Struct Skew3

pub struct Skew3(pub Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>);

Contains a member of the lie algebra so(3), a representation of the tangent space of 3d rotation. This is also known as the lie algebra of the 3d rotation group SO(3).

This is only intended to be used in optimization problems where it is desirable to have unconstranied variables representing the degrees of freedom of the rotation. In all other cases, a rotation matrix should be used to store rotations, since the conversion to and from a rotation matrix is non-trivial.

Tuple Fields

0: Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>

Implementations

impl Skew3

pub fn rotation(self) -> Rotation<f64, U3>

Converts the Skew3 to a Rotation3 matrix.

pub fn vee( mat: Matrix<f64, U3, U3, <DefaultAllocator as Allocator<f64, U3, U3>>::Buffer>, ) -> Skew3

This converts a matrix in skew-symmetric form into a Skew3.

Warning: Does no check to ensure matrix is actually skew-symmetric.

pub fn hat( self, ) -> Matrix<f64, U3, U3, <DefaultAllocator as Allocator<f64, U3, U3>>::Buffer>

This converts the Skew3 into its skew-symmetric matrix form.

pub fn hat2( self, ) -> Matrix<f64, U3, U3, <DefaultAllocator as Allocator<f64, U3, U3>>::Buffer>

This converts the Skew3 into its squared skew-symmetric matrix form efficiently.

pub fn bracket(self, rhs: Skew3) -> Skew3

Computes the lie bracket [self, rhs].

pub fn jacobian_input( self, ) -> Matrix<f64, U4, U4, <DefaultAllocator as Allocator<f64, U4, U4>>::Buffer>

The jacobian of the output of a rotation in respect to the input of a rotation.

y = R * x

dy/dx = R

The formula is pretty simple and is just the rotation matrix created from the exponential map of this so(3) element into SO(3). The result is converted to homogeneous form (by adding a new dimension with a 1 in the diagonal) so that it is compatible with homogeneous coordinates.

If you have the rotation matrix already, please use the rotation matrix itself rather than calling this method. Calling this method will waste time converting the Skew3 back into a Rotation3, which is non-trivial.

pub fn jacobian_self( y: Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>, ) -> Matrix<f64, U3, U3, <DefaultAllocator as Allocator<f64, U3, U3>>::Buffer>

The jacobian of the output of a rotation in respect to the rotation itself.

y = R * x

dy/dR = -hat(y)

The derivative is purely based on the current output vector, and thus doesn’t take self.

Note that when working with homogeneous projective coordinates, only the first three components (the bearing) are relevant, hence the resulting matrix is a Matrix3.

Methods from Deref<Target = Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>>

pub fn icamax(&self) -> usize

Computes the index of the vector component with the largest complex or real absolute value.

Examples:

let vec = Vector3::new(Complex::new(11.0, 3.0), Complex::new(-15.0, 0.0), Complex::new(13.0, 5.0));
assert_eq!(vec.icamax(), 2);

pub fn argmax(&self) -> (usize, N)

Computes the index and value of the vector component with the largest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.argmax(), (2, 13));

pub fn imax(&self) -> usize

Computes the index of the vector component with the largest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.imax(), 2);

pub fn iamax(&self) -> usize

where N: Signed,

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

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.iamax(), 1);

pub fn argmin(&self) -> (usize, N)

Computes the index and value of the vector component with the smallest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.argmin(), (1, -15));

pub fn imin(&self) -> usize

Computes the index of the vector component with the smallest value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.imin(), 1);

pub fn iamin(&self) -> usize

where N: Signed,

Computes the index of the vector component with the smallest absolute value.

Examples:

let vec = Vector3::new(11, -15, 13);
assert_eq!(vec.iamin(), 0);

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

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

Examples:

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

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));

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

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

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

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

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

Examples:

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

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

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

where R2: Dim, C2: Dim, N: SimdComplexField, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

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

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

Examples:

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

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

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

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>,

The dot product between the transpose of self and rhs.

Examples:

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

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

pub fn axcpy<D2, SB>(&mut self, a: N, x: &Matrix<N, D2, U1, SB>, c: N, b: N)

where D2: Dim, SB: Storage<N, D2>, ShapeConstraint: DimEq<D, D2>,

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

If b is zero, self is never read from.

Examples:

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

pub fn axpy<D2, SB>(&mut self, a: N, x: &Matrix<N, D2, U1, SB>, b: N)

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

Computes self = a * x + b * self.

If b is zero, self is never read from.

Examples:

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

pub fn gemv<R2, C2, D3, SB, SC>( &mut self, alpha: N, a: &Matrix<N, R2, C2, SB>, x: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

If beta is zero, self is never read.

Examples:

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

pub fn gemv_symm<D2, D3, SB, SC>( &mut self, alpha: N, a: &Matrix<N, D2, D2, SB>, x: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

Computes self = alpha * a * x + beta * self, where a is a symmetric matrix, x a vector, and alpha, beta two scalars. DEPRECATED: use sygemv instead.

pub fn sygemv<D2, D3, SB, SC>( &mut self, alpha: N, a: &Matrix<N, D2, D2, SB>, x: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

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

Examples:

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


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

pub fn hegemv<D2, D3, SB, SC>( &mut self, alpha: N, a: &Matrix<N, D2, D2, SB>, x: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

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

Examples:

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


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

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

pub fn gemv_tr<R2, C2, D3, SB, SC>( &mut self, alpha: N, a: &Matrix<N, R2, C2, SB>, x: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

If beta is zero, self is never read.

Examples:

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

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

pub fn gemv_ad<R2, C2, D3, SB, SC>( &mut self, alpha: N, a: &Matrix<N, R2, C2, SB>, x: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

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

Examples:

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

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

pub fn ger<D2, D3, SB, SC>( &mut self, alpha: N, x: &Matrix<N, D2, U1, SB>, y: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

If beta is zero, self is never read.

Examples:

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

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

pub fn gerc<D2, D3, SB, SC>( &mut self, alpha: N, x: &Matrix<N, D2, U1, SB>, y: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

If beta is zero, self is never read.

Examples:

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

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

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

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

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

If beta is zero, self is never read.

Examples:

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

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

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

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

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

If beta is zero, self is never read.

Examples:

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

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

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

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

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

If beta is zero, self is never read.

Examples:

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

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

pub fn ger_symm<D2, D3, SB, SC>( &mut self, alpha: N, x: &Matrix<N, D2, U1, SB>, y: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

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

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

Examples:

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

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

pub fn syger<D2, D3, SB, SC>( &mut self, alpha: N, x: &Matrix<N, D2, U1, SB>, y: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

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

Examples:

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

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

pub fn hegerc<D2, D3, SB, SC>( &mut self, alpha: N, x: &Matrix<N, D2, U1, SB>, y: &Matrix<N, D3, U1, SC>, beta: N, )

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

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

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

Examples:

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

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

pub fn quadform_tr_with_workspace<D2, S2, R3, C3, S3, D4, S4>( &mut self, work: &mut Matrix<N, D2, U1, S2>, alpha: N, lhs: &Matrix<N, R3, C3, S3>, mid: &Matrix<N, D4, D4, S4>, beta: N, )

where D2: Dim, R3: Dim, C3: Dim, D4: Dim, S2: StorageMut<N, D2>, S3: Storage<N, R3, C3>, S4: Storage<N, 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: N, lhs: &Matrix<N, R3, C3, S3>, mid: &Matrix<N, D4, D4, S4>, beta: N, )

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

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

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

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<N, D2, U1, S2>, alpha: N, mid: &Matrix<N, D3, D3, S3>, rhs: &Matrix<N, R4, C4, S4>, beta: N, )

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

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

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

// 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: N, mid: &Matrix<N, D2, D2, S2>, rhs: &Matrix<N, R3, C3, S3>, beta: N, )

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

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

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

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);

pub fn neg_mut(&mut self)

Negates self in-place.

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

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

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

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

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

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

pub fn tr_mul<R2, C2, SB>( &self, rhs: &Matrix<N, R2, C2, SB>, ) -> Matrix<N, C1, C2, <DefaultAllocator as Allocator<N, C1, C2>>::Buffer>

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

Equivalent to self.transpose() * rhs.

pub fn ad_mul<R2, C2, SB>( &self, rhs: &Matrix<N, R2, C2, SB>, ) -> Matrix<N, C1, C2, <DefaultAllocator as Allocator<N, C1, C2>>::Buffer>

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

Equivalent to self.adjoint() * rhs.

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

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

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

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

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

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

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

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

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

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

where R2: Dim, C2: Dim, N: ClosedMul, R1: DimMul<R2>, C1: DimMul<C2>, SB: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, <R1 as DimMul<R2>>::Output, <C1 as DimMul<C2>>::Output>,

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

pub fn add_scalar( &self, rhs: N, ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

where DefaultAllocator: Allocator<N, R, C>,

Adds a scalar to self.

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

where S: StorageMut<N, R, C>,

Adds a scalar to self in-place.

pub fn amax(&self) -> N

where N: 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) -> <N as SimdComplexField>::SimdRealField

where N: 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) -> N

where N: 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) -> N

where N: 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) -> <N as SimdComplexField>::SimdRealField

where N: 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) -> N

where N: 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 append_scaling( &self, scaling: N, ) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

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

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

pub fn prepend_scaling( &self, scaling: N, ) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

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

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

pub fn append_nonuniform_scaling<SB>( &self, scaling: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, SB>, ) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>, DefaultAllocator: Allocator<N, D, D>,

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

pub fn prepend_nonuniform_scaling<SB>( &self, scaling: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, SB>, ) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>, DefaultAllocator: Allocator<N, D, D>,

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

pub fn append_translation<SB>( &self, shift: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, SB>, ) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>, DefaultAllocator: Allocator<N, D, D>,

Computes the transformation equal to self followed by a translation.

pub fn prepend_translation<SB>( &self, shift: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, SB>, ) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>, DefaultAllocator: Allocator<N, D, D> + Allocator<N, <D as DimNameSub<U1>>::Output>,

Computes the transformation equal to a translation followed by self.

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

where D: DimNameSub<U1>,

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

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

where D: DimNameSub<U1>,

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

pub fn append_nonuniform_scaling_mut<SB>( &mut self, scaling: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, SB>, )

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>,

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<N, <D as DimNameSub<U1>>::Output, U1, SB>, )

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>,

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<N, <D as DimNameSub<U1>>::Output, U1, SB>, )

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>,

Computes the transformation equal to self followed by a translation.

pub fn prepend_translation_mut<SB>( &mut self, shift: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, SB>, )

where D: DimNameSub<U1>, SB: Storage<N, <D as DimNameSub<U1>>::Output>, DefaultAllocator: Allocator<N, <D as DimNameSub<U1>>::Output>,

Computes the transformation equal to a translation followed by self.

pub fn transform_vector( &self, v: &Matrix<N, <D as DimNameSub<U1>>::Output, U1, <DefaultAllocator as Allocator<N, <D as DimNameSub<U1>>::Output>>::Buffer>, ) -> Matrix<N, <D as DimNameSub<U1>>::Output, U1, <DefaultAllocator as Allocator<N, <D as DimNameSub<U1>>::Output>>::Buffer>

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

pub fn transform_point( &self, pt: &Point<N, <D as DimNameSub<U1>>::Output>, ) -> Point<N, <D as DimNameSub<U1>>::Output>

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

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

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

Computes the component-wise absolute value.

Example

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

pub fn component_mul<R2, C2, SB>( &self, rhs: &Matrix<N, R2, C2, SB>, ) -> Matrix<N, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>

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

Componentwise matrix or vector multiplication.

Example

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

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

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

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

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

Example

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

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

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

where N: ClosedMul, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Inplace componentwise matrix or vector multiplication.

Example

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

a.component_mul_assign(&b);

assert_eq!(a, expected);

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

where N: ClosedMul, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

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

Inplace componentwise matrix or vector multiplication.

Example

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

a.component_mul_assign(&b);

assert_eq!(a, expected);

pub fn component_div<R2, C2, SB>( &self, rhs: &Matrix<N, R2, C2, SB>, ) -> Matrix<N, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<R1, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C1, C2>>::Representative>>::Buffer>

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

Componentwise matrix or vector division.

Example

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

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

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

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

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

Example

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

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

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

where N: ClosedDiv, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

Inplace componentwise matrix or vector division.

Example

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

a.component_div_assign(&b);

assert_eq!(a, expected);

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

where N: ClosedDiv, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,

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

Inplace componentwise matrix or vector division.

Example

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

a.component_div_assign(&b);

assert_eq!(a, expected);

pub fn inf( &self, other: &Matrix<N, R, C, S>, ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

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

pub fn sup( &self, other: &Matrix<N, R, C, S>, ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

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

pub fn inf_sup( &self, other: &Matrix<N, R, C, S>, ) -> (Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>, Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>)

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

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

where DefaultAllocator: Allocator<N, R, C>,

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

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

where DefaultAllocator: Allocator<N, R, C>,

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

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

Sets all the elements of this matrix to val.

pub fn fill_with_identity(&mut self)

where N: Zero + One,

Fills self with the identity matrix.

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

Sets all the diagonal elements of this matrix to val.

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

Sets all the elements of the selected row to val.

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

Sets all the elements of the selected column to val.

pub fn set_diagonal<R2, S2>(&mut self, diag: &Matrix<N, R2, U1, S2>)

where R2: Dim, R: DimMin<C>, S2: Storage<N, R2>, 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 = N>)

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

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

pub fn set_row<C2, S2>(&mut self, i: usize, row: &Matrix<N, U1, C2, S2>)

where C2: Dim, S2: Storage<N, U1, C2>, ShapeConstraint: SameNumberOfColumns<C, C2>,

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

pub fn set_column<R2, S2>(&mut self, i: usize, column: &Matrix<N, R2, U1, S2>)

where R2: Dim, S2: Storage<N, R2>, ShapeConstraint: SameNumberOfRows<R, R2>,

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

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

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

The parameter shift allows some subdiagonals to be left untouched:

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

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

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

The parameter shift allows some superdiagonals to be left untouched:

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

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

Swaps two rows in-place.

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

Swaps two columns in-place.

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.

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

where I: MatrixIndex<'a, N, R, C, S>,

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

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

where S: StorageMut<N, R, C>, I: MatrixIndexMut<'a, N, R, C, S>,

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

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

where I: MatrixIndex<'a, N, R, C, S>,

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

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

where S: StorageMut<N, R, C>, I: MatrixIndexMut<'a, N, R, C, S>,

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

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

where I: MatrixIndex<'a, N, R, C, S>,

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

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

where S: StorageMut<N, R, C>, I: MatrixIndexMut<'a, N, R, C, S>,

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

pub fn len(&self) -> usize

The total number of elements of this matrix.

Examples:

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

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

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

Examples:

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

pub fn nrows(&self) -> usize

The number of rows of this matrix.

Examples:

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

pub fn ncols(&self) -> usize

The number of columns of this matrix.

Examples:

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

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

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

Examples:

let mat = DMatrix::<f32>::zeros(10, 10);
let slice = mat.slice_with_steps((0, 0), (5, 3), (1, 2));
// The column strides is the number of steps (here 2) multiplied by the corresponding dimension.
assert_eq!(mat.strides(), (1, 10));

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

Iterates through this matrix coordinates in column-major order.

Examples:

let mat = Matrix2x3::new(11, 12, 13,
                         21, 22, 23);
let mut it = mat.iter();
assert_eq!(*it.next().unwrap(), 11);
assert_eq!(*it.next().unwrap(), 21);
assert_eq!(*it.next().unwrap(), 12);
assert_eq!(*it.next().unwrap(), 22);
assert_eq!(*it.next().unwrap(), 13);
assert_eq!(*it.next().unwrap(), 23);
assert!(it.next().is_none());

pub fn row_iter(&self) -> RowIter<'_, N, R, C, S>

Iterate through the rows of this matrix.

Example

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

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

Iterate through the columns of this matrix.

Example

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

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

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

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 N

Returns a pointer to the start of the matrix.

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

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<N, R2, C2, SB>, eps: <N as AbsDiffEq>::Epsilon, max_relative: <N as AbsDiffEq>::Epsilon, ) -> bool

where N: RelativeEq, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, <N as AbsDiffEq>::Epsilon: Copy, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

See relative_eq from the RelativeEq trait for more details.

pub fn eq<R2, C2, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> bool

where N: PartialEq, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

Tests whether self and rhs are exactly equal.

pub fn clone_owned( &self, ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>

where DefaultAllocator: Allocator<N, R, C>,

Clones this matrix to one that owns its data.

pub fn clone_owned_sum<R2, C2>( &self, ) -> Matrix<N, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative>>::Buffer>

where R2: Dim, C2: Dim, DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

pub fn map<N2, F>( &self, f: F, ) -> Matrix<N2, R, C, <DefaultAllocator as Allocator<N2, R, C>>::Buffer>

where N2: Scalar, F: FnMut(N) -> N2, DefaultAllocator: Allocator<N2, R, C>,

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

pub fn fold_with<N2>( &self, init_f: impl FnOnce(Option<&N>) -> N2, f: impl FnMut(N2, &N) -> N2, ) -> N2

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<N2, F>( &self, f: F, ) -> Matrix<N2, R, C, <DefaultAllocator as Allocator<N2, R, C>>::Buffer>

where N2: Scalar, F: FnMut(usize, usize, N) -> N2, DefaultAllocator: Allocator<N2, R, C>,

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

pub fn zip_map<N2, N3, S2, F>( &self, rhs: &Matrix<N2, R, C, S2>, f: F, ) -> Matrix<N3, R, C, <DefaultAllocator as Allocator<N3, R, C>>::Buffer>

where N2: Scalar, N3: Scalar, S2: Storage<N2, R, C>, F: FnMut(N, N2) -> N3, DefaultAllocator: Allocator<N3, R, C>,

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

pub fn zip_zip_map<N2, N3, N4, S2, S3, F>( &self, b: &Matrix<N2, R, C, S2>, c: &Matrix<N3, R, C, S3>, f: F, ) -> Matrix<N4, R, C, <DefaultAllocator as Allocator<N4, R, C>>::Buffer>

where N2: Scalar, N3: Scalar, N4: Scalar, S2: Storage<N2, R, C>, S3: Storage<N3, R, C>, F: FnMut(N, N2, N3) -> N4, DefaultAllocator: Allocator<N4, R, C>,

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

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

Folds a function f on each entry of self.

pub fn zip_fold<N2, R2, C2, S2, Acc>( &self, rhs: &Matrix<N2, R2, C2, S2>, init: Acc, f: impl FnMut(Acc, N, N2) -> Acc, ) -> Acc

where N2: Scalar, R2: Dim, C2: Dim, S2: Storage<N2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

pub fn transpose_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>)

where R2: Dim, C2: Dim, SB: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,

Transposes self and store the result into out.

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

where DefaultAllocator: Allocator<N, C, R>,

Transposes self.

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

Mutably iterates through this matrix coordinates.

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

Returns a mutable pointer to the start of the matrix.

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

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

Mutably iterates through this matrix rows.

Example

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

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

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

Mutably iterates through this matrix columns.

Example

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

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

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

Swaps two entries without bound-checking.

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

Swaps two entries.

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

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

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

pub fn copy_from<R2, C2, SB>(&mut self, other: &Matrix<N, R2, C2, SB>)

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

pub fn tr_copy_from<R2, C2, SB>(&mut self, other: &Matrix<N, R2, C2, SB>)

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, C2> + SameNumberOfColumns<C, R2>,

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

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

where F: FnMut(N) -> N,

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

pub fn zip_apply<N2, R2, C2, S2>( &mut self, rhs: &Matrix<N2, R2, C2, S2>, f: impl FnMut(N, N2) -> N, )

where N2: Scalar, R2: Dim, C2: Dim, S2: Storage<N2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

pub fn zip_zip_apply<N2, R2, C2, S2, N3, R3, C3, S3>( &mut self, b: &Matrix<N2, R2, C2, S2>, c: &Matrix<N3, R3, C3, S3>, f: impl FnMut(N, N2, N3) -> N, )

where N2: Scalar, R2: Dim, C2: Dim, S2: Storage<N2, R2, C2>, N3: Scalar, R3: Dim, C3: Dim, S3: Storage<N3, R3, C3>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

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

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

pub unsafe fn vget_unchecked_mut(&mut self, i: usize) -> &mut N

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

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

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

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

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

pub fn transpose_mut(&mut self)

Transposes the square matrix self in-place.

pub fn adjoint_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>)

where R2: Dim, C2: Dim, SB: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,

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

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

where DefaultAllocator: Allocator<N, C, R>,

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

pub fn conjugate_transpose_to<R2, C2, SB>( &self, out: &mut Matrix<N, R2, C2, SB>, )

where R2: Dim, C2: Dim, SB: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2> + SameNumberOfColumns<C, R2>,

👎Deprecated: Renamed self.adjoint_to(out).

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

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

where DefaultAllocator: Allocator<N, C, R>,

👎Deprecated: Renamed self.adjoint().

The conjugate transposition of self.

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

where DefaultAllocator: Allocator<N, R, C>,

The conjugate of self.

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

where DefaultAllocator: Allocator<N, R, C>,

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

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

where DefaultAllocator: Allocator<N, R, C>,

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

pub fn conjugate_mut(&mut self)

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

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

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

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

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

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).

pub fn diagonal( &self, ) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer>

where DefaultAllocator: Allocator<N, D>,

The diagonal of this matrix.

pub fn map_diagonal<N2>( &self, f: impl FnMut(N) -> N2, ) -> Matrix<N2, D, U1, <DefaultAllocator as Allocator<N2, D>>::Buffer>

where N2: Scalar, DefaultAllocator: Allocator<N2, D>,

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

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

pub fn trace(&self) -> N

where N: Scalar + Zero + ClosedAdd,

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

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

where DefaultAllocator: Allocator<N, D, D>,

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

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

where DefaultAllocator: Allocator<N, D, D>,

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

pub fn to_homogeneous( &self, ) -> Matrix<N, <D as DimAdd<U1>>::Output, <D as DimAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimAdd<U1>>::Output, <D as DimAdd<U1>>::Output>>::Buffer>

where DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output, <D as DimAdd<U1>>::Output>,

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

pub fn to_homogeneous( &self, ) -> Matrix<N, <D as DimAdd<U1>>::Output, U1, <DefaultAllocator as Allocator<N, <D as DimAdd<U1>>::Output>>::Buffer>

where DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output>,

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

pub fn push( &self, element: N, ) -> Matrix<N, <D as DimAdd<U1>>::Output, U1, <DefaultAllocator as Allocator<N, <D as DimAdd<U1>>::Output>>::Buffer>

where DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output>,

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

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

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, U2> + SameNumberOfColumns<C, U1> + SameNumberOfRows<R2, U2> + SameNumberOfColumns<C2, U1>,

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

pub fn cross<R2, C2, SB>( &self, b: &Matrix<N, R2, C2, SB>, ) -> Matrix<N, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<R, R2>>::Representative, <ShapeConstraint as SameNumberOfColumns<C, C2>>::Representative>>::Buffer>

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

The 3D cross product between two vectors.

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

pub fn cross_matrix( &self, ) -> Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>

Computes the matrix M such that for all vector v we have M * v == self.cross(&v).

pub fn angle<R2, C2, SB>( &self, other: &Matrix<N, R2, C2, SB>, ) -> <N as SimdComplexField>::SimdRealField

where R2: Dim, C2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,

The smallest angle between two vectors.

pub fn lerp<S2>( &self, rhs: &Matrix<N, D, U1, S2>, t: N, ) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer>

where S2: Storage<N, D>, DefaultAllocator: Allocator<N, D>,

Returns self * (1.0 - t) + rhs * t, i.e., the linear blend of the vectors x and y using the scalar value a.

The value for a is not restricted to the range [0, 1].

Examples:

let x = Vector3::new(1.0, 2.0, 3.0);
let y = Vector3::new(10.0, 20.0, 30.0);
assert_eq!(x.lerp(&y, 0.1), Vector3::new(1.9, 3.8, 5.7));

pub fn row( &self, i: usize, ) -> Matrix<N, U1, C, SliceStorage<'_, N, U1, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

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

pub fn row_part( &self, i: usize, n: usize, ) -> Matrix<N, U1, Dynamic, SliceStorage<'_, N, U1, Dynamic, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, C, SliceStorage<'_, N, Dynamic, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, C, SliceStorage<'_, N, Dynamic, C, Dynamic, <S as Storage<N, R, C>>::CStride>>

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

pub fn fixed_rows<RSlice>( &self, first_row: usize, ) -> Matrix<N, RSlice, C, SliceStorage<'_, N, RSlice, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where RSlice: DimName,

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

pub fn fixed_rows_with_step<RSlice>( &self, first_row: usize, step: usize, ) -> Matrix<N, RSlice, C, SliceStorage<'_, N, RSlice, C, Dynamic, <S as Storage<N, R, C>>::CStride>>

where RSlice: DimName,

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<N, RSlice, C, SliceStorage<'_, N, RSlice, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, RSlice, C, SliceStorage<'_, N, RSlice, C, Dynamic, <S as Storage<N, 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<N, R, U1, SliceStorage<'_, N, R, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

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

pub fn column_part( &self, i: usize, n: usize, ) -> Matrix<N, Dynamic, U1, SliceStorage<'_, N, Dynamic, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, Dynamic, SliceStorage<'_, N, R, Dynamic, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, Dynamic, SliceStorage<'_, N, R, Dynamic, <S as Storage<N, R, C>>::RStride, Dynamic>>

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

pub fn fixed_columns<CSlice>( &self, first_col: usize, ) -> Matrix<N, R, CSlice, SliceStorage<'_, N, R, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where CSlice: DimName,

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

pub fn fixed_columns_with_step<CSlice>( &self, first_col: usize, step: usize, ) -> Matrix<N, R, CSlice, SliceStorage<'_, N, R, CSlice, <S as Storage<N, R, C>>::RStride, Dynamic>>

where CSlice: DimName,

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<N, R, CSlice, SliceStorage<'_, N, R, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, CSlice, SliceStorage<'_, N, R, CSlice, <S as Storage<N, 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<N, Dynamic, Dynamic, SliceStorage<'_, N, Dynamic, Dynamic, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, Dynamic, SliceStorage<'_, N, Dynamic, Dynamic, Dynamic, Dynamic>>

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

pub fn fixed_slice<RSlice, CSlice>( &self, irow: usize, icol: usize, ) -> Matrix<N, RSlice, CSlice, SliceStorage<'_, N, RSlice, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where RSlice: DimName, CSlice: DimName,

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

pub fn fixed_slice_with_steps<RSlice, CSlice>( &self, start: (usize, usize), steps: (usize, usize), ) -> Matrix<N, RSlice, CSlice, SliceStorage<'_, N, RSlice, CSlice, Dynamic, Dynamic>>

where RSlice: DimName, CSlice: DimName,

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

pub fn generic_slice<RSlice, CSlice>( &self, start: (usize, usize), shape: (RSlice, CSlice), ) -> Matrix<N, RSlice, CSlice, SliceStorage<'_, N, RSlice, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, RSlice, CSlice, SliceStorage<'_, N, RSlice, CSlice, Dynamic, Dynamic>>

where RSlice: Dim, CSlice: Dim,

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

pub fn rows_range_pair<Range1, Range2>( &self, r1: Range1, r2: Range2, ) -> (Matrix<N, <Range1 as SliceRange<R>>::Size, C, SliceStorage<'_, N, <Range1 as SliceRange<R>>::Size, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>, Matrix<N, <Range2 as SliceRange<R>>::Size, C, SliceStorage<'_, N, <Range2 as SliceRange<R>>::Size, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, <Range1 as SliceRange<C>>::Size, SliceStorage<'_, N, R, <Range1 as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>, Matrix<N, R, <Range2 as SliceRange<C>>::Size, SliceStorage<'_, N, R, <Range2 as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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.

pub fn row_mut( &mut self, i: usize, ) -> Matrix<N, U1, C, SliceStorageMut<'_, N, U1, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, U1, Dynamic, SliceStorageMut<'_, N, U1, Dynamic, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, C, SliceStorageMut<'_, N, Dynamic, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, C, SliceStorageMut<'_, N, Dynamic, C, Dynamic, <S as Storage<N, R, C>>::CStride>>

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

pub fn fixed_rows_mut<RSlice>( &mut self, first_row: usize, ) -> Matrix<N, RSlice, C, SliceStorageMut<'_, N, RSlice, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where RSlice: DimName,

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

pub fn fixed_rows_with_step_mut<RSlice>( &mut self, first_row: usize, step: usize, ) -> Matrix<N, RSlice, C, SliceStorageMut<'_, N, RSlice, C, Dynamic, <S as Storage<N, R, C>>::CStride>>

where RSlice: DimName,

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<N, RSlice, C, SliceStorageMut<'_, N, RSlice, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, RSlice, C, SliceStorageMut<'_, N, RSlice, C, Dynamic, <S as Storage<N, 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<N, R, U1, SliceStorageMut<'_, N, R, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, U1, SliceStorageMut<'_, N, Dynamic, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, Dynamic, SliceStorageMut<'_, N, R, Dynamic, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, Dynamic, SliceStorageMut<'_, N, R, Dynamic, <S as Storage<N, R, C>>::RStride, Dynamic>>

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

pub fn fixed_columns_mut<CSlice>( &mut self, first_col: usize, ) -> Matrix<N, R, CSlice, SliceStorageMut<'_, N, R, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where CSlice: DimName,

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

pub fn fixed_columns_with_step_mut<CSlice>( &mut self, first_col: usize, step: usize, ) -> Matrix<N, R, CSlice, SliceStorageMut<'_, N, R, CSlice, <S as Storage<N, R, C>>::RStride, Dynamic>>

where CSlice: DimName,

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<N, R, CSlice, SliceStorageMut<'_, N, R, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, CSlice, SliceStorageMut<'_, N, R, CSlice, <S as Storage<N, 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<N, Dynamic, Dynamic, SliceStorageMut<'_, N, Dynamic, Dynamic, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, Dynamic, Dynamic, SliceStorageMut<'_, N, Dynamic, Dynamic, Dynamic, Dynamic>>

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

pub fn fixed_slice_mut<RSlice, CSlice>( &mut self, irow: usize, icol: usize, ) -> Matrix<N, RSlice, CSlice, SliceStorageMut<'_, N, RSlice, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where RSlice: DimName, CSlice: DimName,

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

pub fn fixed_slice_with_steps_mut<RSlice, CSlice>( &mut self, start: (usize, usize), steps: (usize, usize), ) -> Matrix<N, RSlice, CSlice, SliceStorageMut<'_, N, RSlice, CSlice, Dynamic, Dynamic>>

where RSlice: DimName, CSlice: DimName,

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

pub fn generic_slice_mut<RSlice, CSlice>( &mut self, start: (usize, usize), shape: (RSlice, CSlice), ) -> Matrix<N, RSlice, CSlice, SliceStorageMut<'_, N, RSlice, CSlice, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, RSlice, CSlice, SliceStorageMut<'_, N, RSlice, CSlice, Dynamic, Dynamic>>

where RSlice: Dim, CSlice: Dim,

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

pub fn rows_range_pair_mut<Range1, Range2>( &mut self, r1: Range1, r2: Range2, ) -> (Matrix<N, <Range1 as SliceRange<R>>::Size, C, SliceStorageMut<'_, N, <Range1 as SliceRange<R>>::Size, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>, Matrix<N, <Range2 as SliceRange<R>>::Size, C, SliceStorageMut<'_, N, <Range2 as SliceRange<R>>::Size, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, <Range1 as SliceRange<C>>::Size, SliceStorageMut<'_, N, R, <Range1 as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>, Matrix<N, R, <Range2 as SliceRange<C>>::Size, SliceStorageMut<'_, N, R, <Range2 as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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.

pub fn slice_range<RowRange, ColRange>( &self, rows: RowRange, cols: ColRange, ) -> Matrix<N, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, SliceStorage<'_, N, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, <RowRange as SliceRange<R>>::Size, C, SliceStorage<'_, N, <RowRange as SliceRange<R>>::Size, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, <ColRange as SliceRange<C>>::Size, SliceStorage<'_, N, R, <ColRange as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where ColRange: SliceRange<C>,

Slice containing all the columns indexed by the range rows.

pub fn slice_range_mut<RowRange, ColRange>( &mut self, rows: RowRange, cols: ColRange, ) -> Matrix<N, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, SliceStorageMut<'_, N, <RowRange as SliceRange<R>>::Size, <ColRange as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, <RowRange as SliceRange<R>>::Size, C, SliceStorageMut<'_, N, <RowRange as SliceRange<R>>::Size, C, <S as Storage<N, R, C>>::RStride, <S as Storage<N, 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<N, R, <ColRange as SliceRange<C>>::Size, SliceStorageMut<'_, N, R, <ColRange as SliceRange<C>>::Size, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>

where ColRange: SliceRange<C>,

Slice containing all the columns indexed by the range cols.

pub fn norm_squared(&self) -> <N as SimdComplexField>::SimdRealField

The squared L2 norm of this vector.

pub fn norm(&self) -> <N as SimdComplexField>::SimdRealField

The L2 norm of this matrix.

Use .apply_norm to apply a custom norm.

pub fn metric_distance<R2, C2, S2>( &self, rhs: &Matrix<N, R2, C2, S2>, ) -> <N as SimdComplexField>::SimdRealField

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

Use .apply_metric_distance to apply a custom norm.

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

Uses the given norm to compute the norm of self.

Example

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

pub fn apply_metric_distance<R2, C2, S2>( &self, rhs: &Matrix<N, R2, C2, S2>, norm: &impl Norm<N>, ) -> <N as SimdComplexField>::SimdRealField

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,

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

Example

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

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

pub fn magnitude(&self) -> <N as SimdComplexField>::SimdRealField

A synonym for the norm of this matrix.

Aka the length.

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

pub fn magnitude_squared(&self) -> <N as SimdComplexField>::SimdRealField

A synonym for the squared norm of this matrix.

Aka the squared length.

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

pub fn set_magnitude( &mut self, magnitude: <N as SimdComplexField>::SimdRealField, )

where S: StorageMut<N, R, C>,

Sets the magnitude of this vector.

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

where DefaultAllocator: Allocator<N, R, C>,

Returns a normalized version of this matrix.

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

The Lp norm of this matrix.

pub fn simd_try_normalize( &self, min_norm: <N as SimdComplexField>::SimdRealField, ) -> SimdOption<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

where <N as SimdValue>::Element: Scalar, DefaultAllocator: Allocator<N, R, C> + Allocator<<N 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: <N as ComplexField>::RealField, min_magnitude: <N as ComplexField>::RealField, )

where S: StorageMut<N, 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 try_normalize( &self, min_norm: <N as ComplexField>::RealField, ) -> Option<Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>>

where DefaultAllocator: Allocator<N, 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.

pub fn normalize_mut(&mut self) -> <N as SimdComplexField>::SimdRealField

Normalizes this matrix in-place and returns its norm.

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

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

where <N as SimdValue>::Element: Scalar, DefaultAllocator: Allocator<N, R, C> + Allocator<<N 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: <N as ComplexField>::RealField, ) -> Option<<N as ComplexField>::RealField>

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

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

pub fn is_empty(&self) -> bool

Indicates if this is an empty matrix.

pub fn is_square(&self) -> bool

Indicates if this is a square matrix.

pub fn is_identity(&self, eps: <N as AbsDiffEq>::Epsilon) -> bool

where N: Zero + One + RelativeEq, <N as AbsDiffEq>::Epsilon: Copy,

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

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

pub fn is_orthogonal(&self, eps: <N as AbsDiffEq>::Epsilon) -> bool

where N: Zero + One + ClosedAdd + ClosedMul + RelativeEq, S: Storage<N, R, C>, <N as AbsDiffEq>::Epsilon: Copy, DefaultAllocator: Allocator<N, R, C> + Allocator<N, C, C>,

Checks that Mᵀ × M = Id.

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

pub fn is_special_orthogonal(&self, eps: N) -> bool

where D: DimMin<D, Output = D>, DefaultAllocator: Allocator<(usize, usize), D>,

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

pub fn is_invertible(&self) -> bool

Returns true if this matrix is invertible.

pub fn compress_rows( &self, f: impl Fn(Matrix<N, R, U1, SliceStorage<'_, N, R, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>) -> N, ) -> Matrix<N, U1, C, <DefaultAllocator as Allocator<N, U1, C>>::Buffer>

where DefaultAllocator: Allocator<N, U1, C>,

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

pub fn compress_rows_tr( &self, f: impl Fn(Matrix<N, R, U1, SliceStorage<'_, N, R, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>) -> N, ) -> Matrix<N, C, U1, <DefaultAllocator as Allocator<N, C>>::Buffer>

where DefaultAllocator: Allocator<N, C>,

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

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

pub fn compress_columns( &self, init: Matrix<N, R, U1, <DefaultAllocator as Allocator<N, R>>::Buffer>, f: impl Fn(&mut Matrix<N, R, U1, <DefaultAllocator as Allocator<N, R>>::Buffer>, Matrix<N, R, U1, SliceStorage<'_, N, R, U1, <S as Storage<N, R, C>>::RStride, <S as Storage<N, R, C>>::CStride>>), ) -> Matrix<N, R, U1, <DefaultAllocator as Allocator<N, R>>::Buffer>

where DefaultAllocator: Allocator<N, R>,

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

pub fn sum(&self) -> N

The sum of all the elements of this matrix.

Example

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

pub fn row_sum( &self, ) -> Matrix<N, U1, C, <DefaultAllocator as Allocator<N, U1, C>>::Buffer>

where DefaultAllocator: Allocator<N, U1, C>,

The sum of all the rows of this matrix.

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

Example

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

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<N, C, U1, <DefaultAllocator as Allocator<N, C>>::Buffer>

where DefaultAllocator: Allocator<N, C>,

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

Example

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

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<N, R, U1, <DefaultAllocator as Allocator<N, R>>::Buffer>

where DefaultAllocator: Allocator<N, R>,

The sum of all the columns of this matrix.

Example

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

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

pub fn variance(&self) -> N

The variance of all the elements of this matrix.

Example

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

pub fn row_variance( &self, ) -> Matrix<N, U1, C, <DefaultAllocator as Allocator<N, U1, C>>::Buffer>

where DefaultAllocator: Allocator<N, U1, C>,

The variance of all the rows of this matrix.

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

Example

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

pub fn row_variance_tr( &self, ) -> Matrix<N, C, U1, <DefaultAllocator as Allocator<N, C>>::Buffer>

where DefaultAllocator: Allocator<N, C>,

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

Example

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

pub fn column_variance( &self, ) -> Matrix<N, R, U1, <DefaultAllocator as Allocator<N, R>>::Buffer>

where DefaultAllocator: Allocator<N, R>,

The variance of all the columns of this matrix.

Example

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

pub fn mean(&self) -> N

The mean of all the elements of this matrix.

Example

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

pub fn row_mean( &self, ) -> Matrix<N, U1, C, <DefaultAllocator as Allocator<N, U1, C>>::Buffer>

where DefaultAllocator: Allocator<N, U1, C>,

The mean of all the rows of this matrix.

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

Example

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

pub fn row_mean_tr( &self, ) -> Matrix<N, C, U1, <DefaultAllocator as Allocator<N, C>>::Buffer>

where DefaultAllocator: Allocator<N, C>,

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

Example

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

pub fn column_mean( &self, ) -> Matrix<N, R, U1, <DefaultAllocator as Allocator<N, R>>::Buffer>

where DefaultAllocator: Allocator<N, R>,

The mean of all the columns of this matrix.

Example

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

pub fn xx( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn xxx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xy( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn yx( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn yy( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn xxy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xyx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xyy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yxx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yxy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yyx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yyy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xz( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn yz( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn zx( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn zy( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn zz( &self, ) -> Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2>>::Buffer>

Builds a new vector from components of self.

pub fn xxz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xyz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xzx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xzy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn xzz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yxz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yyz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yzx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yzy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn yzz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zxx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zxy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zxz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zyx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zyy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zyz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zzx( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zzy( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn zzz( &self, ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3>>::Buffer>

Builds a new vector from components of self.

pub fn convolve_full<D2, S2>( &self, kernel: Matrix<N, D2, U1, S2>, ) -> Matrix<N, <<D1 as DimAdd<D2>>::Output as DimSub<U1>>::Output, U1, <DefaultAllocator as Allocator<N, <<D1 as DimAdd<D2>>::Output as DimSub<U1>>::Output>>::Buffer>

where D1: DimAdd<D2>, D2: DimAdd<D1, Output = <D1 as DimAdd<D2>>::Output>, <D1 as DimAdd<D2>>::Output: DimSub<U1>, S2: Storage<N, D2>, DefaultAllocator: Allocator<N, <<D1 as DimAdd<D2>>::Output as DimSub<U1>>::Output>,

Returns the convolution of the target vector and a kernel.

Arguments

• kernel - A Vector with size > 0

Errors

Inputs must satisfy vector.len() >= kernel.len() > 0.

pub fn convolve_valid<D2, S2>( &self, kernel: Matrix<N, D2, U1, S2>, ) -> Matrix<N, <<D1 as DimAdd<U1>>::Output as DimSub<D2>>::Output, U1, <DefaultAllocator as Allocator<N, <<D1 as DimAdd<U1>>::Output as DimSub<D2>>::Output>>::Buffer>

where D1: DimAdd<U1>, D2: Dim, <D1 as DimAdd<U1>>::Output: DimSub<D2>, S2: Storage<N, D2>, DefaultAllocator: Allocator<N, <<D1 as DimAdd<U1>>::Output as DimSub<D2>>::Output>,

Returns the convolution of the target vector and a kernel.

The output convolution consists only of those elements that do not rely on the zero-padding.

Arguments

• kernel - A Vector with size > 0

Errors

Inputs must satisfy self.len() >= kernel.len() > 0.

pub fn convolve_same<D2, S2>( &self, kernel: Matrix<N, D2, U1, S2>, ) -> Matrix<N, D1, U1, <DefaultAllocator as Allocator<N, D1>>::Buffer>

where D2: Dim, S2: Storage<N, D2>, DefaultAllocator: Allocator<N, D1>,

Returns the convolution of the target vector and a kernel.

The output convolution is the same size as vector, centered with respect to the ‘full’ output.

Arguments

• kernel - A Vector with size > 0

Errors

Inputs must satisfy self.len() >= kernel.len() > 0.

pub fn determinant(&self) -> N

where DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), D>,

Computes the matrix determinant.

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

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

Computes exponential of this matrix

pub fn try_inverse_mut(&mut self) -> bool

where DefaultAllocator: Allocator<N, D, D>,

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

pub fn eigenvalues( &self, ) -> Option<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer>>

Computes the eigenvalues of this matrix.

pub fn complex_eigenvalues( &self, ) -> Matrix<Complex<N>, D, U1, <DefaultAllocator as Allocator<Complex<N>, D>>::Buffer>

where N: RealField, DefaultAllocator: Allocator<Complex<N>, D>,

Computes the eigenvalues of this matrix.

pub fn solve_lower_triangular<R2, C2, S2>( &self, b: &Matrix<N, R2, C2, S2>, ) -> Option<Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> Option<Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, diag: N, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> Option<Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> Option<Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> Option<Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> Option<Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> bool

where R2: Dim, C2: Dim, S2: StorageMut<N, 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.

pub fn solve_lower_triangular_unchecked<R2, C2, S2>( &self, b: &Matrix<N, R2, C2, S2>, ) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, diag: N, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, ) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, ) -> Matrix<N, R2, C2, <DefaultAllocator as Allocator<N, R2, C2>>::Buffer>

where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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<N, R2, C2, S2>, )

where R2: Dim, C2: Dim, S2: StorageMut<N, 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.

pub fn singular_values( &self, ) -> Matrix<<N as ComplexField>::RealField, <R as DimMin<C>>::Output, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, <R as DimMin<C>>::Output>>::Buffer>

Computes the singular values of this matrix.

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

Computes the rank of this matrix.

All singular values below eps are considered equal to 0.

pub fn symmetric_eigenvalues( &self, ) -> Matrix<<N as ComplexField>::RealField, D, U1, <DefaultAllocator as Allocator<<N as ComplexField>::RealField, D>>::Buffer>

Computes the eigenvalues of this symmetric matrix.

Only the lower-triangular part of the matrix is read.

Trait Implementations

impl AsMut<Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>> for Skew3

fn as_mut( &mut self, ) -> &mut Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>

Converts this type into a mutable reference of the (usually inferred) input type.

impl AsRef<Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>> for Skew3

fn as_ref( &self, ) -> &Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>

Converts this type into a shared reference of the (usually inferred) input type.

impl Clone for Skew3

fn clone(&self) -> Skew3

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Skew3

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Deref for Skew3

type Target = Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>

The resulting type after dereferencing.

fn deref(&self) -> &<Skew3 as Deref>::Target

Dereferences the value.

impl DerefMut for Skew3

fn deref_mut(&mut self) -> &mut <Skew3 as Deref>::Target

Mutably dereferences the value.

impl From<Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>> for Skew3

fn from( original: Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>, ) -> Skew3

Converts to this type from the input type.

impl From<Rotation<f64, U3>> for Skew3

This is the log map.

fn from(r: Rotation<f64, U3>) -> Skew3

Converts to this type from the input type.

impl From<Skew3> for Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>

fn from( original: Skew3, ) -> Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3>>::Buffer>

Converts to this type from the input type.

impl From<Skew3> for Rotation<f64, U3>

This is the exponential map.

fn from(w: Skew3) -> Rotation<f64, U3>

Converts to this type from the input type.

impl PartialEq for Skew3

fn eq(&self, other: &Skew3) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for Skew3

fn partial_cmp(&self, other: &Skew3) -> Option<Ordering>

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

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

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

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

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

impl Copy for Skew3

impl StructuralPartialEq for Skew3