Struct nalgebra::base::Matrix

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

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
Computer graphics utilities for transformations
Common math operations
Statistics
Iteration, map, and fold
Vector and matrix views
In-place modification of a single matrix or vector
Vector and matrix size modification
Matrix decomposition
Vector basis computation

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§

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impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>
where T: Scalar + Zero + ClosedAdd + ClosedMul,

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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);
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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));
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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);
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impl<T, D: Dim, S> Matrix<T, D, Const<1>, S>
where T: Scalar + Zero + ClosedAdd + ClosedMul, S: StorageMut<T, D>,

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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));
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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));
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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));
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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));
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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)));
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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);
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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);
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impl<T, R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>> Matrix<T, R1, C1, S>
where T: Scalar + Zero + ClosedAdd + ClosedMul,

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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);
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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);
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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);
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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);
source

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);
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impl<T, R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>> Matrix<T, R1, C1, S>
where T: Scalar + Zero + ClosedAdd + ClosedMul,

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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.
source

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.
source

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.
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impl<T, D1: Dim, S: StorageMut<T, D1, D1>> Matrix<T, D1, D1, S>
where T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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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);
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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<T, 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);
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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);
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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<T, 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);
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impl<T, R: Dim, C: Dim, S> Matrix<T, R, C, S>
where T: Scalar + ClosedNeg, S: StorageMut<T, R, C>,

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pub fn neg_mut(&mut self)

Negates self in-place.

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

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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.

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

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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.

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impl<T, R1: Dim, C1: Dim, SA> Matrix<T, R1, C1, SA>
where T: Scalar + Zero + One + ClosedAdd + ClosedMul, SA: Storage<T, R1, C1>,

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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<T, C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,

Equivalent to self.transpose() * rhs.

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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<T, C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,

Equivalent to self.adjoint() * rhs.

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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.

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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.

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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.

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

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

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impl<T, D: DimName> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
where T: Scalar + Zero + One, DefaultAllocator: Allocator<T, D, D>,

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pub fn new_scaling(scaling: T) -> Self

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

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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.

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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.

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

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pub fn new_rotation(angle: T) -> Self

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

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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.

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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

Creates a new homogeneous matrix for a perspective projection.

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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.

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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.

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

Builds a right-handed look-at view matrix.

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

Builds a left-handed look-at view matrix.

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impl<T: Scalar + Zero + One + ClosedMul + ClosedAdd, D: DimName, S: Storage<T, D, D>> Matrix<T, D, D, S>

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pub fn append_scaling(&self, scaling: T) -> OMatrix<T, D, D>
where D: DimNameSub<U1>, DefaultAllocator: Allocator<T, D, D>,

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

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pub fn prepend_scaling(&self, scaling: T) -> OMatrix<T, D, D>
where D: DimNameSub<U1>, DefaultAllocator: Allocator<T, D, D>,

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

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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<T, D, D>,

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

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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<T, D, D>,

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

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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<T, D, D>,

Computes the transformation equal to self followed by a translation.

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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<T, D, D> + Allocator<T, DimNameDiff<D, U1>>,

Computes the transformation equal to a translation followed by self.

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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.

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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.

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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.

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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.

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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.

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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<T, DimNameDiff<D, U1>>,

Computes the transformation equal to a translation followed by self.

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

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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.

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

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

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

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

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

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

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

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pub fn abs(&self) -> OMatrix<T, R, C>
where T: Signed, DefaultAllocator: Allocator<T, 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))
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impl<T: Scalar, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>> Matrix<T, R1, C1, SA>

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pub fn component_mul<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB> ) -> MatrixSum<T, R1, C1, R2, C2>
where T: ClosedMul, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, 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);
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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: ClosedMul + 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);
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pub fn component_mul_assign<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)
where T: ClosedMul, 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);
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pub fn component_mul_mut<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)
where T: ClosedMul, 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);
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pub fn component_div<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB> ) -> MatrixSum<T, R1, C1, R2, C2>
where T: ClosedDiv, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, 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);
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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: ClosedDiv + 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);
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pub fn component_div_assign<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)
where T: ClosedDiv, 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);
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pub fn component_div_mut<R2, C2, SB>(&mut self, rhs: &Matrix<T, R2, C2, SB>)
where T: ClosedDiv, 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);
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pub fn inf(&self, other: &Self) -> OMatrix<T, 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)
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pub fn sup(&self, other: &Self) -> OMatrix<T, 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)
source

pub fn inf_sup(&self, other: &Self) -> (OMatrix<T, R1, C1>, OMatrix<T, 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)
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pub fn add_scalar(&self, rhs: T) -> OMatrix<T, R1, C1>
where T: ClosedAdd, DefaultAllocator: Allocator<T, 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)
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pub fn add_scalar_mut(&mut self, rhs: T)
where T: ClosedAdd, 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)
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impl<T: Scalar, R: Dim, C: Dim> Matrix<MaybeUninit<T>, R, C, <DefaultAllocator as Allocator<T, R, C>>::BufferUninit>
where DefaultAllocator: Allocator<T, R, C>,

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

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

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

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

Creates a matrix with all its elements set to elem.

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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.

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

Creates a matrix with all its elements set to 0.

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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.

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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.

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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.

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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).

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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.

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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.

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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.

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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.

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

Creates a matrix filled with random values.

source

pub fn from_distribution_generic<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>( nrows: R, ncols: C, distribution: &Distr, rng: &mut G ) -> Self

Creates a matrix filled with random values from the given distribution.

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pub fn from_vec_generic(nrows: R, ncols: C, data: Vec<T>) -> Self

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

let vec = vec![0, 1, 2, 3, 4, 5];
let vec_ptr = vec.as_ptr();

let matrix = Matrix::from_vec_generic(Dyn(vec.len()), Const::<1>, vec);
let matrix_storage_ptr = matrix.data.as_vec().as_ptr();

// `matrix` is backed by exactly the same `Vec` as it was constructed from.
assert_eq!(matrix_storage_ptr, vec_ptr);
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impl<T, D: Dim> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>
where T: Scalar, DefaultAllocator: Allocator<T, D, D>,

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

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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);
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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);
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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);
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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);
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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);
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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);
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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);
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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);
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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);
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pub fn from_distribution<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>( distribution: &Distr, rng: &mut G ) -> Self

Creates a matrix or vector filled with random values from the given distribution.

source

pub fn new_random() -> Self

Creates a matrix filled with random values.

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

source

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);
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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);
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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);
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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);
source

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);
source

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);
source

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);
source

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);
source

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);
source

pub fn from_distribution<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>( ncols: usize, distribution: &Distr, rng: &mut G ) -> Self

Creates a matrix or vector filled with random values from the given distribution.

source

pub fn new_random(ncols: usize) -> Self

Creates a matrix filled with random values.

source§

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

source

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);
source

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);
source

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);
source

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);
source

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);
source

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);
source

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);
source

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);
source

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);
source

pub fn from_distribution<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>( nrows: usize, distribution: &Distr, rng: &mut G ) -> Self

Creates a matrix or vector filled with random values from the given distribution.

source

pub fn new_random(nrows: usize) -> Self

Creates a matrix filled with random values.

source§

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

source

pub fn from_element(nrows: usize, 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);
source

pub fn repeat(nrows: usize, 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);
source

pub fn zeros(nrows: usize, 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);
source

pub fn from_iterator<I>(nrows: usize, 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);
source

pub fn from_row_iterator<I>(nrows: usize, 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);
source

pub fn from_fn<F>(nrows: usize, 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);
source

pub fn identity(nrows: usize, 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);
source

pub fn from_diagonal_element(nrows: usize, 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);
source

pub fn from_partial_diagonal(nrows: usize, 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);
source

pub fn from_distribution<Distr: Distribution<T> + ?Sized, G: Rng + ?Sized>( nrows: usize, ncols: usize, distribution: &Distr, rng: &mut G ) -> Self

Creates a matrix or vector filled with random values from the given distribution.

source

pub fn new_random(nrows: usize, ncols: usize) -> Self

Creates a matrix filled with random values.

source§

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

source

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);
source

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);
source

pub fn from_vec(data: Vec<T>) -> Self

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);

assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);


// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 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);
source§

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

source

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);
source

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);
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pub fn from_vec(data: Vec<T>) -> Self

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);

assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);


// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 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);
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impl<T: Scalar, C: DimName> Matrix<T, Dyn, C, <DefaultAllocator as Allocator<T, Dyn, C>>::Buffer>

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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);
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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);
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pub fn from_vec(data: Vec<T>) -> Self

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);

assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);


// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 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);
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impl<T: Scalar> Matrix<T, Dyn, Dyn, <DefaultAllocator as Allocator<T, Dyn, Dyn>>::Buffer>

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pub fn from_row_slice(nrows: usize, ncols: usize, 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);
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pub fn from_column_slice(nrows: usize, ncols: usize, 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);
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pub fn from_vec(nrows: usize, ncols: usize, data: Vec<T>) -> Self

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

let m = Matrix2x3::from_vec(vec![0, 1, 2, 3, 4, 5]);

assert!(m.m11 == 0 && m.m12 == 2 && m.m13 == 4 &&
        m.m21 == 1 && m.m22 == 3 && m.m23 == 5);


// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 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);
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impl<T> Matrix<T, Const<2>, Const<2>, ArrayStorage<T, 2, 2>>

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

Initializes this matrix from its components.

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

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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.

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

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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.

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

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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.

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

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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.

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

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

Initializes this matrix from its components.

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

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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.

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

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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.

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

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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.

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

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

Initializes this matrix from its components.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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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.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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

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

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

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

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

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pub fn x() -> Self
where R::Typenum: Cmp<U0, Output = Greater>,

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

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pub fn y() -> Self
where R::Typenum: Cmp<U1, Output = Greater>,

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

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pub fn z() -> Self
where R::Typenum: Cmp<U2, Output = Greater>,

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

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pub fn w() -> Self
where R::Typenum: Cmp<U3, Output = Greater>,

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

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pub fn a() -> Self
where R::Typenum: Cmp<U4, Output = Greater>,

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

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pub fn b() -> Self
where R::Typenum: Cmp<U5, Output = Greater>,

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

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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.

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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.

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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.

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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.

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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.

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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.

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

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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().

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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().

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

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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().

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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().

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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().

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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().

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

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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().

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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().

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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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.

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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.

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

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pub fn upper_triangle(&self) -> OMatrix<T, R, C>
where DefaultAllocator: Allocator<T, R, C>,

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

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pub fn lower_triangle(&self) -> OMatrix<T, R, C>
where DefaultAllocator: Allocator<T, R, C>,

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

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

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pub fn select_rows<'a, I>(&self, irows: I) -> OMatrix<T, Dyn, C>

Creates a new matrix by extracting the given set of rows from self.

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pub fn select_columns<'a, I>(&self, icols: I) -> OMatrix<T, R, Dyn>

Creates a new matrix by extracting the given set of columns from self.

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

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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.

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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).

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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.

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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.

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

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

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

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

Sets all the elements of this matrix to val.

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pub fn fill_with_identity(&mut self)
where T: Scalar + Zero + One,

Fills self with the identity matrix.

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

Sets all the diagonal elements of this matrix to val.

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

Sets all the elements of the selected row to val.

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

Sets all the elements of the selected column to val.

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

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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.

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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.

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

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

Swaps two rows in-place.

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

Swaps two columns in-place.

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

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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.

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pub fn remove_columns_at(self, indices: &[usize]) -> OMatrix<T, R, Dyn>
where C: DimSub<Dyn, Output = Dyn>, DefaultAllocator: Reallocator<T, R, C, R, Dyn>,

Removes all columns in indices

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pub fn remove_rows_at(self, indices: &[usize]) -> OMatrix<T, Dyn, C>
where R: DimSub<Dyn, Output = Dyn>, DefaultAllocator: Reallocator<T, R, C, Dyn, C>,

Removes all rows in indices

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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).

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pub fn remove_columns(self, i: usize, n: usize) -> OMatrix<T, R, Dyn>
where C: DimSub<Dyn, Output = Dyn>, DefaultAllocator: Reallocator<T, R, C, R, Dyn>,

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

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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.

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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.

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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).

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pub fn remove_rows(self, i: usize, n: usize) -> OMatrix<T, Dyn, C>
where R: DimSub<Dyn, Output = Dyn>, DefaultAllocator: Reallocator<T, R, C, Dyn, C>,

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

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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.

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

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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.

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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.

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pub fn insert_columns(self, i: usize, n: usize, val: T) -> OMatrix<T, R, Dyn>
where C: DimAdd<Dyn, Output = Dyn>, DefaultAllocator: Reallocator<T, R, C, R, Dyn>,

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

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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.

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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.

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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.

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pub fn insert_rows(self, i: usize, n: usize, val: T) -> OMatrix<T, Dyn, C>
where R: DimAdd<Dyn, Output = Dyn>, DefaultAllocator: Reallocator<T, R, C, Dyn, C>,

Inserts n rows filled with val starting at the i-th position.

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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.

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

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pub fn resize( self, new_nrows: usize, new_ncols: usize, val: T ) -> OMatrix<T, Dyn, Dyn>
where DefaultAllocator: Reallocator<T, R, C, Dyn, Dyn>,

Resizes this matrix so that it contains new_nrows rows and new_ncols 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.

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pub fn resize_vertically(self, new_nrows: usize, val: T) -> OMatrix<T, Dyn, C>
where DefaultAllocator: Reallocator<T, R, C, Dyn, C>,

Resizes this matrix vertically, i.e., so that it contains new_nrows rows while keeping the same number of columns.

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

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pub fn resize_horizontally(self, new_ncols: usize, val: T) -> OMatrix<T, R, Dyn>
where DefaultAllocator: Reallocator<T, R, C, R, Dyn>,

Resizes this matrix horizontally, i.e., so that it contains new_ncolumns columns while keeping the same number of columns.

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

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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.

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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.

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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);
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impl<T: Scalar> Matrix<T, Dyn, Dyn, <DefaultAllocator as Allocator<T, Dyn, Dyn>>::Buffer>

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pub fn resize_mut(&mut self, new_nrows: usize, new_ncols: usize, val: T)

Resizes this matrix in-place.

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.

Defined only for owned fully-dynamic matrices, i.e., DMatrix.

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

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pub fn resize_vertically_mut(&mut self, new_nrows: usize, val: T)
where DefaultAllocator: Reallocator<T, Dyn, C, Dyn, C>,

Changes the number of rows of this matrix in-place.

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

Defined only for owned matrices with a dynamic number of rows (for example, DVector).

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

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pub fn resize_horizontally_mut(&mut self, new_ncols: usize, val: T)
where DefaultAllocator: Reallocator<T, R, Dyn, R, Dyn>,

Changes the number of column of this matrix in-place.

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

Defined only for owned matrices with a dynamic number of columns (for example, DVector).

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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)));
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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.

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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.

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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.

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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.

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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.

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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.

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

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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.

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impl<T, const R: usize, const C: usize> Matrix<T, Const<R>, Const<C>, ArrayStorage<T, R, C>>

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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.

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impl<T> Matrix<T, Dyn, Dyn, VecStorage<T, Dyn, Dyn>>

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pub const fn from_vec_storage(storage: VecStorage<T, Dyn, Dyn>) -> Self

Creates a new heap-allocated matrix from the given VecStorage.

This method exists primarily as a workaround for the fact that from_data can not work in const fn contexts.

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impl<T> Matrix<T, Dyn, Const<1>, VecStorage<T, Dyn, Const<1>>>

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pub const fn from_vec_storage(storage: VecStorage<T, Dyn, U1>) -> Self

Creates a new heap-allocated matrix from the given VecStorage.

This method exists primarily as a workaround for the fact that from_data can not work in const fn contexts.

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impl<T> Matrix<T, Const<1>, Dyn, VecStorage<T, Const<1>, Dyn>>

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pub const fn from_vec_storage(storage: VecStorage<T, U1, Dyn>) -> Self

Creates a new heap-allocated matrix from the given VecStorage.

This method exists primarily as a workaround for the fact that from_data can not work in const fn contexts.

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

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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.

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

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pub fn from_data(data: S) -> Self

Creates a new matrix with the given data.

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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));
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pub fn shape_generic(&self) -> (R, C)

The shape of this matrix wrapped into their representative types (Const or Dyn).

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pub fn nrows(&self) -> usize

The number of rows of this matrix.

Example
let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.nrows(), 3);
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pub fn ncols(&self) -> usize

The number of columns of this matrix.

Example
let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.ncols(), 4);
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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));
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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]);
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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]);
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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, 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.

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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.

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pub fn into_owned(self) -> OMatrix<T, R, C>
where T: Scalar, S: Storage<T, R, C>, DefaultAllocator: Allocator<T, R, C>,

Moves this matrix into one that owns its data.

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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<T, 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.

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pub fn clone_owned(&self) -> OMatrix<T, R, C>
where T: Scalar, S: Storage<T, R, C>, DefaultAllocator: Allocator<T, R, C>,

Clones this matrix to one that owns its data.

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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<T, 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.

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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.

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pub fn transpose(&self) -> OMatrix<T, C, R>
where T: Scalar, DefaultAllocator: Allocator<T, C, R>,

Transposes self.

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

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pub fn map<T2: Scalar, F: FnMut(T) -> T2>(&self, f: F) -> OMatrix<T2, R, C>
where T: Scalar, DefaultAllocator: Allocator<T2, R, C>,

Returns a matrix containing the result of f applied to each of its entries.

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pub fn cast<T2: Scalar>(self) -> OMatrix<T2, R, C>
where T: Scalar, OMatrix<T2, R, C>: SupersetOf<Self>, DefaultAllocator: Allocator<T2, 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));
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pub fn try_cast<T2: Scalar>(self) -> Option<OMatrix<T2, R, C>>
where T: Scalar, Self: SupersetOf<OMatrix<T2, R, C>>, DefaultAllocator: Allocator<T2, 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)));
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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.
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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<T2, 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).

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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<N3, R, C>,

Returns a matrix containing the result of f applied to each entries of self and rhs.

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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<N4, R, C>,

Returns a matrix containing the result of f applied to each entries of self and b, and c.

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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.

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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.

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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.

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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.

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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.

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

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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());
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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))
}
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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))
}
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pub fn iter_mut(&mut self) -> MatrixIterMut<'_, T, R, C, S>
where S: RawStorageMut<T, R, C>,

Mutably iterates through this matrix coordinates.

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

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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.

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pub unsafe fn swap_unchecked( &mut self, row_cols1: (usize, usize), row_cols2: (usize, usize) )

Swaps two entries without bound-checking.

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pub fn swap(&mut self, row_cols1: (usize, usize), row_cols2: (usize, usize))

Swaps two entries.

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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.

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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.

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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.

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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.

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

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pub unsafe fn vget_unchecked(&self, i: usize) -> &T

Gets a reference to the i-th element of this column vector without bound checking.

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

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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.

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

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pub fn as_slice(&self) -> &[T]

Extracts a slice containing the entire matrix entries ordered column-by-columns.

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

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pub fn as_mut_slice(&mut self) -> &mut [T]

Extracts a mutable slice containing the entire matrix entries ordered column-by-columns.

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

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pub fn transpose_mut(&mut self)

Transposes the square matrix self in-place.

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

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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.

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pub fn adjoint(&self) -> OMatrix<T, C, R>
where DefaultAllocator: Allocator<T, C, R>,

The adjoint (aka. conjugate-transpose) of self.

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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.

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pub fn conjugate_transpose(&self) -> OMatrix<T, C, R>
where DefaultAllocator: Allocator<T, C, R>,

👎Deprecated: Renamed self.adjoint().

The conjugate transposition of self.

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pub fn conjugate(&self) -> OMatrix<T, R, C>
where DefaultAllocator: Allocator<T, R, C>,

The conjugate of self.

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pub fn unscale(&self, real: T::SimdRealField) -> OMatrix<T, R, C>
where DefaultAllocator: Allocator<T, R, C>,

Divides each component of the complex matrix self by the given real.

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pub fn scale(&self, real: T::SimdRealField) -> OMatrix<T, R, C>
where DefaultAllocator: Allocator<T, R, C>,

Multiplies each component of the complex matrix self by the given real.

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

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pub fn conjugate_mut(&mut self)

The conjugate of the complex matrix self computed in-place.

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pub fn unscale_mut(&mut self, real: T::SimdRealField)

Divides each component of the complex matrix self by the given real.

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pub fn scale_mut(&mut self, real: T::SimdRealField)

Multiplies each component of the complex matrix self by the given real.

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

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pub fn conjugate_transform_mut(&mut self)

👎Deprecated: Renamed to self.adjoint_mut().

Sets self to its adjoint.

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pub fn adjoint_mut(&mut self)

Sets self to its adjoint (aka. conjugate-transpose).

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

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pub fn diagonal(&self) -> OVector<T, D>

The diagonal of this matrix.

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pub fn map_diagonal<T2: Scalar>(&self, f: impl FnMut(T) -> T2) -> OVector<T2, 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.

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pub fn trace(&self) -> T
where T: Scalar + Zero + ClosedAdd,

Computes a trace of a square matrix, i.e., the sum of its diagonal elements.

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impl<T: SimdComplexField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>

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pub fn symmetric_part(&self) -> OMatrix<T, D, D>
where DefaultAllocator: Allocator<T, D, D>,

The symmetric part of self, i.e., 0.5 * (self + self.transpose()).

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pub fn hermitian_part(&self) -> OMatrix<T, D, D>
where DefaultAllocator: Allocator<T, D, D>,

The hermitian part of self, i.e., 0.5 * (self + self.adjoint()).

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impl<T: Scalar + Zero + One, D: DimAdd<U1> + IsNotStaticOne, S: RawStorage<T, D, D>> Matrix<T, D, D, S>

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pub fn to_homogeneous(&self) -> OMatrix<T, 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.

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impl<T: Scalar + Zero, D: DimAdd<U1>, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

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pub fn to_homogeneous(&self) -> OVector<T, DimSum<D, U1>>

Computes the coordinates in projective space of this vector, i.e., appends a 0 to its coordinates.

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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<T, 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.

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impl<T: Scalar, D: DimAdd<U1>, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>

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pub fn push(&self, element: T) -> OVector<T, DimSum<D, U1>>

Constructs a new vector of higher dimension by appending element to the end of self.

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impl<T: Scalar + ClosedAdd + ClosedSub + ClosedMul, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>

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pub fn perp<R2, C2, SB>(&self, b: &Matrix<T, R2, C2, SB>) -> T

The perpendicular product between two 2D column vectors, i.e. a.x * b.y - a.y * b.x.

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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<T, 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.

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impl<T: Scalar + Field, S: RawStorage<T, U3>> Matrix<T, Const<3>, Const<1>, S>

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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).

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

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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.

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impl<T, S> Matrix<T, U1, U1, S>
where S: RawStorage<T, U1, U1>,

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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.
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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.;
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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();
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impl<T> Matrix<T, Const<1>, Const<1>, ArrayStorage<T, 1, 1>>

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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 (R::dim(), CView::dim()) consecutive components.

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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 (R::dim(), CView::dim()) consecutive components.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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 (R::dim(), CView::dim()) consecutive components.

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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 (R::dim(), CView::dim()) consecutive components.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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

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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.

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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.

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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.

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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.

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

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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.

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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.

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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.

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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.

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

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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();
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impl<T, R, C, S> Matrix<T, R, C, S>
where R: Dim, C: Dim, S: RawStorageMut<T, R, C>,

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

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pub fn norm_squared(&self) -> T::SimdRealField

The squared L2 norm of this vector.

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pub fn norm(&self) -> T::SimdRealField

The L2 norm of this matrix.

Use .apply_norm to apply a custom norm.

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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.

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pub fn apply_norm(&self, norm: &impl Norm<T>) -> T::SimdRealField

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());
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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());
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pub fn magnitude(&self) -> T::SimdRealField

A synonym for the norm of this matrix.

Aka the length.

This function is simply implemented as a call to norm()

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pub fn magnitude_squared(&self) -> T::SimdRealField

A synonym for the squared norm of this matrix.

Aka the squared length.

This function is simply implemented as a call to norm_squared()

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pub fn set_magnitude(&mut self, magnitude: T::SimdRealField)
where T: SimdComplexField, S: StorageMut<T, R, C>,

Sets the magnitude of this vector.

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

Returns a normalized version of this matrix.

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pub fn lp_norm(&self, p: i32) -> T::SimdRealField

The Lp norm of this matrix.

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pub fn simd_try_normalize( &self, min_norm: T::SimdRealField ) -> SimdOption<OMatrix<T, R, C>>

Attempts to normalize self.

The components of this matrix can be SIMD types.

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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.

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pub fn cap_magnitude(&self, max: T::RealField) -> OMatrix<T, R, C>

Returns a new vector with the same magnitude as self clamped between 0.0 and max.

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pub fn simd_cap_magnitude(&self, max: T::SimdRealField) -> OMatrix<T, R, C>

Returns a new vector with the same magnitude as self clamped between 0.0 and max.

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pub fn try_normalize(&self, min_norm: T::RealField) -> Option<OMatrix<T, 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.

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

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pub fn normalize_mut(&mut self) -> T::SimdRealField

Normalizes this matrix in-place and returns its norm.

The components of the matrix cannot be SIMD types (see simd_try_normalize_mut instead).

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pub fn simd_try_normalize_mut( &mut self, min_norm: T::SimdRealField ) -> SimdOption<T::SimdRealField>

Normalizes this matrix in-place and return its norm.

The components of the matrix can be SIMD types.

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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.

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impl<T: ComplexField, D: DimName> Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<T, D>>::Buffer>

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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.

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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.

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

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pub fn len(&self) -> usize

The total number of elements of this matrix.

Examples:
let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.len(), 12);
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pub fn is_empty(&self) -> bool

Returns true if the matrix contains no elements.

Examples:
let mat = Matrix3x4::<f32>::zeros();
assert!(!mat.is_empty());
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pub fn is_square(&self) -> bool

Indicates if this is a square matrix.

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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.

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

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pub fn is_orthogonal(&self, eps: T::Epsilon) -> bool
where T: Zero + One + ClosedAdd + ClosedMul + RelativeEq, S: Storage<T, R, C>, T::Epsilon: Clone, DefaultAllocator: Allocator<T, R, C> + Allocator<T, 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.

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impl<T: RealField, D: Dim, S: Storage<T, D, D>> Matrix<T, D, D, S>
where DefaultAllocator: Allocator<T, D, D>,

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pub fn is_special_orthogonal(&self, eps: T) -> bool
where D: DimMin<D, Output = D>, DefaultAllocator: Allocator<(usize, usize), D>,

Checks that this matrix is orthogonal and has a determinant equal to 1.

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pub fn is_invertible(&self) -> bool

Returns true if this matrix is invertible.

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

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pub fn compress_rows( &self, f: impl Fn(VectorView<'_, T, R, S::RStride, S::CStride>) -> T ) -> RowOVector<T, C>

Returns a row vector where each element is the result of the application of f on the corresponding column of the original matrix.

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pub fn compress_rows_tr( &self, f: impl Fn(VectorView<'_, T, R, S::RStride, S::CStride>) -> T ) -> OVector<T, 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().

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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>

Returns a column vector resulting from the folding of f on each column of this matrix.

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

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pub fn sum(&self) -> T
where T: ClosedAdd + 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);
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pub fn row_sum(&self) -> RowOVector<T, 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));
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pub fn row_sum_tr(&self) -> OVector<T, 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));
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pub fn column_sum(&self) -> OVector<T, 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));
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pub fn product(&self) -> T
where T: ClosedMul + 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);
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pub fn row_product(&self) -> RowOVector<T, 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));
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pub fn row_product_tr(&self) -> OVector<T, 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));
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pub fn column_product(&self) -> OVector<T, 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));
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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);
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pub fn row_variance(&self) -> RowOVector<T, 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));
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pub fn row_variance_tr(&self) -> OVector<T, 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));
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pub fn column_variance(&self) -> OVector<T, 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);
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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);
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pub fn row_mean(&self) -> RowOVector<T, 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));
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pub fn row_mean_tr(&self) -> OVector<T, 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));
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pub fn column_mean(&self) -> OVector<T, 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));
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impl<T: Scalar, D, S: RawStorage<T, D>> Matrix<T, D, Const<1>, S>
where D: DimName + ToTypenum,

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pub fn xx(&self) -> Vector2<T>
where D::Typenum: Cmp<U0, Output = Greater>,

Builds a new vector from components of self.

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pub fn xxx(&self) -> Vector3<T>
where D::Typenum: Cmp<U0, Output = Greater>,

Builds a new vector from components of self.

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pub fn xy(&self) -> Vector2<T>
where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

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pub fn yx(&self) -> Vector2<T>
where D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.