Struct nalgebra::base::Matrix

#[repr(C)]
pub struct Matrix<N: Scalar, R: Dim, C: Dim, S> {
    pub data: S,
    // some fields omitted
}

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

It combines four type parameters:

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

Fields

data: S

The data storage that contains all the matrix components and informations about its number of rows and column (if needed).

Methods

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

pub fn icamax_full(&self) -> (usize, usize)

Computes the index of the matrix component with the largest absolute value.

Examples:

let mat = Matrix2x3::new(Complex::new(11.0, 1.0), Complex::new(-12.0, 2.0), Complex::new(13.0, 3.0),
                         Complex::new(21.0, 43.0), Complex::new(22.0, 5.0), Complex::new(-23.0, 0.0));
assert_eq!(mat.icamax_full(), (1, 0));

impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>

pub fn iamax_full(&self) -> (usize, usize)

Computes the index of the matrix component with the largest absolute value.

Examples:

let mat = Matrix2x3::new(11, -12, 13,
                         21, 22, -23);
assert_eq!(mat.iamax_full(), (1, 2));

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

pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N where
    SB: Storage<N, 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.

Examples:

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

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

pub fn dotc<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N where
    N: ComplexField,
    SB: Storage<N, 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.

Examples:

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

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

pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N where
    SB: Storage<N, R2, C2>,
    ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>, 

The dot product between the transpose of self and rhs.

Examples:

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

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

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

pub fn ger<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: N,
    x: &Vector<N, D2, SB>,
    y: &Vector<N, D3, SC>,
    beta: N
) where
    N: One,
    SB: Storage<N, D2>,
    SC: Storage<N, D3>,
    ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>, 

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

If beta is zero, self is never read.

Examples:

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

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

pub fn gerc<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: N,
    x: &Vector<N, D2, SB>,
    y: &Vector<N, D3, SC>,
    beta: N
) where
    N: ComplexField,
    SB: Storage<N, D2>,
    SC: Storage<N, D3>,
    ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>, 

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

If beta is zero, self is never read.

Examples:

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

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

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

Examples:

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

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

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

Examples:

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

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

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

Examples:

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

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

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

pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: N,
    x: &Vector<N, D2, SB>,
    y: &Vector<N, D3, SC>,
    beta: N
) where
    N: One,
    SB: Storage<N, D2>,
    SC: Storage<N, 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.

Examples:

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

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

pub fn syger<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: N,
    x: &Vector<N, D2, SB>,
    y: &Vector<N, D3, SC>,
    beta: N
) where
    N: One,
    SB: Storage<N, D2>,
    SC: Storage<N, 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.

Examples:

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

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

pub fn hegerc<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: N,
    x: &Vector<N, D2, SB>,
    y: &Vector<N, D3, SC>,
    beta: N
) where
    N: ComplexField,
    SB: Storage<N, D2>,
    SC: Storage<N, 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.

Examples:

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

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

impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S> where
    N: Scalar + ClosedNeg,
    S: StorageMut<N, R, C>, 

pub fn neg_mut(&mut self)

Negates self in-place.

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

pub fn add_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>,
    out: &mut Matrix<N, R3, C3, SC>
) where
    SB: Storage<N, R2, C2>,
    SC: StorageMut<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>, 

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

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

pub fn sub_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>,
    out: &mut Matrix<N, R3, C3, SC>
) where
    SB: Storage<N, R2, C2>,
    SC: StorageMut<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>, 

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

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

pub fn tr_mul<R2: Dim, C2: Dim, SB>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>
) -> MatrixMN<N, C1, C2> where
    SB: Storage<N, R2, C2>,
    DefaultAllocator: Allocator<N, C1, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2>, 

Equivalent to self.transpose() * rhs.

pub fn ad_mul<R2: Dim, C2: Dim, SB>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>
) -> MatrixMN<N, C1, C2> where
    N: ComplexField,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: Allocator<N, C1, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2>, 

Equivalent to self.adjoint() * rhs.

pub fn tr_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>,
    out: &mut Matrix<N, R3, C3, SC>
) where
    SB: Storage<N, R2, C2>,
    SC: StorageMut<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>, 

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

pub fn ad_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>,
    out: &mut Matrix<N, R3, C3, SC>
) where
    N: ComplexField,
    SB: Storage<N, R2, C2>,
    SC: StorageMut<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>, 

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

pub fn mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>,
    out: &mut Matrix<N, R3, C3, SC>
) where
    SB: Storage<N, R2, C2>,
    SC: StorageMut<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R3, R1> + SameNumberOfColumns<C3, C2> + AreMultipliable<R1, C1, R2, C2>, 

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

pub fn kronecker<R2: Dim, C2: Dim, SB>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>
) -> MatrixMN<N, DimProd<R1, R2>, DimProd<C1, C2>> where
    N: ClosedMul,
    R1: DimMul<R2>,
    C1: DimMul<C2>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: Allocator<N, DimProd<R1, R2>, DimProd<C1, C2>>, 

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

impl<N: Scalar + ClosedAdd, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>

pub fn add_scalar(&self, rhs: N) -> MatrixMN<N, R, C> where
    DefaultAllocator: Allocator<N, R, C>, 

Adds a scalar to self.

pub fn add_scalar_mut(&mut self, rhs: N) where
    S: StorageMut<N, R, C>, 

Adds a scalar to self in-place.

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

pub fn amax(&self) -> N where
    N: PartialOrd + Signed, 

Returns the absolute value of the component with the largest absolute value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).amax(), 3.0);
assert_eq!(Vector3::new(-1.0, -2.0, -3.0).amax(), 3.0);

pub fn camax(&self) -> N::RealField where
    N: ComplexField, 

Returns the the 1-norm of the complex component with the largest 1-norm.

Example

assert_eq!(Vector3::new(
    Complex::new(-3.0, -2.0),
    Complex::new(1.0, 2.0),
    Complex::new(1.0, 3.0)).camax(), 5.0);

pub fn max(&self) -> N where
    N: PartialOrd + Signed, 

Returns the component with the largest value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).max(), 3.0);
assert_eq!(Vector3::new(-1.0, -2.0, -3.0).max(), -1.0);

pub fn amin(&self) -> N where
    N: PartialOrd + Signed, 

Returns the absolute value of the component with the smallest absolute value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, -3.0).amin(), 1.0);
assert_eq!(Vector3::new(10.0, 2.0, 30.0).amin(), 2.0);

pub fn camin(&self) -> N::RealField where
    N: ComplexField, 

Returns the the 1-norm of the complex component with the smallest 1-norm.

Example

assert_eq!(Vector3::new(
    Complex::new(-3.0, -2.0),
    Complex::new(1.0, 2.0),
    Complex::new(1.0, 3.0)).camin(), 3.0);

pub fn min(&self) -> N where
    N: PartialOrd + Signed, 

Returns the component with the smallest value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).min(), -1.0);
assert_eq!(Vector3::new(1.0, 2.0, 3.0).min(), 1.0);

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

pub fn abs(&self) -> MatrixMN<N, R, C> where
    N: Signed,
    DefaultAllocator: Allocator<N, R, C>, 

Computes the component-wise absolute value.

Example

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

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

pub fn component_mul<R2, C2, SB>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>
) -> MatrixSum<N, R1, C1, R2, C2> where
    N: ClosedMul,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, 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);

impl<N: Scalar, R1: Dim, C1: Dim, SA: StorageMut<N, R1, C1>> Matrix<N, R1, C1, SA>

pub fn cmpy<R2, C2, SB, R3, C3, SC>(
    &mut self,
    alpha: N,
    a: &Matrix<N, R2, C2, SB>,
    b: &Matrix<N, R3, C3, SC>,
    beta: N
) where
    N: ClosedMul + Zero + Mul<N, Output = N> + Add<N, Output = N>,
    R2: Dim,
    C2: Dim,
    R3: Dim,
    C3: Dim,
    SB: Storage<N, R2, C2>,
    SC: Storage<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>, 

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

Example

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

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

pub fn component_mul_assign<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>) where
    N: ClosedMul,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

Inplace componentwise matrix or vector multiplication.

Example

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

a.component_mul_assign(&b);

assert_eq!(a, expected);

pub fn component_mul_mut<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>) where
    N: ClosedMul,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, 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);

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

pub fn component_div<R2, C2, SB>(
    &self,
    rhs: &Matrix<N, R2, C2, SB>
) -> MatrixSum<N, R1, C1, R2, C2> where
    N: ClosedDiv,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, 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);

impl<N: Scalar, R1: Dim, C1: Dim, SA: StorageMut<N, R1, C1>> Matrix<N, R1, C1, SA>

pub fn cdpy<R2, C2, SB, R3, C3, SC>(
    &mut self,
    alpha: N,
    a: &Matrix<N, R2, C2, SB>,
    b: &Matrix<N, R3, C3, SC>,
    beta: N
) where
    N: ClosedDiv + Zero + Mul<N, Output = N> + Add<N, Output = N>,
    R2: Dim,
    C2: Dim,
    R3: Dim,
    C3: Dim,
    SB: Storage<N, R2, C2>,
    SC: Storage<N, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> + SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3>, 

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

Example

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

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

pub fn component_div_assign<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>) where
    N: ClosedDiv,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

Inplace componentwise matrix or vector division.

Example

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

a.component_div_assign(&b);

assert_eq!(a, expected);

pub fn component_div_mut<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>) where
    N: ClosedDiv,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, 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);

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

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

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

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

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

pub fn select_rows<'a, I>(&self, irows: I) -> MatrixMN<N, Dynamic, C> where
    I: IntoIterator<Item = &'a usize>,
    I::IntoIter: ExactSizeIterator + Clone,
    DefaultAllocator: Allocator<N, Dynamic, C>, 

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

pub fn select_columns<'a, I>(&self, icols: I) -> MatrixMN<N, R, Dynamic> where
    I: IntoIterator<Item = &'a usize>,
    I::IntoIter: ExactSizeIterator,
    DefaultAllocator: Allocator<N, R, Dynamic>, 

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

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

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

Sets all the elements of this matrix to val.

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

Fills self with the identity matrix.

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

Sets all the diagonal elements of this matrix to val.

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

Sets all the elements of the selected row to val.

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

Sets all the elements of the selected column to val.

pub fn set_diagonal<R2: Dim, S2>(&mut self, diag: &Vector<N, R2, S2>) where
    R: DimMin<C>,
    S2: Storage<N, R2>,
    ShapeConstraint: DimEq<DimMinimum<R, C>, R2>, 

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

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

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

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

pub fn set_row<C2: Dim, S2>(&mut self, i: usize, row: &RowVector<N, C2, S2>) where
    S2: Storage<N, U1, C2>,
    ShapeConstraint: SameNumberOfColumns<C, C2>, 

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

pub fn set_column<R2: Dim, S2>(&mut self, i: usize, column: &Vector<N, R2, S2>) where
    S2: Storage<N, R2, U1>,
    ShapeConstraint: SameNumberOfRows<R, R2>, 

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

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

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

The parameter shift allows some subdiagonals to be left untouched:

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

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

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.

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

Swaps two rows in-place.

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

Swaps two columns in-place.

impl<N: Scalar, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S>

pub fn fill_lower_triangle_with_upper_triangle(&mut self)

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

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

pub fn fill_upper_triangle_with_lower_triangle(&mut self)

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

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

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

pub fn remove_column(self, i: usize) -> MatrixMN<N, R, DimDiff<C, U1>> where
    C: DimSub<U1>,
    DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, U1>>, 

Removes the i-th column from this matrix.

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

Removes all columns in indices

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

Removes all rows in indices

pub fn remove_fixed_columns<D>(self, i: usize) -> MatrixMN<N, R, DimDiff<C, D>> where
    D: DimName,
    C: DimSub<D>,
    DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, D>>, 

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

pub fn remove_columns(self, i: usize, n: usize) -> MatrixMN<N, R, Dynamic> where
    C: DimSub<Dynamic, Output = Dynamic>,
    DefaultAllocator: Reallocator<N, R, C, R, Dynamic>, 

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

pub fn remove_columns_generic<D>(
    self,
    i: usize,
    nremove: D
) -> MatrixMN<N, R, DimDiff<C, D>> where
    D: Dim,
    C: DimSub<D>,
    DefaultAllocator: Reallocator<N, R, C, R, DimDiff<C, D>>, 

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

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

pub fn remove_row(self, i: usize) -> MatrixMN<N, DimDiff<R, U1>, C> where
    R: DimSub<U1>,
    DefaultAllocator: Reallocator<N, R, C, DimDiff<R, U1>, C>, 

Removes the i-th row from this matrix.

pub fn remove_fixed_rows<D>(self, i: usize) -> MatrixMN<N, DimDiff<R, D>, C> where
    D: DimName,
    R: DimSub<D>,
    DefaultAllocator: Reallocator<N, R, C, DimDiff<R, D>, C>, 

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

pub fn remove_rows(self, i: usize, n: usize) -> MatrixMN<N, Dynamic, C> where
    R: DimSub<Dynamic, Output = Dynamic>,
    DefaultAllocator: Reallocator<N, R, C, Dynamic, C>, 

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

pub fn remove_rows_generic<D>(
    self,
    i: usize,
    nremove: D
) -> MatrixMN<N, DimDiff<R, D>, C> where
    D: Dim,
    R: DimSub<D>,
    DefaultAllocator: Reallocator<N, 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.

pub fn insert_column(self, i: usize, val: N) -> MatrixMN<N, R, DimSum<C, U1>> where
    C: DimAdd<U1>,
    DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, U1>>, 

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

pub fn insert_fixed_columns<D>(
    self,
    i: usize,
    val: N
) -> MatrixMN<N, R, DimSum<C, D>> where
    D: DimName,
    C: DimAdd<D>,
    DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, D>>, 

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

pub fn insert_columns(
    self,
    i: usize,
    n: usize,
    val: N
) -> MatrixMN<N, R, Dynamic> where
    C: DimAdd<Dynamic, Output = Dynamic>,
    DefaultAllocator: Reallocator<N, R, C, R, Dynamic>, 

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

pub unsafe fn insert_columns_generic_uninitialized<D>(
    self,
    i: usize,
    ninsert: D
) -> MatrixMN<N, R, DimSum<C, D>> where
    D: Dim,
    C: DimAdd<D>,
    DefaultAllocator: Reallocator<N, R, C, R, DimSum<C, D>>, 

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

The added column values are not initialized.

pub fn insert_row(self, i: usize, val: N) -> MatrixMN<N, DimSum<R, U1>, C> where
    R: DimAdd<U1>,
    DefaultAllocator: Reallocator<N, R, C, DimSum<R, U1>, C>, 

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

pub fn insert_fixed_rows<D>(
    self,
    i: usize,
    val: N
) -> MatrixMN<N, DimSum<R, D>, C> where
    D: DimName,
    R: DimAdd<D>,
    DefaultAllocator: Reallocator<N, R, C, DimSum<R, D>, C>, 

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

pub fn insert_rows(self, i: usize, n: usize, val: N) -> MatrixMN<N, Dynamic, C> where
    R: DimAdd<Dynamic, Output = Dynamic>,
    DefaultAllocator: Reallocator<N, R, C, Dynamic, C>, 

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

pub unsafe fn insert_rows_generic_uninitialized<D>(
    self,
    i: usize,
    ninsert: D
) -> MatrixMN<N, DimSum<R, D>, C> where
    D: Dim,
    R: DimAdd<D>,
    DefaultAllocator: Reallocator<N, R, C, DimSum<R, D>, C>, 

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

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

pub fn resize(self, new_nrows: usize, new_ncols: usize, val: N) -> DMatrix<N> where
    DefaultAllocator: Reallocator<N, R, C, Dynamic, Dynamic>, 

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.

pub fn resize_vertically(
    self,
    new_nrows: usize,
    val: N
) -> MatrixMN<N, Dynamic, C> where
    DefaultAllocator: Reallocator<N, R, C, Dynamic, 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.

pub fn resize_horizontally(
    self,
    new_ncols: usize,
    val: N
) -> MatrixMN<N, R, Dynamic> where
    DefaultAllocator: Reallocator<N, R, C, R, Dynamic>, 

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.

pub fn fixed_resize<R2: DimName, C2: DimName>(
    self,
    val: N
) -> MatrixMN<N, R2, C2> where
    DefaultAllocator: Reallocator<N, R, C, R2, C2>, 

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

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

pub fn resize_generic<R2: Dim, C2: Dim>(
    self,
    new_nrows: R2,
    new_ncols: C2,
    val: N
) -> MatrixMN<N, R2, C2> where
    DefaultAllocator: Reallocator<N, R, C, R2, C2>, 

Resizes self such that it has dimensions new_nrows × now_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.

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

Indexing Operations

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((U1.., 0))
    .eq(&Matrix2x1::new(1,
                        2)));

Indices to Ranges of Rows and Columns

Index to a Range of Rows

let matrix = Matrix3::new(0, 3, 6,
                          1, 4, 7,
                          2, 5, 8);

assert!(matrix.index((1..3, ..))
    .eq(&Matrix2x3::new(1, 4, 7,
                        2, 5, 8)));

Index to a Range of Columns

let matrix = Matrix3::new(0, 3, 6,
                          1, 4, 7,
                          2, 5, 8);

assert!(matrix.index((.., 1..3))
    .eq(&Matrix3x2::new(3, 6,
                        4, 7,
                        5, 8)));

pub fn get<'a, I>(&'a self, index: I) -> Option<I::Output> where
    I: MatrixIndex<'a, N, R, C, S>, 

Produces a view of the data at the given index, or None if the index is out of bounds.

pub fn get_mut<'a, I>(&'a mut self, index: I) -> Option<I::OutputMut> where
    S: StorageMut<N, R, C>,
    I: MatrixIndexMut<'a, N, R, C, S>, 

Produces a mutable view of the data at the given index, or None if the index is out of bounds.

pub fn index<'a, I>(&'a self, index: I) -> I::Output where
    I: MatrixIndex<'a, N, R, C, S>, 

Produces a view of the data at the given index, or panics if the index is out of bounds.

pub fn index_mut<'a, I>(&'a mut self, index: I) -> I::OutputMut where
    S: StorageMut<N, R, C>,
    I: MatrixIndexMut<'a, N, R, C, S>, 

Produces a mutable view of the data at the given index, or panics if the index is out of bounds.

pub unsafe fn get_unchecked<'a, I>(&'a self, index: I) -> I::Output where
    I: MatrixIndex<'a, N, R, C, S>, 

Produces a view of the data at the given index, without doing any bounds checking.

pub unsafe fn get_unchecked_mut<'a, I>(&'a mut self, index: I) -> I::OutputMut where
    S: StorageMut<N, R, C>,
    I: MatrixIndexMut<'a, N, R, C, S>, 

Returns a mutable view of the data at the given index, without doing any bounds checking.

impl<N: Scalar, R: Dim, C: Dim, S> Matrix<N, R, C, S>

pub unsafe fn from_data_statically_unchecked(data: S) -> Matrix<N, R, C, S>

Creates a new matrix with the given data without statically checking that the matrix dimension matches the storage dimension.

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

pub fn from_data(data: S) -> Self

Creates a new matrix with the given data.

pub fn len(&self) -> usize

The total number of elements of this matrix.

Examples:

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.len(), 12);

pub fn shape(&self) -> (usize, usize)

The shape of this matrix returned as the tuple (number of rows, number of columns).

Examples:

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.shape(), (3, 4));

pub fn nrows(&self) -> usize

The number of rows of this matrix.

Examples:

let mat = Matrix3x4::<f32>::zeros();
assert_eq!(mat.nrows(), 3);

pub fn ncols(&self) -> usize

The number of columns of this matrix.

Examples:

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

pub fn strides(&self) -> (usize, usize)

The strides (row stride, column stride) of this matrix.

Examples:

let mat = DMatrix::<f32>::zeros(10, 10);
let slice = mat.slice_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));

Important traits for MatrixIter<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for MatrixIter<'a, N, R, C, S> type Item = &'a N;

pub fn iter(&self) -> MatrixIter<N, R, C, S>

Iterates through this matrix coordinates in column-major order.

Examples:

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());

Important traits for RowIter<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for RowIter<'a, N, R, C, S> type Item = MatrixSlice<'a, N, U1, C, S::RStride, S::CStride>;

pub fn row_iter(&self) -> RowIter<N, 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))
}

Important traits for ColumnIter<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for ColumnIter<'a, N, R, C, S> type Item = MatrixSlice<'a, N, R, U1, S::RStride, S::CStride>;

pub fn column_iter(&self) -> ColumnIter<N, R, C, S>

Iterate through the columns of this matrix.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, column) in a.column_iter().enumerate() {
    assert_eq!(column, a.column(i))
}

pub fn 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.

pub fn as_ptr(&self) -> *const N

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.

pub fn relative_eq<R2, C2, SB>(
    &self,
    other: &Matrix<N, R2, C2, SB>,
    eps: N::Epsilon,
    max_relative: N::Epsilon
) -> bool where
    N: RelativeEq,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    N::Epsilon: Copy,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Tests whether self and rhs are equal up to a given epsilon.

See relative_eq from the RelativeEq trait for more details.

pub fn eq<R2, C2, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> bool where
    N: PartialEq,
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Tests whether self and rhs are exactly equal.

pub fn into_owned(self) -> MatrixMN<N, R, C> where
    DefaultAllocator: Allocator<N, R, C>, 

Moves this matrix into one that owns its data.

pub fn into_owned_sum<R2, C2>(self) -> MatrixSum<N, R, C, R2, C2> where
    R2: Dim,
    C2: Dim,
    DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Moves this matrix into one that owns its data. The actual type of the result depends on matrix storage combination rules for addition.

pub fn clone_owned(&self) -> MatrixMN<N, R, C> where
    DefaultAllocator: Allocator<N, R, C>, 

Clones this matrix to one that owns its data.

pub fn clone_owned_sum<R2, C2>(&self) -> MatrixSum<N, R, C, R2, C2> where
    R2: Dim,
    C2: Dim,
    DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Clones this matrix into one that owns its data. The actual type of the result depends on matrix storage combination rules for addition.

pub fn map<N2: Scalar, F: FnMut(N) -> N2>(&self, f: F) -> MatrixMN<N2, R, C> where
    DefaultAllocator: Allocator<N2, R, C>, 

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

pub fn map_with_location<N2: Scalar, F: FnMut(usize, usize, N) -> N2>(
    &self,
    f: F
) -> MatrixMN<N2, R, C> where
    DefaultAllocator: Allocator<N2, R, C>, 

Returns a matrix containing the result of f applied to each of its entries. Unlike map, f also gets passed the row and column index, i.e. f(row, col, value).

pub fn zip_map<N2, N3, S2, F>(
    &self,
    rhs: &Matrix<N2, R, C, S2>,
    f: F
) -> MatrixMN<N3, R, C> where
    N2: Scalar,
    N3: Scalar,
    S2: Storage<N2, R, C>,
    F: FnMut(N, N2) -> N3,
    DefaultAllocator: Allocator<N3, R, C>, 

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

pub fn zip_zip_map<N2, N3, N4, S2, S3, F>(
    &self,
    b: &Matrix<N2, R, C, S2>,
    c: &Matrix<N3, R, C, S3>,
    f: F
) -> MatrixMN<N4, R, C> where
    N2: Scalar,
    N3: Scalar,
    N4: Scalar,
    S2: Storage<N2, R, C>,
    S3: Storage<N3, R, C>,
    F: FnMut(N, N2, 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.

pub fn fold<Acc>(&self, init: Acc, f: impl FnMut(Acc, N) -> Acc) -> Acc

Folds a function f on each entry of self.

pub fn zip_fold<N2, R2, C2, S2, Acc>(
    &self,
    rhs: &Matrix<N2, R2, C2, S2>,
    init: Acc,
    f: impl FnMut(Acc, N, N2) -> Acc
) -> Acc where
    N2: Scalar,
    R2: Dim,
    C2: Dim,
    S2: Storage<N2, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Folds a function f on each pairs of entries from self and rhs.

pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>) where
    R2: Dim,
    C2: Dim,
    SB: StorageMut<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>, 

Transposes self and store the result into out.

pub fn transpose(&self) -> MatrixMN<N, C, R> where
    DefaultAllocator: Allocator<N, C, R>, 

Transposes self.

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

Important traits for MatrixIterMut<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for MatrixIterMut<'a, N, R, C, S> type Item = &'a mut N;

pub fn iter_mut(&mut self) -> MatrixIterMut<N, R, C, S>

Mutably iterates through this matrix coordinates.

pub fn as_mut_ptr(&mut self) -> *mut N

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.

Important traits for RowIterMut<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for RowIterMut<'a, N, R, C, S> type Item = MatrixSliceMut<'a, N, U1, C, S::RStride, S::CStride>;

pub fn row_iter_mut(&mut self) -> RowIterMut<N, R, C, S>

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);

Important traits for ColumnIterMut<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for ColumnIterMut<'a, N, R, C, S> type Item = MatrixSliceMut<'a, N, R, U1, S::RStride, S::CStride>;

pub fn column_iter_mut(&mut self) -> ColumnIterMut<N, R, C, S>

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);

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

Swaps two entries without bound-checking.

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

Swaps two entries.

pub fn copy_from_slice(&mut self, slice: &[N])

Fills this matrix with the content of a slice. Both must hold the same number of elements.

The components of the slice are assumed to be ordered in column-major order.

pub fn copy_from<R2, C2, SB>(&mut self, other: &Matrix<N, R2, C2, SB>) where
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Fills this matrix with the content of another one. Both must have the same shape.

pub fn tr_copy_from<R2, C2, SB>(&mut self, other: &Matrix<N, R2, C2, SB>) where
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: DimEq<R, C2> + SameNumberOfColumns<C, R2>, 

Fills this matrix with the content of the transpose another one.

pub fn apply_into<F: FnMut(N) -> N>(self, f: F) -> Self

Returns self with each of its components replaced by the result of a closure f applied on it.

pub fn apply<F: FnMut(N) -> N>(&mut self, f: F)

Replaces each component of self by the result of a closure f applied on it.

pub fn zip_apply<N2, R2, C2, S2>(
    &mut self,
    rhs: &Matrix<N2, R2, C2, S2>,
    f: impl FnMut(N, N2) -> N
) where
    N2: Scalar,
    R2: Dim,
    C2: Dim,
    S2: Storage<N2, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Replaces each component of self by the result of a closure f applied on its components joined with the components from rhs.

pub fn zip_zip_apply<N2, R2, C2, S2, N3, R3, C3, S3>(
    &mut self,
    b: &Matrix<N2, R2, C2, S2>,
    c: &Matrix<N3, R3, C3, S3>,
    f: impl FnMut(N, N2, N3) -> N
) where
    N2: Scalar,
    R2: Dim,
    C2: Dim,
    S2: Storage<N2, R2, C2>,
    N3: Scalar,
    R3: Dim,
    C3: Dim,
    S3: Storage<N3, R3, C3>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, 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 b and c.

impl<N: Scalar, R: Dim, C: Dim, S: ContiguousStorage<N, R, C>> Matrix<N, R, C, S>

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

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

impl<N: Scalar, R: Dim, C: Dim, S: ContiguousStorageMut<N, R, C>> Matrix<N, R, C, S>

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

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

impl<N: Scalar, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S>

pub fn transpose_mut(&mut self)

Transposes the square matrix self in-place.

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

pub fn adjoint_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>) where
    R2: Dim,
    C2: Dim,
    SB: StorageMut<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>, 

Takes the adjoint (aka. conjugate-transpose) of self and store the result into out.

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

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

pub fn conjugate_transpose_to<R2, C2, SB>(
    &self,
    out: &mut Matrix<N, R2, C2, SB>
) where
    R2: Dim,
    C2: Dim,
    SB: StorageMut<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>, 

Deprecated:

Renamed self.adjoint_to(out).

Takes the conjugate and transposes self and store the result into out.

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

Deprecated:

Renamed self.adjoint().

The conjugate transposition of self.

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

The conjugate of self.

pub fn unscale(&self, real: N::RealField) -> MatrixMN<N, R, C> where
    DefaultAllocator: Allocator<N, R, C>, 

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

pub fn scale(&self, real: N::RealField) -> MatrixMN<N, R, C> where
    DefaultAllocator: Allocator<N, R, C>, 

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

impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S>

pub fn conjugate_mut(&mut self)

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

pub fn unscale_mut(&mut self, real: N::RealField)

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

pub fn scale_mut(&mut self, real: N::RealField)

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

impl<N: ComplexField, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S>

pub fn conjugate_transform_mut(&mut self)

Deprecated:

Renamed to self.adjoint_mut().

Sets self to its adjoint.

pub fn adjoint_mut(&mut self)

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

impl<N: Scalar + One + Zero, D: DimAdd<U1> + IsNotStaticOne, S: Storage<N, D, D>> Matrix<N, D, D, S>

pub fn to_homogeneous(&self) -> MatrixN<N, DimSum<D, U1>> where
    DefaultAllocator: Allocator<N, DimSum<D, U1>, DimSum<D, U1>>, 

Yields the homogeneous matrix for this matrix, i.e., appending an additional dimension and and setting the diagonal element to 1.

impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>

pub fn perp<R2, C2, SB>(&self, b: &Matrix<N, R2, C2, SB>) -> N where
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, U2> + SameNumberOfColumns<C, U1> + SameNumberOfRows<R2, U2> + SameNumberOfColumns<C2, U1>, 

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

pub fn cross<R2, C2, SB>(
    &self,
    b: &Matrix<N, R2, C2, SB>
) -> MatrixCross<N, R, C, R2, C2> where
    R2: Dim,
    C2: Dim,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

The 3D cross product between two vectors.

Panics if the shape is not 3D vector. In the future, this will be implemented only for dynamically-sized matrices and statically-sized 3D matrices.

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

pub fn angle<R2: Dim, C2: Dim, SB>(
    &self,
    other: &Matrix<N, R2, C2, SB>
) -> N::RealField where
    SB: Storage<N, R2, C2>,
    ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>, 

The smallest angle between two vectors.

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

pub fn row(&self, i: usize) -> MatrixSlice<N, U1, C, S::RStride, S::CStride>

Returns a slice containing the i-th row of this matrix.

pub fn row_part(
    &self,
    i: usize,
    n: usize
) -> MatrixSlice<N, U1, Dynamic, S::RStride, S::CStride>

Returns a slice containing the n first elements of the i-th row of this matrix.

pub fn rows(
    &self,
    first_row: usize,
    nrows: usize
) -> MatrixSlice<N, Dynamic, C, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive rows.

pub fn rows_with_step(
    &self,
    first_row: usize,
    nrows: usize,
    step: usize
) -> MatrixSlice<N, Dynamic, C, Dynamic, S::CStride>

Extracts from this matrix a set of consecutive rows regularly skipping step rows.

pub fn fixed_rows<RSlice: DimName>(
    &self,
    first_row: usize
) -> MatrixSlice<N, RSlice, C, S::RStride, S::CStride>

Extracts a compile-time number of consecutive rows from this matrix.

pub fn fixed_rows_with_step<RSlice: DimName>(
    &self,
    first_row: usize,
    step: usize
) -> MatrixSlice<N, RSlice, C, Dynamic, S::CStride>

Extracts from this matrix a compile-time number of rows regularly skipping step rows.

pub fn rows_generic<RSlice: Dim>(
    &self,
    row_start: usize,
    nrows: RSlice
) -> MatrixSlice<N, RSlice, C, S::RStride, S::CStride>

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn rows_generic_with_step<RSlice>(
    &self,
    row_start: usize,
    nrows: RSlice,
    step: usize
) -> MatrixSlice<N, RSlice, C, Dynamic, S::CStride> where
    RSlice: Dim, 

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn column(&self, i: usize) -> MatrixSlice<N, R, U1, S::RStride, S::CStride>

Returns a slice containing the i-th column of this matrix.

pub fn column_part(
    &self,
    i: usize,
    n: usize
) -> MatrixSlice<N, Dynamic, U1, S::RStride, S::CStride>

Returns a slice containing the n first elements of the i-th column of this matrix.

pub fn columns(
    &self,
    first_col: usize,
    ncols: usize
) -> MatrixSlice<N, R, Dynamic, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive columns.

pub fn columns_with_step(
    &self,
    first_col: usize,
    ncols: usize,
    step: usize
) -> MatrixSlice<N, R, Dynamic, S::RStride, Dynamic>

Extracts from this matrix a set of consecutive columns regularly skipping step columns.

pub fn fixed_columns<CSlice: DimName>(
    &self,
    first_col: usize
) -> MatrixSlice<N, R, CSlice, S::RStride, S::CStride>

Extracts a compile-time number of consecutive columns from this matrix.

pub fn fixed_columns_with_step<CSlice: DimName>(
    &self,
    first_col: usize,
    step: usize
) -> MatrixSlice<N, R, CSlice, S::RStride, Dynamic>

Extracts from this matrix a compile-time number of columns regularly skipping step columns.

pub fn columns_generic<CSlice: Dim>(
    &self,
    first_col: usize,
    ncols: CSlice
) -> MatrixSlice<N, R, CSlice, S::RStride, S::CStride>

Extracts from this matrix ncols columns. The number of columns may or may not be known at compile-time.

pub fn columns_generic_with_step<CSlice: Dim>(
    &self,
    first_col: usize,
    ncols: CSlice,
    step: usize
) -> MatrixSlice<N, R, CSlice, S::RStride, Dynamic>

Extracts from this matrix ncols columns skipping step columns. Both argument may or may not be values known at compile-time.

pub fn slice(
    &self,
    start: (usize, usize),
    shape: (usize, usize)
) -> MatrixSlice<N, Dynamic, Dynamic, S::RStride, S::CStride>

Slices this matrix starting at its component (irow, icol) and with (nrows, ncols) consecutive elements.

pub fn slice_with_steps(
    &self,
    start: (usize, usize),
    shape: (usize, usize),
    steps: (usize, usize)
) -> MatrixSlice<N, Dynamic, Dynamic, Dynamic, Dynamic>

Slices this matrix starting at its component (start.0, start.1) and with (shape.0, shape.1) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn fixed_slice<RSlice, CSlice>(
    &self,
    irow: usize,
    icol: usize
) -> MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride> where
    RSlice: DimName,
    CSlice: DimName, 

Slices this matrix starting at its component (irow, icol) and with (R::dim(), CSlice::dim()) consecutive components.

pub fn fixed_slice_with_steps<RSlice, CSlice>(
    &self,
    start: (usize, usize),
    steps: (usize, usize)
) -> MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic> where
    RSlice: DimName,
    CSlice: DimName, 

Slices this matrix starting at its component (start.0, start.1) and with (R::dim(), CSlice::dim()) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn generic_slice<RSlice, CSlice>(
    &self,
    start: (usize, usize),
    shape: (RSlice, CSlice)
) -> MatrixSlice<N, RSlice, CSlice, S::RStride, S::CStride> where
    RSlice: Dim,
    CSlice: Dim, 

Creates a slice that may or may not have a fixed size and stride.

pub fn generic_slice_with_steps<RSlice, CSlice>(
    &self,
    start: (usize, usize),
    shape: (RSlice, CSlice),
    steps: (usize, usize)
) -> MatrixSlice<N, RSlice, CSlice, Dynamic, Dynamic> where
    RSlice: Dim,
    CSlice: Dim, 

Creates a slice that may or may not have a fixed size and stride.

pub fn rows_range_pair<Range1: SliceRange<R>, Range2: SliceRange<R>>(
    &self,
    r1: Range1,
    r2: Range2
) -> (MatrixSlice<N, Range1::Size, C, S::RStride, S::CStride>, MatrixSlice<N, Range2::Size, C, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

pub fn columns_range_pair<Range1: SliceRange<C>, Range2: SliceRange<C>>(
    &self,
    r1: Range1,
    r2: Range2
) -> (MatrixSlice<N, R, Range1::Size, S::RStride, S::CStride>, MatrixSlice<N, R, Range2::Size, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

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

pub fn row_mut(
    &mut self,
    i: usize
) -> MatrixSliceMut<N, U1, C, S::RStride, S::CStride>

Returns a slice containing the i-th row of this matrix.

pub fn row_part_mut(
    &mut self,
    i: usize,
    n: usize
) -> MatrixSliceMut<N, U1, Dynamic, S::RStride, S::CStride>

Returns a slice containing the n first elements of the i-th row of this matrix.

pub fn rows_mut(
    &mut self,
    first_row: usize,
    nrows: usize
) -> MatrixSliceMut<N, Dynamic, C, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive rows.

pub fn rows_with_step_mut(
    &mut self,
    first_row: usize,
    nrows: usize,
    step: usize
) -> MatrixSliceMut<N, Dynamic, C, Dynamic, S::CStride>

Extracts from this matrix a set of consecutive rows regularly skipping step rows.

pub fn fixed_rows_mut<RSlice: DimName>(
    &mut self,
    first_row: usize
) -> MatrixSliceMut<N, RSlice, C, S::RStride, S::CStride>

Extracts a compile-time number of consecutive rows from this matrix.

pub fn fixed_rows_with_step_mut<RSlice: DimName>(
    &mut self,
    first_row: usize,
    step: usize
) -> MatrixSliceMut<N, RSlice, C, Dynamic, S::CStride>

Extracts from this matrix a compile-time number of rows regularly skipping step rows.

pub fn rows_generic_mut<RSlice: Dim>(
    &mut self,
    row_start: usize,
    nrows: RSlice
) -> MatrixSliceMut<N, RSlice, C, S::RStride, S::CStride>

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn rows_generic_with_step_mut<RSlice>(
    &mut self,
    row_start: usize,
    nrows: RSlice,
    step: usize
) -> MatrixSliceMut<N, RSlice, C, Dynamic, S::CStride> where
    RSlice: Dim, 

Extracts from this matrix nrows rows regularly skipping step rows. Both argument may or may not be values known at compile-time.

pub fn column_mut(
    &mut self,
    i: usize
) -> MatrixSliceMut<N, R, U1, S::RStride, S::CStride>

Returns a slice containing the i-th column of this matrix.

pub fn column_part_mut(
    &mut self,
    i: usize,
    n: usize
) -> MatrixSliceMut<N, Dynamic, U1, S::RStride, S::CStride>

Returns a slice containing the n first elements of the i-th column of this matrix.

pub fn columns_mut(
    &mut self,
    first_col: usize,
    ncols: usize
) -> MatrixSliceMut<N, R, Dynamic, S::RStride, S::CStride>

Extracts from this matrix a set of consecutive columns.

pub fn columns_with_step_mut(
    &mut self,
    first_col: usize,
    ncols: usize,
    step: usize
) -> MatrixSliceMut<N, R, Dynamic, S::RStride, Dynamic>

Extracts from this matrix a set of consecutive columns regularly skipping step columns.

pub fn fixed_columns_mut<CSlice: DimName>(
    &mut self,
    first_col: usize
) -> MatrixSliceMut<N, R, CSlice, S::RStride, S::CStride>

Extracts a compile-time number of consecutive columns from this matrix.

pub fn fixed_columns_with_step_mut<CSlice: DimName>(
    &mut self,
    first_col: usize,
    step: usize
) -> MatrixSliceMut<N, R, CSlice, S::RStride, Dynamic>

Extracts from this matrix a compile-time number of columns regularly skipping step columns.

pub fn columns_generic_mut<CSlice: Dim>(
    &mut self,
    first_col: usize,
    ncols: CSlice
) -> MatrixSliceMut<N, R, CSlice, S::RStride, S::CStride>

Extracts from this matrix ncols columns. The number of columns may or may not be known at compile-time.

pub fn columns_generic_with_step_mut<CSlice: Dim>(
    &mut self,
    first_col: usize,
    ncols: CSlice,
    step: usize
) -> MatrixSliceMut<N, R, CSlice, S::RStride, Dynamic>

Extracts from this matrix ncols columns skipping step columns. Both argument may or may not be values known at compile-time.

pub fn slice_mut(
    &mut self,
    start: (usize, usize),
    shape: (usize, usize)
) -> MatrixSliceMut<N, Dynamic, Dynamic, S::RStride, S::CStride>

Slices this matrix starting at its component (irow, icol) and with (nrows, ncols) consecutive elements.

pub fn slice_with_steps_mut(
    &mut self,
    start: (usize, usize),
    shape: (usize, usize),
    steps: (usize, usize)
) -> MatrixSliceMut<N, Dynamic, Dynamic, Dynamic, Dynamic>

Slices this matrix starting at its component (start.0, start.1) and with (shape.0, shape.1) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn fixed_slice_mut<RSlice, CSlice>(
    &mut self,
    irow: usize,
    icol: usize
) -> MatrixSliceMut<N, RSlice, CSlice, S::RStride, S::CStride> where
    RSlice: DimName,
    CSlice: DimName, 

Slices this matrix starting at its component (irow, icol) and with (R::dim(), CSlice::dim()) consecutive components.

pub fn fixed_slice_with_steps_mut<RSlice, CSlice>(
    &mut self,
    start: (usize, usize),
    steps: (usize, usize)
) -> MatrixSliceMut<N, RSlice, CSlice, Dynamic, Dynamic> where
    RSlice: DimName,
    CSlice: DimName, 

Slices this matrix starting at its component (start.0, start.1) and with (R::dim(), CSlice::dim()) components. Each row (resp. column) of the sliced matrix is separated by steps.0 (resp. steps.1) ignored rows (resp. columns) of the original matrix.

pub fn generic_slice_mut<RSlice, CSlice>(
    &mut self,
    start: (usize, usize),
    shape: (RSlice, CSlice)
) -> MatrixSliceMut<N, RSlice, CSlice, S::RStride, S::CStride> where
    RSlice: Dim,
    CSlice: Dim, 

Creates a slice that may or may not have a fixed size and stride.

pub fn generic_slice_with_steps_mut<RSlice, CSlice>(
    &mut self,
    start: (usize, usize),
    shape: (RSlice, CSlice),
    steps: (usize, usize)
) -> MatrixSliceMut<N, RSlice, CSlice, Dynamic, Dynamic> where
    RSlice: Dim,
    CSlice: Dim, 

Creates a slice that may or may not have a fixed size and stride.

pub fn rows_range_pair_mut<Range1: SliceRange<R>, Range2: SliceRange<R>>(
    &mut self,
    r1: Range1,
    r2: Range2
) -> (MatrixSliceMut<N, Range1::Size, C, S::RStride, S::CStride>, MatrixSliceMut<N, Range2::Size, C, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

pub fn columns_range_pair_mut<Range1: SliceRange<C>, Range2: SliceRange<C>>(
    &mut self,
    r1: Range1,
    r2: Range2
) -> (MatrixSliceMut<N, R, Range1::Size, S::RStride, S::CStride>, MatrixSliceMut<N, R, Range2::Size, S::RStride, S::CStride>)

Splits this NxM matrix into two parts delimited by two ranges.

Panics if the ranges overlap or if the first range is empty.

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

pub fn slice_range<RowRange, ColRange>(
    &self,
    rows: RowRange,
    cols: ColRange
) -> MatrixSlice<N, RowRange::Size, ColRange::Size, S::RStride, S::CStride> where
    RowRange: SliceRange<R>,
    ColRange: SliceRange<C>, 

Slices a sub-matrix containing the rows indexed by the range rows and the columns indexed by the range cols.

pub fn rows_range<RowRange: SliceRange<R>>(
    &self,
    rows: RowRange
) -> MatrixSlice<N, RowRange::Size, C, S::RStride, S::CStride>

Slice containing all the rows indexed by the range rows.

pub fn columns_range<ColRange: SliceRange<C>>(
    &self,
    cols: ColRange
) -> MatrixSlice<N, R, ColRange::Size, S::RStride, S::CStride>

Slice containing all the columns indexed by the range rows.

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

pub fn slice_range_mut<RowRange, ColRange>(
    &mut self,
    rows: RowRange,
    cols: ColRange
) -> MatrixSliceMut<N, RowRange::Size, ColRange::Size, S::RStride, S::CStride> where
    RowRange: SliceRange<R>,
    ColRange: SliceRange<C>, 

Slices a mutable sub-matrix containing the rows indexed by the range rows and the columns indexed by the range cols.

pub fn rows_range_mut<RowRange: SliceRange<R>>(
    &mut self,
    rows: RowRange
) -> MatrixSliceMut<N, RowRange::Size, C, S::RStride, S::CStride>

Slice containing all the rows indexed by the range rows.

pub fn columns_range_mut<ColRange: SliceRange<C>>(
    &mut self,
    cols: ColRange
) -> MatrixSliceMut<N, R, ColRange::Size, S::RStride, S::CStride>

Slice containing all the columns indexed by the range cols.

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

pub fn is_empty(&self) -> bool

Indicates if this is an empty matrix.

pub fn is_square(&self) -> bool

Indicates if this is a square matrix.

pub fn is_identity(&self, eps: N::Epsilon) -> bool where
    N: Zero + One + RelativeEq,
    N::Epsilon: Copy, 

Indicated if this is the identity matrix within a relative error of eps.

If the matrix is diagonal, this checks that diagonal elements (i.e. at coordinates (i, i) for i from 0 to min(R, C)) are equal one; and that all other elements are zero.

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

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

Checks that Mᵀ × M = Id.

In this definition Id is approximately equal to the identity matrix with a relative error equal to eps.

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

pub fn compress_rows(
    &self,
    f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N
) -> RowVectorN<N, C> where
    DefaultAllocator: Allocator<N, U1, C>, 

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

pub fn compress_rows_tr(
    &self,
    f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N
) -> VectorN<N, C> where
    DefaultAllocator: Allocator<N, C>, 

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

This is the same as self.compress_rows(f).transpose().

pub fn compress_columns(
    &self,
    init: VectorN<N, R>,
    f: impl Fn(&mut VectorN<N, R>, VectorSliceN<N, R, S::RStride, S::CStride>)
) -> VectorN<N, R> where
    DefaultAllocator: Allocator<N, R>, 

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

impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>

pub fn sum(&self) -> N

The sum of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.sum(), 21.0);

pub fn row_sum(&self) -> RowVectorN<N, C> where
    DefaultAllocator: Allocator<N, U1, C>, 

The sum 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_sum(), RowVector3::new(5.0, 7.0, 9.0));

pub fn row_sum_tr(&self) -> VectorN<N, C> where
    DefaultAllocator: Allocator<N, 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));

pub fn column_sum(&self) -> VectorN<N, R> where
    DefaultAllocator: Allocator<N, 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));

pub fn variance(&self) -> N

The variance of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_relative_eq!(m.variance(), 35.0 / 12.0, epsilon = 1.0e-8);

pub fn row_variance(&self) -> RowVectorN<N, C> where
    DefaultAllocator: Allocator<N, U1, C>, 

The variance of all the rows of this matrix.

Use .row_variance_tr if you need the result in a column vector instead.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_variance(), RowVector3::new(2.25, 2.25, 2.25));

pub fn row_variance_tr(&self) -> VectorN<N, C> where
    DefaultAllocator: Allocator<N, C>, 

The variance of all the rows of this matrix. The result is transposed and returned as a column vector.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_variance_tr(), Vector3::new(2.25, 2.25, 2.25));

pub fn column_variance(&self) -> VectorN<N, R> where
    DefaultAllocator: Allocator<N, R>, 

The variance of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_relative_eq!(m.column_variance(), Vector2::new(2.0 / 3.0, 2.0 / 3.0), epsilon = 1.0e-8);

pub fn mean(&self) -> N

The mean of all the elements of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.mean(), 3.5);

pub fn row_mean(&self) -> RowVectorN<N, C> where
    DefaultAllocator: Allocator<N, U1, C>, 

The mean of all the rows of this matrix.

Use .row_mean_tr if you need the result in a column vector instead.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_mean(), RowVector3::new(2.5, 3.5, 4.5));

pub fn row_mean_tr(&self) -> VectorN<N, C> where
    DefaultAllocator: Allocator<N, C>, 

The mean of all the rows of this matrix. The result is transposed and returned as a column vector.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_mean_tr(), Vector3::new(2.5, 3.5, 4.5));

pub fn column_mean(&self) -> VectorN<N, R> where
    DefaultAllocator: Allocator<N, R>, 

The mean of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.column_mean(), Vector2::new(2.0, 5.0));

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

pub fn norm_squared(&self) -> N::RealField

The squared L2 norm of this vector.

pub fn norm(&self) -> N::RealField

The L2 norm of this matrix.

Use .apply_norm to apply a custom norm.

pub fn metric_distance<R2, C2, S2>(
    &self,
    rhs: &Matrix<N, R2, C2, S2>
) -> N::RealField where
    R2: Dim,
    C2: Dim,
    S2: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Compute the distance between self and rhs using the metric induced by the euclidean norm.

Use .apply_metric_distance to apply a custom norm.

pub fn apply_norm(&self, norm: &impl Norm<N>) -> N::RealField

Uses the given norm to compute the norm of self.

Example

let v = Vector3::new(1.0, 2.0, 3.0);
assert_eq!(v.apply_norm(&UniformNorm), 3.0);
assert_eq!(v.apply_norm(&LpNorm(1)), 6.0);
assert_eq!(v.apply_norm(&EuclideanNorm), v.norm());

pub fn apply_metric_distance<R2, C2, S2>(
    &self,
    rhs: &Matrix<N, R2, C2, S2>,
    norm: &impl Norm<N>
) -> N::RealField where
    R2: Dim,
    C2: Dim,
    S2: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>, 

Uses the metric induced by the given norm to compute the metric distance between self and rhs.

Example

let v1 = Vector3::new(1.0, 2.0, 3.0);
let v2 = Vector3::new(10.0, 20.0, 30.0);

assert_eq!(v1.apply_metric_distance(&v2, &UniformNorm), 27.0);
assert_eq!(v1.apply_metric_distance(&v2, &LpNorm(1)), 27.0 + 18.0 + 9.0);
assert_eq!(v1.apply_metric_distance(&v2, &EuclideanNorm), (v1 - v2).norm());

pub fn magnitude(&self) -> N::RealField

A synonym for the norm of this matrix.

Aka the length.

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

pub fn magnitude_squared(&self) -> N::RealField

A synonym for the squared norm of this matrix.

Aka the squared length.

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

pub fn normalize(&self) -> MatrixMN<N, R, C> where
    DefaultAllocator: Allocator<N, R, C>, 

Returns a normalized version of this matrix.

pub fn try_normalize(&self, min_norm: N::RealField) -> Option<MatrixMN<N, R, C>> where
    DefaultAllocator: Allocator<N, R, C>, 

Returns a normalized version of this matrix unless its norm as smaller or equal to eps.

pub fn lp_norm(&self, p: i32) -> N::RealField

The Lp norm of this matrix.

impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S>

pub fn normalize_mut(&mut self) -> N::RealField

Normalizes this matrix in-place and returns its norm.

pub fn try_normalize_mut(
    &mut self,
    min_norm: N::RealField
) -> Option<N::RealField>

Normalizes this matrix in-place or does nothing if its norm is smaller or equal to eps.

If the normalization succeeded, returns the old normal of this matrix.

impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> where
    DimMinimum<R, C>: DimSub<U1>,
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>>, 

pub fn bidiagonalize(self) -> Bidiagonal<N, R, C>

Computes the bidiagonalization using householder reflections.

impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>, 

pub fn full_piv_lu(self) -> FullPivLU<N, R, C>

Computes the LU decomposition with full pivoting of matrix.

This effectively computes P, L, U, Q such that P * matrix * Q = LU.

impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>, 

pub fn lu(self) -> LU<N, R, C>

Computes the LU decomposition with partial (row) pivoting of matrix.

impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> where
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>>, 

pub fn qr(self) -> QR<N, R, C>

Computes the QR decomposition of this matrix.

impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> where
    DimMinimum<R, C>: DimSub<U1>,
    DefaultAllocator: Allocator<N, R, C> + Allocator<N, C> + Allocator<N, R> + Allocator<N, DimDiff<DimMinimum<R, C>, U1>> + Allocator<N, DimMinimum<R, C>, C> + Allocator<N, R, DimMinimum<R, C>> + Allocator<N, DimMinimum<R, C>> + Allocator<N::RealField, DimMinimum<R, C>> + Allocator<N::RealField, DimDiff<DimMinimum<R, C>, U1>>, 

pub fn svd(self, compute_u: bool, compute_v: bool) -> SVD<N, R, C>

Computes the Singular Value Decomposition using implicit shift.

pub fn try_svd(
    self,
    compute_u: bool,
    compute_v: bool,
    eps: N::RealField,
    max_niter: usize
) -> Option<SVD<N, R, C>>

Attempts to compute the Singular Value Decomposition of matrix using implicit shift.

Arguments

• compute_u − set this to true to enable the computation of left-singular vectors.
• compute_v − set this to true to enable the computation of left-singular vectors.
• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn singular_values(&self) -> VectorN<N::RealField, DimMinimum<R, C>>

Computes the singular values of this matrix.

pub fn rank(&self, eps: N::RealField) -> usize

Computes the rank of this matrix.

All singular values below eps are considered equal to 0.

pub fn pseudo_inverse(
    self,
    eps: N::RealField
) -> Result<MatrixMN<N, C, R>, &'static str> where
    DefaultAllocator: Allocator<N, C, R>, 

Computes the pseudo-inverse of this matrix.

All singular values below eps are considered equal to 0.

Trait Implementations

impl<N: Copy + Scalar, R: Copy + Dim, C: Copy + Dim, S: Copy> Copy for Matrix<N, R, C, S>

impl<N, S> AsRef<[N; 1]> for Matrix<N, U1, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U1>, 

fn as_ref(&self) -> &[N; 1]

Performs the conversion.

impl<N, S> AsRef<[N; 2]> for Matrix<N, U1, U2, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U2>, 

fn as_ref(&self) -> &[N; 2]

Performs the conversion.

impl<N, S> AsRef<[N; 3]> for Matrix<N, U1, U3, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U3>, 

fn as_ref(&self) -> &[N; 3]

Performs the conversion.

impl<N, S> AsRef<[N; 4]> for Matrix<N, U1, U4, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U4>, 

fn as_ref(&self) -> &[N; 4]

Performs the conversion.

impl<N, S> AsRef<[N; 5]> for Matrix<N, U1, U5, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U5>, 

fn as_ref(&self) -> &[N; 5]

Performs the conversion.

impl<N, S> AsRef<[N; 6]> for Matrix<N, U1, U6, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U6>, 

fn as_ref(&self) -> &[N; 6]

Performs the conversion.

impl<N, S> AsRef<[N; 7]> for Matrix<N, U1, U7, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U7>, 

fn as_ref(&self) -> &[N; 7]

Performs the conversion.

impl<N, S> AsRef<[N; 8]> for Matrix<N, U1, U8, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U8>, 

fn as_ref(&self) -> &[N; 8]

Performs the conversion.

impl<N, S> AsRef<[N; 9]> for Matrix<N, U1, U9, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U9>, 

fn as_ref(&self) -> &[N; 9]

Performs the conversion.

impl<N, S> AsRef<[N; 10]> for Matrix<N, U1, U10, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U10>, 

fn as_ref(&self) -> &[N; 10]

Performs the conversion.

impl<N, S> AsRef<[N; 11]> for Matrix<N, U1, U11, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U11>, 

fn as_ref(&self) -> &[N; 11]

Performs the conversion.

impl<N, S> AsRef<[N; 12]> for Matrix<N, U1, U12, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U12>, 

fn as_ref(&self) -> &[N; 12]

Performs the conversion.

impl<N, S> AsRef<[N; 13]> for Matrix<N, U1, U13, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U13>, 

fn as_ref(&self) -> &[N; 13]

Performs the conversion.

impl<N, S> AsRef<[N; 14]> for Matrix<N, U1, U14, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U14>, 

fn as_ref(&self) -> &[N; 14]

Performs the conversion.

impl<N, S> AsRef<[N; 15]> for Matrix<N, U1, U15, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U15>, 

fn as_ref(&self) -> &[N; 15]

Performs the conversion.

impl<N, S> AsRef<[N; 16]> for Matrix<N, U1, U16, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U16>, 

fn as_ref(&self) -> &[N; 16]

Performs the conversion.

impl<N, S> AsRef<[N; 2]> for Matrix<N, U2, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U2, U1>, 

fn as_ref(&self) -> &[N; 2]

Performs the conversion.

impl<N, S> AsRef<[N; 3]> for Matrix<N, U3, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U3, U1>, 

fn as_ref(&self) -> &[N; 3]

Performs the conversion.

impl<N, S> AsRef<[N; 4]> for Matrix<N, U4, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U4, U1>, 

fn as_ref(&self) -> &[N; 4]

Performs the conversion.

impl<N, S> AsRef<[N; 5]> for Matrix<N, U5, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U5, U1>, 

fn as_ref(&self) -> &[N; 5]

Performs the conversion.

impl<N, S> AsRef<[N; 6]> for Matrix<N, U6, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U6, U1>, 

fn as_ref(&self) -> &[N; 6]

Performs the conversion.

impl<N, S> AsRef<[N; 7]> for Matrix<N, U7, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U7, U1>, 

fn as_ref(&self) -> &[N; 7]

Performs the conversion.

impl<N, S> AsRef<[N; 8]> for Matrix<N, U8, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U8, U1>, 

fn as_ref(&self) -> &[N; 8]

Performs the conversion.

impl<N, S> AsRef<[N; 9]> for Matrix<N, U9, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U9, U1>, 

fn as_ref(&self) -> &[N; 9]

Performs the conversion.

impl<N, S> AsRef<[N; 10]> for Matrix<N, U10, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U10, U1>, 

fn as_ref(&self) -> &[N; 10]

Performs the conversion.

impl<N, S> AsRef<[N; 11]> for Matrix<N, U11, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U11, U1>, 

fn as_ref(&self) -> &[N; 11]

Performs the conversion.

impl<N, S> AsRef<[N; 12]> for Matrix<N, U12, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U12, U1>, 

fn as_ref(&self) -> &[N; 12]

Performs the conversion.

impl<N, S> AsRef<[N; 13]> for Matrix<N, U13, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U13, U1>, 

fn as_ref(&self) -> &[N; 13]

Performs the conversion.

impl<N, S> AsRef<[N; 14]> for Matrix<N, U14, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U14, U1>, 

fn as_ref(&self) -> &[N; 14]

Performs the conversion.

impl<N, S> AsRef<[N; 15]> for Matrix<N, U15, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U15, U1>, 

fn as_ref(&self) -> &[N; 15]

Performs the conversion.

impl<N, S> AsRef<[N; 16]> for Matrix<N, U16, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U16, U1>, 

fn as_ref(&self) -> &[N; 16]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 2]; 2]> for Matrix<N, U2, U2, S> where
    S: ContiguousStorage<N, U2, U2>, 

fn as_ref(&self) -> &[[N; 2]; 2]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 2]; 3]> for Matrix<N, U2, U3, S> where
    S: ContiguousStorage<N, U2, U3>, 

fn as_ref(&self) -> &[[N; 2]; 3]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 2]; 4]> for Matrix<N, U2, U4, S> where
    S: ContiguousStorage<N, U2, U4>, 

fn as_ref(&self) -> &[[N; 2]; 4]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 2]; 5]> for Matrix<N, U2, U5, S> where
    S: ContiguousStorage<N, U2, U5>, 

fn as_ref(&self) -> &[[N; 2]; 5]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 2]; 6]> for Matrix<N, U2, U6, S> where
    S: ContiguousStorage<N, U2, U6>, 

fn as_ref(&self) -> &[[N; 2]; 6]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 3]; 2]> for Matrix<N, U3, U2, S> where
    S: ContiguousStorage<N, U3, U2>, 

fn as_ref(&self) -> &[[N; 3]; 2]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 3]; 3]> for Matrix<N, U3, U3, S> where
    S: ContiguousStorage<N, U3, U3>, 

fn as_ref(&self) -> &[[N; 3]; 3]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 3]; 4]> for Matrix<N, U3, U4, S> where
    S: ContiguousStorage<N, U3, U4>, 

fn as_ref(&self) -> &[[N; 3]; 4]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 3]; 5]> for Matrix<N, U3, U5, S> where
    S: ContiguousStorage<N, U3, U5>, 

fn as_ref(&self) -> &[[N; 3]; 5]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 3]; 6]> for Matrix<N, U3, U6, S> where
    S: ContiguousStorage<N, U3, U6>, 

fn as_ref(&self) -> &[[N; 3]; 6]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 4]; 2]> for Matrix<N, U4, U2, S> where
    S: ContiguousStorage<N, U4, U2>, 

fn as_ref(&self) -> &[[N; 4]; 2]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 4]; 3]> for Matrix<N, U4, U3, S> where
    S: ContiguousStorage<N, U4, U3>, 

fn as_ref(&self) -> &[[N; 4]; 3]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 4]; 4]> for Matrix<N, U4, U4, S> where
    S: ContiguousStorage<N, U4, U4>, 

fn as_ref(&self) -> &[[N; 4]; 4]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 4]; 5]> for Matrix<N, U4, U5, S> where
    S: ContiguousStorage<N, U4, U5>, 

fn as_ref(&self) -> &[[N; 4]; 5]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 4]; 6]> for Matrix<N, U4, U6, S> where
    S: ContiguousStorage<N, U4, U6>, 

fn as_ref(&self) -> &[[N; 4]; 6]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 5]; 2]> for Matrix<N, U5, U2, S> where
    S: ContiguousStorage<N, U5, U2>, 

fn as_ref(&self) -> &[[N; 5]; 2]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 5]; 3]> for Matrix<N, U5, U3, S> where
    S: ContiguousStorage<N, U5, U3>, 

fn as_ref(&self) -> &[[N; 5]; 3]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 5]; 4]> for Matrix<N, U5, U4, S> where
    S: ContiguousStorage<N, U5, U4>, 

fn as_ref(&self) -> &[[N; 5]; 4]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 5]; 5]> for Matrix<N, U5, U5, S> where
    S: ContiguousStorage<N, U5, U5>, 

fn as_ref(&self) -> &[[N; 5]; 5]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 5]; 6]> for Matrix<N, U5, U6, S> where
    S: ContiguousStorage<N, U5, U6>, 

fn as_ref(&self) -> &[[N; 5]; 6]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 6]; 2]> for Matrix<N, U6, U2, S> where
    S: ContiguousStorage<N, U6, U2>, 

fn as_ref(&self) -> &[[N; 6]; 2]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 6]; 3]> for Matrix<N, U6, U3, S> where
    S: ContiguousStorage<N, U6, U3>, 

fn as_ref(&self) -> &[[N; 6]; 3]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 6]; 4]> for Matrix<N, U6, U4, S> where
    S: ContiguousStorage<N, U6, U4>, 

fn as_ref(&self) -> &[[N; 6]; 4]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 6]; 5]> for Matrix<N, U6, U5, S> where
    S: ContiguousStorage<N, U6, U5>, 

fn as_ref(&self) -> &[[N; 6]; 5]

Performs the conversion.

impl<N: Scalar, S> AsRef<[[N; 6]; 6]> for Matrix<N, U6, U6, S> where
    S: ContiguousStorage<N, U6, U6>, 

fn as_ref(&self) -> &[[N; 6]; 6]

Performs the conversion.

impl<N, S> AsRef<Vector2<N>> for Matrix<N, U2, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U2, U1>, 

fn as_ref(&self) -> &Vector2<N>

Performs the conversion.

impl<N, S> AsRef<Vector3<N>> for Matrix<N, U3, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U3, U1>, 

fn as_ref(&self) -> &Vector3<N>

Performs the conversion.

impl<N, S> AsRef<Vector4<N>> for Matrix<N, U4, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U4, U1>, 

fn as_ref(&self) -> &Vector4<N>

Performs the conversion.

impl<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> IntoIterator for &'a Matrix<N, R, C, S>

type Item = &'a N

The type of the elements being iterated over.

type IntoIter = MatrixIter<'a, N, R, C, S>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> IntoIterator for &'a mut Matrix<N, R, C, S>

type Item = &'a mut N

The type of the elements being iterated over.

type IntoIter = MatrixIterMut<'a, N, R, C, S>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl<N, R: Dim, C: Dim, S> Eq for Matrix<N, R, C, S> where
    N: Scalar + Eq,
    S: Storage<N, R, C>, 

impl<N: Clone + Scalar, R: Clone + Dim, C: Clone + Dim, S: Clone> Clone for Matrix<N, R, C, S>

fn clone(&self) -> Matrix<N, R, C, S>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<N, R: Dim, C: Dim, S> PartialOrd<Matrix<N, R, C, S>> for Matrix<N, R, C, S> where
    N: Scalar + PartialOrd,
    S: Storage<N, R, C>, 

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, right: &Self) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, right: &Self) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, right: &Self) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, right: &Self) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<N, R, S> Extend<N> for Matrix<N, R, Dynamic, S> where
    N: Scalar,
    R: Dim,
    S: Extend<N>, 

Extend the number of columns of the Matrix with elements from a given iterator.

fn extend<I: IntoIterator<Item = N>>(&mut self, iter: I)

Extend the number of columns of the Matrix with elements from the given iterator.

Example

let data = vec![0, 1, 2,      // column 1
                3, 4, 5];     // column 2

let mut matrix = DMatrix::from_vec(3, 2, data);

matrix.extend(vec![6, 7, 8]); // column 3

assert!(matrix.eq(&Matrix3::new(0, 3, 6,
                                1, 4, 7,
                                2, 5, 8)));

Panics

This function panics if the number of elements yielded by the given iterator is not a multiple of the number of rows of the Matrix.

let data = vec![0, 1, 2,  // column 1
                3, 4, 5]; // column 2

let mut matrix = DMatrix::from_vec(3, 2, data);

// The following panics because the vec length is not a multiple of 3.
matrix.extend(vec![6, 7, 8, 9]);

impl<N, S> Extend<N> for Matrix<N, Dynamic, U1, S> where
    N: Scalar,
    S: Extend<N>, 

Extend the number of rows of the Vector with elements from a given iterator.

fn extend<I: IntoIterator<Item = N>>(&mut self, iter: I)

Extend the number of rows of a Vector with elements from the given iterator.

Example

let mut vector = DVector::from_vec(vec![0, 1, 2]);
vector.extend(vec![3, 4, 5]);
assert!(vector.eq(&DVector::from_vec(vec![0, 1, 2, 3, 4, 5])));

impl<N, R, S, RV, SV> Extend<Matrix<N, RV, U1, SV>> for Matrix<N, R, Dynamic, S> where
    N: Scalar,
    R: Dim,
    S: Extend<Vector<N, RV, SV>>,
    RV: Dim,
    SV: Storage<N, RV>,
    ShapeConstraint: SameNumberOfRows<R, RV>, 

fn extend<I: IntoIterator<Item = Vector<N, RV, SV>>>(&mut self, iter: I)

Extends the number of columns of a Matrix with Vectors from a given iterator.

Example

let data = vec![0, 1, 2,          // column 1
                3, 4, 5];         // column 2

let mut matrix = DMatrix::from_vec(3, 2, data);

matrix.extend(
  vec![Vector3::new(6,  7,  8),   // column 3
       Vector3::new(9, 10, 11)]); // column 4

assert!(matrix.eq(&Matrix3x4::new(0, 3, 6,  9,
                                  1, 4, 7, 10,
                                  2, 5, 8, 11)));

Panics

This function panics if the dimension of each Vector yielded by the given iterator is not equal to the number of rows of this Matrix.

let mut matrix =
  DMatrix::from_vec(3, 2,
                    vec![0, 1, 2,   // column 1
                         3, 4, 5]); // column 2

// The following panics because this matrix can only be extended with 3-dimensional vectors.
matrix.extend(
  vec![Vector2::new(6,  7)]); // too few dimensions!

let mut matrix =
  DMatrix::from_vec(3, 2,
                    vec![0, 1, 2,   // column 1
                         3, 4, 5]); // column 2

// The following panics because this matrix can only be extended with 3-dimensional vectors.
matrix.extend(
  vec![Vector4::new(6, 7, 8, 9)]); // too few dimensions!

impl<N, R, RV, SV> Extend<Matrix<N, RV, U1, SV>> for VecStorage<N, R, Dynamic> where
    N: Scalar,
    R: Dim,
    RV: Dim,
    SV: Storage<N, RV>,
    ShapeConstraint: SameNumberOfRows<R, RV>, 

fn extend<I: IntoIterator<Item = Vector<N, RV, SV>>>(&mut self, iter: I)

Extends the number of columns of the VecStorage with vectors from the given iterator.

Panics

This function panics if the number of rows of each Vector yielded by the iterator is not equal to the number of rows of this VecStorage.

impl<N, R: Dim, C: Dim, S> PartialEq<Matrix<N, R, C, S>> for Matrix<N, R, C, S> where
    N: Scalar,
    S: Storage<N, R, C>, 

fn eq(&self, right: &Matrix<N, R, C, S>) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<'a, N, R, C, RStride, CStride> From<Matrix<N, R, C, SliceStorage<'a, N, R, C, RStride, CStride>>> for Matrix<N, R, C, ArrayStorage<N, R, C>> where
    N: Scalar,
    R: DimName,
    C: DimName,
    RStride: Dim,
    CStride: Dim,
    R::Value: Mul<C::Value>,
    Prod<R::Value, C::Value>: ArrayLength<N>, 

fn from(matrix_slice: MatrixSlice<'a, N, R, C, RStride, CStride>) -> Self

Performs the conversion.

impl<'a, N, C, RStride, CStride> From<Matrix<N, Dynamic, C, SliceStorage<'a, N, Dynamic, C, RStride, CStride>>> for Matrix<N, Dynamic, C, VecStorage<N, Dynamic, C>> where
    N: Scalar,
    C: Dim,
    RStride: Dim,
    CStride: Dim, 

fn from(matrix_slice: MatrixSlice<'a, N, Dynamic, C, RStride, CStride>) -> Self

Performs the conversion.

impl<'a, N, R, RStride, CStride> From<Matrix<N, R, Dynamic, SliceStorage<'a, N, R, Dynamic, RStride, CStride>>> for Matrix<N, R, Dynamic, VecStorage<N, R, Dynamic>> where
    N: Scalar,
    R: DimName,
    RStride: Dim,
    CStride: Dim, 

fn from(matrix_slice: MatrixSlice<'a, N, R, Dynamic, RStride, CStride>) -> Self

Performs the conversion.

impl<'a, N, R, C, RStride, CStride> From<Matrix<N, R, C, SliceStorageMut<'a, N, R, C, RStride, CStride>>> for Matrix<N, R, C, ArrayStorage<N, R, C>> where
    N: Scalar,
    R: DimName,
    C: DimName,
    RStride: Dim,
    CStride: Dim,
    R::Value: Mul<C::Value>,
    Prod<R::Value, C::Value>: ArrayLength<N>, 

fn from(matrix_slice: MatrixSliceMut<'a, N, R, C, RStride, CStride>) -> Self

Performs the conversion.

impl<'a, N, C, RStride, CStride> From<Matrix<N, Dynamic, C, SliceStorageMut<'a, N, Dynamic, C, RStride, CStride>>> for Matrix<N, Dynamic, C, VecStorage<N, Dynamic, C>> where
    N: Scalar,
    C: Dim,
    RStride: Dim,
    CStride: Dim, 

fn from(
    matrix_slice: MatrixSliceMut<'a, N, Dynamic, C, RStride, CStride>
) -> Self

Performs the conversion.

impl<'a, N, R, RStride, CStride> From<Matrix<N, R, Dynamic, SliceStorageMut<'a, N, R, Dynamic, RStride, CStride>>> for Matrix<N, R, Dynamic, VecStorage<N, R, Dynamic>> where
    N: Scalar,
    R: DimName,
    RStride: Dim,
    CStride: Dim, 

fn from(
    matrix_slice: MatrixSliceMut<'a, N, R, Dynamic, RStride, CStride>
) -> Self

Performs the conversion.

impl<'a, N, R, C, RStride, CStride> From<Matrix<N, R, C, SliceStorageMut<'a, N, R, C, RStride, CStride>>> for MatrixSlice<'a, N, R, C, RStride, CStride> where
    N: Scalar,
    R: Dim,
    C: Dim,
    RStride: Dim,
    CStride: Dim, 

fn from(slice_mut: MatrixSliceMut<'a, N, R, C, RStride, CStride>) -> Self

Performs the conversion.

impl<N: Scalar, D: DimName> From<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Point<N, D> where
    DefaultAllocator: Allocator<N, D>, 

fn from(coords: VectorN<N, D>) -> Self

Performs the conversion.

impl<N: RealField> From<Matrix<N, U4, U1, <DefaultAllocator as Allocator<N, U4, U1>>::Buffer>> for Quaternion<N>

fn from(coords: Vector4<N>) -> Self

Performs the conversion.

impl<N: Scalar, D: DimName> From<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>, 

fn from(vector: VectorN<N, D>) -> Self

Performs the conversion.

impl<N, S> Into<[N; 1]> for Matrix<N, U1, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U1>, 

fn into(self) -> [N; 1]

Performs the conversion.

impl<N, S> Into<[N; 2]> for Matrix<N, U1, U2, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U2>, 

fn into(self) -> [N; 2]

Performs the conversion.

impl<N, S> Into<[N; 3]> for Matrix<N, U1, U3, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U3>, 

fn into(self) -> [N; 3]

Performs the conversion.

impl<N, S> Into<[N; 4]> for Matrix<N, U1, U4, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U4>, 

fn into(self) -> [N; 4]

Performs the conversion.

impl<N, S> Into<[N; 5]> for Matrix<N, U1, U5, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U5>, 

fn into(self) -> [N; 5]

Performs the conversion.

impl<N, S> Into<[N; 6]> for Matrix<N, U1, U6, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U6>, 

fn into(self) -> [N; 6]

Performs the conversion.

impl<N, S> Into<[N; 7]> for Matrix<N, U1, U7, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U7>, 

fn into(self) -> [N; 7]

Performs the conversion.

impl<N, S> Into<[N; 8]> for Matrix<N, U1, U8, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U8>, 

fn into(self) -> [N; 8]

Performs the conversion.

impl<N, S> Into<[N; 9]> for Matrix<N, U1, U9, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U9>, 

fn into(self) -> [N; 9]

Performs the conversion.

impl<N, S> Into<[N; 10]> for Matrix<N, U1, U10, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U10>, 

fn into(self) -> [N; 10]

Performs the conversion.

impl<N, S> Into<[N; 11]> for Matrix<N, U1, U11, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U11>, 

fn into(self) -> [N; 11]

Performs the conversion.

impl<N, S> Into<[N; 12]> for Matrix<N, U1, U12, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U12>, 

fn into(self) -> [N; 12]

Performs the conversion.

impl<N, S> Into<[N; 13]> for Matrix<N, U1, U13, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U13>, 

fn into(self) -> [N; 13]

Performs the conversion.

impl<N, S> Into<[N; 14]> for Matrix<N, U1, U14, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U14>, 

fn into(self) -> [N; 14]

Performs the conversion.

impl<N, S> Into<[N; 15]> for Matrix<N, U1, U15, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U15>, 

fn into(self) -> [N; 15]

Performs the conversion.

impl<N, S> Into<[N; 16]> for Matrix<N, U1, U16, S> where
    N: Scalar,
    S: ContiguousStorage<N, U1, U16>, 

fn into(self) -> [N; 16]

Performs the conversion.

impl<N, S> Into<[N; 2]> for Matrix<N, U2, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U2, U1>, 

fn into(self) -> [N; 2]

Performs the conversion.

impl<N, S> Into<[N; 3]> for Matrix<N, U3, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U3, U1>, 

fn into(self) -> [N; 3]

Performs the conversion.

impl<N, S> Into<[N; 4]> for Matrix<N, U4, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U4, U1>, 

fn into(self) -> [N; 4]

Performs the conversion.

impl<N, S> Into<[N; 5]> for Matrix<N, U5, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U5, U1>, 

fn into(self) -> [N; 5]

Performs the conversion.

impl<N, S> Into<[N; 6]> for Matrix<N, U6, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U6, U1>, 

fn into(self) -> [N; 6]

Performs the conversion.

impl<N, S> Into<[N; 7]> for Matrix<N, U7, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U7, U1>, 

fn into(self) -> [N; 7]

Performs the conversion.

impl<N, S> Into<[N; 8]> for Matrix<N, U8, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U8, U1>, 

fn into(self) -> [N; 8]

Performs the conversion.

impl<N, S> Into<[N; 9]> for Matrix<N, U9, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U9, U1>, 

fn into(self) -> [N; 9]

Performs the conversion.

impl<N, S> Into<[N; 10]> for Matrix<N, U10, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U10, U1>, 

fn into(self) -> [N; 10]

Performs the conversion.

impl<N, S> Into<[N; 11]> for Matrix<N, U11, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U11, U1>, 

fn into(self) -> [N; 11]

Performs the conversion.

impl<N, S> Into<[N; 12]> for Matrix<N, U12, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U12, U1>, 

fn into(self) -> [N; 12]

Performs the conversion.

impl<N, S> Into<[N; 13]> for Matrix<N, U13, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U13, U1>, 

fn into(self) -> [N; 13]

Performs the conversion.

impl<N, S> Into<[N; 14]> for Matrix<N, U14, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U14, U1>, 

fn into(self) -> [N; 14]

Performs the conversion.

impl<N, S> Into<[N; 15]> for Matrix<N, U15, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U15, U1>, 

fn into(self) -> [N; 15]

Performs the conversion.

impl<N, S> Into<[N; 16]> for Matrix<N, U16, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U16, U1>, 

fn into(self) -> [N; 16]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 2]; 2]> for Matrix<N, U2, U2, S> where
    S: ContiguousStorage<N, U2, U2>, 

fn into(self) -> [[N; 2]; 2]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 2]; 3]> for Matrix<N, U2, U3, S> where
    S: ContiguousStorage<N, U2, U3>, 

fn into(self) -> [[N; 2]; 3]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 2]; 4]> for Matrix<N, U2, U4, S> where
    S: ContiguousStorage<N, U2, U4>, 

fn into(self) -> [[N; 2]; 4]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 2]; 5]> for Matrix<N, U2, U5, S> where
    S: ContiguousStorage<N, U2, U5>, 

fn into(self) -> [[N; 2]; 5]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 2]; 6]> for Matrix<N, U2, U6, S> where
    S: ContiguousStorage<N, U2, U6>, 

fn into(self) -> [[N; 2]; 6]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 3]; 2]> for Matrix<N, U3, U2, S> where
    S: ContiguousStorage<N, U3, U2>, 

fn into(self) -> [[N; 3]; 2]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 3]; 3]> for Matrix<N, U3, U3, S> where
    S: ContiguousStorage<N, U3, U3>, 

fn into(self) -> [[N; 3]; 3]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 3]; 4]> for Matrix<N, U3, U4, S> where
    S: ContiguousStorage<N, U3, U4>, 

fn into(self) -> [[N; 3]; 4]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 3]; 5]> for Matrix<N, U3, U5, S> where
    S: ContiguousStorage<N, U3, U5>, 

fn into(self) -> [[N; 3]; 5]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 3]; 6]> for Matrix<N, U3, U6, S> where
    S: ContiguousStorage<N, U3, U6>, 

fn into(self) -> [[N; 3]; 6]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 4]; 2]> for Matrix<N, U4, U2, S> where
    S: ContiguousStorage<N, U4, U2>, 

fn into(self) -> [[N; 4]; 2]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 4]; 3]> for Matrix<N, U4, U3, S> where
    S: ContiguousStorage<N, U4, U3>, 

fn into(self) -> [[N; 4]; 3]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 4]; 4]> for Matrix<N, U4, U4, S> where
    S: ContiguousStorage<N, U4, U4>, 

fn into(self) -> [[N; 4]; 4]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 4]; 5]> for Matrix<N, U4, U5, S> where
    S: ContiguousStorage<N, U4, U5>, 

fn into(self) -> [[N; 4]; 5]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 4]; 6]> for Matrix<N, U4, U6, S> where
    S: ContiguousStorage<N, U4, U6>, 

fn into(self) -> [[N; 4]; 6]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 5]; 2]> for Matrix<N, U5, U2, S> where
    S: ContiguousStorage<N, U5, U2>, 

fn into(self) -> [[N; 5]; 2]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 5]; 3]> for Matrix<N, U5, U3, S> where
    S: ContiguousStorage<N, U5, U3>, 

fn into(self) -> [[N; 5]; 3]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 5]; 4]> for Matrix<N, U5, U4, S> where
    S: ContiguousStorage<N, U5, U4>, 

fn into(self) -> [[N; 5]; 4]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 5]; 5]> for Matrix<N, U5, U5, S> where
    S: ContiguousStorage<N, U5, U5>, 

fn into(self) -> [[N; 5]; 5]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 5]; 6]> for Matrix<N, U5, U6, S> where
    S: ContiguousStorage<N, U5, U6>, 

fn into(self) -> [[N; 5]; 6]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 6]; 2]> for Matrix<N, U6, U2, S> where
    S: ContiguousStorage<N, U6, U2>, 

fn into(self) -> [[N; 6]; 2]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 6]; 3]> for Matrix<N, U6, U3, S> where
    S: ContiguousStorage<N, U6, U3>, 

fn into(self) -> [[N; 6]; 3]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 6]; 4]> for Matrix<N, U6, U4, S> where
    S: ContiguousStorage<N, U6, U4>, 

fn into(self) -> [[N; 6]; 4]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 6]; 5]> for Matrix<N, U6, U5, S> where
    S: ContiguousStorage<N, U6, U5>, 

fn into(self) -> [[N; 6]; 5]

Performs the conversion.

impl<N: Scalar, S> Into<[[N; 6]; 6]> for Matrix<N, U6, U6, S> where
    S: ContiguousStorage<N, U6, U6>, 

fn into(self) -> [[N; 6]; 6]

Performs the conversion.

impl<N, S> Into<Vector2<N>> for Matrix<N, U2, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U2, U1>, 

fn into(self) -> Vector2<N>

Performs the conversion.

impl<N, S> Into<Vector3<N>> for Matrix<N, U3, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U3, U1>, 

fn into(self) -> Vector3<N>

Performs the conversion.

impl<N, S> Into<Vector4<N>> for Matrix<N, U4, U1, S> where
    N: Scalar,
    S: ContiguousStorage<N, U4, U1>, 

fn into(self) -> Vector4<N>

Performs the conversion.

impl<N, S> AsMut<[N; 1]> for Matrix<N, U1, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U1>, 

fn as_mut(&mut self) -> &mut [N; 1]

Performs the conversion.

impl<N, S> AsMut<[N; 2]> for Matrix<N, U1, U2, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U2>, 

fn as_mut(&mut self) -> &mut [N; 2]

Performs the conversion.

impl<N, S> AsMut<[N; 3]> for Matrix<N, U1, U3, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U3>, 

fn as_mut(&mut self) -> &mut [N; 3]

Performs the conversion.

impl<N, S> AsMut<[N; 4]> for Matrix<N, U1, U4, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U4>, 

fn as_mut(&mut self) -> &mut [N; 4]

Performs the conversion.

impl<N, S> AsMut<[N; 5]> for Matrix<N, U1, U5, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U5>, 

fn as_mut(&mut self) -> &mut [N; 5]

Performs the conversion.

impl<N, S> AsMut<[N; 6]> for Matrix<N, U1, U6, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U6>, 

fn as_mut(&mut self) -> &mut [N; 6]

Performs the conversion.

impl<N, S> AsMut<[N; 7]> for Matrix<N, U1, U7, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U7>, 

fn as_mut(&mut self) -> &mut [N; 7]

Performs the conversion.

impl<N, S> AsMut<[N; 8]> for Matrix<N, U1, U8, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U8>, 

fn as_mut(&mut self) -> &mut [N; 8]

Performs the conversion.

impl<N, S> AsMut<[N; 9]> for Matrix<N, U1, U9, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U9>, 

fn as_mut(&mut self) -> &mut [N; 9]

Performs the conversion.

impl<N, S> AsMut<[N; 10]> for Matrix<N, U1, U10, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U10>, 

fn as_mut(&mut self) -> &mut [N; 10]

Performs the conversion.

impl<N, S> AsMut<[N; 11]> for Matrix<N, U1, U11, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U11>, 

fn as_mut(&mut self) -> &mut [N; 11]

Performs the conversion.

impl<N, S> AsMut<[N; 12]> for Matrix<N, U1, U12, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U12>, 

fn as_mut(&mut self) -> &mut [N; 12]

Performs the conversion.

impl<N, S> AsMut<[N; 13]> for Matrix<N, U1, U13, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U13>, 

fn as_mut(&mut self) -> &mut [N; 13]

Performs the conversion.

impl<N, S> AsMut<[N; 14]> for Matrix<N, U1, U14, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U14>, 

fn as_mut(&mut self) -> &mut [N; 14]

Performs the conversion.

impl<N, S> AsMut<[N; 15]> for Matrix<N, U1, U15, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U15>, 

fn as_mut(&mut self) -> &mut [N; 15]

Performs the conversion.

impl<N, S> AsMut<[N; 16]> for Matrix<N, U1, U16, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U1, U16>, 

fn as_mut(&mut self) -> &mut [N; 16]

Performs the conversion.

impl<N, S> AsMut<[N; 2]> for Matrix<N, U2, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U2, U1>, 

fn as_mut(&mut self) -> &mut [N; 2]

Performs the conversion.

impl<N, S> AsMut<[N; 3]> for Matrix<N, U3, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U3, U1>, 

fn as_mut(&mut self) -> &mut [N; 3]

Performs the conversion.

impl<N, S> AsMut<[N; 4]> for Matrix<N, U4, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U4, U1>, 

fn as_mut(&mut self) -> &mut [N; 4]

Performs the conversion.

impl<N, S> AsMut<[N; 5]> for Matrix<N, U5, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U5, U1>, 

fn as_mut(&mut self) -> &mut [N; 5]

Performs the conversion.

impl<N, S> AsMut<[N; 6]> for Matrix<N, U6, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U6, U1>, 

fn as_mut(&mut self) -> &mut [N; 6]

Performs the conversion.

impl<N, S> AsMut<[N; 7]> for Matrix<N, U7, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U7, U1>, 

fn as_mut(&mut self) -> &mut [N; 7]

Performs the conversion.

impl<N, S> AsMut<[N; 8]> for Matrix<N, U8, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U8, U1>, 

fn as_mut(&mut self) -> &mut [N; 8]

Performs the conversion.

impl<N, S> AsMut<[N; 9]> for Matrix<N, U9, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U9, U1>, 

fn as_mut(&mut self) -> &mut [N; 9]

Performs the conversion.

impl<N, S> AsMut<[N; 10]> for Matrix<N, U10, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U10, U1>, 

fn as_mut(&mut self) -> &mut [N; 10]

Performs the conversion.

impl<N, S> AsMut<[N; 11]> for Matrix<N, U11, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U11, U1>, 

fn as_mut(&mut self) -> &mut [N; 11]

Performs the conversion.

impl<N, S> AsMut<[N; 12]> for Matrix<N, U12, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U12, U1>, 

fn as_mut(&mut self) -> &mut [N; 12]

Performs the conversion.

impl<N, S> AsMut<[N; 13]> for Matrix<N, U13, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U13, U1>, 

fn as_mut(&mut self) -> &mut [N; 13]

Performs the conversion.

impl<N, S> AsMut<[N; 14]> for Matrix<N, U14, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U14, U1>, 

fn as_mut(&mut self) -> &mut [N; 14]

Performs the conversion.

impl<N, S> AsMut<[N; 15]> for Matrix<N, U15, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U15, U1>, 

fn as_mut(&mut self) -> &mut [N; 15]

Performs the conversion.

impl<N, S> AsMut<[N; 16]> for Matrix<N, U16, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U16, U1>, 

fn as_mut(&mut self) -> &mut [N; 16]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 2]; 2]> for Matrix<N, U2, U2, S> where
    S: ContiguousStorageMut<N, U2, U2>, 

fn as_mut(&mut self) -> &mut [[N; 2]; 2]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 2]; 3]> for Matrix<N, U2, U3, S> where
    S: ContiguousStorageMut<N, U2, U3>, 

fn as_mut(&mut self) -> &mut [[N; 2]; 3]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 2]; 4]> for Matrix<N, U2, U4, S> where
    S: ContiguousStorageMut<N, U2, U4>, 

fn as_mut(&mut self) -> &mut [[N; 2]; 4]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 2]; 5]> for Matrix<N, U2, U5, S> where
    S: ContiguousStorageMut<N, U2, U5>, 

fn as_mut(&mut self) -> &mut [[N; 2]; 5]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 2]; 6]> for Matrix<N, U2, U6, S> where
    S: ContiguousStorageMut<N, U2, U6>, 

fn as_mut(&mut self) -> &mut [[N; 2]; 6]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 3]; 2]> for Matrix<N, U3, U2, S> where
    S: ContiguousStorageMut<N, U3, U2>, 

fn as_mut(&mut self) -> &mut [[N; 3]; 2]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 3]; 3]> for Matrix<N, U3, U3, S> where
    S: ContiguousStorageMut<N, U3, U3>, 

fn as_mut(&mut self) -> &mut [[N; 3]; 3]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 3]; 4]> for Matrix<N, U3, U4, S> where
    S: ContiguousStorageMut<N, U3, U4>, 

fn as_mut(&mut self) -> &mut [[N; 3]; 4]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 3]; 5]> for Matrix<N, U3, U5, S> where
    S: ContiguousStorageMut<N, U3, U5>, 

fn as_mut(&mut self) -> &mut [[N; 3]; 5]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 3]; 6]> for Matrix<N, U3, U6, S> where
    S: ContiguousStorageMut<N, U3, U6>, 

fn as_mut(&mut self) -> &mut [[N; 3]; 6]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 4]; 2]> for Matrix<N, U4, U2, S> where
    S: ContiguousStorageMut<N, U4, U2>, 

fn as_mut(&mut self) -> &mut [[N; 4]; 2]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 4]; 3]> for Matrix<N, U4, U3, S> where
    S: ContiguousStorageMut<N, U4, U3>, 

fn as_mut(&mut self) -> &mut [[N; 4]; 3]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 4]; 4]> for Matrix<N, U4, U4, S> where
    S: ContiguousStorageMut<N, U4, U4>, 

fn as_mut(&mut self) -> &mut [[N; 4]; 4]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 4]; 5]> for Matrix<N, U4, U5, S> where
    S: ContiguousStorageMut<N, U4, U5>, 

fn as_mut(&mut self) -> &mut [[N; 4]; 5]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 4]; 6]> for Matrix<N, U4, U6, S> where
    S: ContiguousStorageMut<N, U4, U6>, 

fn as_mut(&mut self) -> &mut [[N; 4]; 6]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 5]; 2]> for Matrix<N, U5, U2, S> where
    S: ContiguousStorageMut<N, U5, U2>, 

fn as_mut(&mut self) -> &mut [[N; 5]; 2]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 5]; 3]> for Matrix<N, U5, U3, S> where
    S: ContiguousStorageMut<N, U5, U3>, 

fn as_mut(&mut self) -> &mut [[N; 5]; 3]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 5]; 4]> for Matrix<N, U5, U4, S> where
    S: ContiguousStorageMut<N, U5, U4>, 

fn as_mut(&mut self) -> &mut [[N; 5]; 4]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 5]; 5]> for Matrix<N, U5, U5, S> where
    S: ContiguousStorageMut<N, U5, U5>, 

fn as_mut(&mut self) -> &mut [[N; 5]; 5]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 5]; 6]> for Matrix<N, U5, U6, S> where
    S: ContiguousStorageMut<N, U5, U6>, 

fn as_mut(&mut self) -> &mut [[N; 5]; 6]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 6]; 2]> for Matrix<N, U6, U2, S> where
    S: ContiguousStorageMut<N, U6, U2>, 

fn as_mut(&mut self) -> &mut [[N; 6]; 2]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 6]; 3]> for Matrix<N, U6, U3, S> where
    S: ContiguousStorageMut<N, U6, U3>, 

fn as_mut(&mut self) -> &mut [[N; 6]; 3]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 6]; 4]> for Matrix<N, U6, U4, S> where
    S: ContiguousStorageMut<N, U6, U4>, 

fn as_mut(&mut self) -> &mut [[N; 6]; 4]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 6]; 5]> for Matrix<N, U6, U5, S> where
    S: ContiguousStorageMut<N, U6, U5>, 

fn as_mut(&mut self) -> &mut [[N; 6]; 5]

Performs the conversion.

impl<N: Scalar, S> AsMut<[[N; 6]; 6]> for Matrix<N, U6, U6, S> where
    S: ContiguousStorageMut<N, U6, U6>, 

fn as_mut(&mut self) -> &mut [[N; 6]; 6]

Performs the conversion.

impl<N, S> AsMut<Vector2<N>> for Matrix<N, U2, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U2, U1>, 

fn as_mut(&mut self) -> &mut Vector2<N>

Performs the conversion.

impl<N, S> AsMut<Vector3<N>> for Matrix<N, U3, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U3, U1>, 

fn as_mut(&mut self) -> &mut Vector3<N>

Performs the conversion.

impl<N, S> AsMut<Vector4<N>> for Matrix<N, U4, U1, S> where
    N: Scalar,
    S: ContiguousStorageMut<N, U4, U1>, 

fn as_mut(&mut self) -> &mut Vector4<N>

Performs the conversion.

impl<N: Scalar, S> Deref for Matrix<N, U1, U1, S> where
    S: ContiguousStorage<N, U1, U1>, 

type Target = X<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U2, U1, S> where
    S: ContiguousStorage<N, U2, U1>, 

type Target = XY<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U3, U1, S> where
    S: ContiguousStorage<N, U3, U1>, 

type Target = XYZ<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U4, U1, S> where
    S: ContiguousStorage<N, U4, U1>, 

type Target = XYZW<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U5, U1, S> where
    S: ContiguousStorage<N, U5, U1>, 

type Target = XYZWA<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U6, U1, S> where
    S: ContiguousStorage<N, U6, U1>, 

type Target = XYZWAB<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U1, U2, S> where
    S: ContiguousStorage<N, U1, U2>, 

type Target = XY<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U1, U3, S> where
    S: ContiguousStorage<N, U1, U3>, 

type Target = XYZ<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U1, U4, S> where
    S: ContiguousStorage<N, U1, U4>, 

type Target = XYZW<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U1, U5, S> where
    S: ContiguousStorage<N, U1, U5>, 

type Target = XYZWA<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U1, U6, S> where
    S: ContiguousStorage<N, U1, U6>, 

type Target = XYZWAB<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U2, U2, S> where
    S: ContiguousStorage<N, U2, U2>, 

type Target = M2x2<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U2, U3, S> where
    S: ContiguousStorage<N, U2, U3>, 

type Target = M2x3<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U2, U4, S> where
    S: ContiguousStorage<N, U2, U4>, 

type Target = M2x4<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U2, U5, S> where
    S: ContiguousStorage<N, U2, U5>, 

type Target = M2x5<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U2, U6, S> where
    S: ContiguousStorage<N, U2, U6>, 

type Target = M2x6<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U3, U2, S> where
    S: ContiguousStorage<N, U3, U2>, 

type Target = M3x2<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U3, U3, S> where
    S: ContiguousStorage<N, U3, U3>, 

type Target = M3x3<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U3, U4, S> where
    S: ContiguousStorage<N, U3, U4>, 

type Target = M3x4<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U3, U5, S> where
    S: ContiguousStorage<N, U3, U5>, 

type Target = M3x5<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U3, U6, S> where
    S: ContiguousStorage<N, U3, U6>, 

type Target = M3x6<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U4, U2, S> where
    S: ContiguousStorage<N, U4, U2>, 

type Target = M4x2<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U4, U3, S> where
    S: ContiguousStorage<N, U4, U3>, 

type Target = M4x3<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U4, U4, S> where
    S: ContiguousStorage<N, U4, U4>, 

type Target = M4x4<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U4, U5, S> where
    S: ContiguousStorage<N, U4, U5>, 

type Target = M4x5<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U4, U6, S> where
    S: ContiguousStorage<N, U4, U6>, 

type Target = M4x6<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U5, U2, S> where
    S: ContiguousStorage<N, U5, U2>, 

type Target = M5x2<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U5, U3, S> where
    S: ContiguousStorage<N, U5, U3>, 

type Target = M5x3<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U5, U4, S> where
    S: ContiguousStorage<N, U5, U4>, 

type Target = M5x4<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U5, U5, S> where
    S: ContiguousStorage<N, U5, U5>, 

type Target = M5x5<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U5, U6, S> where
    S: ContiguousStorage<N, U5, U6>, 

type Target = M5x6<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U6, U2, S> where
    S: ContiguousStorage<N, U6, U2>, 

type Target = M6x2<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U6, U3, S> where
    S: ContiguousStorage<N, U6, U3>, 

type Target = M6x3<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U6, U4, S> where
    S: ContiguousStorage<N, U6, U4>, 

type Target = M6x4<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U6, U5, S> where
    S: ContiguousStorage<N, U6, U5>, 

type Target = M6x5<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> Deref for Matrix<N, U6, U6, S> where
    S: ContiguousStorage<N, U6, U6>, 

type Target = M6x6<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U1, U1, S> where
    S: ContiguousStorageMut<N, U1, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U2, U1, S> where
    S: ContiguousStorageMut<N, U2, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U3, U1, S> where
    S: ContiguousStorageMut<N, U3, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U4, U1, S> where
    S: ContiguousStorageMut<N, U4, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U5, U1, S> where
    S: ContiguousStorageMut<N, U5, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U6, U1, S> where
    S: ContiguousStorageMut<N, U6, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U1, U2, S> where
    S: ContiguousStorageMut<N, U1, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U1, U3, S> where
    S: ContiguousStorageMut<N, U1, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U1, U4, S> where
    S: ContiguousStorageMut<N, U1, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U1, U5, S> where
    S: ContiguousStorageMut<N, U1, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U1, U6, S> where
    S: ContiguousStorageMut<N, U1, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U2, U2, S> where
    S: ContiguousStorageMut<N, U2, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U2, U3, S> where
    S: ContiguousStorageMut<N, U2, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U2, U4, S> where
    S: ContiguousStorageMut<N, U2, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U2, U5, S> where
    S: ContiguousStorageMut<N, U2, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U2, U6, S> where
    S: ContiguousStorageMut<N, U2, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U3, U2, S> where
    S: ContiguousStorageMut<N, U3, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U3, U3, S> where
    S: ContiguousStorageMut<N, U3, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U3, U4, S> where
    S: ContiguousStorageMut<N, U3, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U3, U5, S> where
    S: ContiguousStorageMut<N, U3, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U3, U6, S> where
    S: ContiguousStorageMut<N, U3, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U4, U2, S> where
    S: ContiguousStorageMut<N, U4, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U4, U3, S> where
    S: ContiguousStorageMut<N, U4, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U4, U4, S> where
    S: ContiguousStorageMut<N, U4, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U4, U5, S> where
    S: ContiguousStorageMut<N, U4, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U4, U6, S> where
    S: ContiguousStorageMut<N, U4, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U5, U2, S> where
    S: ContiguousStorageMut<N, U5, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U5, U3, S> where
    S: ContiguousStorageMut<N, U5, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U5, U4, S> where
    S: ContiguousStorageMut<N, U5, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U5, U5, S> where
    S: ContiguousStorageMut<N, U5, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U5, U6, S> where
    S: ContiguousStorageMut<N, U5, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U6, U2, S> where
    S: ContiguousStorageMut<N, U6, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U6, U3, S> where
    S: ContiguousStorageMut<N, U6, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U6, U4, S> where
    S: ContiguousStorageMut<N, U6, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U6, U5, S> where
    S: ContiguousStorageMut<N, U6, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar, S> DerefMut for Matrix<N, U6, U6, S> where
    S: ContiguousStorageMut<N, U6, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N, R, C, S> Hash for Matrix<N, R, C, S> where
    N: Scalar + Hash,
    R: Dim,
    C: Dim,
    S: Storage<N, R, C>, 

fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given [Hasher].

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given [Hasher].

impl<N, R: Dim, C: Dim, S> Display for Matrix<N, R, C, S> where
    N: Scalar + Display,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<usize, R, C>, 

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<N: Scalar, R: Dim, C: Dim, S: Debug> Debug for Matrix<N, R, C, S>

fn fmt(&self, formatter: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<'b, N, R1, C1, R2, C2, SA, SB> Add<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedAdd,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

type Output = MatrixSum<N, R1, C1, R2, C2>

The resulting type after applying the + operator.

fn add(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<'a, N, R1, C1, R2, C2, SA, SB> Add<Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedAdd,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R2, C2, R1, C1>,
    ShapeConstraint: SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1>, 

type Output = MatrixSum<N, R2, C2, R1, C1>

The resulting type after applying the + operator.

fn add(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<N, R1, C1, R2, C2, SA, SB> Add<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedAdd,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

type Output = MatrixSum<N, R1, C1, R2, C2>

The resulting type after applying the + operator.

fn add(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<'a, 'b, N, R1, C1, R2, C2, SA, SB> Add<&'b Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedAdd,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

type Output = MatrixSum<N, R1, C1, R2, C2>

The resulting type after applying the + operator.

fn add(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the + operation.

impl<'a, 'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<&'b Matrix<N, D2, U1, SB>> for &'a Point<N, D1> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<'a, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<Matrix<N, D2, U1, SB>> for &'a Point<N, D1> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<&'b Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<'b, N, R1, C1, R2, C2, SA, SB> Sub<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedSub,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

type Output = MatrixSum<N, R1, C1, R2, C2>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<'a, N, R1, C1, R2, C2, SA, SB> Sub<Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedSub,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R2, C2, R1, C1>,
    ShapeConstraint: SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1>, 

type Output = MatrixSum<N, R2, C2, R1, C1>

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<N, R1, C1, R2, C2, SA, SB> Sub<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedSub,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

type Output = MatrixSum<N, R1, C1, R2, C2>

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<'a, 'b, N, R1, C1, R2, C2, SA, SB> Sub<&'b Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedSub,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

type Output = MatrixSum<N, R1, C1, R2, C2>

The resulting type after applying the - operator.

fn sub(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the - operation.

impl<'a, 'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<&'b Matrix<N, D2, U1, SB>> for &'a Point<N, D1> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<'a, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<Matrix<N, D2, U1, SB>> for &'a Point<N, D1> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<&'b Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>, 

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<N, R: Dim, C: Dim, S> Mul<N> for Matrix<N, R, C, S> where
    N: Scalar + ClosedMul,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = MatrixMN<N, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: N) -> Self::Output

Performs the * operation.

impl<'a, N, R: Dim, C: Dim, S> Mul<N> for &'a Matrix<N, R, C, S> where
    N: Scalar + ClosedMul,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = MatrixMN<N, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: N) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u8, R, C>> Mul<Matrix<u8, R, C, S>> for u8 where
    DefaultAllocator: Allocator<u8, R, C>, 

type Output = MatrixMN<u8, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u8, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u8, R, C>> Mul<&'b Matrix<u8, R, C, S>> for u8 where
    DefaultAllocator: Allocator<u8, R, C>, 

type Output = MatrixMN<u8, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u8, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u16, R, C>> Mul<Matrix<u16, R, C, S>> for u16 where
    DefaultAllocator: Allocator<u16, R, C>, 

type Output = MatrixMN<u16, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u16, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u16, R, C>> Mul<&'b Matrix<u16, R, C, S>> for u16 where
    DefaultAllocator: Allocator<u16, R, C>, 

type Output = MatrixMN<u16, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u16, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u32, R, C>> Mul<Matrix<u32, R, C, S>> for u32 where
    DefaultAllocator: Allocator<u32, R, C>, 

type Output = MatrixMN<u32, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u32, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u32, R, C>> Mul<&'b Matrix<u32, R, C, S>> for u32 where
    DefaultAllocator: Allocator<u32, R, C>, 

type Output = MatrixMN<u32, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u32, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<u64, R, C>> Mul<Matrix<u64, R, C, S>> for u64 where
    DefaultAllocator: Allocator<u64, R, C>, 

type Output = MatrixMN<u64, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<u64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<u64, R, C>> Mul<&'b Matrix<u64, R, C, S>> for u64 where
    DefaultAllocator: Allocator<u64, R, C>, 

type Output = MatrixMN<u64, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<u64, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<usize, R, C>> Mul<Matrix<usize, R, C, S>> for usize where
    DefaultAllocator: Allocator<usize, R, C>, 

type Output = MatrixMN<usize, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<usize, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<usize, R, C>> Mul<&'b Matrix<usize, R, C, S>> for usize where
    DefaultAllocator: Allocator<usize, R, C>, 

type Output = MatrixMN<usize, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<usize, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i8, R, C>> Mul<Matrix<i8, R, C, S>> for i8 where
    DefaultAllocator: Allocator<i8, R, C>, 

type Output = MatrixMN<i8, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i8, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i8, R, C>> Mul<&'b Matrix<i8, R, C, S>> for i8 where
    DefaultAllocator: Allocator<i8, R, C>, 

type Output = MatrixMN<i8, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i8, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i16, R, C>> Mul<Matrix<i16, R, C, S>> for i16 where
    DefaultAllocator: Allocator<i16, R, C>, 

type Output = MatrixMN<i16, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i16, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i16, R, C>> Mul<&'b Matrix<i16, R, C, S>> for i16 where
    DefaultAllocator: Allocator<i16, R, C>, 

type Output = MatrixMN<i16, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i16, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i32, R, C>> Mul<Matrix<i32, R, C, S>> for i32 where
    DefaultAllocator: Allocator<i32, R, C>, 

type Output = MatrixMN<i32, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i32, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i32, R, C>> Mul<&'b Matrix<i32, R, C, S>> for i32 where
    DefaultAllocator: Allocator<i32, R, C>, 

type Output = MatrixMN<i32, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i32, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<i64, R, C>> Mul<Matrix<i64, R, C, S>> for i64 where
    DefaultAllocator: Allocator<i64, R, C>, 

type Output = MatrixMN<i64, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<i64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<i64, R, C>> Mul<&'b Matrix<i64, R, C, S>> for i64 where
    DefaultAllocator: Allocator<i64, R, C>, 

type Output = MatrixMN<i64, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<i64, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<isize, R, C>> Mul<Matrix<isize, R, C, S>> for isize where
    DefaultAllocator: Allocator<isize, R, C>, 

type Output = MatrixMN<isize, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<isize, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<isize, R, C>> Mul<&'b Matrix<isize, R, C, S>> for isize where
    DefaultAllocator: Allocator<isize, R, C>, 

type Output = MatrixMN<isize, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<isize, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<f32, R, C>> Mul<Matrix<f32, R, C, S>> for f32 where
    DefaultAllocator: Allocator<f32, R, C>, 

type Output = MatrixMN<f32, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<f32, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<f32, R, C>> Mul<&'b Matrix<f32, R, C, S>> for f32 where
    DefaultAllocator: Allocator<f32, R, C>, 

type Output = MatrixMN<f32, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<f32, R, C, S>) -> Self::Output

Performs the * operation.

impl<R: Dim, C: Dim, S: Storage<f64, R, C>> Mul<Matrix<f64, R, C, S>> for f64 where
    DefaultAllocator: Allocator<f64, R, C>, 

type Output = MatrixMN<f64, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<f64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'b, R: Dim, C: Dim, S: Storage<f64, R, C>> Mul<&'b Matrix<f64, R, C, S>> for f64 where
    DefaultAllocator: Allocator<f64, R, C>, 

type Output = MatrixMN<f64, R, C>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<f64, R, C, S>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    SA: Storage<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    DefaultAllocator: Allocator<N, R1, C2>,
    ShapeConstraint: AreMultipliable<R1, C1, R2, C2>, 

type Output = MatrixMN<N, R1, C2>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'a, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    SB: Storage<N, R2, C2>,
    SA: Storage<N, R1, C1>,
    DefaultAllocator: Allocator<N, R1, C2>,
    ShapeConstraint: AreMultipliable<R1, C1, R2, C2>, 

type Output = MatrixMN<N, R1, C2>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    SB: Storage<N, R2, C2>,
    SA: Storage<N, R1, C1>,
    DefaultAllocator: Allocator<N, R1, C2>,
    ShapeConstraint: AreMultipliable<R1, C1, R2, C2>, 

type Output = MatrixMN<N, R1, C2>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    SB: Storage<N, R2, C2>,
    SA: Storage<N, R1, C1>,
    DefaultAllocator: Allocator<N, R1, C2>,
    ShapeConstraint: AreMultipliable<R1, C1, R2, C2>, 

type Output = MatrixMN<N, R1, C2>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Point<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>, 

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Point<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>, 

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D2>) -> Self::Output

Performs the * operation.

impl<'b, N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Point<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>, 

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Point<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>, 

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D2>) -> Self::Output

Performs the * operation.

impl<N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<Matrix<N, R2, C2, SB>> for Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

fn mul(self, right: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'a, N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<Matrix<N, R2, C2, SB>> for &'a Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

fn mul(self, right: Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'b, N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<&'b Matrix<N, R2, C2, SB>> for Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<&'b Matrix<N, R2, C2, SB>> for &'a Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: RealField, SB: Storage<N, U3>> Mul<&'b Matrix<N, U3, U1, SB>> for &'a UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Vector3<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<N, U3, SB>) -> Self::Output

Performs the * operation.

impl<'a, N: RealField, SB: Storage<N, U3>> Mul<Matrix<N, U3, U1, SB>> for &'a UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Vector3<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<N, U3, SB>) -> Self::Output

Performs the * operation.

impl<'b, N: RealField, SB: Storage<N, U3>> Mul<&'b Matrix<N, U3, U1, SB>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Vector3<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<N, U3, SB>) -> Self::Output

Performs the * operation.

impl<N: RealField, SB: Storage<N, U3>> Mul<Matrix<N, U3, U1, SB>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Vector3<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<N, U3, SB>) -> Self::Output

Performs the * operation.

impl<N: RealField, S: Storage<N, U2>> Mul<Matrix<N, U2, U1, S>> for UnitComplex<N> where
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Vector2<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<N, U2, S>) -> Self::Output

Performs the * operation.

impl<'a, N: RealField, S: Storage<N, U2>> Mul<Matrix<N, U2, U1, S>> for &'a UnitComplex<N> where
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Vector2<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector<N, U2, S>) -> Self::Output

Performs the * operation.

impl<'b, N: RealField, S: Storage<N, U2>> Mul<&'b Matrix<N, U2, U1, S>> for UnitComplex<N> where
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Vector2<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<N, U2, S>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: RealField, S: Storage<N, U2>> Mul<&'b Matrix<N, U2, U1, S>> for &'a UnitComplex<N> where
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Vector2<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Vector<N, U2, S>) -> Self::Output

Performs the * operation.

impl<N: RealField, D: DimName, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Isometry<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N: RealField, D: DimName, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Isometry<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: RealField, D: DimName, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Isometry<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: RealField, D: DimName, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Isometry<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<N: RealField, D: DimName, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Similarity<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N: RealField, D: DimName, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Similarity<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: RealField, D: DimName, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Similarity<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: RealField, D: DimName, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Similarity<N, D, R> where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<N, D: DimNameAdd<U1>, C: TCategory> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategory> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategory> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategory> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>, 

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<N, R: Dim, C: Dim, S> Div<N> for Matrix<N, R, C, S> where
    N: Scalar + ClosedDiv,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = MatrixMN<N, R, C>

The resulting type after applying the / operator.

fn div(self, rhs: N) -> Self::Output

Performs the / operation.

impl<'a, N, R: Dim, C: Dim, S> Div<N> for &'a Matrix<N, R, C, S> where
    N: Scalar + ClosedDiv,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = MatrixMN<N, R, C>

The resulting type after applying the / operator.

fn div(self, rhs: N) -> Self::Output

Performs the / operation.

impl<N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<'a, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<&'b Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<&'b Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S> where
    N: Scalar + ClosedNeg,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = MatrixMN<N, R, C>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<'a, N, R: Dim, C: Dim, S> Neg for &'a Matrix<N, R, C, S> where
    N: Scalar + ClosedNeg,
    S: Storage<N, R, C>,
    DefaultAllocator: Allocator<N, R, C>, 

type Output = MatrixMN<N, R, C>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<'b, N, R1, C1, R2, C2, SA, SB> AddAssign<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedAdd,
    SA: StorageMut<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

fn add_assign(&mut self, rhs: &'b Matrix<N, R2, C2, SB>)

Performs the += operation.

impl<N, R1, C1, R2, C2, SA, SB> AddAssign<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedAdd,
    SA: StorageMut<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

fn add_assign(&mut self, rhs: Matrix<N, R2, C2, SB>)

Performs the += operation.

impl<'b, N, D1: DimName, D2: Dim, SB> AddAssign<&'b Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedAdd,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>, 

fn add_assign(&mut self, right: &'b Vector<N, D2, SB>)

Performs the += operation.

impl<N, D1: DimName, D2: Dim, SB> AddAssign<Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedAdd,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>, 

fn add_assign(&mut self, right: Vector<N, D2, SB>)

Performs the += operation.

impl<'b, N, R1, C1, R2, C2, SA, SB> SubAssign<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedSub,
    SA: StorageMut<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

fn sub_assign(&mut self, rhs: &'b Matrix<N, R2, C2, SB>)

Performs the -= operation.

impl<N, R1, C1, R2, C2, SA, SB> SubAssign<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N: Scalar + ClosedSub,
    SA: StorageMut<N, R1, C1>,
    SB: Storage<N, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

fn sub_assign(&mut self, rhs: Matrix<N, R2, C2, SB>)

Performs the -= operation.

impl<'b, N, D1: DimName, D2: Dim, SB> SubAssign<&'b Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedSub,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>, 

fn sub_assign(&mut self, right: &'b Vector<N, D2, SB>)

Performs the -= operation.

impl<N, D1: DimName, D2: Dim, SB> SubAssign<Matrix<N, D2, U1, SB>> for Point<N, D1> where
    N: Scalar + ClosedSub,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>, 

fn sub_assign(&mut self, right: Vector<N, D2, SB>)

Performs the -= operation.

impl<N, R: Dim, C: Dim, S> MulAssign<N> for Matrix<N, R, C, S> where
    N: Scalar + ClosedMul,
    S: StorageMut<N, R, C>, 

fn mul_assign(&mut self, rhs: N)

Performs the *= operation.

impl<N, R1, C1, R2, SA, SB> MulAssign<Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    SB: Storage<N, R2, C1>,
    SA: ContiguousStorageMut<N, R1, C1> + Clone,
    ShapeConstraint: AreMultipliable<R1, C1, R2, C1>,
    DefaultAllocator: Allocator<N, R1, C1, Buffer = SA>, 

fn mul_assign(&mut self, rhs: Matrix<N, R2, C1, SB>)

Performs the *= operation.

impl<'b, N, R1, C1, R2, SA, SB> MulAssign<&'b Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    SB: Storage<N, R2, C1>,
    SA: ContiguousStorageMut<N, R1, C1> + Clone,
    ShapeConstraint: AreMultipliable<R1, C1, R2, C1>,
    DefaultAllocator: Allocator<N, R1, C1, Buffer = SA>, 

fn mul_assign(&mut self, rhs: &'b Matrix<N, R2, C1, SB>)

Performs the *= operation.

impl<N, R: Dim, C: Dim, S> DivAssign<N> for Matrix<N, R, C, S> where
    N: Scalar + ClosedDiv,
    S: StorageMut<N, R, C>, 

fn div_assign(&mut self, rhs: N)

Performs the /= operation.

impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Index<usize> for Matrix<N, R, C, S>

type Output = N

The returned type after indexing.

fn index(&self, i: usize) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<N, R: Dim, C: Dim, S> Index<(usize, usize)> for Matrix<N, R, C, S> where
    N: Scalar,
    S: Storage<N, R, C>, 

type Output = N

The returned type after indexing.

fn index(&self, ij: (usize, usize)) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> IndexMut<usize> for Matrix<N, R, C, S>

fn index_mut(&mut self, i: usize) -> &mut N

Performs the mutable indexing (container[index]) operation.

impl<N, R: Dim, C: Dim, S> IndexMut<(usize, usize)> for Matrix<N, R, C, S> where
    N: Scalar,
    S: StorageMut<N, R, C>, 

fn index_mut(&mut self, ij: (usize, usize)) -> &mut N

Performs the mutable indexing (container[index]) operation.

impl<N, D: DimName> Product<Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>> for MatrixN<N, D> where
    N: Scalar + Zero + One + ClosedMul + ClosedAdd,
    DefaultAllocator: Allocator<N, D, D>, 

fn product<I: Iterator<Item = MatrixN<N, D>>>(iter: I) -> MatrixN<N, D>

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, N, D: DimName> Product<&'a Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>> for MatrixN<N, D> where
    N: Scalar + Zero + One + ClosedMul + ClosedAdd,
    DefaultAllocator: Allocator<N, D, D>, 

fn product<I: Iterator<Item = &'a MatrixN<N, D>>>(iter: I) -> MatrixN<N, D>

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<N, R: DimName, C: DimName> Sum<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> for MatrixMN<N, R, C> where
    N: Scalar + ClosedAdd + Zero,
    DefaultAllocator: Allocator<N, R, C>, 

fn sum<I: Iterator<Item = MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C>

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl<N, C: Dim> Sum<Matrix<N, Dynamic, C, <DefaultAllocator as Allocator<N, Dynamic, C>>::Buffer>> for MatrixMN<N, Dynamic, C> where
    N: Scalar + ClosedAdd + Zero,
    DefaultAllocator: Allocator<N, Dynamic, C>, 

fn sum<I: Iterator<Item = MatrixMN<N, Dynamic, C>>>(
    iter: I
) -> MatrixMN<N, Dynamic, C>

Example

assert_eq!(vec![DVector::repeat(3, 1.0f64),
                DVector::repeat(3, 1.0f64),
                DVector::repeat(3, 1.0f64)].into_iter().sum::<DVector<f64>>(),
           DVector::repeat(3, 1.0f64) + DVector::repeat(3, 1.0f64) + DVector::repeat(3, 1.0f64));

Panics

Panics if the iterator is empty:

iter::empty::<DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!

impl<'a, N, R: DimName, C: DimName> Sum<&'a Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> for MatrixMN<N, R, C> where
    N: Scalar + ClosedAdd + Zero,
    DefaultAllocator: Allocator<N, R, C>, 

fn sum<I: Iterator<Item = &'a MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C>

Method which takes an iterator and generates Self from the elements by "summing up" the items.

impl<'a, N, C: Dim> Sum<&'a Matrix<N, Dynamic, C, <DefaultAllocator as Allocator<N, Dynamic, C>>::Buffer>> for MatrixMN<N, Dynamic, C> where
    N: Scalar + ClosedAdd + Zero,
    DefaultAllocator: Allocator<N, Dynamic, C>, 

fn sum<I: Iterator<Item = &'a MatrixMN<N, Dynamic, C>>>(
    iter: I
) -> MatrixMN<N, Dynamic, C>

Example

let v = &DVector::repeat(3, 1.0f64);

assert_eq!(vec![v, v, v].into_iter().sum::<DVector<f64>>(),
           v + v + v);

Panics

Panics if the iterator is empty:

iter::empty::<&DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!

impl<N, R, C, S> Serialize for Matrix<N, R, C, S> where
    N: Scalar,
    R: Dim,
    C: Dim,
    S: Serialize, 

fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error> where
    T: Serializer, 

Serialize this value into the given Serde serializer.

impl<'de, N, R, C, S> Deserialize<'de> for Matrix<N, R, C, S> where
    N: Scalar,
    R: Dim,
    C: Dim,
    S: Deserialize<'de>, 

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error> where
    D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl<N, R: Dim, C: Dim, S> AbsDiffEq<Matrix<N, R, C, S>> for Matrix<N, R, C, S> where
    N: Scalar + AbsDiffEq,
    S: Storage<N, R, C>,
    N::Epsilon: Copy, 

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of ApproxEq::abs_diff_eq.

impl<N, R: Dim, C: Dim, S> RelativeEq<Matrix<N, R, C, S>> for Matrix<N, R, C, S> where
    N: Scalar + RelativeEq,
    S: Storage<N, R, C>,
    N::Epsilon: Copy, 

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq(
    &self,
    other: &Self,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of ApproxEq::relative_eq.

impl<N, R: Dim, C: Dim, S> UlpsEq<Matrix<N, R, C, S>> for Matrix<N, R, C, S> where
    N: Scalar + UlpsEq,
    S: Storage<N, R, C>,
    N::Epsilon: Copy, 

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of ApproxEq::ulps_eq.

impl<N: Scalar, R: Dim, C: Dim> Distribution<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>> for Standard where
    DefaultAllocator: Allocator<N, R, C>,
    Standard: Distribution<N>, 

fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> MatrixMN<N, R, C>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

impl<N1, N2, R1, C1, R2, C2> SubsetOf<Matrix<N2, R2, C2, <DefaultAllocator as Allocator<N2, R2, C2>>::Buffer>> for MatrixMN<N1, R1, C1> where
    R1: Dim,
    C1: Dim,
    R2: Dim,
    C2: Dim,
    N1: Scalar,
    N2: Scalar + SupersetOf<N1>,
    DefaultAllocator: Allocator<N2, R2, C2> + Allocator<N1, R1, C1> + SameShapeAllocator<N1, R1, C1, R2, C2>,
    ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>, 

fn to_superset(&self) -> MatrixMN<N2, R2, C2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixMN<N2, R2, C2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &MatrixMN<N2, R2, C2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, U1, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, U1>>::Buffer>> for Point<N1, D> where
    D: DimNameAdd<U1>,
    N1: Scalar,
    N2: Scalar + Zero + One + ClosedDiv + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N1, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>> + Allocator<N2, D>, 

fn to_superset(&self) -> VectorN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(v: &VectorN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Rotation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D>, 

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix<N2, U4, U4, <DefaultAllocator as Allocator<N2, U4, U4>>::Buffer>> for UnitQuaternion<N1>

fn to_superset(&self) -> Matrix4<N2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &Matrix4<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &Matrix4<N2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix<N2, U3, U3, <DefaultAllocator as Allocator<N2, U3, U3>>::Buffer>> for UnitComplex<N1>

fn to_superset(&self) -> Matrix3<N2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &Matrix3<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &Matrix3<N2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Translation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D, R> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Isometry<N1, D, R> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N1, D>> + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N1, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D> + Allocator<N2, D, D> + Allocator<N2, D>, 

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D, R> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Similarity<N1, D, R> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N1, D>> + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N1, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D> + Allocator<N2, D, D> + Allocator<N2, D>, 

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D: DimName, C> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Transform<N1, D, C> where
    N1: RealField + SubsetOf<N2>,
    N2: RealField,
    C: TCategory,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    N1::Epsilon: Copy,
    N2::Epsilon: Copy, 

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.