Type Alias oxygengine_physics_2d::prelude::nalgebra::base::MatrixSliceMut2xX

pub type MatrixSliceMut2xX<'a, T, RStride = Const<1>, CStride = Const<nalgebra::::base::dimension::U2::{constant#0}>> = Matrix<T, Const<nalgebra::::base::dimension::U2::{constant#0}>, Dynamic, SliceStorageMut<'a, T, Const<nalgebra::::base::dimension::U2::{constant#0}>, Dynamic, RStride, CStride>>;

A column-major matrix slice with 2 rows and a number of columns chosen at runtime.

Aliased Type

struct MatrixSliceMut2xX<'a, T, RStride = Const<1>, CStride = Const<nalgebra::::base::dimension::U2::{constant#0}>> {
    pub data: SliceStorageMut<'a, T, Const<2>, Dynamic, RStride, CStride>,
    /* private fields */
}

Fields

data: SliceStorageMut<'a, T, Const<2>, Dynamic, RStride, CStride>

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

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

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

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

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

Implementations

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

Dot/scalar product

pub fn dot<R2, C2, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> Twhere R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

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

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

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

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, C2, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> Twhere R2: Dim, C2: Dim, T: SimdComplexField, SB: RawStorage<T, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

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

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

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, C2, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> Twhere R2: Dim, C2: Dim, SB: RawStorage<T, 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<T, R1, C1, S> Matrix<T, R1, C1, S>where R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>, T: Scalar + Zero + ClosedAdd<T> + ClosedMul<T>,

pub fn ger<D2, D3, SB, SC>( &mut self, alpha: T, x: &Matrix<T, D2, Const<1>, SB>, y: &Matrix<T, D3, Const<1>, SC>, beta: T )where D2: Dim, D3: Dim, T: One, SB: Storage<T, D2, Const<1>>, SC: Storage<T, D3, Const<1>>, 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, D3, SB, SC>( &mut self, alpha: T, x: &Matrix<T, D2, Const<1>, SB>, y: &Matrix<T, D3, Const<1>, SC>, beta: T )where D2: Dim, D3: Dim, T: SimdComplexField, SB: Storage<T, D2, Const<1>>, SC: Storage<T, D3, Const<1>>, 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, C2, R3, C3, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T )where R2: Dim, C2: Dim, R3: Dim, C3: Dim, T: One, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C3> + AreMultipliable<R2, C2, R3, C3>,

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

If beta is zero, self is never read.

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, C2, R3, C3, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T )where R2: Dim, C2: Dim, R3: Dim, C3: Dim, T: One, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, C2> + SameNumberOfColumns<C1, C3> + AreMultipliable<C2, R2, R3, C3>,

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

If beta is zero, self is never read.

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, C2, R3, C3, SB, SC>( &mut self, alpha: T, a: &Matrix<T, R2, C2, SB>, b: &Matrix<T, R3, C3, SC>, beta: T )where R2: Dim, C2: Dim, R3: Dim, C3: Dim, T: SimdComplexField, SB: Storage<T, R2, C2>, SC: Storage<T, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, C2> + SameNumberOfColumns<C1, C3> + AreMultipliable<C2, R2, R3, C3>,

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

If beta is zero, self is never read.

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

pub fn ger_symm<D2, D3, SB, SC>( &mut self, alpha: T, x: &Matrix<T, D2, Const<1>, SB>, y: &Matrix<T, D3, Const<1>, SC>, beta: T )where D2: Dim, D3: Dim, T: One, SB: Storage<T, D2, Const<1>>, SC: Storage<T, D3, Const<1>>, 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, D3, SB, SC>( &mut self, alpha: T, x: &Matrix<T, D2, Const<1>, SB>, y: &Matrix<T, D3, Const<1>, SC>, beta: T )where D2: Dim, D3: Dim, T: One, SB: Storage<T, D2, Const<1>>, SC: Storage<T, D3, Const<1>>, 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, D3, SB, SC>( &mut self, alpha: T, x: &Matrix<T, D2, Const<1>, SB>, y: &Matrix<T, D3, Const<1>, SC>, beta: T )where D2: Dim, D3: Dim, T: SimdComplexField, SB: Storage<T, D2, Const<1>>, SC: Storage<T, D3, Const<1>>, 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<T, D1, S> Matrix<T, D1, D1, S>where D1: Dim, S: StorageMut<T, D1, D1>, T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>,

pub fn quadform_tr_with_workspace<D2, S2, R3, C3, S3, D4, S4>( &mut self, work: &mut Matrix<T, D2, Const<1>, S2>, alpha: T, lhs: &Matrix<T, R3, C3, S3>, mid: &Matrix<T, D4, D4, S4>, beta: T )where D2: Dim, R3: Dim, C3: Dim, D4: Dim, S2: StorageMut<T, D2, Const<1>>, S3: Storage<T, R3, C3>, S4: Storage<T, D4, D4>, ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,

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

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

Examples:

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

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

pub fn quadform_tr<R3, C3, S3, D4, S4>( &mut self, alpha: T, lhs: &Matrix<T, R3, C3, S3>, mid: &Matrix<T, D4, D4, S4>, beta: T )where R3: Dim, C3: Dim, D4: Dim, S3: Storage<T, R3, C3>, S4: Storage<T, D4, D4>, ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>, DefaultAllocator: Allocator<T, D1, Const<1>>,

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

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

Examples:

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

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

pub fn quadform_with_workspace<D2, S2, D3, S3, R4, C4, S4>( &mut self, work: &mut Matrix<T, D2, Const<1>, S2>, alpha: T, mid: &Matrix<T, D3, D3, S3>, rhs: &Matrix<T, R4, C4, S4>, beta: T )where D2: Dim, D3: Dim, R4: Dim, C4: Dim, S2: StorageMut<T, D2, Const<1>>, S3: Storage<T, D3, D3>, S4: Storage<T, R4, C4>, ShapeConstraint: DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, Const<1>>,

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

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

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

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

pub fn quadform<D2, S2, R3, C3, S3>( &mut self, alpha: T, mid: &Matrix<T, D2, D2, S2>, rhs: &Matrix<T, R3, C3, S3>, beta: T )where D2: Dim, R3: Dim, C3: Dim, S2: Storage<T, D2, D2>, S3: Storage<T, R3, C3>, ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, Const<1>>, DefaultAllocator: Allocator<T, D2, Const<1>>,

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

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

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

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

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

pub fn neg_mut(&mut self)

Negates self in-place.

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

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

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

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

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

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

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

Special multiplications.

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

Equivalent to self.transpose() * rhs.

pub fn ad_mul<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB> ) -> Matrix<T, C1, C2, <DefaultAllocator as Allocator<T, C1, C2>>::Buffer>where R2: Dim, C2: Dim, T: SimdComplexField, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,

Equivalent to self.adjoint() * rhs.

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

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

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

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

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

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

pub fn kronecker<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB> ) -> Matrix<T, <R1 as DimMul<R2>>::Output, <C1 as DimMul<C2>>::Output, <DefaultAllocator as Allocator<T, <R1 as DimMul<R2>>::Output, <C1 as DimMul<C2>>::Output>>::Buffer>where R2: Dim, C2: Dim, T: ClosedMul<T>, R1: DimMul<R2>, C1: DimMul<C2>, SB: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, <R1 as DimMul<R2>>::Output, <C1 as DimMul<C2>>::Output>,

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

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

Translation and scaling in any dimension

pub fn new_scaling( scaling: T ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>

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

pub fn new_nonuniform_scaling<SB>( scaling: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

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

pub fn new_translation<SB>( translation: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

Creates a new homogeneous matrix that applies a pure translation.

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

Append/prepend translation and scaling

pub fn append_scaling( &self, scaling: T ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, DefaultAllocator: Allocator<T, D, D>,

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

pub fn prepend_scaling( &self, scaling: T ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, DefaultAllocator: Allocator<T, D, D>,

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

pub fn append_nonuniform_scaling<SB>( &self, scaling: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>, DefaultAllocator: Allocator<T, D, D>,

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

pub fn prepend_nonuniform_scaling<SB>( &self, scaling: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>, DefaultAllocator: Allocator<T, D, D>,

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

pub fn append_translation<SB>( &self, shift: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>, DefaultAllocator: Allocator<T, D, D>,

Computes the transformation equal to self followed by a translation.

pub fn prepend_translation<SB>( &self, shift: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

Computes the transformation equal to a translation followed by self.

pub fn append_scaling_mut(&mut self, scaling: T)where S: StorageMut<T, D, D>, D: DimNameSub<Const<1>>,

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

pub fn prepend_scaling_mut(&mut self, scaling: T)where S: StorageMut<T, D, D>, D: DimNameSub<Const<1>>,

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

pub fn append_nonuniform_scaling_mut<SB>( &mut self, scaling: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> )where S: StorageMut<T, D, D>, D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

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

pub fn prepend_nonuniform_scaling_mut<SB>( &mut self, scaling: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> )where S: StorageMut<T, D, D>, D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

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

pub fn append_translation_mut<SB>( &mut self, shift: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> )where S: StorageMut<T, D, D>, D: DimNameSub<Const<1>>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

Computes the transformation equal to self followed by a translation.

pub fn prepend_translation_mut<SB>( &mut self, shift: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, SB> )where D: DimNameSub<Const<1>>, S: StorageMut<T, D, D>, SB: Storage<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>, DefaultAllocator: Allocator<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>,

Computes the transformation equal to a translation followed by self.

impl<T, D, S> Matrix<T, D, D, S>where T: RealField, D: DimNameSub<Const<1>>, S: Storage<T, D, D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, <D as DimNameSub<Const<1>>>::Output, Const<1>> + Allocator<T, <D as DimNameSub<Const<1>>>::Output, <D as DimNameSub<Const<1>>>::Output>,

Transformation of vectors and points

pub fn transform_vector( &self, v: &Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, <DefaultAllocator as Allocator<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>>::Buffer> ) -> Matrix<T, <D as DimNameSub<Const<1>>>::Output, Const<1>, <DefaultAllocator as Allocator<T, <D as DimNameSub<Const<1>>>::Output, Const<1>>>::Buffer>

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

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

pub fn abs( &self ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Signed, DefaultAllocator: Allocator<T, R, C>,

Computes the component-wise absolute value.

Example

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

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

Componentwise operations

pub fn component_mul<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB> ) -> Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>where T: ClosedMul<T>, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Componentwise matrix or vector multiplication.

Example

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

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

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

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

Example

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

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

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

Inplace componentwise matrix or vector multiplication.

Example

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

a.component_mul_assign(&b);

assert_eq!(a, expected);

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

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

Inplace componentwise matrix or vector multiplication.

Example

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

a.component_mul_assign(&b);

assert_eq!(a, expected);

pub fn component_div<R2, C2, SB>( &self, rhs: &Matrix<T, R2, C2, SB> ) -> Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>where T: ClosedDiv<T>, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Componentwise matrix or vector division.

Example

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

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

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

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

Example

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

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

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

Inplace componentwise matrix or vector division.

Example

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

a.component_div_assign(&b);

assert_eq!(a, expected);

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

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

Inplace componentwise matrix or vector division.

Example

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

a.component_div_assign(&b);

assert_eq!(a, expected);

pub fn inf( &self, other: &Matrix<T, R1, C1, SA> ) -> Matrix<T, R1, C1, <DefaultAllocator as Allocator<T, R1, C1>>::Buffer>where T: SimdPartialOrd, DefaultAllocator: Allocator<T, R1, C1>,

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

Example

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

pub fn sup( &self, other: &Matrix<T, R1, C1, SA> ) -> Matrix<T, R1, C1, <DefaultAllocator as Allocator<T, R1, C1>>::Buffer>where T: SimdPartialOrd, DefaultAllocator: Allocator<T, R1, C1>,

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

Example

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

pub fn inf_sup( &self, other: &Matrix<T, R1, C1, SA> ) -> (Matrix<T, R1, C1, <DefaultAllocator as Allocator<T, R1, C1>>::Buffer>, Matrix<T, R1, C1, <DefaultAllocator as Allocator<T, R1, C1>>::Buffer>)where T: SimdPartialOrd, DefaultAllocator: Allocator<T, R1, C1>,

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

Example

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

pub fn add_scalar( &self, rhs: T ) -> Matrix<T, R1, C1, <DefaultAllocator as Allocator<T, R1, C1>>::Buffer>where T: ClosedAdd<T>, DefaultAllocator: Allocator<T, R1, C1>,

Adds a scalar to self.

Example

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

pub fn add_scalar_mut(&mut self, rhs: T)where T: ClosedAdd<T>, SA: StorageMut<T, R1, C1>,

Adds a scalar to self in-place.

Example

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

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

pub fn uninit( nrows: R, ncols: C ) -> Matrix<MaybeUninit<T>, R, C, <DefaultAllocator as Allocator<T, R, C>>::BufferUninit>

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

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

Generic constructors

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

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

pub fn from_element_generic( nrows: R, ncols: C, elem: T ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Creates a matrix with all its elements set to elem.

pub fn repeat_generic( nrows: R, ncols: C, elem: T ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Creates a matrix with all its elements set to elem.

Same as from_element_generic.

pub fn zeros_generic( nrows: R, ncols: C ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero,

Creates a matrix with all its elements set to 0.

pub fn from_iterator_generic<I>( nrows: R, ncols: C, iter: I ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where I: IntoIterator<Item = T>,

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

pub fn from_row_slice_generic( nrows: R, ncols: C, slice: &[T] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

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

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

pub fn from_column_slice_generic( nrows: R, ncols: C, slice: &[T] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

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

pub fn from_fn_generic<F>( nrows: R, ncols: C, f: F ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where F: FnMut(usize, usize) -> T,

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

pub fn identity_generic( nrows: R, ncols: C ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero + One,

Creates a new identity matrix.

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

pub fn from_diagonal_element_generic( nrows: R, ncols: C, elt: T ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero + One,

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

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

pub fn from_partial_diagonal_generic( nrows: R, ncols: C, elts: &[T] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero,

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

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

pub fn from_rows<SB>( rows: &[Matrix<T, Const<1>, C, SB>] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where SB: RawStorage<T, Const<1>, C>,

Builds a new matrix from its rows.

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

Example

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

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

pub fn from_columns<SB>( columns: &[Matrix<T, R, Const<1>, SB>] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where SB: RawStorage<T, R, Const<1>>,

Builds a new matrix from its columns.

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

Example

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

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

pub fn from_vec_generic( nrows: R, ncols: C, data: Vec<T, Global> ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

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

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

// `matrix` is backed by exactly the same `Vec` as it was constructed from.
assert_eq!(matrix_storage_ptr, vec_ptr);

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

pub fn from_diagonal<SB>( diag: &Matrix<T, D, Const<1>, SB> ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where SB: RawStorage<T, D, Const<1>>, T: Zero,

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

Example

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

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

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

Constructors of statically-sized vectors or statically-sized matrices

pub fn from_element( elem: T ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

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

Example

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

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

pub fn repeat( elem: T ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

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

Same as .from_element.

Example

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

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

pub fn zeros( ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero,

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

Example

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

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

pub fn from_iterator<I>( iter: I ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where I: IntoIterator<Item = T>,

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

The output matrix is filled column-by-column.

Example

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

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

pub fn from_fn<F>( f: F ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where F: FnMut(usize, usize) -> T,

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

Example

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

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

pub fn identity( ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero + One,

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

Example

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

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

pub fn from_diagonal_element( elt: T ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero + One,

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

Example

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

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

pub fn from_partial_diagonal( elts: &[T] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Zero,

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

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

Example

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

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

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

Constructors of matrices with a dynamic number of columns

pub fn from_element( ncols: usize, elem: T ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>

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

Example

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

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

pub fn repeat( ncols: usize, elem: T ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>

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

Same as .from_element.

Example

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

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

pub fn zeros( ncols: usize ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where T: Zero,

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

Example

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

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

pub fn from_iterator<I>( ncols: usize, iter: I ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where I: IntoIterator<Item = T>,

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

The output matrix is filled column-by-column.

Example

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

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

pub fn from_fn<F>( ncols: usize, f: F ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where F: FnMut(usize, usize) -> T,

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

Example

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

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

pub fn identity( ncols: usize ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where T: Zero + One,

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

Example

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

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

pub fn from_diagonal_element( ncols: usize, elt: T ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where T: Zero + One,

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

Example

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

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

pub fn from_partial_diagonal( ncols: usize, elts: &[T] ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where T: Zero,

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

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

Example

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

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

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

pub fn from_row_slice( data: &[T] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

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

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

Example

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

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

pub fn from_column_slice( data: &[T] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

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

Example

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

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

pub fn from_vec( data: Vec<T, Global> ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

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

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


// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 5]);

assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

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

pub fn from_row_slice( data: &[T] ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>

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

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

Example

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

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

pub fn from_column_slice( data: &[T] ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>

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

Example

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

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

pub fn from_vec( data: Vec<T, Global> ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>

Creates a matrix backed by a given Vec.

The output matrix is filled column-by-column.

Example

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

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


// The two additional arguments represent the matrix dimensions.
let dm = DMatrix::from_vec(2, 3, vec![0, 1, 2, 3, 4, 5]);

assert!(dm[(0, 0)] == 0 && dm[(0, 1)] == 2 && dm[(0, 2)] == 4 &&
        dm[(1, 0)] == 1 && dm[(1, 1)] == 3 && dm[(1, 2)] == 5);

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

Creating mutable matrix slices from &mut [T]

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

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

Safety

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

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

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

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

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

pub unsafe fn from_slice_generic_unchecked( data: &'a mut [T], start: usize, nrows: R, ncols: C ) -> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Const<1>, R>>

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

Safety

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

pub fn from_slice_generic( data: &'a mut [T], nrows: R, ncols: C ) -> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Const<1>, R>>

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

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

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

pub fn from_slice( data: &'a mut [T] ) -> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Const<1>, R>>

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

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a mut [T], start: usize ) -> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Const<1>, R>>

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

impl<'a, T, R, C> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Dynamic, Dynamic>>where T: Scalar, R: DimName, C: DimName,

pub fn from_slice_with_strides_mut( data: &'a mut [T], rstride: usize, cstride: usize ) -> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Dynamic, Dynamic>>

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

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a mut [T], start: usize, rstride: usize, cstride: usize ) -> Matrix<T, R, C, SliceStorageMut<'a, T, R, C, Dynamic, Dynamic>>

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

impl<'a, T, R> Matrix<T, R, Dynamic, SliceStorageMut<'a, T, R, Dynamic, Const<1>, R>>where T: Scalar, R: DimName,

pub fn from_slice( data: &'a mut [T], ncols: usize ) -> Matrix<T, R, Dynamic, SliceStorageMut<'a, T, R, Dynamic, Const<1>, R>>

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

Panics if data does not contain enough elements.

pub unsafe fn from_slice_unchecked( data: &'a mut [T], start: usize, ncols: usize ) -> Matrix<T, R, Dynamic, SliceStorageMut<'a, T, R, Dynamic, Const<1>, R>>

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

impl<'a, T, R> Matrix<T, R, Dynamic, SliceStorageMut<'a, T, R, Dynamic, Dynamic, Dynamic>>where T: Scalar, R: DimName,

pub fn from_slice_with_strides_mut( data: &'a mut [T], ncols: usize, rstride: usize, cstride: usize ) -> Matrix<T, R, Dynamic, SliceStorageMut<'a, T, R, Dynamic, Dynamic, Dynamic>>

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

Panics if data does not contain enough elements.

pub unsafe fn from_slice_with_strides_unchecked( data: &'a mut [T], start: usize, ncols: usize, rstride: usize, cstride: usize ) -> Matrix<T, R, Dynamic, SliceStorageMut<'a, T, R, Dynamic, Dynamic, Dynamic>>

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

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

Rows and columns extraction

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

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

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

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

pub fn select_rows<'a, I>( &self, irows: I ) -> Matrix<T, Dynamic, C, <DefaultAllocator as Allocator<T, Dynamic, C>>::Buffer>where I: IntoIterator<Item = &'a usize>, <I as IntoIterator>::IntoIter: ExactSizeIterator + Clone, DefaultAllocator: Allocator<T, Dynamic, C>,

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

pub fn select_columns<'a, I>( &self, icols: I ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where I: IntoIterator<Item = &'a usize>, <I as IntoIterator>::IntoIter: ExactSizeIterator, DefaultAllocator: Allocator<T, R, Dynamic>,

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

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

Set rows, columns, and diagonal

pub fn set_diagonal<R2, S2>(&mut self, diag: &Matrix<T, R2, Const<1>, S2>)where R2: Dim, R: DimMin<C>, S2: RawStorage<T, R2, Const<1>>, ShapeConstraint: DimEq<<R as DimMin<C>>::Output, R2>,

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

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

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

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

pub fn set_row<C2, S2>(&mut self, i: usize, row: &Matrix<T, Const<1>, C2, S2>)where C2: Dim, S2: RawStorage<T, Const<1>, C2>, ShapeConstraint: SameNumberOfColumns<C, C2>,

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

pub fn set_column<R2, S2>( &mut self, i: usize, column: &Matrix<T, R2, Const<1>, S2> )where R2: Dim, S2: RawStorage<T, R2, Const<1>>, ShapeConstraint: SameNumberOfRows<R, R2>,

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

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

In-place filling

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

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

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

Sets all the elements of this matrix to val.

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

Fills self with the identity matrix.

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

Sets all the diagonal elements of this matrix to val.

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

Sets all the elements of the selected row to val.

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

Sets all the elements of the selected column to val.

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

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

The parameter shift allows some subdiagonals to be left untouched:

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

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

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

The parameter shift allows some superdiagonals to be left untouched:

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

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

pub fn fill_lower_triangle_with_upper_triangle(&mut self)

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

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

pub fn fill_upper_triangle_with_lower_triangle(&mut self)

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

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

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

In-place swapping

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

Swaps two rows in-place.

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

Swaps two columns in-place.

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

Rows and columns removal

pub fn remove_column( self, i: usize ) -> Matrix<T, R, <C as DimSub<Const<1>>>::Output, <DefaultAllocator as Allocator<T, R, <C as DimSub<Const<1>>>::Output>>::Buffer>where C: DimSub<Const<1>>, DefaultAllocator: Reallocator<T, R, C, R, <C as DimSub<Const<1>>>::Output>,

Removes the i-th column from this matrix.

pub fn remove_columns_at( self, indices: &[usize] ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where C: DimSub<Dynamic, Output = Dynamic>, DefaultAllocator: Reallocator<T, R, C, R, Dynamic>,

Removes all columns in indices

pub fn remove_rows_at( self, indices: &[usize] ) -> Matrix<T, Dynamic, C, <DefaultAllocator as Allocator<T, Dynamic, C>>::Buffer>where R: DimSub<Dynamic, Output = Dynamic>, DefaultAllocator: Reallocator<T, R, C, Dynamic, C>,

Removes all rows in indices

pub fn remove_fixed_columns<const D: usize>( self, i: usize ) -> Matrix<T, R, <C as DimSub<Const<D>>>::Output, <DefaultAllocator as Allocator<T, R, <C as DimSub<Const<D>>>::Output>>::Buffer>where C: DimSub<Const<D>>, DefaultAllocator: Reallocator<T, R, C, R, <C as DimSub<Const<D>>>::Output>,

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

pub fn remove_columns( self, i: usize, n: usize ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where C: DimSub<Dynamic, Output = Dynamic>, DefaultAllocator: Reallocator<T, 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 ) -> Matrix<T, R, <C as DimSub<D>>::Output, <DefaultAllocator as Allocator<T, R, <C as DimSub<D>>::Output>>::Buffer>where D: Dim, C: DimSub<D>, DefaultAllocator: Reallocator<T, R, C, R, <C as DimSub<D>>::Output>,

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 ) -> Matrix<T, <R as DimSub<Const<1>>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimSub<Const<1>>>::Output, C>>::Buffer>where R: DimSub<Const<1>>, DefaultAllocator: Reallocator<T, R, C, <R as DimSub<Const<1>>>::Output, C>,

Removes the i-th row from this matrix.

pub fn remove_fixed_rows<const D: usize>( self, i: usize ) -> Matrix<T, <R as DimSub<Const<D>>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimSub<Const<D>>>::Output, C>>::Buffer>where R: DimSub<Const<D>>, DefaultAllocator: Reallocator<T, R, C, <R as DimSub<Const<D>>>::Output, C>,

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

pub fn remove_rows( self, i: usize, n: usize ) -> Matrix<T, Dynamic, C, <DefaultAllocator as Allocator<T, Dynamic, C>>::Buffer>where R: DimSub<Dynamic, Output = Dynamic>, DefaultAllocator: Reallocator<T, 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 ) -> Matrix<T, <R as DimSub<D>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimSub<D>>::Output, C>>::Buffer>where D: Dim, R: DimSub<D>, DefaultAllocator: Reallocator<T, R, C, <R as DimSub<D>>::Output, C>,

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

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

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

Rows and columns insertion

pub fn insert_column( self, i: usize, val: T ) -> Matrix<T, R, <C as DimAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, R, <C as DimAdd<Const<1>>>::Output>>::Buffer>where C: DimAdd<Const<1>>, DefaultAllocator: Reallocator<T, R, C, R, <C as DimAdd<Const<1>>>::Output>,

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

pub fn insert_fixed_columns<const D: usize>( self, i: usize, val: T ) -> Matrix<T, R, <C as DimAdd<Const<D>>>::Output, <DefaultAllocator as Allocator<T, R, <C as DimAdd<Const<D>>>::Output>>::Buffer>where C: DimAdd<Const<D>>, DefaultAllocator: Reallocator<T, R, C, R, <C as DimAdd<Const<D>>>::Output>,

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

pub fn insert_columns( self, i: usize, n: usize, val: T ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where C: DimAdd<Dynamic, Output = Dynamic>, DefaultAllocator: Reallocator<T, 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 ) -> Matrix<MaybeUninit<T>, R, <C as DimAdd<D>>::Output, <DefaultAllocator as Allocator<T, R, <C as DimAdd<D>>::Output>>::BufferUninit>where D: Dim, C: DimAdd<D>, DefaultAllocator: Reallocator<T, R, C, R, <C as DimAdd<D>>::Output>,

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

Safety

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

pub fn insert_row( self, i: usize, val: T ) -> Matrix<T, <R as DimAdd<Const<1>>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimAdd<Const<1>>>::Output, C>>::Buffer>where R: DimAdd<Const<1>>, DefaultAllocator: Reallocator<T, R, C, <R as DimAdd<Const<1>>>::Output, C>,

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

pub fn insert_fixed_rows<const D: usize>( self, i: usize, val: T ) -> Matrix<T, <R as DimAdd<Const<D>>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimAdd<Const<D>>>::Output, C>>::Buffer>where R: DimAdd<Const<D>>, DefaultAllocator: Reallocator<T, R, C, <R as DimAdd<Const<D>>>::Output, C>,

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

pub fn insert_rows( self, i: usize, n: usize, val: T ) -> Matrix<T, Dynamic, C, <DefaultAllocator as Allocator<T, Dynamic, C>>::Buffer>where R: DimAdd<Dynamic, Output = Dynamic>, DefaultAllocator: Reallocator<T, 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 ) -> Matrix<MaybeUninit<T>, <R as DimAdd<D>>::Output, C, <DefaultAllocator as Allocator<T, <R as DimAdd<D>>::Output, C>>::BufferUninit>where D: Dim, R: DimAdd<D>, DefaultAllocator: Reallocator<T, R, C, <R as DimAdd<D>>::Output, C>,

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

Safety

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

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

Resizing and reshaping

pub fn resize( self, new_nrows: usize, new_ncols: usize, val: T ) -> Matrix<T, Dynamic, Dynamic, <DefaultAllocator as Allocator<T, Dynamic, Dynamic>>::Buffer>where DefaultAllocator: Reallocator<T, 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: T ) -> Matrix<T, Dynamic, C, <DefaultAllocator as Allocator<T, Dynamic, C>>::Buffer>where DefaultAllocator: Reallocator<T, 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: T ) -> Matrix<T, R, Dynamic, <DefaultAllocator as Allocator<T, R, Dynamic>>::Buffer>where DefaultAllocator: Reallocator<T, 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<const R2: usize, const C2: usize>( self, val: T ) -> Matrix<T, Const<R2>, Const<C2>, <DefaultAllocator as Allocator<T, Const<R2>, Const<C2>>>::Buffer>where DefaultAllocator: Reallocator<T, R, C, Const<R2>, Const<C2>>,

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

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

pub fn resize_generic<R2, C2>( self, new_nrows: R2, new_ncols: C2, val: T ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, DefaultAllocator: Reallocator<T, R, C, R2, C2>,

Resizes self such that it has dimensions new_nrows × new_ncols.

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

pub fn reshape_generic<R2, C2>( self, new_nrows: R2, new_ncols: C2 ) -> Matrix<T, R2, C2, <S as ReshapableStorage<T, R, C, R2, C2>>::Output>where R2: Dim, C2: Dim, S: ReshapableStorage<T, R, C, R2, C2>,

Reshapes self such that it has dimensions new_nrows × new_ncols.

This will reinterpret self as if it is a matrix with new_nrows rows and new_ncols columns. The arrangements of the component in the output matrix are the same as what would be obtained by Matrix::from_slice_generic(self.as_slice(), new_nrows, new_ncols).

If self is a dynamically-sized matrix, then its components are neither copied nor moved. If self is staticyll-sized, then a copy may happen in some situations. This function will panic if the given dimensions are such that the number of elements of the input matrix are not equal to the number of elements of the output matrix.

Examples

let m1 = Matrix2x3::new(
    1.1, 1.2, 1.3,
    2.1, 2.2, 2.3
);
let m2 = Matrix3x2::new(
    1.1, 2.2,
    2.1, 1.3,
    1.2, 2.3
);
let reshaped = m1.reshape_generic(Const::<3>, Const::<2>);
assert_eq!(reshaped, m2);

let dm1 = DMatrix::from_row_slice(
    4,
    3,
    &[
        1.0, 0.0, 0.0,
        0.0, 0.0, 1.0,
        0.0, 0.0, 0.0,
        0.0, 1.0, 0.0
    ],
);
let dm2 = DMatrix::from_row_slice(
    6,
    2,
    &[
        1.0, 0.0,
        0.0, 1.0,
        0.0, 0.0,
        0.0, 1.0,
        0.0, 0.0,
        0.0, 0.0,
    ],
);
let reshaped = dm1.reshape_generic(Dynamic::new(6), Dynamic::new(2));
assert_eq!(reshaped, dm2);

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

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

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

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

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

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

Slicing based on ranges

Indices to Individual Elements

Two-Dimensional Indices

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert_eq!(matrix.index((0, 0)), &0);
assert_eq!(matrix.index((1, 0)), &1);
assert_eq!(matrix.index((0, 1)), &2);
assert_eq!(matrix.index((1, 1)), &3);

Linear Address Indexing

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert_eq!(matrix.get(0), Some(&0));
assert_eq!(matrix.get(1), Some(&1));
assert_eq!(matrix.get(2), Some(&2));
assert_eq!(matrix.get(3), Some(&3));

Indices to Individual Rows and Columns

Index to a Row

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert!(matrix.index((0, ..))
    .eq(&Matrix1x2::new(0, 2)));

Index to a Column

let matrix = Matrix2::new(0, 2,
                          1, 3);

assert!(matrix.index((.., 0))
    .eq(&Matrix2x1::new(0,
                        1)));

Indices to Parts of Individual Rows and Columns

Index to a Partial Row

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

assert!(matrix.index((0, ..2))
    .eq(&Matrix1x2::new(0, 3)));

Index to a Partial Column

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

assert!(matrix.index((..2, 0))
    .eq(&Matrix2x1::new(0,
                        1)));

assert!(matrix.index((Const::<1>.., 0))
    .eq(&Matrix2x1::new(1,
                        2)));

Indices to Ranges of Rows and Columns

Index to a Range of Rows

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

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

Index to a Range of Columns

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

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

pub fn get<'a, I>( &'a self, index: I ) -> Option<<I as MatrixIndex<'a, T, R, C, S>>::Output>where I: MatrixIndex<'a, T, R, C, S>,

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

pub fn get_mut<'a, I>( &'a mut self, index: I ) -> Option<<I as MatrixIndexMut<'a, T, R, C, S>>::OutputMut>where S: RawStorageMut<T, R, C>, I: MatrixIndexMut<'a, T, R, C, S>,

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

pub fn index<'a, I>( &'a self, index: I ) -> <I as MatrixIndex<'a, T, R, C, S>>::Outputwhere I: MatrixIndex<'a, T, R, C, S>,

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

pub fn index_mut<'a, I>( &'a mut self, index: I ) -> <I as MatrixIndexMut<'a, T, R, C, S>>::OutputMutwhere S: RawStorageMut<T, R, C>, I: MatrixIndexMut<'a, T, R, C, S>,

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

pub unsafe fn get_unchecked<'a, I>( &'a self, index: I ) -> <I as MatrixIndex<'a, T, R, C, S>>::Outputwhere I: MatrixIndex<'a, T, 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 as MatrixIndexMut<'a, T, R, C, S>>::OutputMutwhere S: RawStorageMut<T, R, C>, I: MatrixIndexMut<'a, T, R, C, S>,

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

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

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

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

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

pub unsafe fn assume_init( self ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Assumes a matrix’s entries to be initialized. This operation should be near zero-cost.

For the similar method that operates on matrix slices, see [slice_assume_init].

Safety

The user must make sure that every single entry of the buffer has been initialized, or Undefined Behavior will immediately occur.

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

pub fn from_data(data: S) -> Matrix<T, R, C, S>

Creates a new matrix with the given data.

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

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

Examples:

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

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

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

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));

pub fn vector_to_matrix_index(&self, i: usize) -> (usize, usize)

Computes the row and column coordinates of the i-th element of this matrix seen as a vector.

Example

let m = Matrix2::new(1, 2,
                     3, 4);
let i = m.vector_to_matrix_index(3);
assert_eq!(i, (1, 1));
assert_eq!(m[i], m[3]);

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

Returns a pointer to the start of the matrix.

If the matrix is not empty, this pointer is guaranteed to be aligned and non-null.

Example

let m = Matrix2::new(1, 2,
                     3, 4);
let ptr = m.as_ptr();
assert_eq!(unsafe { *ptr }, m[0]);

pub fn relative_eq<R2, C2, SB>( &self, other: &Matrix<T, R2, C2, SB>, eps: <T as AbsDiffEq<T>>::Epsilon, max_relative: <T as AbsDiffEq<T>>::Epsilon ) -> boolwhere T: RelativeEq<T>, R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, <T as AbsDiffEq<T>>::Epsilon: Clone, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

See relative_eq from the RelativeEq trait for more details.

pub fn eq<R2, C2, SB>(&self, other: &Matrix<T, R2, C2, SB>) -> boolwhere T: PartialEq<T>, R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Tests whether self and rhs are exactly equal.

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

Moves this matrix into one that owns its data.

pub fn into_owned_sum<R2, C2>( self ) -> Matrix<T, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative>>::Buffer>where T: Scalar, S: Storage<T, R, C>, R2: Dim, C2: Dim, DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

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

Clones this matrix to one that owns its data.

pub fn clone_owned_sum<R2, C2>( &self ) -> Matrix<T, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative>>::Buffer>where T: Scalar, S: Storage<T, R, C>, R2: Dim, C2: Dim, DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

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

Transposes self and store the result into out.

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

Transposes self.

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

Elementwise mapping and folding

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

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

pub fn cast<T2>( self ) -> Matrix<T2, R, C, <DefaultAllocator as Allocator<T2, R, C>>::Buffer>where T2: Scalar, T: Scalar, Matrix<T2, R, C, <DefaultAllocator as Allocator<T2, R, C>>::Buffer>: SupersetOf<Matrix<T, R, C, S>>, DefaultAllocator: Allocator<T2, R, C>,

Cast the components of self to another type.

Example

let q = Vector3::new(1.0f64, 2.0, 3.0);
let q2 = q.cast::<f32>();
assert_eq!(q2, Vector3::new(1.0f32, 2.0, 3.0));

pub fn fold_with<T2>( &self, init_f: impl FnOnce(Option<&T>) -> T2, f: impl FnMut(T2, &T) -> T2 ) -> T2where T: Scalar,

Similar to self.iter().fold(init, f) except that init is replaced by a closure.

The initialization closure is given the first component of this matrix:

• If the matrix has no component (0 rows or 0 columns) then init_f is called with None and its return value is the value returned by this method.
• If the matrix has has least one component, then init_f is called with the first component to compute the initial value. Folding then continues on all the remaining components of the matrix.

pub fn map_with_location<T2, F>( &self, f: F ) -> Matrix<T2, R, C, <DefaultAllocator as Allocator<T2, R, C>>::Buffer>where T2: Scalar, F: FnMut(usize, usize, T) -> T2, T: Scalar, DefaultAllocator: Allocator<T2, R, C>,

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

pub fn zip_map<T2, N3, S2, F>( &self, rhs: &Matrix<T2, R, C, S2>, f: F ) -> Matrix<N3, R, C, <DefaultAllocator as Allocator<N3, R, C>>::Buffer>where T: Scalar, T2: Scalar, N3: Scalar, S2: RawStorage<T2, R, C>, F: FnMut(T, T2) -> N3, DefaultAllocator: Allocator<N3, R, C>,

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

pub fn zip_zip_map<T2, N3, N4, S2, S3, F>( &self, b: &Matrix<T2, R, C, S2>, c: &Matrix<N3, R, C, S3>, f: F ) -> Matrix<N4, R, C, <DefaultAllocator as Allocator<N4, R, C>>::Buffer>where T: Scalar, T2: Scalar, N3: Scalar, N4: Scalar, S2: RawStorage<T2, R, C>, S3: RawStorage<N3, R, C>, F: FnMut(T, T2, N3) -> N4, DefaultAllocator: Allocator<N4, R, C>,

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

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

Folds a function f on each entry of self.

pub fn zip_fold<T2, R2, C2, S2, Acc>( &self, rhs: &Matrix<T2, R2, C2, S2>, init: Acc, f: impl FnMut(Acc, T, T2) -> Acc ) -> Accwhere T: Scalar, T2: Scalar, R2: Dim, C2: Dim, S2: RawStorage<T2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

pub fn apply<F>(&mut self, f: F)where F: FnMut(&mut T), S: RawStorageMut<T, R, C>,

Applies a closure f to modify each component of self.

pub fn zip_apply<T2, R2, C2, S2>( &mut self, rhs: &Matrix<T2, R2, C2, S2>, f: impl FnMut(&mut T, T2) )where S: RawStorageMut<T, R, C>, T2: Scalar, R2: Dim, C2: Dim, S2: RawStorage<T2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

pub fn zip_zip_apply<T2, R2, C2, S2, N3, R3, C3, S3>( &mut self, b: &Matrix<T2, R2, C2, S2>, c: &Matrix<N3, R3, C3, S3>, f: impl FnMut(&mut T, T2, N3) )where S: RawStorageMut<T, R, C>, T2: Scalar, R2: Dim, C2: Dim, S2: RawStorage<T2, R2, C2>, N3: Scalar, R3: Dim, C3: Dim, S3: RawStorage<N3, R3, C3>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

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

Iteration on components, rows, and columns

pub fn iter(&self) -> MatrixIter<'_, T, 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());

pub fn row_iter(&self) -> RowIter<'_, T, R, C, S>

Iterate through the rows of this matrix.

Example

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

pub fn column_iter(&self) -> ColumnIter<'_, T, R, C, S>

Iterate through the columns of this matrix.

Example

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

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

Mutably iterates through this matrix coordinates.

pub fn row_iter_mut(&mut self) -> RowIterMut<'_, T, R, C, S> where S: RawStorageMut<T, R, C>,

Mutably iterates through this matrix rows.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, mut row) in a.row_iter_mut().enumerate() {
    row *= (i + 1) * 10;
}

let expected = Matrix2x3::new(10, 20, 30,
                              80, 100, 120);
assert_eq!(a, expected);

pub fn column_iter_mut(&mut self) -> ColumnIterMut<'_, T, R, C, S> where S: RawStorageMut<T, R, C>,

Mutably iterates through this matrix columns.

Example

let mut a = Matrix2x3::new(1, 2, 3,
                           4, 5, 6);
for (i, mut col) in a.column_iter_mut().enumerate() {
    col *= (i + 1) * 10;
}

let expected = Matrix2x3::new(10, 40, 90,
                              40, 100, 180);
assert_eq!(a, expected);

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

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

Returns a mutable pointer to the start of the matrix.

If the matrix is not empty, this pointer is guaranteed to be aligned and non-null.

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

Swaps two entries without bound-checking.

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

Swaps two entries.

pub fn copy_from_slice(&mut self, slice: &[T])where T: Scalar,

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

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

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

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

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

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

pub fn apply_into<F>(self, f: F) -> Matrix<T, R, C, S>where F: FnMut(&mut T),

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

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

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

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

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

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

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

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

pub fn transpose_mut(&mut self)

Transposes the square matrix self in-place.

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

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

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

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

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

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

👎Deprecated: Renamed self.adjoint_to(out).

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

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

👎Deprecated: Renamed self.adjoint().

The conjugate transposition of self.

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

The conjugate of self.

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

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

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

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

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

pub fn conjugate_mut(&mut self)

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

pub fn unscale_mut(&mut self, real: <T as SimdComplexField>::SimdRealField)

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

pub fn scale_mut(&mut self, real: <T as SimdComplexField>::SimdRealField)

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

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

pub fn conjugate_transform_mut(&mut self)

👎Deprecated: Renamed to self.adjoint_mut().

Sets self to its adjoint.

pub fn adjoint_mut(&mut self)

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

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

pub fn diagonal( &self ) -> Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<T, D, Const<1>>>::Buffer>where DefaultAllocator: Allocator<T, D, Const<1>>,

The diagonal of this matrix.

pub fn map_diagonal<T2>( &self, f: impl FnMut(T) -> T2 ) -> Matrix<T2, D, Const<1>, <DefaultAllocator as Allocator<T2, D, Const<1>>>::Buffer>where T2: Scalar, DefaultAllocator: Allocator<T2, D, Const<1>>,

Apply the given function to this matrix’s diagonal and returns it.

This is a more efficient version of self.diagonal().map(f) since this allocates only once.

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

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

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

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

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

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

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

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

pub fn to_homogeneous( &self ) -> Matrix<T, <D as DimAdd<Const<1>>>::Output, <D as DimAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <D as DimAdd<Const<1>>>::Output, <D as DimAdd<Const<1>>>::Output>>::Buffer>where DefaultAllocator: Allocator<T, <D as DimAdd<Const<1>>>::Output, <D as DimAdd<Const<1>>>::Output>,

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

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

Cross product

pub fn perp<R2, C2, SB>(&self, b: &Matrix<T, R2, C2, SB>) -> Twhere R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, Const<nalgebra::::base::dimension::U2::{constant#0}>> + SameNumberOfColumns<C, Const<1>> + SameNumberOfRows<R2, Const<nalgebra::::base::dimension::U2::{constant#0}>> + SameNumberOfColumns<C2, Const<1>>,

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

pub fn cross<R2, C2, SB>( &self, b: &Matrix<T, R2, C2, SB> ) -> Matrix<T, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative>>::Buffer>where R2: Dim, C2: Dim, SB: RawStorage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

The 3D cross product between two vectors.

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

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

pub fn angle<R2, C2, SB>( &self, other: &Matrix<T, R2, C2, SB> ) -> <T as SimdComplexField>::SimdRealFieldwhere R2: Dim, C2: Dim, SB: Storage<T, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

The smallest angle between two vectors.

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

Slicing based on index and length

pub fn row( &self, i: usize ) -> Matrix<T, Const<1>, C, SliceStorage<'_, T, Const<1>, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn row_part( &self, i: usize, n: usize ) -> Matrix<T, Const<1>, Dynamic, SliceStorage<'_, T, Const<1>, Dynamic, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, Dynamic, C, SliceStorage<'_, T, Dynamic, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

Extracts from this matrix a set of consecutive rows.

pub fn rows_with_step( &self, first_row: usize, nrows: usize, step: usize ) -> Matrix<T, Dynamic, C, SliceStorage<'_, T, Dynamic, C, Dynamic, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_rows<const RSLICE: usize>( &self, first_row: usize ) -> Matrix<T, Const<RSLICE>, C, SliceStorage<'_, T, Const<RSLICE>, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_rows_with_step<const RSLICE: usize>( &self, first_row: usize, step: usize ) -> Matrix<T, Const<RSLICE>, C, SliceStorage<'_, T, Const<RSLICE>, C, Dynamic, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn rows_generic<RSlice>( &self, row_start: usize, nrows: RSlice ) -> Matrix<T, RSlice, C, SliceStorage<'_, T, RSlice, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 rows_generic_with_step<RSlice>( &self, row_start: usize, nrows: RSlice, step: usize ) -> Matrix<T, RSlice, C, SliceStorage<'_, T, RSlice, C, Dynamic, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, R, Const<1>, SliceStorage<'_, T, R, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn column_part( &self, i: usize, n: usize ) -> Matrix<T, Dynamic, Const<1>, SliceStorage<'_, T, Dynamic, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, R, Dynamic, SliceStorage<'_, T, R, Dynamic, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

Extracts from this matrix a set of consecutive columns.

pub fn columns_with_step( &self, first_col: usize, ncols: usize, step: usize ) -> Matrix<T, R, Dynamic, SliceStorage<'_, T, R, Dynamic, <S as RawStorage<T, R, C>>::RStride, Dynamic>>

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

pub fn fixed_columns<const CSLICE: usize>( &self, first_col: usize ) -> Matrix<T, R, Const<CSLICE>, SliceStorage<'_, T, R, Const<CSLICE>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_columns_with_step<const CSLICE: usize>( &self, first_col: usize, step: usize ) -> Matrix<T, R, Const<CSLICE>, SliceStorage<'_, T, R, Const<CSLICE>, <S as RawStorage<T, R, C>>::RStride, Dynamic>>

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

pub fn columns_generic<CSlice>( &self, first_col: usize, ncols: CSlice ) -> Matrix<T, R, CSlice, SliceStorage<'_, T, R, CSlice, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>where CSlice: Dim,

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>( &self, first_col: usize, ncols: CSlice, step: usize ) -> Matrix<T, R, CSlice, SliceStorage<'_, T, R, CSlice, <S as RawStorage<T, R, C>>::RStride, Dynamic>>where CSlice: Dim,

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) ) -> Matrix<T, Dynamic, Dynamic, SliceStorage<'_, T, Dynamic, Dynamic, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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) ) -> Matrix<T, Dynamic, Dynamic, SliceStorage<'_, T, 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<const RSLICE: usize, const CSLICE: usize>( &self, irow: usize, icol: usize ) -> Matrix<T, Const<RSLICE>, Const<CSLICE>, SliceStorage<'_, T, Const<RSLICE>, Const<CSLICE>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_slice_with_steps<const RSLICE: usize, const CSLICE: usize>( &self, start: (usize, usize), steps: (usize, usize) ) -> Matrix<T, Const<RSLICE>, Const<CSLICE>, SliceStorage<'_, T, Const<RSLICE>, Const<CSLICE>, Dynamic, Dynamic>>

Slices this matrix starting at its component (start.0, start.1) and with (RSLICE, CSLICE) 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) ) -> Matrix<T, RSlice, CSlice, SliceStorage<'_, T, RSlice, CSlice, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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) ) -> Matrix<T, RSlice, CSlice, SliceStorage<'_, T, 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, Range2>( &self, r1: Range1, r2: Range2 ) -> (Matrix<T, <Range1 as SliceRange<R>>::Size, C, SliceStorage<'_, T, <Range1 as SliceRange<R>>::Size, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>, Matrix<T, <Range2 as SliceRange<R>>::Size, C, SliceStorage<'_, T, <Range2 as SliceRange<R>>::Size, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>)where Range1: SliceRange<R>, Range2: SliceRange<R>,

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, Range2>( &self, r1: Range1, r2: Range2 ) -> (Matrix<T, R, <Range1 as SliceRange<C>>::Size, SliceStorage<'_, T, R, <Range1 as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>, Matrix<T, R, <Range2 as SliceRange<C>>::Size, SliceStorage<'_, T, R, <Range2 as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>)where Range1: SliceRange<C>, Range2: SliceRange<C>,

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

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

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

Mutable slicing based on index and length

pub fn row_mut( &mut self, i: usize ) -> Matrix<T, Const<1>, C, SliceStorageMut<'_, T, Const<1>, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn row_part_mut( &mut self, i: usize, n: usize ) -> Matrix<T, Const<1>, Dynamic, SliceStorageMut<'_, T, Const<1>, Dynamic, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, Dynamic, C, SliceStorageMut<'_, T, Dynamic, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, Dynamic, C, SliceStorageMut<'_, T, Dynamic, C, Dynamic, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_rows_mut<const RSLICE: usize>( &mut self, first_row: usize ) -> Matrix<T, Const<RSLICE>, C, SliceStorageMut<'_, T, Const<RSLICE>, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_rows_with_step_mut<const RSLICE: usize>( &mut self, first_row: usize, step: usize ) -> Matrix<T, Const<RSLICE>, C, SliceStorageMut<'_, T, Const<RSLICE>, C, Dynamic, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn rows_generic_mut<RSlice>( &mut self, row_start: usize, nrows: RSlice ) -> Matrix<T, RSlice, C, SliceStorageMut<'_, T, RSlice, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 rows_generic_with_step_mut<RSlice>( &mut self, row_start: usize, nrows: RSlice, step: usize ) -> Matrix<T, RSlice, C, SliceStorageMut<'_, T, RSlice, C, Dynamic, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, R, Const<1>, SliceStorageMut<'_, T, R, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn column_part_mut( &mut self, i: usize, n: usize ) -> Matrix<T, Dynamic, Const<1>, SliceStorageMut<'_, T, Dynamic, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, R, Dynamic, SliceStorageMut<'_, T, R, Dynamic, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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 ) -> Matrix<T, R, Dynamic, SliceStorageMut<'_, T, R, Dynamic, <S as RawStorage<T, R, C>>::RStride, Dynamic>>

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

pub fn fixed_columns_mut<const CSLICE: usize>( &mut self, first_col: usize ) -> Matrix<T, R, Const<CSLICE>, SliceStorageMut<'_, T, R, Const<CSLICE>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_columns_with_step_mut<const CSLICE: usize>( &mut self, first_col: usize, step: usize ) -> Matrix<T, R, Const<CSLICE>, SliceStorageMut<'_, T, R, Const<CSLICE>, <S as RawStorage<T, R, C>>::RStride, Dynamic>>

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

pub fn columns_generic_mut<CSlice>( &mut self, first_col: usize, ncols: CSlice ) -> Matrix<T, R, CSlice, SliceStorageMut<'_, T, R, CSlice, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>where CSlice: Dim,

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>( &mut self, first_col: usize, ncols: CSlice, step: usize ) -> Matrix<T, R, CSlice, SliceStorageMut<'_, T, R, CSlice, <S as RawStorage<T, R, C>>::RStride, Dynamic>>where CSlice: Dim,

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) ) -> Matrix<T, Dynamic, Dynamic, SliceStorageMut<'_, T, Dynamic, Dynamic, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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) ) -> Matrix<T, Dynamic, Dynamic, SliceStorageMut<'_, T, 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<const RSLICE: usize, const CSLICE: usize>( &mut self, irow: usize, icol: usize ) -> Matrix<T, Const<RSLICE>, Const<CSLICE>, SliceStorageMut<'_, T, Const<RSLICE>, Const<CSLICE>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>

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

pub fn fixed_slice_with_steps_mut<const RSLICE: usize, const CSLICE: usize>( &mut self, start: (usize, usize), steps: (usize, usize) ) -> Matrix<T, Const<RSLICE>, Const<CSLICE>, SliceStorageMut<'_, T, Const<RSLICE>, Const<CSLICE>, Dynamic, Dynamic>>

Slices this matrix starting at its component (start.0, start.1) and with (RSLICE, CSLICE) 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) ) -> Matrix<T, RSlice, CSlice, SliceStorageMut<'_, T, RSlice, CSlice, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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) ) -> Matrix<T, RSlice, CSlice, SliceStorageMut<'_, T, 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, Range2>( &mut self, r1: Range1, r2: Range2 ) -> (Matrix<T, <Range1 as SliceRange<R>>::Size, C, SliceStorageMut<'_, T, <Range1 as SliceRange<R>>::Size, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>, Matrix<T, <Range2 as SliceRange<R>>::Size, C, SliceStorageMut<'_, T, <Range2 as SliceRange<R>>::Size, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>)where Range1: SliceRange<R>, Range2: SliceRange<R>,

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, Range2>( &mut self, r1: Range1, r2: Range2 ) -> (Matrix<T, R, <Range1 as SliceRange<C>>::Size, SliceStorageMut<'_, T, R, <Range1 as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>, Matrix<T, R, <Range2 as SliceRange<C>>::Size, SliceStorageMut<'_, T, R, <Range2 as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>)where Range1: SliceRange<C>, Range2: SliceRange<C>,

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

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

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

pub fn slice_range<RowRange, ColRange>( &self, rows: RowRange, cols: ColRange ) -> Matrix<T, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, SliceStorage<'_, T, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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>( &self, rows: RowRange ) -> Matrix<T, <RowRange as SliceRange<R>>::Size, C, SliceStorage<'_, T, <RowRange as SliceRange<R>>::Size, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>where RowRange: SliceRange<R>,

Slice containing all the rows indexed by the range rows.

pub fn columns_range<ColRange>( &self, cols: ColRange ) -> Matrix<T, R, <ColRange as SliceRange<C>>::Size, SliceStorage<'_, T, R, <ColRange as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>where ColRange: SliceRange<C>,

Slice containing all the columns indexed by the range rows.

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

pub fn slice_range_mut<RowRange, ColRange>( &mut self, rows: RowRange, cols: ColRange ) -> Matrix<T, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, SliceStorageMut<'_, T, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::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>( &mut self, rows: RowRange ) -> Matrix<T, <RowRange as SliceRange<R>>::Size, C, SliceStorageMut<'_, T, <RowRange as SliceRange<R>>::Size, C, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>where RowRange: SliceRange<R>,

Slice containing all the rows indexed by the range rows.

pub fn columns_range_mut<ColRange>( &mut self, cols: ColRange ) -> Matrix<T, R, <ColRange as SliceRange<C>>::Size, SliceStorageMut<'_, T, R, <ColRange as SliceRange<C>>::Size, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>where ColRange: SliceRange<C>,

Slice containing all the columns indexed by the range cols.

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

Magnitude and norms

pub fn norm_squared(&self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

The squared L2 norm of this vector.

pub fn norm(&self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

The L2 norm of this matrix.

Use .apply_norm to apply a custom norm.

pub fn metric_distance<R2, C2, S2>( &self, rhs: &Matrix<T, R2, C2, S2> ) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField, R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

Use .apply_metric_distance to apply a custom norm.

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

Uses the given norm to compute the norm of self.

Example

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

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

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

Example

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

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

pub fn magnitude(&self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

A synonym for the norm of this matrix.

Aka the length.

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

pub fn magnitude_squared(&self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

A synonym for the squared norm of this matrix.

Aka the squared length.

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

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

Sets the magnitude of this vector.

pub fn normalize( &self ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: SimdComplexField, DefaultAllocator: Allocator<T, R, C>,

Returns a normalized version of this matrix.

pub fn lp_norm(&self, p: i32) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

The Lp norm of this matrix.

pub fn simd_try_normalize( &self, min_norm: <T as SimdComplexField>::SimdRealField ) -> SimdOption<Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>>where T: SimdComplexField, <T as SimdValue>::Element: Scalar, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

Attempts to normalize self.

The components of this matrix can be SIMD types.

pub fn try_set_magnitude( &mut self, magnitude: <T as ComplexField>::RealField, min_magnitude: <T as ComplexField>::RealField )where T: ComplexField, S: StorageMut<T, R, C>,

Sets the magnitude of this vector unless it is smaller than min_magnitude.

If self.magnitude() is smaller than min_magnitude, it will be left unchanged. Otherwise this is equivalent to: `*self = self.normalize() * magnitude.

pub fn cap_magnitude( &self, max: <T as ComplexField>::RealField ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: ComplexField, DefaultAllocator: Allocator<T, R, C>,

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

pub fn simd_cap_magnitude( &self, max: <T as SimdComplexField>::SimdRealField ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: SimdComplexField, <T as SimdValue>::Element: Scalar, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

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

pub fn try_normalize( &self, min_norm: <T as ComplexField>::RealField ) -> Option<Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>>where T: ComplexField, DefaultAllocator: Allocator<T, R, C>,

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

The components of this matrix cannot be SIMD types (see simd_try_normalize) instead.

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

In-place normalization

pub fn normalize_mut(&mut self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

Normalizes this matrix in-place and returns its norm.

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

pub fn simd_try_normalize_mut( &mut self, min_norm: <T as SimdComplexField>::SimdRealField ) -> SimdOption<<T as SimdComplexField>::SimdRealField>where T: SimdComplexField, <T as SimdValue>::Element: Scalar, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

Normalizes this matrix in-place and return its norm.

The components of the matrix can be SIMD types.

pub fn try_normalize_mut( &mut self, min_norm: <T as ComplexField>::RealField ) -> Option<<T as ComplexField>::RealField>where T: ComplexField,

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

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

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

pub fn len(&self) -> usize

The total number of elements of this matrix.

Examples:

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

pub fn is_empty(&self) -> bool

Returns true if the matrix contains no elements.

Examples:

let mat = Matrix3x4::<f32>::zeros();
assert!(!mat.is_empty());

pub fn is_square(&self) -> bool

Indicates if this is a square matrix.

pub fn is_identity(&self, eps: <T as AbsDiffEq<T>>::Epsilon) -> boolwhere T: Zero + One + RelativeEq<T>, <T as AbsDiffEq<T>>::Epsilon: Clone,

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

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

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

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

Checks that Mᵀ × M = Id.

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

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

pub fn is_special_orthogonal(&self, eps: T) -> boolwhere D: DimMin<D, Output = D>, DefaultAllocator: Allocator<(usize, usize), D, Const<1>>,

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

pub fn is_invertible(&self) -> bool

Returns true if this matrix is invertible.

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

Folding on columns and rows

pub fn compress_rows( &self, f: impl Fn(Matrix<T, R, Const<1>, SliceStorage<'_, T, R, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>) -> T ) -> Matrix<T, Const<1>, C, <DefaultAllocator as Allocator<T, Const<1>, C>>::Buffer>where DefaultAllocator: Allocator<T, Const<1>, 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(Matrix<T, R, Const<1>, SliceStorage<'_, T, R, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>) -> T ) -> Matrix<T, C, Const<1>, <DefaultAllocator as Allocator<T, C, Const<1>>>::Buffer>where DefaultAllocator: Allocator<T, C, Const<1>>,

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: Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<T, R, Const<1>>>::Buffer>, f: impl Fn(&mut Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<T, R, Const<1>>>::Buffer>, Matrix<T, R, Const<1>, SliceStorage<'_, T, R, Const<1>, <S as RawStorage<T, R, C>>::RStride, <S as RawStorage<T, R, C>>::CStride>>) ) -> Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<T, R, Const<1>>>::Buffer>where DefaultAllocator: Allocator<T, R, Const<1>>,

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

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

Common statistics operations

pub fn sum(&self) -> Twhere T: ClosedAdd<T> + Zero,

The sum of all the elements of this matrix.

Example

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

pub fn row_sum( &self ) -> Matrix<T, Const<1>, C, <DefaultAllocator as Allocator<T, Const<1>, C>>::Buffer>where T: ClosedAdd<T> + Zero, DefaultAllocator: Allocator<T, Const<1>, C>,

The sum of all the rows of this matrix.

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

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_sum(), RowVector3::new(5.0, 7.0, 9.0));

let mint = Matrix3x2::new(1,2,3,4,5,6);
assert_eq!(mint.row_sum(), RowVector2::new(9,12));

pub fn row_sum_tr( &self ) -> Matrix<T, C, Const<1>, <DefaultAllocator as Allocator<T, C, Const<1>>>::Buffer>where T: ClosedAdd<T> + Zero, DefaultAllocator: Allocator<T, C, Const<1>>,

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

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.row_sum_tr(), Vector3::new(5.0, 7.0, 9.0));

let mint = Matrix3x2::new(1,2,3,4,5,6);
assert_eq!(mint.row_sum_tr(), Vector2::new(9,12));

pub fn column_sum( &self ) -> Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<T, R, Const<1>>>::Buffer>where T: ClosedAdd<T> + Zero, DefaultAllocator: Allocator<T, R, Const<1>>,

The sum of all the columns of this matrix.

Example

let m = Matrix2x3::new(1.0, 2.0, 3.0,
                       4.0, 5.0, 6.0);
assert_eq!(m.column_sum(), Vector2::new(6.0, 15.0));

let mint = Matrix3x2::new(1,2,3,4,5,6);
assert_eq!(mint.column_sum(), Vector3::new(3,7,11));

pub fn variance(&self) -> Twhere T: Field + SupersetOf<f64>,

The variance of all the elements of this matrix.

Example

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

pub fn row_variance( &self ) -> Matrix<T, Const<1>, C, <DefaultAllocator as Allocator<T, Const<1>, C>>::Buffer>where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<T, Const<1>, 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 ) -> Matrix<T, C, Const<1>, <DefaultAllocator as Allocator<T, C, Const<1>>>::Buffer>where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<T, C, Const<1>>,

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 ) -> Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<T, R, Const<1>>>::Buffer>where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<T, R, Const<1>>,

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) -> Twhere T: Field + SupersetOf<f64>,

The mean of all the elements of this matrix.

Example

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

pub fn row_mean( &self ) -> Matrix<T, Const<1>, C, <DefaultAllocator as Allocator<T, Const<1>, C>>::Buffer>where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<T, Const<1>, 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 ) -> Matrix<T, C, Const<1>, <DefaultAllocator as Allocator<T, C, Const<1>>>::Buffer>where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<T, C, Const<1>>,

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 ) -> Matrix<T, R, Const<1>, <DefaultAllocator as Allocator<T, R, Const<1>>>::Buffer>where T: Field + SupersetOf<f64>, DefaultAllocator: Allocator<T, R, Const<1>>,

The mean of all the columns of this matrix.

Example

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

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

Find the min and max components

pub fn amax(&self) -> Twhere T: Zero + SimdSigned + SimdPartialOrd,

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

Example

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

pub fn camax(&self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

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

Example

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

pub fn max(&self) -> Twhere T: SimdPartialOrd + Zero,

Returns the component with the largest value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).max(), 3.0);
assert_eq!(Vector3::new(-1.0, -2.0, -3.0).max(), -1.0);
assert_eq!(Vector3::new(5u32, 2, 3).max(), 5);

pub fn amin(&self) -> Twhere T: Zero + SimdPartialOrd + SimdSigned,

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

Example

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

pub fn camin(&self) -> <T as SimdComplexField>::SimdRealFieldwhere T: SimdComplexField,

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

Example

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

pub fn min(&self) -> Twhere T: SimdPartialOrd + Zero,

Returns the component with the smallest value.

Example

assert_eq!(Vector3::new(-1.0, 2.0, 3.0).min(), -1.0);
assert_eq!(Vector3::new(1.0, 2.0, 3.0).min(), 1.0);
assert_eq!(Vector3::new(5u32, 2, 3).min(), 2);

pub fn icamax_full(&self) -> (usize, usize)where T: ComplexField,

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

Examples:

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

impl<T, R, C, S> Matrix<T, R, C, S>where T: Scalar + PartialOrd<T> + Signed, R: Dim, C: Dim, S: RawStorage<T, R, C>,

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

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

Examples:

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

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: DimMin<D, Output = D>, S: Storage<T, D, D>,

pub fn determinant(&self) -> Twhere DefaultAllocator: Allocator<T, D, D> + Allocator<(usize, usize), D, Const<1>>,

Computes the matrix determinant.

If the matrix has a dimension larger than 3, an LU decomposition is used.

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

Rectangular matrix decomposition

This section contains the methods for computing some common decompositions of rectangular matrices with real or complex components. The following are currently supported:

Decomposition	Factors	Details
QR	Q * R	Q is an unitary matrix, and R is upper-triangular.
QR with column pivoting	Q * R * P⁻¹	Q is an unitary matrix, and R is upper-triangular. P is a permutation matrix.
LU with partial pivoting	P⁻¹ * L * U	L is lower-triangular with a diagonal filled with 1 and U is upper-triangular. P is a permutation matrix.
LU with full pivoting	P⁻¹ * L * U * Q⁻¹	L is lower-triangular with a diagonal filled with 1 and U is upper-triangular. P and Q are permutation matrices.
SVD	U * Σ * Vᵀ	U and V are two orthogonal matrices and Σ is a diagonal matrix containing the singular values.

pub fn bidiagonalize(self) -> Bidiagonal<T, R, C>where R: DimMin<C>, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,

Computes the bidiagonalization using householder reflections.

pub fn full_piv_lu(self) -> FullPivLU<T, R, C>where R: DimMin<C>, DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1>>,

Computes the LU decomposition with full pivoting of matrix.

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

pub fn lu(self) -> LU<T, R, C>where R: DimMin<C>, DefaultAllocator: Allocator<T, R, C> + Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1>>,

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

pub fn qr(self) -> QR<T, R, C>where R: DimMin<C>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, R, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, Const<1>>,

Computes the QR decomposition of this matrix.

pub fn col_piv_qr(self) -> ColPivQR<T, R, C>where R: DimMin<C>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, R, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<(usize, usize), <R as DimMin<C>>::Output, Const<1>>,

Computes the QR decomposition (with column pivoting) of this matrix.

pub fn svd(self, compute_u: bool, compute_v: bool) -> SVD<T, R, C>where R: DimMin<C>, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,

Computes the Singular Value Decomposition using implicit shift.

pub fn try_svd( self, compute_u: bool, compute_v: bool, eps: <T as ComplexField>::RealField, max_niter: usize ) -> Option<SVD<T, R, C>>where R: DimMin<C>, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,

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

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: Dim, S: Storage<T, D, D>,

Square matrix decomposition

This section contains the methods for computing some common decompositions of square matrices with real or complex components. The following are currently supported:

Decomposition	Factors	Details
Hessenberg	Q * H * Qᵀ	Q is a unitary matrix and H an upper-Hessenberg matrix.
Cholesky	L * Lᵀ	L is a lower-triangular matrix.
UDU	U * D * Uᵀ	U is a upper-triangular matrix, and D a diagonal matrix.
Schur decomposition	Q * T * Qᵀ	Q is an unitary matrix and T a quasi-upper-triangular matrix.
Symmetric eigendecomposition	Q ~ Λ ~ Qᵀ	Q is an unitary matrix, and Λ is a real diagonal matrix.
Symmetric tridiagonalization	Q ~ T ~ Qᵀ	Q is an unitary matrix, and T is a tridiagonal matrix.

pub fn cholesky(self) -> Option<Cholesky<T, D>>where DefaultAllocator: Allocator<T, D, D>,

Attempts to compute the Cholesky decomposition of this matrix.

Returns None if the input matrix is not definite-positive. The input matrix is assumed to be symmetric and only the lower-triangular part is read.

pub fn udu(self) -> Option<UDU<T, D>>where T: RealField, DefaultAllocator: Allocator<T, D, Const<1>> + Allocator<T, D, D>,

Attempts to compute the UDU decomposition of this matrix.

The input matrix self is assumed to be symmetric and this decomposition will only read the upper-triangular part of self.

pub fn hessenberg(self) -> Hessenberg<T, D>where D: DimSub<Const<1>>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, D, Const<1>> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>>,

Computes the Hessenberg decomposition of this matrix using householder reflections.

pub fn schur(self) -> Schur<T, D>where D: DimSub<Const<1>>, DefaultAllocator: Allocator<T, D, <D as DimSub<Const<1>>>::Output> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, D, D> + Allocator<T, D, Const<1>>,

Computes the Schur decomposition of a square matrix.

pub fn try_schur( self, eps: <T as ComplexField>::RealField, max_niter: usize ) -> Option<Schur<T, D>>where D: DimSub<Const<1>>, DefaultAllocator: Allocator<T, D, <D as DimSub<Const<1>>>::Output> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, D, D> + Allocator<T, D, Const<1>>,

Attempts to compute the Schur decomposition of a square matrix.

If only eigenvalues are needed, it is more efficient to call the matrix method .eigenvalues() instead.

Arguments

• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn symmetric_eigen(self) -> SymmetricEigen<T, D>where D: DimSub<Const<1>>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, D, Const<1>> + Allocator<<T as ComplexField>::RealField, <D as DimSub<Const<1>>>::Output, Const<1>>,

Computes the eigendecomposition of this symmetric matrix.

Only the lower-triangular part (including the diagonal) of m is read.

pub fn try_symmetric_eigen( self, eps: <T as ComplexField>::RealField, max_niter: usize ) -> Option<SymmetricEigen<T, D>>where D: DimSub<Const<1>>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, D, Const<1>> + Allocator<<T as ComplexField>::RealField, <D as DimSub<Const<1>>>::Output, Const<1>>,

Computes the eigendecomposition of the given symmetric matrix with user-specified convergence parameters.

Only the lower-triangular part (including the diagonal) of m is read.

Arguments

• eps − tolerance used to determine when a value converged to 0.
• max_niter − maximum total number of iterations performed by the algorithm. If this number of iteration is exceeded, None is returned. If niter == 0, then the algorithm continues indefinitely until convergence.

pub fn symmetric_tridiagonalize(self) -> SymmetricTridiagonal<T, D>where D: DimSub<Const<1>>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>>,

Computes the tridiagonalization of this symmetric matrix.

Only the lower-triangular part (including the diagonal) of m is read.

impl<T, D> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where T: ComplexField, D: DimMin<D, Output = D>, DefaultAllocator: Allocator<T, D, D> + Allocator<(usize, usize), <D as DimMin<D>>::Output, Const<1>> + Allocator<T, D, Const<1>> + Allocator<<T as ComplexField>::RealField, D, Const<1>> + Allocator<<T as ComplexField>::RealField, D, D>,

pub fn exp( &self ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>

Computes exponential of this matrix

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: Dim, S: Storage<T, D, D>,

pub fn try_inverse( self ) -> Option<Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>>where DefaultAllocator: Allocator<T, D, D>,

Attempts to invert this matrix.

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: Dim, S: StorageMut<T, D, D>,

pub fn try_inverse_mut(&mut self) -> boolwhere DefaultAllocator: Allocator<T, D, D>,

Attempts to invert this matrix in-place. Returns false and leaves self untouched if inversion fails.

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: DimMin<D, Output = D>, S: StorageMut<T, D, D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, D, Const<1>>,

pub fn pow_mut<I>(&mut self, e: I) -> boolwhere I: PrimInt + DivAssign<I>,

Attempts to raise this matrix to an integral power e in-place. If this matrix is non-invertible and e is negative, it leaves this matrix untouched and returns false. Otherwise, it returns true and overwrites this matrix with the result.

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, S: Storage<T, D, D> + StorageMut<T, D, D>, D: DimMin<D, Output = D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, D, Const<1>>,

pub fn pow<I>( &self, e: I ) -> Option<Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>>where I: PrimInt + DivAssign<I>,

Attempts to raise this matrix to an integral power e. If this matrix is non-invertible and e is negative, it returns None. Otherwise, it returns the result as a new matrix. Uses exponentiation by squares.

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: Dim + DimSub<Const<1>>, S: Storage<T, D, D>, DefaultAllocator: Allocator<T, D, <D as DimSub<Const<1>>>::Output> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, D, D> + Allocator<T, D, Const<1>>,

pub fn eigenvalues( &self ) -> Option<Matrix<T, D, Const<1>, <DefaultAllocator as Allocator<T, D, Const<1>>>::Buffer>>

Computes the eigenvalues of this matrix.

pub fn complex_eigenvalues( &self ) -> Matrix<Complex<T>, D, Const<1>, <DefaultAllocator as Allocator<Complex<T>, D, Const<1>>>::Buffer>where T: RealField, DefaultAllocator: Allocator<Complex<T>, D, Const<1>>,

Computes the eigenvalues of this matrix.

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: Dim, S: Storage<T, D, D>,

pub fn solve_lower_triangular<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_upper_triangular<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_with_diag_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, diag: T ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self is considered not-zero. The diagonal is never read as it is assumed to be equal to diag. Returns false and does not modify its inputs if diag is zero.

pub fn solve_upper_triangular_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Option<Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> ) -> boolwhere R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

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

pub fn solve_lower_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_upper_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn solve_lower_triangular_with_diag_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2>, diag: T )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the lower-triangular part of self is considered not-zero. The diagonal is never read as it is assumed to be equal to diag. Returns false and does not modify its inputs if diag is zero.

pub fn solve_upper_triangular_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_lower_triangular_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn tr_solve_upper_triangular_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.transpose() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<T, R2, C2, S2> ) -> Matrix<T, R2, C2, <DefaultAllocator as Allocator<T, R2, C2>>::Buffer>where R2: Dim, C2: Dim, S2: Storage<T, R2, C2>, DefaultAllocator: Allocator<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Computes the solution of the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_lower_triangular_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the lower-triangular part of self (including the diagonal) is considered not-zero.

pub fn ad_solve_upper_triangular_unchecked_mut<R2, C2, S2>( &self, b: &mut Matrix<T, R2, C2, S2> )where R2: Dim, C2: Dim, S2: StorageMut<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,

Solves the linear system self.adjoint() . x = b where x is the unknown and only the upper-triangular part of self (including the diagonal) is considered not-zero.

impl<T, R, C, S> Matrix<T, R, C, S>where T: ComplexField, R: DimMin<C>, C: Dim, S: Storage<T, R, C>, <R as DimMin<C>>::Output: DimSub<Const<1>>, DefaultAllocator: Allocator<T, R, C> + Allocator<T, C, Const<1>> + Allocator<T, R, Const<1>> + Allocator<T, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>> + Allocator<T, <R as DimMin<C>>::Output, C> + Allocator<T, R, <R as DimMin<C>>::Output> + Allocator<T, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, <<R as DimMin<C>>::Output as DimSub<Const<1>>>::Output, Const<1>>,

pub fn singular_values( &self ) -> Matrix<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, <R as DimMin<C>>::Output, Const<1>>>::Buffer>

Computes the singular values of this matrix.

pub fn rank(&self, eps: <T as ComplexField>::RealField) -> usize

Computes the rank of this matrix.

All singular values below eps are considered equal to 0.

pub fn pseudo_inverse( self, eps: <T as ComplexField>::RealField ) -> Result<Matrix<T, C, R, <DefaultAllocator as Allocator<T, C, R>>::Buffer>, &'static str>where DefaultAllocator: Allocator<T, C, R>,

Computes the pseudo-inverse of this matrix.

All singular values below eps are considered equal to 0.

impl<T, D, S> Matrix<T, D, D, S>where T: ComplexField, D: DimSub<Const<1>>, S: Storage<T, D, D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, <D as DimSub<Const<1>>>::Output, Const<1>> + Allocator<<T as ComplexField>::RealField, D, Const<1>> + Allocator<<T as ComplexField>::RealField, <D as DimSub<Const<1>>>::Output, Const<1>>,

pub fn symmetric_eigenvalues( &self ) -> Matrix<<T as ComplexField>::RealField, D, Const<1>, <DefaultAllocator as Allocator<<T as ComplexField>::RealField, D, Const<1>>>::Buffer>

Computes the eigenvalues of this symmetric matrix.

Only the lower-triangular part of the matrix is read.

Trait Implementations

impl<T, R, C, S> AbsDiffEq<Matrix<T, R, C, S>> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + AbsDiffEq<T>, S: RawStorage<T, R, C>, <T as AbsDiffEq<T>>::Epsilon: Clone,

type Epsilon = <T as AbsDiffEq<T>>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon( ) -> <Matrix<T, R, C, S> as AbsDiffEq<Matrix<T, R, C, S>>>::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq( &self, other: &Matrix<T, R, C, S>, epsilon: <Matrix<T, R, C, S> as AbsDiffEq<Matrix<T, R, C, S>>>::Epsilon ) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of [AbsDiffEq::abs_diff_eq].

impl<'b, T, R1, C1, R2, C2, SA, SB> Add<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAdd<T>, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>

The resulting type after applying the + operator.

fn add( self, rhs: &'b Matrix<T, R2, C2, SB> ) -> <Matrix<T, R1, C1, SA> as Add<&'b Matrix<T, R2, C2, SB>>>::Output

Performs the + operation.

impl<T, R1, C1, R2, C2, SA, SB> Add<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAdd<T>, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>

The resulting type after applying the + operator.

fn add( self, rhs: Matrix<T, R2, C2, SB> ) -> <Matrix<T, R1, C1, SA> as Add<Matrix<T, R2, C2, SB>>>::Output

Performs the + operation.

impl<'b, T, R1, C1, R2, C2, SA, SB> AddAssign<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAdd<T>, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn add_assign(&mut self, rhs: &'b Matrix<T, R2, C2, SB>)

Performs the += operation.

impl<T, R1, C1, R2, C2, SA, SB> AddAssign<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedAdd<T>, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

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

Performs the += operation.

impl<T, R, C, S> Binary for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + Binary, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

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

fn max_value( ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Returns the largest finite number this type can represent

fn min_value( ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Returns the smallest finite number this type can represent

impl<T, R, C, S> Clone for Matrix<T, R, C, S>where T: Clone, R: Clone, C: Clone, S: Clone,

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

fn fmt(&self, formatter: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T, R, C, S> Default for Matrix<T, R, C, S>where T: Scalar, R: Dim, C: Dim, S: Default,

fn default() -> Matrix<T, R, C, S>

Returns the “default value” for a type.

impl<'de, T, R, C, S> Deserialize<'de> for Matrix<T, R, C, S>where T: Scalar, R: Dim, C: Dim, S: Deserialize<'de>,

fn deserialize<D>( deserializer: D ) -> Result<Matrix<T, R, C, S>, <D as Deserializer<'de>>::Error>where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T, R, C, S> Display for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + Display, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for Matrix<T, R1, C1, SA>where T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<T, R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the / operator.

fn div( self, right: &'b Rotation<T, D2> ) -> <Matrix<T, R1, C1, SA> as Div<&'b Rotation<T, D2>>>::Output

Performs the / operation.

impl<T, R1, C1, SA, const D2: usize> Div<Rotation<T, D2>> for Matrix<T, R1, C1, SA>where T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<T, R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the / operator.

fn div( self, right: Rotation<T, D2> ) -> <Matrix<T, R1, C1, SA> as Div<Rotation<T, D2>>>::Output

Performs the / operation.

impl<T, R, C, S> Div<T> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + ClosedDiv<T>, S: Storage<T, R, C>, DefaultAllocator: Allocator<T, R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

The resulting type after applying the / operator.

fn div(self, rhs: T) -> <Matrix<T, R, C, S> as Div<T>>::Output

Performs the / operation.

impl<T, R, C, S> DivAssign<T> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + ClosedDiv<T>, S: StorageMut<T, R, C>,

fn div_assign(&mut self, rhs: T)

Performs the /= operation.

impl<T, R, S, RV, SV> Extend<Matrix<T, RV, Const<1>, SV>> for Matrix<T, R, Dynamic, S>where T: Scalar, R: Dim, S: Extend<Matrix<T, RV, Const<1>, SV>>, RV: Dim, SV: RawStorage<T, RV, Const<1>>, ShapeConstraint: SameNumberOfRows<R, RV>,

fn extend<I>(&mut self, iter: I)where I: IntoIterator<Item = Matrix<T, RV, Const<1>, SV>>,

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!

fn extend_one(&mut self, item: A)

🔬This is a nightly-only experimental API. (extend_one)

Extends a collection with exactly one element.

fn extend_reserve(&mut self, additional: usize)

🔬This is a nightly-only experimental API. (extend_one)

Reserves capacity in a collection for the given number of additional elements.

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

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

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

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]);

fn extend_one(&mut self, item: A)

🔬This is a nightly-only experimental API. (extend_one)

Extends a collection with exactly one element.

fn extend_reserve(&mut self, additional: usize)

🔬This is a nightly-only experimental API. (extend_one)

Reserves capacity in a collection for the given number of additional elements.

impl<'a, T, R, C, RSlice, CSlice, RStride, CStride, S> From<&'a mut Matrix<T, R, C, S>> for Matrix<T, RSlice, CSlice, SliceStorageMut<'a, T, RSlice, CSlice, RStride, CStride>>where T: Scalar, R: Dim, C: Dim, RSlice: Dim, CSlice: Dim, RStride: Dim, CStride: Dim, S: RawStorageMut<T, R, C>, ShapeConstraint: DimEq<R, RSlice> + DimEq<C, CSlice> + DimEq<RStride, <S as RawStorage<T, R, C>>::RStride> + DimEq<CStride, <S as RawStorage<T, R, C>>::CStride>,

fn from( m: &'a mut Matrix<T, R, C, S> ) -> Matrix<T, RSlice, CSlice, SliceStorageMut<'a, T, RSlice, CSlice, RStride, CStride>>

Converts to this type from the input type.

impl<T, R, C> From<[Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 16]> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Scalar + PrimitiveSimdValue + From<[<T as SimdValue>::Element; 16]>, R: Dim, C: Dim, <T as SimdValue>::Element: Scalar + SimdValue, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

fn from( arr: [Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 16] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Converts to this type from the input type.

impl<T, R, C> From<[Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 2]> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Scalar + PrimitiveSimdValue + From<[<T as SimdValue>::Element; 2]>, R: Dim, C: Dim, <T as SimdValue>::Element: Scalar + SimdValue, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

fn from( arr: [Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 2] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Converts to this type from the input type.

impl<T, R, C> From<[Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 4]> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Scalar + PrimitiveSimdValue + From<[<T as SimdValue>::Element; 4]>, R: Dim, C: Dim, <T as SimdValue>::Element: Scalar + SimdValue, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

fn from( arr: [Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 4] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Converts to this type from the input type.

impl<T, R, C> From<[Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 8]> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Scalar + PrimitiveSimdValue + From<[<T as SimdValue>::Element; 8]>, R: Dim, C: Dim, <T as SimdValue>::Element: Scalar + SimdValue, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

fn from( arr: [Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>; 8] ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Converts to this type from the input type.

impl<'a, T, R, C, S> From<CsMatrix<T, R, C, S>> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Scalar + Zero, R: Dim, C: Dim, S: CsStorage<T, R, C>, DefaultAllocator: Allocator<T, R, C>,

fn from( m: CsMatrix<T, R, C, S> ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Converts to this type from the input type.

impl<T, R, const D: usize> From<Isometry<T, R, D>> for Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>where T: SimdRealField, Const<D>: DimNameAdd<Const<1>>, R: SubsetOf<Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

fn from( iso: Isometry<T, R, D> ) -> Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>

Converts to this type from the input type.

impl<T, R, const D: usize> From<Similarity<T, R, D>> for Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>where T: SimdRealField, Const<D>: DimNameAdd<Const<1>>, R: SubsetOf<Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

fn from( sim: Similarity<T, R, D> ) -> Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>

Converts to this type from the input type.

impl<T, C, const D: usize> From<Transform<T, C, D>> for Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>where T: RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategory, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

fn from( t: Transform<T, C, D> ) -> Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>

Converts to this type from the input type.

impl<T, const D: usize> From<Translation<T, D>> for Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>where T: Scalar + Zero + One, Const<D>: DimNameAdd<Const<1>>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output> + Allocator<T, Const<D>, Const<1>>,

fn from( t: Translation<T, D> ) -> Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>

Converts to this type from the input type.

impl<T, R, C, S> Hash for Matrix<T, R, C, S>where T: Scalar + Hash, R: Dim, C: Dim, S: RawStorage<T, R, C>,

fn hash<H>(&self, state: &mut H)where H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T, R, C, S> Index<(usize, usize)> for Matrix<T, R, C, S>where R: Dim, C: Dim, S: RawStorage<T, R, C>,

type Output = T

The returned type after indexing.

fn index( &self, ij: (usize, usize) ) -> &<Matrix<T, R, C, S> as Index<(usize, usize)>>::Output

Performs the indexing (container[index]) operation.

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

type Output = T

The returned type after indexing.

fn index(&self, i: usize) -> &<Matrix<T, R, C, S> as Index<usize>>::Output

Performs the indexing (container[index]) operation.

impl<T, R, C, S> IndexMut<(usize, usize)> for Matrix<T, R, C, S>where R: Dim, C: Dim, S: RawStorageMut<T, R, C>,

fn index_mut(&mut self, ij: (usize, usize)) -> &mut T

Performs the mutable indexing (container[index]) operation.

impl<T, R, C, S> IndexMut<usize> for Matrix<T, R, C, S>where R: Dim, C: Dim, S: RawStorageMut<T, R, C>,

fn index_mut(&mut self, i: usize) -> &mut T

Performs the mutable indexing (container[index]) operation.

impl<T, R, C, S> LowerExp for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + LowerExp, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T, R, C, S> LowerHex for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + LowerHex, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<'b, T, R1, C1, R2, C2, SA, SB> Mul<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, SB: Storage<T, R2, C2>, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<T, R1, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,

type Output = Matrix<T, R1, C2, <DefaultAllocator as Allocator<T, R1, C2>>::Buffer>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Matrix<T, R2, C2, SB> ) -> <Matrix<T, R1, C1, SA> as Mul<&'b Matrix<T, R2, C2, SB>>>::Output

Performs the * operation.

impl<'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for Matrix<T, R1, C1, SA>where T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<T, R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the * operator.

fn mul( self, right: &'b Rotation<T, D2> ) -> <Matrix<T, R1, C1, SA> as Mul<&'b Rotation<T, D2>>>::Output

Performs the * operation.

impl<T, R1, C1, R2, C2, SA, SB> Mul<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, SB: Storage<T, R2, C2>, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<T, R1, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,

type Output = Matrix<T, R1, C2, <DefaultAllocator as Allocator<T, R1, C2>>::Buffer>

The resulting type after applying the * operator.

fn mul( self, rhs: Matrix<T, R2, C2, SB> ) -> <Matrix<T, R1, C1, SA> as Mul<Matrix<T, R2, C2, SB>>>::Output

Performs the * operation.

impl<T, R1, C1, SA, const D2: usize> Mul<Rotation<T, D2>> for Matrix<T, R1, C1, SA>where T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, R1: Dim, C1: Dim, SA: Storage<T, R1, C1>, DefaultAllocator: Allocator<T, R1, Const<D2>>, ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the * operator.

fn mul( self, right: Rotation<T, D2> ) -> <Matrix<T, R1, C1, SA> as Mul<Rotation<T, D2>>>::Output

Performs the * operation.

impl<T, R, C, S> Mul<T> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + ClosedMul<T>, S: Storage<T, R, C>, DefaultAllocator: Allocator<T, R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> <Matrix<T, R, C, S> as Mul<T>>::Output

Performs the * operation.

impl<'b, T, R1, C1, R2, SA, SB> MulAssign<&'b Matrix<T, R2, C1, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, SB: Storage<T, R2, C1>, SA: StorageMut<T, R1, C1> + IsContiguous + Clone, ShapeConstraint: AreMultipliable<R1, C1, R2, C1>, DefaultAllocator: Allocator<T, R1, C1, Buffer = SA>,

fn mul_assign(&mut self, rhs: &'b Matrix<T, R2, C1, SB>)

Performs the *= operation.

impl<T, R1, C1, R2, SA, SB> MulAssign<Matrix<T, R2, C1, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T>, SB: Storage<T, R2, C1>, SA: StorageMut<T, R1, C1> + IsContiguous + Clone, ShapeConstraint: AreMultipliable<R1, C1, R2, C1>, DefaultAllocator: Allocator<T, R1, C1, Buffer = SA>,

fn mul_assign(&mut self, rhs: Matrix<T, R2, C1, SB>)

Performs the *= operation.

impl<T, R, C, S> MulAssign<T> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + ClosedMul<T>, S: StorageMut<T, R, C>,

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T, R, C, S> Neg for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + ClosedNeg, S: Storage<T, R, C>, DefaultAllocator: Allocator<T, R, C>,

type Output = Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

The resulting type after applying the - operator.

fn neg(self) -> <Matrix<T, R, C, S> as Neg>::Output

Performs the unary - operation.

impl<T, R, C> Normed for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: SimdComplexField, R: Dim, C: Dim, DefaultAllocator: Allocator<T, R, C>,

type Norm = <T as SimdComplexField>::SimdRealField

The type of the norm.

fn norm(&self) -> <T as SimdComplexField>::SimdRealField

Computes the norm.

fn norm_squared(&self) -> <T as SimdComplexField>::SimdRealField

Computes the squared norm.

fn scale_mut( &mut self, n: <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as Normed>::Norm )

Multiply self by n.

fn unscale_mut( &mut self, n: <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as Normed>::Norm )

Divides self by n.

impl<T, R, C, S> Octal for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + Octal, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

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

fn one() -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> boolwhere Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

impl<T, R, R2, C, C2, S, S2> PartialEq<Matrix<T, R2, C2, S2>> for Matrix<T, R, C, S>where T: Scalar + PartialEq<T>, C: Dim, C2: Dim, R: Dim, R2: Dim, S: RawStorage<T, R, C>, S2: RawStorage<T, R2, C2>,

fn eq(&self, right: &Matrix<T, R2, C2, S2>) -> bool

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

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T, R, C, S> PartialOrd<Matrix<T, R, C, S>> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + PartialOrd<T>, S: RawStorage<T, R, C>,

fn partial_cmp(&self, other: &Matrix<T, R, C, S>) -> Option<Ordering>

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

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

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

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

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

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

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

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

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

impl<T, R, C, S> Pointer for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + Pointer, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<'a, T, D> Product<&'a Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>> for Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where D: DimName, T: Scalar + Zero + One + ClosedMul<T> + ClosedAdd<T>, DefaultAllocator: Allocator<T, D, D>,

fn product<I>( iter: I ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where I: Iterator<Item = &'a Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

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

fn product<I>( iter: I ) -> Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>where I: Iterator<Item = Matrix<T, D, D, <DefaultAllocator as Allocator<T, D, D>>::Buffer>>,

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<T, R, C, S> RelativeEq<Matrix<T, R, C, S>> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + RelativeEq<T>, S: Storage<T, R, C>, <T as AbsDiffEq<T>>::Epsilon: Clone,

fn default_max_relative( ) -> <Matrix<T, R, C, S> as AbsDiffEq<Matrix<T, R, C, S>>>::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Matrix<T, R, C, S>, epsilon: <Matrix<T, R, C, S> as AbsDiffEq<Matrix<T, R, C, S>>>::Epsilon, max_relative: <Matrix<T, R, C, S> as AbsDiffEq<Matrix<T, R, C, S>>>::Epsilon ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool

The inverse of [RelativeEq::relative_eq].

impl<T, R, C, S> Serialize for Matrix<T, R, C, S>where T: Scalar, R: Dim, C: Dim, S: Serialize,

fn serialize<Ser>( &self, serializer: Ser ) -> Result<<Ser as Serializer>::Ok, <Ser as Serializer>::Error>where Ser: Serializer,

Serialize this value into the given Serde serializer.

impl<T, R, C> SimdValue for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where T: Scalar + SimdValue, R: Dim, C: Dim, <T as SimdValue>::Element: Scalar, DefaultAllocator: Allocator<T, R, C> + Allocator<<T as SimdValue>::Element, R, C>,

type Element = Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>

The type of the elements of each lane of this SIMD value.

type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.

fn lanes() -> usize

The number of lanes of this SIMD value.

fn splat( val: <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as SimdValue>::Element ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Initializes an SIMD value with each lanes set to val.

fn extract( &self, i: usize ) -> <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as SimdValue>::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked( &self, i: usize ) -> <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as SimdValue>::Element

Extracts the i-th lane of self without bound-checking.

fn replace( &mut self, i: usize, val: <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as SimdValue>::Element )

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked( &mut self, i: usize, val: <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as SimdValue>::Element )

Replaces the i-th lane of self by val without bound-checking.

fn select( self, cond: <Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> as SimdValue>::SimdBool, other: Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer> ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Merges self and other depending on the lanes of cond.

fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere Self: Clone,

Applies a function to each lane of self.

fn zip_map_lanes( self, b: Self, f: impl Fn(Self::Element, Self::Element) -> Self::Element ) -> Selfwhere Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b.

impl<'b, T, R1, C1, R2, C2, SA, SB> Sub<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSub<T>, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>

The resulting type after applying the - operator.

fn sub( self, rhs: &'b Matrix<T, R2, C2, SB> ) -> <Matrix<T, R1, C1, SA> as Sub<&'b Matrix<T, R2, C2, SB>>>::Output

Performs the - operation.

impl<T, R1, C1, R2, C2, SA, SB> Sub<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSub<T>, SA: Storage<T, R1, C1>, SB: Storage<T, R2, C2>, DefaultAllocator: SameShapeAllocator<T, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

type Output = Matrix<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<T, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>

The resulting type after applying the - operator.

fn sub( self, rhs: Matrix<T, R2, C2, SB> ) -> <Matrix<T, R1, C1, SA> as Sub<Matrix<T, R2, C2, SB>>>::Output

Performs the - operation.

impl<'b, T, R1, C1, R2, C2, SA, SB> SubAssign<&'b Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSub<T>, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn sub_assign(&mut self, rhs: &'b Matrix<T, R2, C2, SB>)

Performs the -= operation.

impl<T, R1, C1, R2, C2, SA, SB> SubAssign<Matrix<T, R2, C2, SB>> for Matrix<T, R1, C1, SA>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T: Scalar + ClosedSub<T>, SA: StorageMut<T, R1, C1>, SB: Storage<T, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

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

Performs the -= operation.

impl<T1, T2, R1, C1, R2, C2> SubsetOf<Matrix<T2, R2, C2, <DefaultAllocator as Allocator<T2, R2, C2>>::Buffer>> for Matrix<T1, R1, C1, <DefaultAllocator as Allocator<T1, R1, C1>>::Buffer>where R1: Dim, C1: Dim, R2: Dim, C2: Dim, T1: Scalar, T2: Scalar + SupersetOf<T1>, DefaultAllocator: Allocator<T2, R2, C2> + Allocator<T1, R1, C1> + SameShapeAllocator<T1, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

fn to_superset( &self ) -> Matrix<T2, R2, C2, <DefaultAllocator as Allocator<T2, R2, C2>>::Buffer>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset( m: &Matrix<T2, R2, C2, <DefaultAllocator as Allocator<T2, R2, C2>>::Buffer> ) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked( m: &Matrix<T2, R2, C2, <DefaultAllocator as Allocator<T2, R2, C2>>::Buffer> ) -> Matrix<T1, R1, C1, <DefaultAllocator as Allocator<T1, R1, C1>>::Buffer>

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<'a, T, R, C> Sum<&'a Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where R: DimName, C: DimName, T: Scalar + ClosedAdd<T> + Zero, DefaultAllocator: Allocator<T, R, C>,

fn sum<I>( iter: I ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where I: Iterator<Item = &'a Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<T, R, C> Sum<Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>> for Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where R: DimName, C: DimName, T: Scalar + ClosedAdd<T> + Zero, DefaultAllocator: Allocator<T, R, C>,

fn sum<I>( iter: I ) -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>where I: Iterator<Item = Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>>,

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<T, R, C, S> UlpsEq<Matrix<T, R, C, S>> for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + UlpsEq<T>, S: RawStorage<T, R, C>, <T as AbsDiffEq<T>>::Epsilon: Clone,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq( &self, other: &Matrix<T, R, C, S>, epsilon: <Matrix<T, R, C, S> as AbsDiffEq<Matrix<T, R, C, S>>>::Epsilon, max_ulps: u32 ) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of [UlpsEq::ulps_eq].

impl<T, R, C, S> UpperExp for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + UpperExp, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<T, R, C, S> UpperHex for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + UpperHex, S: RawStorage<T, R, C>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

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

fn zero() -> Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<T, R, C, S> Copy for Matrix<T, R, C, S>where T: Copy, R: Copy, C: Copy, S: Copy,

impl<T, R, C, S> Eq for Matrix<T, R, C, S>where R: Dim, C: Dim, T: Scalar + Eq, S: RawStorage<T, R, C>,