_ref(&self) -> &[[T; 3]; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 3]; 4]> for Matrix<T, U3, U4, S>

where S: RawStorage<T, U3, U4> + IsContiguous,

fn as_ref(&self) -> &[[T; 3]; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 3]; 5]> for Matrix<T, U3, U5, S>

where S: RawStorage<T, U3, U5> + IsContiguous,

fn as_ref(&self) -> &[[T; 3]; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 3]; 6]> for Matrix<T, U3, U6, S>

where S: RawStorage<T, U3, U6> + IsContiguous,

fn as_ref(&self) -> &[[T; 3]; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 4]; 2]> for Matrix<T, U4, U2, S>

where S: RawStorage<T, U4, U2> + IsContiguous,

fn as_ref(&self) -> &[[T; 4]; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 4]; 3]> for Matrix<T, U4, U3, S>

where S: RawStorage<T, U4, U3> + IsContiguous,

fn as_ref(&self) -> &[[T; 4]; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 4]; 4]> for Matrix<T, U4, U4, S>

where S: RawStorage<T, U4, U4> + IsContiguous,

fn as_ref(&self) -> &[[T; 4]; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 4]; 5]> for Matrix<T, U4, U5, S>

where S: RawStorage<T, U4, U5> + IsContiguous,

fn as_ref(&self) -> &[[T; 4]; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 4]; 6]> for Matrix<T, U4, U6, S>

where S: RawStorage<T, U4, U6> + IsContiguous,

fn as_ref(&self) -> &[[T; 4]; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 5]; 2]> for Matrix<T, U5, U2, S>

where S: RawStorage<T, U5, U2> + IsContiguous,

fn as_ref(&self) -> &[[T; 5]; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 5]; 3]> for Matrix<T, U5, U3, S>

where S: RawStorage<T, U5, U3> + IsContiguous,

fn as_ref(&self) -> &[[T; 5]; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 5]; 4]> for Matrix<T, U5, U4, S>

where S: RawStorage<T, U5, U4> + IsContiguous,

fn as_ref(&self) -> &[[T; 5]; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 5]; 5]> for Matrix<T, U5, U5, S>

where S: RawStorage<T, U5, U5> + IsContiguous,

fn as_ref(&self) -> &[[T; 5]; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 5]; 6]> for Matrix<T, U5, U6, S>

where S: RawStorage<T, U5, U6> + IsContiguous,

fn as_ref(&self) -> &[[T; 5]; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 6]; 2]> for Matrix<T, U6, U2, S>

where S: RawStorage<T, U6, U2> + IsContiguous,

fn as_ref(&self) -> &[[T; 6]; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 6]; 3]> for Matrix<T, U6, U3, S>

where S: RawStorage<T, U6, U3> + IsContiguous,

fn as_ref(&self) -> &[[T; 6]; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 6]; 4]> for Matrix<T, U6, U4, S>

where S: RawStorage<T, U6, U4> + IsContiguous,

fn as_ref(&self) -> &[[T; 6]; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 6]; 5]> for Matrix<T, U6, U5, S>

where S: RawStorage<T, U6, U5> + IsContiguous,

fn as_ref(&self) -> &[[T; 6]; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T: Scalar, S> AsRef<[[T; 6]; 6]> for Matrix<T, U6, U6, S>

where S: RawStorage<T, U6, U6> + IsContiguous,

fn as_ref(&self) -> &[[T; 6]; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C> + IsContiguous> AsRef<[T]> for Matrix<T, R, C, S>

fn as_ref(&self) -> &[T]

Extracts a slice containing the entire matrix entries ordered column-by-columns.

impl<T, S> AsRef<[T; 1]> for Matrix<T, U1, U1, S>

where T: Scalar, S: RawStorage<T, U1, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 1]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 10]> for Matrix<T, U1, U10, S>

where T: Scalar, S: RawStorage<T, U1, U10> + IsContiguous,

fn as_ref(&self) -> &[T; 10]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 10]> for Matrix<T, U10, U1, S>

where T: Scalar, S: RawStorage<T, U10, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 10]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 11]> for Matrix<T, U1, U11, S>

where T: Scalar, S: RawStorage<T, U1, U11> + IsContiguous,

fn as_ref(&self) -> &[T; 11]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 11]> for Matrix<T, U11, U1, S>

where T: Scalar, S: RawStorage<T, U11, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 11]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 12]> for Matrix<T, U1, U12, S>

where T: Scalar, S: RawStorage<T, U1, U12> + IsContiguous,

fn as_ref(&self) -> &[T; 12]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 12]> for Matrix<T, U12, U1, S>

where T: Scalar, S: RawStorage<T, U12, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 12]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 13]> for Matrix<T, U1, U13, S>

where T: Scalar, S: RawStorage<T, U1, U13> + IsContiguous,

fn as_ref(&self) -> &[T; 13]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 13]> for Matrix<T, U13, U1, S>

where T: Scalar, S: RawStorage<T, U13, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 13]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 14]> for Matrix<T, U1, U14, S>

where T: Scalar, S: RawStorage<T, U1, U14> + IsContiguous,

fn as_ref(&self) -> &[T; 14]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 14]> for Matrix<T, U14, U1, S>

where T: Scalar, S: RawStorage<T, U14, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 14]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 15]> for Matrix<T, U1, U15, S>

where T: Scalar, S: RawStorage<T, U1, U15> + IsContiguous,

fn as_ref(&self) -> &[T; 15]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 15]> for Matrix<T, U15, U1, S>

where T: Scalar, S: RawStorage<T, U15, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 15]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 16]> for Matrix<T, U1, U16, S>

where T: Scalar, S: RawStorage<T, U1, U16> + IsContiguous,

fn as_ref(&self) -> &[T; 16]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 16]> for Matrix<T, U16, U1, S>

where T: Scalar, S: RawStorage<T, U16, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 16]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 2]> for Matrix<T, U1, U2, S>

where T: Scalar, S: RawStorage<T, U1, U2> + IsContiguous,

fn as_ref(&self) -> &[T; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 2]> for Matrix<T, U2, U1, S>

where T: Scalar, S: RawStorage<T, U2, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 2]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 3]> for Matrix<T, U1, U3, S>

where T: Scalar, S: RawStorage<T, U1, U3> + IsContiguous,

fn as_ref(&self) -> &[T; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 3]> for Matrix<T, U3, U1, S>

where T: Scalar, S: RawStorage<T, U3, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 3]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 4]> for Matrix<T, U1, U4, S>

where T: Scalar, S: RawStorage<T, U1, U4> + IsContiguous,

fn as_ref(&self) -> &[T; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 4]> for Matrix<T, U4, U1, S>

where T: Scalar, S: RawStorage<T, U4, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 5]> for Matrix<T, U1, U5, S>

where T: Scalar, S: RawStorage<T, U1, U5> + IsContiguous,

fn as_ref(&self) -> &[T; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 5]> for Matrix<T, U5, U1, S>

where T: Scalar, S: RawStorage<T, U5, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 5]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 6]> for Matrix<T, U1, U6, S>

where T: Scalar, S: RawStorage<T, U1, U6> + IsContiguous,

fn as_ref(&self) -> &[T; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 6]> for Matrix<T, U6, U1, S>

where T: Scalar, S: RawStorage<T, U6, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 6]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 7]> for Matrix<T, U1, U7, S>

where T: Scalar, S: RawStorage<T, U1, U7> + IsContiguous,

fn as_ref(&self) -> &[T; 7]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 7]> for Matrix<T, U7, U1, S>

where T: Scalar, S: RawStorage<T, U7, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 7]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 8]> for Matrix<T, U1, U8, S>

where T: Scalar, S: RawStorage<T, U1, U8> + IsContiguous,

fn as_ref(&self) -> &[T; 8]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 8]> for Matrix<T, U8, U1, S>

where T: Scalar, S: RawStorage<T, U8, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 8]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 9]> for Matrix<T, U1, U9, S>

where T: Scalar, S: RawStorage<T, U1, U9> + IsContiguous,

fn as_ref(&self) -> &[T; 9]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, S> AsRef<[T; 9]> for Matrix<T, U9, U1, S>

where T: Scalar, S: RawStorage<T, U9, U1> + IsContiguous,

fn as_ref(&self) -> &[T; 9]

Converts this type into a shared reference of the (usually inferred) input type.

impl<T, R: Dim, C: Dim, S> Binary for Matrix<T, R, C, S>

where T: Scalar + Binary, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Scalar, S> Borrow<[[T; 2]; 2]> for Matrix<T, U2, U2, S>

where S: RawStorage<T, U2, U2> + IsContiguous,

fn borrow(&self) -> &[[T; 2]; 2]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 2]; 3]> for Matrix<T, U2, U3, S>

where S: RawStorage<T, U2, U3> + IsContiguous,

fn borrow(&self) -> &[[T; 2]; 3]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 2]; 4]> for Matrix<T, U2, U4, S>

where S: RawStorage<T, U2, U4> + IsContiguous,

fn borrow(&self) -> &[[T; 2]; 4]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 2]; 5]> for Matrix<T, U2, U5, S>

where S: RawStorage<T, U2, U5> + IsContiguous,

fn borrow(&self) -> &[[T; 2]; 5]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 2]; 6]> for Matrix<T, U2, U6, S>

where S: RawStorage<T, U2, U6> + IsContiguous,

fn borrow(&self) -> &[[T; 2]; 6]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 3]; 2]> for Matrix<T, U3, U2, S>

where S: RawStorage<T, U3, U2> + IsContiguous,

fn borrow(&self) -> &[[T; 3]; 2]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 3]; 3]> for Matrix<T, U3, U3, S>

where S: RawStorage<T, U3, U3> + IsContiguous,

fn borrow(&self) -> &[[T; 3]; 3]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 3]; 4]> for Matrix<T, U3, U4, S>

where S: RawStorage<T, U3, U4> + IsContiguous,

fn borrow(&self) -> &[[T; 3]; 4]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 3]; 5]> for Matrix<T, U3, U5, S>

where S: RawStorage<T, U3, U5> + IsContiguous,

fn borrow(&self) -> &[[T; 3]; 5]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 3]; 6]> for Matrix<T, U3, U6, S>

where S: RawStorage<T, U3, U6> + IsContiguous,

fn borrow(&self) -> &[[T; 3]; 6]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 4]; 2]> for Matrix<T, U4, U2, S>

where S: RawStorage<T, U4, U2> + IsContiguous,

fn borrow(&self) -> &[[T; 4]; 2]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 4]; 3]> for Matrix<T, U4, U3, S>

where S: RawStorage<T, U4, U3> + IsContiguous,

fn borrow(&self) -> &[[T; 4]; 3]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 4]; 4]> for Matrix<T, U4, U4, S>

where S: RawStorage<T, U4, U4> + IsContiguous,

fn borrow(&self) -> &[[T; 4]; 4]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 4]; 5]> for Matrix<T, U4, U5, S>

where S: RawStorage<T, U4, U5> + IsContiguous,

fn borrow(&self) -> &[[T; 4]; 5]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 4]; 6]> for Matrix<T, U4, U6, S>

where S: RawStorage<T, U4, U6> + IsContiguous,

fn borrow(&self) -> &[[T; 4]; 6]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 5]; 2]> for Matrix<T, U5, U2, S>

where S: RawStorage<T, U5, U2> + IsContiguous,

fn borrow(&self) -> &[[T; 5]; 2]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 5]; 3]> for Matrix<T, U5, U3, S>

where S: RawStorage<T, U5, U3> + IsContiguous,

fn borrow(&self) -> &[[T; 5]; 3]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 5]; 4]> for Matrix<T, U5, U4, S>

where S: RawStorage<T, U5, U4> + IsContiguous,

fn borrow(&self) -> &[[T; 5]; 4]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 5]; 5]> for Matrix<T, U5, U5, S>

where S: RawStorage<T, U5, U5> + IsContiguous,

fn borrow(&self) -> &[[T; 5]; 5]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 5]; 6]> for Matrix<T, U5, U6, S>

where S: RawStorage<T, U5, U6> + IsContiguous,

fn borrow(&self) -> &[[T; 5]; 6]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 6]; 2]> for Matrix<T, U6, U2, S>

where S: RawStorage<T, U6, U2> + IsContiguous,

fn borrow(&self) -> &[[T; 6]; 2]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 6]; 3]> for Matrix<T, U6, U3, S>

where S: RawStorage<T, U6, U3> + IsContiguous,

fn borrow(&self) -> &[[T; 6]; 3]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 6]; 4]> for Matrix<T, U6, U4, S>

where S: RawStorage<T, U6, U4> + IsContiguous,

fn borrow(&self) -> &[[T; 6]; 4]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 6]; 5]> for Matrix<T, U6, U5, S>

where S: RawStorage<T, U6, U5> + IsContiguous,

fn borrow(&self) -> &[[T; 6]; 5]

Immutably borrows from an owned value.

impl<T: Scalar, S> Borrow<[[T; 6]; 6]> for Matrix<T, U6, U6, S>

where S: RawStorage<T, U6, U6> + IsContiguous,

fn borrow(&self) -> &[[T; 6]; 6]

Immutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 2]; 2]> for Matrix<T, U2, U2, S>

where S: RawStorageMut<T, U2, U2> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 2]; 2]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 2]; 3]> for Matrix<T, U2, U3, S>

where S: RawStorageMut<T, U2, U3> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 2]; 3]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 2]; 4]> for Matrix<T, U2, U4, S>

where S: RawStorageMut<T, U2, U4> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 2]; 4]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 2]; 5]> for Matrix<T, U2, U5, S>

where S: RawStorageMut<T, U2, U5> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 2]; 5]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 2]; 6]> for Matrix<T, U2, U6, S>

where S: RawStorageMut<T, U2, U6> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 2]; 6]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 3]; 2]> for Matrix<T, U3, U2, S>

where S: RawStorageMut<T, U3, U2> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 3]; 2]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 3]; 3]> for Matrix<T, U3, U3, S>

where S: RawStorageMut<T, U3, U3> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 3]; 3]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 3]; 4]> for Matrix<T, U3, U4, S>

where S: RawStorageMut<T, U3, U4> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 3]; 4]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 3]; 5]> for Matrix<T, U3, U5, S>

where S: RawStorageMut<T, U3, U5> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 3]; 5]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 3]; 6]> for Matrix<T, U3, U6, S>

where S: RawStorageMut<T, U3, U6> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 3]; 6]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 4]; 2]> for Matrix<T, U4, U2, S>

where S: RawStorageMut<T, U4, U2> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 4]; 2]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 4]; 3]> for Matrix<T, U4, U3, S>

where S: RawStorageMut<T, U4, U3> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 4]; 3]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 4]; 4]> for Matrix<T, U4, U4, S>

where S: RawStorageMut<T, U4, U4> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 4]; 4]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 4]; 5]> for Matrix<T, U4, U5, S>

where S: RawStorageMut<T, U4, U5> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 4]; 5]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 4]; 6]> for Matrix<T, U4, U6, S>

where S: RawStorageMut<T, U4, U6> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 4]; 6]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 5]; 2]> for Matrix<T, U5, U2, S>

where S: RawStorageMut<T, U5, U2> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 5]; 2]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 5]; 3]> for Matrix<T, U5, U3, S>

where S: RawStorageMut<T, U5, U3> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 5]; 3]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 5]; 4]> for Matrix<T, U5, U4, S>

where S: RawStorageMut<T, U5, U4> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 5]; 4]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 5]; 5]> for Matrix<T, U5, U5, S>

where S: RawStorageMut<T, U5, U5> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 5]; 5]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 5]; 6]> for Matrix<T, U5, U6, S>

where S: RawStorageMut<T, U5, U6> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 5]; 6]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 6]; 2]> for Matrix<T, U6, U2, S>

where S: RawStorageMut<T, U6, U2> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 6]; 2]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 6]; 3]> for Matrix<T, U6, U3, S>

where S: RawStorageMut<T, U6, U3> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 6]; 3]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 6]; 4]> for Matrix<T, U6, U4, S>

where S: RawStorageMut<T, U6, U4> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 6]; 4]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 6]; 5]> for Matrix<T, U6, U5, S>

where S: RawStorageMut<T, U6, U5> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 6]; 5]

Mutably borrows from an owned value.

impl<T: Scalar, S> BorrowMut<[[T; 6]; 6]> for Matrix<T, U6, U6, S>

where S: RawStorageMut<T, U6, U6> + IsContiguous,

fn borrow_mut(&mut self) -> &mut [[T; 6]; 6]

Mutably borrows from an owned value.

impl<T: Clone, R: Clone, C: Clone, S: Clone> Clone for Matrix<T, R, C, S>

fn clone(&self) -> Matrix<T, R, C, S>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T, R: Dim, C: Dim, S: Debug> Debug for Matrix<T, R, C, S>

fn fmt(&self, formatter: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T, R, C, S> Default for Matrix<T, R, C, S>

where T: Scalar, R: Dim, C: Dim, S: Default,

fn default() -> Self

Returns the “default value” for a type.

impl<T: Scalar, S> Deref for Matrix<T, U1, U1, S>

where S: RawStorage<T, U1, U1> + IsContiguous,

type Target = X<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U1, U2, S>

where S: RawStorage<T, U1, U2> + IsContiguous,

type Target = XY<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U1, U3, S>

where S: RawStorage<T, U1, U3> + IsContiguous,

type Target = XYZ<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U1, U4, S>

where S: RawStorage<T, U1, U4> + IsContiguous,

type Target = XYZW<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U1, U5, S>

where S: RawStorage<T, U1, U5> + IsContiguous,

type Target = XYZWA<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U1, U6, S>

where S: RawStorage<T, U1, U6> + IsContiguous,

type Target = XYZWAB<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U2, U1, S>

where S: RawStorage<T, U2, U1> + IsContiguous,

type Target = XY<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U2, U2, S>

where S: RawStorage<T, U2, U2> + IsContiguous,

type Target = M2x2<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U2, U3, S>

where S: RawStorage<T, U2, U3> + IsContiguous,

type Target = M2x3<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U2, U4, S>

where S: RawStorage<T, U2, U4> + IsContiguous,

type Target = M2x4<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U2, U5, S>

where S: RawStorage<T, U2, U5> + IsContiguous,

type Target = M2x5<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U2, U6, S>

where S: RawStorage<T, U2, U6> + IsContiguous,

type Target = M2x6<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U3, U1, S>

where S: RawStorage<T, U3, U1> + IsContiguous,

type Target = XYZ<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U3, U2, S>

where S: RawStorage<T, U3, U2> + IsContiguous,

type Target = M3x2<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U3, U3, S>

where S: RawStorage<T, U3, U3> + IsContiguous,

type Target = M3x3<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U3, U4, S>

where S: RawStorage<T, U3, U4> + IsContiguous,

type Target = M3x4<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U3, U5, S>

where S: RawStorage<T, U3, U5> + IsContiguous,

type Target = M3x5<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U3, U6, S>

where S: RawStorage<T, U3, U6> + IsContiguous,

type Target = M3x6<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U4, U1, S>

where S: RawStorage<T, U4, U1> + IsContiguous,

type Target = XYZW<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U4, U2, S>

where S: RawStorage<T, U4, U2> + IsContiguous,

type Target = M4x2<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U4, U3, S>

where S: RawStorage<T, U4, U3> + IsContiguous,

type Target = M4x3<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U4, U4, S>

where S: RawStorage<T, U4, U4> + IsContiguous,

type Target = M4x4<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U4, U5, S>

where S: RawStorage<T, U4, U5> + IsContiguous,

type Target = M4x5<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U4, U6, S>

where S: RawStorage<T, U4, U6> + IsContiguous,

type Target = M4x6<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U5, U1, S>

where S: RawStorage<T, U5, U1> + IsContiguous,

type Target = XYZWA<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U5, U2, S>

where S: RawStorage<T, U5, U2> + IsContiguous,

type Target = M5x2<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U5, U3, S>

where S: RawStorage<T, U5, U3> + IsContiguous,

type Target = M5x3<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U5, U4, S>

where S: RawStorage<T, U5, U4> + IsContiguous,

type Target = M5x4<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U5, U5, S>

where S: RawStorage<T, U5, U5> + IsContiguous,

type Target = M5x5<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U5, U6, S>

where S: RawStorage<T, U5, U6> + IsContiguous,

type Target = M5x6<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U6, U1, S>

where S: RawStorage<T, U6, U1> + IsContiguous,

type Target = XYZWAB<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U6, U2, S>

where S: RawStorage<T, U6, U2> + IsContiguous,

type Target = M6x2<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U6, U3, S>

where S: RawStorage<T, U6, U3> + IsContiguous,

type Target = M6x3<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U6, U4, S>

where S: RawStorage<T, U6, U4> + IsContiguous,

type Target = M6x4<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U6, U5, S>

where S: RawStorage<T, U6, U5> + IsContiguous,

type Target = M6x5<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> Deref for Matrix<T, U6, U6, S>

where S: RawStorage<T, U6, U6> + IsContiguous,

type Target = M6x6<T>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U1, U1, S>

where S: RawStorageMut<T, U1, U1> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U1, U2, S>

where S: RawStorageMut<T, U1, U2> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U1, U3, S>

where S: RawStorageMut<T, U1, U3> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U1, U4, S>

where S: RawStorageMut<T, U1, U4> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U1, U5, S>

where S: RawStorageMut<T, U1, U5> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U1, U6, S>

where S: RawStorageMut<T, U1, U6> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U2, U1, S>

where S: RawStorageMut<T, U2, U1> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U2, U2, S>

where S: RawStorageMut<T, U2, U2> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U2, U3, S>

where S: RawStorageMut<T, U2, U3> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U2, U4, S>

where S: RawStorageMut<T, U2, U4> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U2, U5, S>

where S: RawStorageMut<T, U2, U5> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U2, U6, S>

where S: RawStorageMut<T, U2, U6> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U3, U1, S>

where S: RawStorageMut<T, U3, U1> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U3, U2, S>

where S: RawStorageMut<T, U3, U2> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U3, U3, S>

where S: RawStorageMut<T, U3, U3> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U3, U4, S>

where S: RawStorageMut<T, U3, U4> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U3, U5, S>

where S: RawStorageMut<T, U3, U5> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U3, U6, S>

where S: RawStorageMut<T, U3, U6> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U4, U1, S>

where S: RawStorageMut<T, U4, U1> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U4, U2, S>

where S: RawStorageMut<T, U4, U2> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U4, U3, S>

where S: RawStorageMut<T, U4, U3> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U4, U4, S>

where S: RawStorageMut<T, U4, U4> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U4, U5, S>

where S: RawStorageMut<T, U4, U5> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U4, U6, S>

where S: RawStorageMut<T, U4, U6> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U5, U1, S>

where S: RawStorageMut<T, U5, U1> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U5, U2, S>

where S: RawStorageMut<T, U5, U2> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U5, U3, S>

where S: RawStorageMut<T, U5, U3> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U5, U4, S>

where S: RawStorageMut<T, U5, U4> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U5, U5, S>

where S: RawStorageMut<T, U5, U5> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U5, U6, S>

where S: RawStorageMut<T, U5, U6> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U6, U1, S>

where S: RawStorageMut<T, U6, U1> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U6, U2, S>

where S: RawStorageMut<T, U6, U2> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U6, U3, S>

where S: RawStorageMut<T, U6, U3> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U6, U4, S>

where S: RawStorageMut<T, U6, U4> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U6, U5, S>

where S: RawStorageMut<T, U6, U5> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<T: Scalar, S> DerefMut for Matrix<T, U6, U6, S>

where S: RawStorageMut<T, U6, U6> + IsContiguous,

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<'de, T, R, C, S> Deserialize<'de> for Matrix<T, R, C, S>

where T: Scalar, R: Dim, C: Dim, S: Deserialize<'de>,

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T, R: Dim, C: Dim, S> Display for Matrix<T, R, C, S>

where T: Scalar + Display, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, 'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the / operation.

impl<'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the / operation.

impl<'a, T, R1, C1, SA, const D2: usize> Div<Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the / operator.

fn div(self, right: Rotation<T, D2>) -> Self::Output

Performs the / operation.

impl<T, R1, C1, SA, const D2: usize> Div<Rotation<T, D2>> for Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the / operator.

fn div(self, right: Rotation<T, D2>) -> Self::Output

Performs the / operation.

impl<'a, T, R: Dim, C: Dim, S> Div<T> for &'a Matrix<T, R, C, S>

where T: Scalar + ClosedDivAssign, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Self::Output

Performs the / operation.

impl<T, R: Dim, C: Dim, S> Div<T> for Matrix<T, R, C, S>

where T: Scalar + ClosedDivAssign, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> Self::Output

Performs the / operation.

impl<T, R: Dim, C: Dim, S> DivAssign<T> for Matrix<T, R, C, S>

where T: Scalar + ClosedDivAssign, S: StorageMut<T, R, C>,

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<'a, T: Scalar + Copy, R: Dim, C: Dim, S: RawStorage<T, R, C> + IsContiguous> From<&'a Matrix<T, R, C, S>> for &'a [T]

fn from(matrix: &'a Matrix<T, R, C, S>) -> Self

Converts to this type from the input type.

impl<'a, T, R, C, RView, CView, RStride, CStride, S> From<&'a Matrix<T, R, C, S>> for MatrixView<'a, T, RView, CView, RStride, CStride>

where R: Dim, C: Dim, RView: Dim, CView: Dim, RStride: Dim, CStride: Dim, S: RawStorage<T, R, C>, ShapeConstraint: DimEq<R, RView> + DimEq<C, CView> + DimEq<RStride, S::RStride> + DimEq<CStride, S::CStride>,

fn from(m: &'a Matrix<T, R, C, S>) -> Self

Converts to this type from the input type.

impl<'a, T: Scalar + Copy, R: Dim, C: Dim, S: RawStorageMut<T, R, C> + IsContiguous> From<&'a mut Matrix<T, R, C, S>> for &'a mut [T]

fn from(matrix: &'a mut Matrix<T, R, C, S>) -> Self

Converts to this type from the input type.

impl<'a, T, R, C, RView, CView, RStride, CStride, S> From<&'a mut Matrix<T, R, C, S>> for MatrixView<'a, T, RView, CView, RStride, CStride>

where R: Dim, C: Dim, RView: Dim, CView: Dim, RStride: Dim, CStride: Dim, S: RawStorage<T, R, C>, ShapeConstraint: DimEq<R, RView> + DimEq<C, CView> + DimEq<RStride, S::RStride> + DimEq<CStride, S::CStride>,

fn from(m: &'a mut Matrix<T, R, C, S>) -> Self

Converts to this type from the input type.

impl<'a, T, R, C, RView, CView, RStride, CStride, S> From<&'a mut Matrix<T, R, C, S>> for MatrixViewMut<'a, T, RView, CView, RStride, CStride>

where R: Dim, C: Dim, RView: Dim, CView: Dim, RStride: Dim, CStride: Dim, S: RawStorageMut<T, R, C>, ShapeConstraint: DimEq<R, RView> + DimEq<C, CView> + DimEq<RStride, S::RStride> + DimEq<CStride, S::CStride>,

fn from(m: &'a mut Matrix<T, R, C, S>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Matrix<T, Const<1>, Const<D>, ArrayStorage<T, 1, D>>> for [T; D]

where Const<D>: IsNotStaticOne,

fn from(vec: RowSVector<T, D>) -> [T; D]

Converts to this type from the input type.

impl<T: Scalar> From<Matrix<T, Const<4>, Const<1>, ArrayStorage<T, 4, 1>>> for Quaternion<T>

fn from(coords: Vector4<T>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Matrix<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<Const<D>>>::Buffer<T>>> for Scale<T, D>

fn from(vector: OVector<T, Const<D>>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Matrix<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<Const<D>>>::Buffer<T>>> for Translation<T, D>

fn from(vector: OVector<T, Const<D>>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for [T; D]

fn from(vec: SVector<T, D>) -> Self

Converts to this type from the input type.

impl<T: SimdRealField, R, const D: usize> From<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Isometry<T, R, D>

where R: AbstractRotation<T, D>,

fn from(coords: SVector<T, D>) -> Self

Converts to this type from the input type.

impl<'a, T: Scalar, RStride: Dim, CStride: Dim, const D: usize> From<Matrix<T, Const<D>, Const<1>, ViewStorage<'a, T, Const<D>, Const<1>, RStride, CStride>>> for [T; D]

fn from(vec: VectorView<'a, T, Const<D>, RStride, CStride>) -> Self

Converts to this type from the input type.

impl<'a, T: Scalar, RStride: Dim, CStride: Dim, const D: usize> From<Matrix<T, Const<D>, Const<1>, ViewStorageMut<'a, T, Const<D>, Const<1>, RStride, CStride>>> for [T; D]

fn from(vec: VectorViewMut<'a, T, Const<D>, RStride, CStride>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const R: usize, const C: usize> From<Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>> for [[T; R]; C]

fn from(mat: SMatrix<T, R, C>) -> Self

Converts to this type from the input type.

impl<'a, T: Scalar, RStride: Dim, CStride: Dim, const R: usize, const C: usize> From<Matrix<T, Const<R>, Const<C>, ViewStorage<'a, T, Const<R>, Const<C>, RStride, CStride>>> for [[T; R]; C]

fn from(mat: MatrixView<'a, T, Const<R>, Const<C>, RStride, CStride>) -> Self

Converts to this type from the input type.

impl<'a, T, RStride, CStride, const R: usize, const C: usize> From<Matrix<T, Const<R>, Const<C>, ViewStorage<'a, T, Const<R>, Const<C>, RStride, CStride>>> for Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>

where T: Scalar, RStride: Dim, CStride: Dim,

fn from( matrix_view: MatrixView<'a, T, Const<R>, Const<C>, RStride, CStride>, ) -> Self

Converts to this type from the input type.

impl<'a, T: Scalar, RStride: Dim, CStride: Dim, const R: usize, const C: usize> From<Matrix<T, Const<R>, Const<C>, ViewStorageMut<'a, T, Const<R>, Const<C>, RStride, CStride>>> for [[T; R]; C]

fn from(mat: MatrixViewMut<'a, T, Const<R>, Const<C>, RStride, CStride>) -> Self

Converts to this type from the input type.

impl<'a, T, RStride, CStride, const R: usize, const C: usize> From<Matrix<T, Const<R>, Const<C>, ViewStorageMut<'a, T, Const<R>, Const<C>, RStride, CStride>>> for Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>

where T: Scalar, RStride: Dim, CStride: Dim,

fn from( matrix_view: MatrixViewMut<'a, T, Const<R>, Const<C>, RStride, CStride>, ) -> Self

Converts to this type from the input type.

impl<T: Scalar, D: DimName> From<Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<T>>> for OPoint<T, D>

where DefaultAllocator: Allocator<D>,

fn from(coords: OVector<T, D>) -> Self

Converts to this type from the input type.

impl<'a, T: Scalar> From<Matrix<T, Dyn, Const<1>, ViewStorage<'a, T, Dyn, Const<1>, Const<1>, Dyn>>> for &'a [T]

fn from(vec: DVectorView<'a, T>) -> &'a [T]

Converts to this type from the input type.

impl<'a, T: Scalar> From<Matrix<T, Dyn, Const<1>, ViewStorageMut<'a, T, Dyn, Const<1>, Const<1>, Dyn>>> for &'a mut [T]

fn from(vec: DVectorViewMut<'a, T>) -> &'a mut [T]

Converts to this type from the input type.

impl<'a, T, R, C, RStride, CStride> From<Matrix<T, R, C, ViewStorageMut<'a, T, R, C, RStride, CStride>>> for MatrixView<'a, T, R, C, RStride, CStride>

where R: Dim, C: Dim, RStride: Dim, CStride: Dim,

fn from(view_mut: MatrixViewMut<'a, T, R, C, RStride, CStride>) -> Self

Converts to this type from the input type.

impl<S> From<Matrix<bool, Const<2>, Const<1>, S>> for BVec2

where S: RawStorage<bool, U2>,

fn from(e: Vector<bool, U2, S>) -> BVec2

Converts to this type from the input type.

impl<S> From<Matrix<bool, Const<3>, Const<1>, S>> for BVec3

where S: RawStorage<bool, U3>,

fn from(e: Vector<bool, U3, S>) -> BVec3

Converts to this type from the input type.

impl<S> From<Matrix<bool, Const<4>, Const<1>, S>> for BVec4

where S: RawStorage<bool, U4>,

fn from(e: Vector<bool, U4, S>) -> BVec4

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<2>, Const<1>, S>> for Vec2

where S: RawStorage<f32, U2>,

fn from(e: Vector<f32, U2, S>) -> Vec2

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<2>, Const<2>, S>> for Mat2

where S: RawStorage<f32, U2, U2>,

fn from(e: Matrix<f32, U2, U2, S>) -> Mat2

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<3>, Const<1>, S>> for Vec3

where S: RawStorage<f32, U3>,

fn from(e: Vector<f32, U3, S>) -> Vec3

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<3>, Const<1>, S>> for Vec3A

where S: RawStorage<f32, U3>,

fn from(e: Vector<f32, U3, S>) -> Vec3A

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<3>, Const<3>, S>> for Mat3

where S: RawStorage<f32, U3, U3>,

fn from(e: Matrix<f32, U3, U3, S>) -> Mat3

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<4>, Const<1>, S>> for Vec4

where S: RawStorage<f32, U4>,

fn from(e: Vector<f32, U4, S>) -> Vec4

Converts to this type from the input type.

impl<S> From<Matrix<f32, Const<4>, Const<4>, S>> for Mat4

where S: RawStorage<f32, U4, U4>,

fn from(e: Matrix<f32, U4, U4, S>) -> Mat4

Converts to this type from the input type.

impl<S> From<Matrix<f64, Const<2>, Const<1>, S>> for DVec2

where S: RawStorage<f64, U2>,

fn from(e: Vector<f64, U2, S>) -> DVec2

Converts to this type from the input type.

impl<S> From<Matrix<f64, Const<2>, Const<2>, S>> for DMat2

where S: RawStorage<f64, U2, U2>,

fn from(e: Matrix<f64, U2, U2, S>) -> DMat2

Converts to this type from the input type.

impl<S> From<Matrix<f64, Const<3>, Const<1>, S>> for DVec3

where S: RawStorage<f64, U3>,

fn from(e: Vector<f64, U3, S>) -> DVec3

Converts to this type from the input type.

impl<S> From<Matrix<f64, Const<3>, Const<3>, S>> for DMat3

where S: RawStorage<f64, U3, U3>,

fn from(e: Matrix<f64, U3, U3, S>) -> DMat3

Converts to this type from the input type.

impl<S> From<Matrix<f64, Const<4>, Const<1>, S>> for DVec4

where S: RawStorage<f64, U4>,

fn from(e: Vector<f64, U4, S>) -> DVec4

Converts to this type from the input type.

impl<S> From<Matrix<f64, Const<4>, Const<4>, S>> for DMat4

where S: RawStorage<f64, U4, U4>,

fn from(e: Matrix<f64, U4, U4, S>) -> DMat4

Converts to this type from the input type.

impl<S> From<Matrix<i32, Const<2>, Const<1>, S>> for IVec2

where S: RawStorage<i32, U2>,

fn from(e: Vector<i32, U2, S>) -> IVec2

Converts to this type from the input type.

impl<S> From<Matrix<i32, Const<3>, Const<1>, S>> for IVec3

where S: RawStorage<i32, U3>,

fn from(e: Vector<i32, U3, S>) -> IVec3

Converts to this type from the input type.

impl<S> From<Matrix<i32, Const<4>, Const<1>, S>> for IVec4

where S: RawStorage<i32, U4>,

fn from(e: Vector<i32, U4, S>) -> IVec4

Converts to this type from the input type.

impl<S> From<Matrix<u32, Const<2>, Const<1>, S>> for UVec2

where S: RawStorage<u32, U2>,

fn from(e: Vector<u32, U2, S>) -> UVec2

Converts to this type from the input type.

impl<S> From<Matrix<u32, Const<3>, Const<1>, S>> for UVec3

where S: RawStorage<u32, U3>,

fn from(e: Vector<u32, U3, S>) -> UVec3

Converts to this type from the input type.

impl<S> From<Matrix<u32, Const<4>, Const<1>, S>> for UVec4

where S: RawStorage<u32, U4>,

fn from(e: Vector<u32, U4, S>) -> UVec4

Converts to this type from the input type.

impl<T, R, C, S> Hash for Matrix<T, R, C, S>

where T: Scalar + Hash, R: Dim, C: Dim, S: RawStorage<T, R, C>,

fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Index<(usize, usize)> for Matrix<T, R, C, S>

type Output = T

The returned type after indexing.

fn index(&self, ij: (usize, usize)) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Index<usize> for Matrix<T, R, C, S>

type Output = T

The returned type after indexing.

fn index(&self, i: usize) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> IndexMut<(usize, usize)> for Matrix<T, R, C, S>

fn index_mut(&mut self, ij: (usize, usize)) -> &mut T

Performs the mutable indexing (container[index]) operation.

impl<T, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> IndexMut<usize> for Matrix<T, R, C, S>

fn index_mut(&mut self, i: usize) -> &mut T

Performs the mutable indexing (container[index]) operation.

impl<'a, T: Scalar, R: Dim, C: Dim, S: RawStorage<T, R, C>> IntoIterator for &'a Matrix<T, R, C, S>

type Item = &'a T

The type of the elements being iterated over.

type IntoIter = MatrixIter<'a, T, R, C, S>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<'a, T: Scalar, R: Dim, C: Dim, S: RawStorageMut<T, R, C>> IntoIterator for &'a mut Matrix<T, R, C, S>

type Item = &'a mut T

The type of the elements being iterated over.

type IntoIter = MatrixIterMut<'a, T, R, C, S>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<'a, T: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> IntoIterator for Matrix<T, R, C, ViewStorage<'a, T, R, C, RStride, CStride>>

type Item = &'a T

The type of the elements being iterated over.

type IntoIter = MatrixIter<'a, T, R, C, ViewStorage<'a, T, R, C, RStride, CStride>>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<'a, T: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> IntoIterator for Matrix<T, R, C, ViewStorageMut<'a, T, R, C, RStride, CStride>>

type Item = &'a mut T

The type of the elements being iterated over.

type IntoIter = MatrixIterMut<'a, T, R, C, ViewStorageMut<'a, T, R, C, RStride, CStride>>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<T, R: Dim, C: Dim, S> LowerExp for Matrix<T, R, C, S>

where T: Scalar + LowerExp, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, R: Dim, C: Dim, S> LowerHex for Matrix<T, R, C, S>

where T: Scalar + LowerHex, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, 'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Matrix<T, Const<2>, Const<1>, S>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<T, Const<2>, S>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Matrix<T, Const<2>, Const<1>, S>> for UnitComplex<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<T, Const<2>, S>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<T, Const<3>, SB>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Matrix<T, Const<3>, Const<1>, SB>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Isometry<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Scale<T, D>

where T: Scalar + ClosedMulAssign, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Similarity<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Transform<T, C, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, Const<D>: DimNameAdd<U1>, C: TCategory, DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Isometry<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Scale<T, D>

where T: Scalar + ClosedMulAssign, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Similarity<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Transform<T, C, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, Const<D>: DimNameAdd<U1>, C: TCategory, DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<T, R2, C2, SB>> for &'a Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<R1, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,

type Output = Matrix<T, R1, C2, <DefaultAllocator as Allocator<R1, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, R2, C2, SB, const D1: usize> Mul<&'b Matrix<T, R2, C2, SB>> for &'a Rotation<T, D1>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<Const<D1>, C2>, ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<Const<D1>, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'b, T, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SB: Storage<T, R2, C2>, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,

type Output = Matrix<T, R1, C2, <DefaultAllocator as Allocator<R1, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'b, T, R2, C2, SB, const D1: usize> Mul<&'b Matrix<T, R2, C2, SB>> for Rotation<T, D1>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<Const<D1>, C2>, ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<Const<D1>, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<f32, R, C>> Mul<&'b Matrix<f32, R, C, S>> for f32

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<f32, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<f32>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<f32, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<f64, R, C>> Mul<&'b Matrix<f64, R, C, S>> for f64

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<f64, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<f64>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<f64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i16, R, C>> Mul<&'b Matrix<i16, R, C, S>> for i16

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i16, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i16>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i16, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i32, R, C>> Mul<&'b Matrix<i32, R, C, S>> for i32

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i32, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i32>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i32, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i64, R, C>> Mul<&'b Matrix<i64, R, C, S>> for i64

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i64, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i64>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i8, R, C>> Mul<&'b Matrix<i8, R, C, S>> for i8

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i8, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i8>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i8, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<isize, R, C>> Mul<&'b Matrix<isize, R, C, S>> for isize

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<isize, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<isize>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<isize, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u16, R, C>> Mul<&'b Matrix<u16, R, C, S>> for u16

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u16, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u16>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u16, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u32, R, C>> Mul<&'b Matrix<u32, R, C, S>> for u32

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u32, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u32>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u32, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u64, R, C>> Mul<&'b Matrix<u64, R, C, S>> for u64

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u64, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u64>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u8, R, C>> Mul<&'b Matrix<u8, R, C, S>> for u8

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u8, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u8>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u8, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<usize, R, C>> Mul<&'b Matrix<usize, R, C, S>> for usize

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<usize, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<usize>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<usize, R, C, S>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, SA, const D2: usize, const R1: usize, const C1: usize> Mul<&'b OPoint<T, Const<D2>>> for &'a Matrix<T, Const<R1>, Const<C1>, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SA: Storage<T, Const<R1>, Const<C1>>, ShapeConstraint: AreMultipliable<Const<R1>, Const<C1>, Const<D2>, U1>,

type Output = OPoint<T, Const<R1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D2>) -> Self::Output

Performs the * operation.

impl<'b, T, SA, const D2: usize, const R1: usize, const C1: usize> Mul<&'b OPoint<T, Const<D2>>> for Matrix<T, Const<R1>, Const<C1>, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SA: Storage<T, Const<R1>, Const<C1>>, ShapeConstraint: AreMultipliable<Const<R1>, Const<C1>, Const<D2>, U1>,

type Output = OPoint<T, Const<R1>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the * operation.

impl<'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, S: Storage<T, Const<2>>> Mul<Matrix<T, Const<2>, Const<1>, S>> for &'a UnitComplex<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<T, Const<2>, S>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, S: Storage<T, Const<2>>> Mul<Matrix<T, Const<2>, Const<1>, S>> for UnitComplex<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<T, Const<2>, S>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, SB: Storage<T, U3>> Mul<Matrix<T, Const<3>, Const<1>, SB>> for &'a UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Matrix<T, Const<3>, Const<1>, SB>> for &'a UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, SB: Storage<T, U3>> Mul<Matrix<T, Const<3>, Const<1>, SB>> for UnitDualQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Matrix<T, Const<3>, Const<1>, SB>> for UnitQuaternion<T>

where T::Element: SimdRealField,

type Output = Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<T, U3, SB>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Isometry<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, T, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Scale<T, D>

where T: Scalar + ClosedMulAssign, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Similarity<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Transform<T, C, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, Const<D>: DimNameAdd<U1>, C: TCategory, DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Isometry<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<T, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Scale<T, D>

where T: Scalar + ClosedMulAssign, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Similarity<T, R, D>

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<T, C, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Transform<T, C, D>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign + RealField, Const<D>: DimNameAdd<U1>, C: TCategory, DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the * operator.

fn mul(self, rhs: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, T, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<T, R2, C2, SB>> for &'a Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SB: Storage<T, R2, C2>, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,

type Output = Matrix<T, R1, C2, <DefaultAllocator as Allocator<R1, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'a, T, R2, C2, SB, const D1: usize> Mul<Matrix<T, R2, C2, SB>> for &'a Rotation<T, D1>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<Const<D1>, C2>, ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<Const<D1>, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<T, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SB: Storage<T, R2, C2>, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,

type Output = Matrix<T, R1, C2, <DefaultAllocator as Allocator<R1, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<T, R2, C2, SB, const D1: usize> Mul<Matrix<T, R2, C2, SB>> for Rotation<T, D1>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<Const<D1>, C2>, ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<Const<D1>, C2>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<f32, R, C>> Mul<Matrix<f32, R, C, S>> for f32

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<f32, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<f32>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<f32, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<f64, R, C>> Mul<Matrix<f64, R, C, S>> for f64

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<f64, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<f64>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<f64, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i16, R, C>> Mul<Matrix<i16, R, C, S>> for i16

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i16, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i16>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i16, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i32, R, C>> Mul<Matrix<i32, R, C, S>> for i32

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i32, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i32>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i32, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i64, R, C>> Mul<Matrix<i64, R, C, S>> for i64

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i64, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i64>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i64, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i8, R, C>> Mul<Matrix<i8, R, C, S>> for i8

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<i8, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<i8>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i8, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<isize, R, C>> Mul<Matrix<isize, R, C, S>> for isize

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<isize, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<isize>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<isize, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u16, R, C>> Mul<Matrix<u16, R, C, S>> for u16

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u16, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u16>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u16, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u32, R, C>> Mul<Matrix<u32, R, C, S>> for u32

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u32, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u32>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u32, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u64, R, C>> Mul<Matrix<u64, R, C, S>> for u64

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u64, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u64>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u64, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u8, R, C>> Mul<Matrix<u8, R, C, S>> for u8

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<u8, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<u8>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u8, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<usize, R, C>> Mul<Matrix<usize, R, C, S>> for usize

where DefaultAllocator: Allocator<R, C>,

type Output = Matrix<usize, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<usize>>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<usize, R, C, S>) -> Self::Output

Performs the * operation.

impl<'a, T, SA, const D2: usize, const R1: usize, const C1: usize> Mul<OPoint<T, Const<D2>>> for &'a Matrix<T, Const<R1>, Const<C1>, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SA: Storage<T, Const<R1>, Const<C1>>, ShapeConstraint: AreMultipliable<Const<R1>, Const<C1>, Const<D2>, U1>,

type Output = OPoint<T, Const<R1>>

The resulting type after applying the * operator.

fn mul(self, right: Point<T, D2>) -> Self::Output

Performs the * operation.

impl<T, SA, const D2: usize, const R1: usize, const C1: usize> Mul<OPoint<T, Const<D2>>> for Matrix<T, Const<R1>, Const<C1>, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SA: Storage<T, Const<R1>, Const<C1>>, ShapeConstraint: AreMultipliable<Const<R1>, Const<C1>, Const<D2>, U1>,

type Output = OPoint<T, Const<R1>>

The resulting type after applying the * operator.

fn mul(self, right: Point<T, D2>) -> Self::Output

Performs the * operation.

impl<'a, T, R1, C1, SA, const D2: usize> Mul<Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: Rotation<T, D2>) -> Self::Output

Performs the * operation.

impl<T, R1, C1, SA, const D2: usize> Mul<Rotation<T, D2>> for Matrix<T, R1, C1, SA>

where T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<R1, Const<D2>>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, right: Rotation<T, D2>) -> Self::Output

Performs the * operation.

impl<'a, T, R: Dim, C: Dim, S> Mul<T> for &'a Matrix<T, R, C, S>

where T: Scalar + ClosedMulAssign, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self::Output

Performs the * operation.

impl<T, R: Dim, C: Dim, S> Mul<T> for Matrix<T, R, C, S>

where T: Scalar + ClosedMulAssign, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Self::Output

Performs the * operation.

impl<'b, T, R1, C1, R2, SA, SB> MulAssign<&'b Matrix<T, R2, C1, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SB: Storage<T, R2, C1>, SA: StorageMut<T, R1, C1> + IsContiguous + Clone, ShapeConstraint: AreMultipliable<R1, C1, R2, C1>, DefaultAllocator: Allocator<R1, C1, Buffer<T> = SA>,

fn mul_assign(&mut self, rhs: &'b Matrix<T, R2, C1, SB>)

Performs the *= operation.

impl<T, R1, C1, R2, SA, SB> MulAssign<Matrix<T, R2, C1, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, T: Scalar + Zero + One + ClosedAddAssign + ClosedMulAssign, SB: Storage<T, R2, C1>, SA: StorageMut<T, R1, C1> + IsContiguous + Clone, ShapeConstraint: AreMultipliable<R1, C1, R2, C1>, DefaultAllocator: Allocator<R1, C1, Buffer<T> = SA>,

fn mul_assign(&mut self, rhs: Matrix<T, R2, C1, SB>)

Performs the *= operation.

impl<T, R: Dim, C: Dim, S> MulAssign<T> for Matrix<T, R, C, S>

where T: Scalar + ClosedMulAssign, S: StorageMut<T, R, C>,

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<'a, T, R: Dim, C: Dim, S> Neg for &'a Matrix<T, R, C, S>

where T: Scalar + ClosedNeg, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T, R: Dim, C: Dim, S> Neg for Matrix<T, R, C, S>

where T: Scalar + ClosedNeg, S: Storage<T, R, C>, DefaultAllocator: Allocator<R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T, R: Dim, C: Dim, S> Octal for Matrix<T, R, C, S>

where T: Scalar + Octal, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, R, R2, C, C2, S, S2> PartialEq<Matrix<T, R2, C2, S2>> for Matrix<T, R, C, S>

where T: PartialEq, C: Dim, C2: Dim, R: Dim, R2: Dim, S: RawStorage<T, R, C>, S2: RawStorage<T, R2, C2>,

fn eq(&self, right: &Matrix<T, R2, C2, S2>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T, R: Dim, C: Dim, S> PartialOrd for Matrix<T, R, C, S>

where T: Scalar + PartialOrd, S: RawStorage<T, R, C>,

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, right: &Self) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, right: &Self) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, right: &Self) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, right: &Self) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<T, R: Dim, C: Dim, S> Pointer for Matrix<T, R, C, S>

where T: Scalar + Pointer, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'a, T, D: DimName> Product<&'a Matrix<T, D, D, <DefaultAllocator as Allocator<D, D>>::Buffer<T>>> for OMatrix<T, D, D>

where T: Scalar + Zero + One + ClosedMulAssign + ClosedAddAssign, DefaultAllocator: Allocator<D, D>,

fn product<I: Iterator<Item = &'a OMatrix<T, D, D>>>( iter: I, ) -> OMatrix<T, D, D>

Takes an iterator and generates Self from the elements by multiplying the items.

impl<T, R: Dim, C: Dim, S> RelativeEq for Matrix<T, R, C, S>

where T: Scalar + RelativeEq, S: Storage<T, R, C>, T::Epsilon: Clone,

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl<T, R, C, S> Serialize for Matrix<T, R, C, S>

where T: Scalar, R: Dim, C: Dim, S: Serialize,

fn serialize<Ser>(&self, serializer: Ser) -> Result<Ser::Ok, Ser::Error>

where Ser: Serializer,

Serialize this value into the given Serde serializer.

impl<'a, 'b, T, D1, D2, SB> Sub<&'b Matrix<T, D2, Const<1>, SB>> for &'a OPoint<T, D1>

where T: Scalar + ClosedSubAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the - operator.

fn sub(self, right: &'b Vector<T, D2, SB>) -> Self::Output

Performs the - operation.

impl<'b, T, D1, D2, SB> Sub<&'b Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedSubAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the - operator.

fn sub(self, right: &'b Vector<T, D2, SB>) -> Self::Output

Performs the - operation.

impl<'a, 'b, T, R1, C1, R2, C2, SA, SB> Sub<&'b Matrix<T, R2, C2, SB>> for &'a Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSubAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer<T>>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<'b, T, R1, C1, R2, C2, SA, SB> Sub<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSubAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer<T>>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<'a, T, D1, D2, SB> Sub<Matrix<T, D2, Const<1>, SB>> for &'a OPoint<T, D1>

where T: Scalar + ClosedSubAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the - operator.

fn sub(self, right: Vector<T, D2, SB>) -> Self::Output

Performs the - operation.

impl<T, D1, D2, SB> Sub<Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedSubAssign, ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1, Representative = U1>, D1: DimName, D2: Dim, SB: Storage<T, D2>, DefaultAllocator: Allocator<D1>,

type Output = OPoint<T, D1>

The resulting type after applying the - operator.

fn sub(self, right: Vector<T, D2, SB>) -> Self::Output

Performs the - operation.

impl<'a, T, R1, C1, R2, C2, SA, SB> Sub<Matrix<T, R2, C2, SB>> for &'a Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSubAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R2, C2, R1, C1>, ShapeConstraint: SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R2, R1>>::Representative, <ShapeConstraint as SameNumberOfColumns<C2, C1>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R2, R1>>::Representative, <ShapeConstraint as SameNumberOfColumns<C2, C1>>::Representative>>::Buffer<T>>

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<T, R1, C1, R2, C2, SA, SB> Sub<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSubAssign, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<<ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer<T>>

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<'b, T, D1: DimName, D2: Dim, SB> SubAssign<&'b Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedSubAssign, SB: Storage<T, D2>, ShapeConstraint: SameNumberOfRows<D1, D2>, DefaultAllocator: Allocator<D1>,

fn sub_assign(&mut self, right: &'b Vector<T, D2, SB>)

Performs the -= operation.

impl<'b, T, R1, C1, R2, C2, SA, SB> SubAssign<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSubAssign, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn sub_assign(&mut self, rhs: &'b Matrix<T, R2, C2, SB>)

Performs the -= operation.

impl<T, D1: DimName, D2: Dim, SB> SubAssign<Matrix<T, D2, Const<1>, SB>> for OPoint<T, D1>

where T: Scalar + ClosedSubAssign, SB: Storage<T, D2>, ShapeConstraint: SameNumberOfRows<D1, D2>, DefaultAllocator: Allocator<D1>,

fn sub_assign(&mut self, right: Vector<T, D2, SB>)

Performs the -= operation.

impl<T, R1, C1, R2, C2, SA, SB> SubAssign<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSubAssign, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn sub_assign(&mut self, rhs: Matrix<T, R2, C2, SB>)

Performs the -= operation.

impl<T1, T2, R, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for Isometry<T1, R, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, DefaultAllocator: Allocator<Const<D>, Const<1>, Buffer<T1> = ArrayStorage<T1, D, 1>> + Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for Rotation<T1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, DefaultAllocator: Allocator<Const<D>, Const<D>, Buffer<T1> = ArrayStorage<T1, D, D>> + Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for Scale<T1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, Const<D>: DimNameAdd<U1>, DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<DimNameSum<Const<D>, U1>, U1>,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, R, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for Similarity<T1, R, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, DefaultAllocator: Allocator<Const<D>, Const<1>, Buffer<T1> = ArrayStorage<T1, D, 1>> + Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, C, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for Transform<T1, C, D>

where T1: RealField + SubsetOf<T2>, T2: RealField, C: TCategory, Const<D>: DimNameAdd<U1>, DefaultAllocator: Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, T1::Epsilon: Copy, T2::Epsilon: Copy,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for Translation<T1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, Const<D>: DimNameAdd<U1>, DefaultAllocator: Allocator<Const<D>, Buffer<T1> = ArrayStorage<T1, D, 1>> + Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset( &self, ) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, ) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, D> SubsetOf<Matrix<T2, <D as DimNameAdd<Const<1>>>::Output, Const<1>, <DefaultAllocator as Allocator<<D as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> for OPoint<T1, D>

where D: DimNameAdd<U1>, T1: Scalar, T2: Scalar + Zero + One + ClosedDivAssign + SupersetOf<T1>, DefaultAllocator: Allocator<D> + Allocator<DimNameSum<D, U1>>,

fn to_superset(&self) -> OVector<T2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(v: &OVector<T2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(v: &OVector<T2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1: RealField, T2: RealField + SupersetOf<T1>> SubsetOf<Matrix<T2, Const<3>, Const<3>, ArrayStorage<T2, 3, 3>>> for UnitComplex<T1>

fn to_superset(&self) -> Matrix3<T2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &Matrix3<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(m: &Matrix3<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1: RealField, T2: RealField + SupersetOf<T1>> SubsetOf<Matrix<T2, Const<4>, Const<4>, ArrayStorage<T2, 4, 4>>> for UnitDualQuaternion<T1>

fn to_superset(&self) -> Matrix4<T2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &Matrix4<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(m: &Matrix4<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1: RealField, T2: RealField + SupersetOf<T1>> SubsetOf<Matrix<T2, Const<4>, Const<4>, ArrayStorage<T2, 4, 4>>> for UnitQuaternion<T1>

fn to_superset(&self) -> Matrix4<T2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &Matrix4<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(m: &Matrix4<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<T1, T2, R1, C1, R2, C2> SubsetOf<Matrix<T2, R2, C2, <DefaultAllocator as Allocator<R2, C2>>::Buffer<T2>>> for OMatrix<T1, R1, C1>

where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T1: Scalar, T2: Scalar + SupersetOf<T1>, DefaultAllocator: Allocator<R2, C2> + Allocator<R1, C1> + SameShapeAllocator<R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn to_superset(&self) -> OMatrix<T2, R2, C2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &OMatrix<T2, R2, C2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(m: &OMatrix<T2, R2, C2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<'a, T, C: Dim> Sum<&'a Matrix<T, Dyn, C, <DefaultAllocator as Allocator<Dyn, C>>::Buffer<T>>> for OMatrix<T, Dyn, C>

where T: Scalar + ClosedAddAssign + Zero, DefaultAllocator: Allocator<Dyn, C>,

fn sum<I: Iterator<Item = &'a OMatrix<T, Dyn, C>>>( iter: I, ) -> OMatrix<T, Dyn, C>

Example

let v = &DVector::repeat(3, 1.0f64);

assert_eq!(vec![v, v, v].into_iter().sum::<DVector<f64>>(),
           v + v + v);

Panics

Panics if the iterator is empty:

iter::empty::<&DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!

impl<'a, T, R: DimName, C: DimName> Sum<&'a Matrix<T, R, C, <DefaultAllocator as Allocator<R, C>>::Buffer<T>>> for OMatrix<T, R, C>

where T: Scalar + ClosedAddAssign + Zero, DefaultAllocator: Allocator<R, C>,

fn sum<I: Iterator<Item = &'a OMatrix<T, R, C>>>(iter: I) -> OMatrix<T, R, C>

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<T, R: Dim, C: Dim, S> UlpsEq for Matrix<T, R, C, S>

where T: Scalar + UlpsEq, S: RawStorage<T, R, C>, T::Epsilon: Clone,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

impl<T, R: Dim, C: Dim, S> UpperExp for Matrix<T, R, C, S>

where T: Scalar + UpperExp, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T, R: Dim, C: Dim, S> UpperHex for Matrix<T, R, C, S>

where T: Scalar + UpperHex, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Copy, R: Copy, C: Copy, S: Copy> Copy for Matrix<T, R, C, S>

impl<T, R: Dim, C: Dim, S> Eq for Matrix<T, R, C, S>

where T: Eq, S: RawStorage<T, R, C>,