[−][src]Struct cv::EssentialMatrix

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

This stores an essential matrix, which is satisfied by the following constraint:

transpose(x') * E * x = 0

Where x' and x are homogeneous normalized image coordinates. You can get a homogeneous normalized image coordinate by appending 1.0 to a NormalizedKeyPoint.

The essential matrix embodies the epipolar constraint between two images. Given that light travels in a perfectly straight line (it will not, but for short distances it mostly does) and assuming a pinhole camera model, for any point on the camera sensor, the light source for that point exists somewhere along a line extending out from the bearing (direction of travel) of that point. For a normalized image coordinate, that bearing is (x, y, 1.0). That is because normalized image coordinates exist on a virtual plane (the sensor) a distance z = 1.0 from the optical center (the location of the focal point) where the unit of distance is the focal length. In epipolar geometry, the point on the virtual plane pointing towards the second camera is called an epipole. The line through the image created by the projected points is called an epipolar line, and it extends from the epipole.

If you look at every point along a projection out of the camera, each one of those points would project onto the epipolar line on the camera sensor of another image. If you traced every point along the projection to where it would appear on the sensor of the camera (projection of the 3d points into normalized image coordinates), then the points would form the epipolar line. This means that you can draw epipolar lines so long as the projection does not pass through the optical center of both cameras. However, that situation is usually impossible, as one camera would be obscuring the feature for the other camera.

The essential matrix makes it possible to create a vector that is perpendicular to all bearings that are formed from the epipolar line on the second image's sensor. This is done by computing E * x, where x is a homogeneous normalized image coordinate from the first image. The transpose of the resulting vector then has a dot product with the transpose of the second image coordinate x' which is equal to 0.0. This can be written as:

dot(transpose(E * x), x') = 0

This can be re-written into the form given above:

transpose(x') * E * x = 0

Where the first operation creates a pependicular vector to the epipoles on the first image and the second takes the dot product which should result in 0.

With a EssentialMatrix, you can retrieve the rotation and translation given one normalized image coordinate and one bearing that is scaled to the depth of the point relative to the current reconstruction. This kind of point can be computed using WorldPose::transform to convert a WorldPoint to a CameraPoint.

Implementations

`impl EssentialMatrix`[src]

`pub fn recondition( self, epsilon: f64, max_iterations: usize ) -> Option<EssentialMatrix>`[src]

Can be used to enforce the constraints of an essential matrix to fix it.

This finds the closest essential matrix in frobenius form. This just means that the two singular values are averaged and the null singular value is forced to zero.

`pub fn possible_rotations_unscaled_translation( &self, epsilon: f64, max_iterations: usize ) -> Option<(Rotation<f64, U3>, Rotation<f64, U3>, Matrix<f64, U3, U1, <DefaultAllocator as Allocator<f64, U3, U1>>::Buffer>)>`[src]

Returns two possible rotations for the essential matrix along with a translation bearing of arbitrary length. The translation bearing is not yet in the correct space and the inverse rotation (transpose) must be multiplied by the translation bearing to make the translation bearing be post-rotation. The translation's length is unknown and of unknown sign and must be solved for by using a prior.

epsilon is the threshold by which the singular value decomposition is considered complete. Making this smaller may improve the precision. It is recommended to set this to no higher than 1e-6.

max_iterations is the maximum number of iterations that singular value decomposition will run on this matrix. Use this in soft realtime systems to cap the execution time. A max_iterations of 0 may execute indefinitely and is not recommended.

let pose = RelativeCameraPose(IsometryMatrix3::from_parts(
    Vector3::new(-0.8, 0.4, 0.5).into(),
    Rotation3::from_euler_angles(0.2, 0.3, 0.4),
));
// Get the possible poses for the essential matrix created from `pose`.
let (rot_a, rot_b, t) = pose.essential_matrix().possible_rotations_unscaled_translation(1e-6, 50).unwrap();
// Compute residual rotations.
let a_res = rot_a.rotation_to(&pose.rotation).angle();
let b_res = rot_b.rotation_to(&pose.rotation).angle();
let a_close = a_res < 1e-4;
let b_close = b_res < 1e-4;
// At least one rotation is correct.
assert!(a_close || b_close);
// The translation points in the same (or reverse) direction
let t_res = 1.0 - t.normalize().dot(&pose.translation.vector.normalize()).abs();
assert!(t_res < 1e-4);

`pub fn possible_rotations( &self, epsilon: f64, max_iterations: usize ) -> Option<[Rotation<f64, U3>; 2]>`[src]

See EssentialMatrix::possible_rotations_unscaled_translation.

This returns only the two rotations that are possible.

let pose = RelativeCameraPose(IsometryMatrix3::from_parts(
    Vector3::new(-0.8, 0.4, 0.5).into(),
    Rotation3::from_euler_angles(0.2, 0.3, 0.4),
));
// Get the possible rotations for the essential matrix created from `pose`.
let rbs = pose.essential_matrix().possible_rotations(1e-6, 50).unwrap();
let one_correct = rbs.iter().any(|&rot| {
    let angle_residual = rot.rotation_to(&pose.rotation).angle();
    angle_residual < 1e-4
});
assert!(one_correct);

`pub fn possible_unscaled_poses( &self, epsilon: f64, max_iterations: usize ) -> Option<[UnscaledRelativeCameraPose; 4]>`[src]

See EssentialMatrix::possible_rotations_unscaled_translation.

This returns the rotations and their corresponding post-rotation translation bearing.

let pose = RelativeCameraPose(IsometryMatrix3::from_parts(
    Vector3::new(-0.8, 0.4, 0.5).into(),
    Rotation3::from_euler_angles(0.2, 0.3, 0.4),
));
// Get the possible poses for the essential matrix created from `pose`.
let rbs = pose.essential_matrix().possible_unscaled_poses(1e-6, 50).unwrap();
let one_correct = rbs.iter().any(|&upose| {
    let angle_residual =
        upose.rotation.rotation_to(&pose.rotation).angle();
    let translation_residual =
        1.0 - upose.translation.vector.normalize()
                   .dot(&pose.translation.vector.normalize());
    angle_residual < 1e-4 && translation_residual < 1e-4
});
assert!(one_correct);

`pub fn possible_unscaled_poses_bearing( &self, epsilon: f64, max_iterations: usize ) -> Option<[UnscaledRelativeCameraPose; 2]>`[src]

Same as EssentialMatrix::possible_unscaled_poses, but it doesn't return 4 unscaled poses since it doesn't bother to give back the different translation directions and instead only gives one. This is useful if your algorithm doesn't care about the direction of translation.

`pub fn pose_solver(&self) -> PoseSolver`[src]

See PoseSolver.

Creates a solver that allows you to solve for the pose using correspondences. The pose may be scaled or unscaled, and if the alloc feature is enabled, you can retrieve the inliers as well.

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

`pub fn icamax(&self) -> usize`[src]

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)`[src]

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`[src]

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,` [src]

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)`[src]

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`[src]

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,` [src]

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)`[src]

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)`[src]

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, R2>, ShapeConstraint: DimEq<C, C2>,` [src]

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 C2: Dim, N: SimdComplexField, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, R2>, ShapeConstraint: DimEq<C, C2>,` [src]

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<C, R2>, ShapeConstraint: DimEq<R, C2>,` [src]

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, U1>, ShapeConstraint: DimEq<D, D2>,` [src]

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, U1>, ShapeConstraint: DimEq<D, D2>,` [src]

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 C2: Dim, D3: Dim, N: One, R2: Dim, SB: Storage<N, R2, C2>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<D, R2>, ShapeConstraint: AreMultipliable<R2, C2, D3, U1>,` [src]

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, U1>, ShapeConstraint: DimEq<D, D2>, ShapeConstraint: AreMultipliable<D2, D2, D3, U1>,` [src]

👎 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, U1>, ShapeConstraint: DimEq<D, D2>, ShapeConstraint: AreMultipliable<D2, D2, D3, U1>,` [src]

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, U1>, ShapeConstraint: DimEq<D, D2>, ShapeConstraint: AreMultipliable<D2, D2, D3, U1>,` [src]

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 C2: Dim, D3: Dim, N: One, R2: Dim, SB: Storage<N, R2, C2>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<D, C2>, ShapeConstraint: AreMultipliable<C2, R2, D3, U1>,` [src]

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 C2: Dim, D3: Dim, N: SimdComplexField, R2: Dim, SB: Storage<N, R2, C2>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<D, C2>, ShapeConstraint: AreMultipliable<C2, R2, D3, U1>,` [src]

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, U1>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<R1, D2>, ShapeConstraint: DimEq<C1, D3>,` [src]

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, U1>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<R1, D2>, ShapeConstraint: DimEq<C1, D3>,` [src]

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 C2: Dim, C3: Dim, N: One, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: Storage<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C3>, ShapeConstraint: AreMultipliable<R2, C2, R3, C3>,` [src]

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 C2: Dim, C3: Dim, N: One, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: Storage<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, C2>, ShapeConstraint: SameNumberOfColumns<C1, C3>, ShapeConstraint: AreMultipliable<C2, R2, R3, C3>,` [src]

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 C2: Dim, C3: Dim, N: SimdComplexField, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: Storage<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, C2>, ShapeConstraint: SameNumberOfColumns<C1, C3>, ShapeConstraint: AreMultipliable<C2, R2, R3, C3>,` [src]

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, U1>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<R1, D2>, ShapeConstraint: DimEq<C1, D3>,` [src]

👎 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, U1>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<R1, D2>, ShapeConstraint: DimEq<C1, D3>,` [src]

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, U1>, SC: Storage<N, D3, U1>, ShapeConstraint: DimEq<R1, D2>, ShapeConstraint: DimEq<C1, D3>,` [src]

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 C3: Dim, D2: Dim, D4: Dim, R3: Dim, S2: StorageMut<N, D2, U1>, S3: Storage<N, R3, C3>, S4: Storage<N, D4, D4>, ShapeConstraint: DimEq<D1, D2>, ShapeConstraint: DimEq<D1, R3>, ShapeConstraint: DimEq<D2, R3>, ShapeConstraint: DimEq<C3, D4>, [src]

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 C3: Dim, D4: Dim, R3: Dim, S3: Storage<N, R3, C3>, S4: Storage<N, D4, D4>, ShapeConstraint: DimEq<D1, D1>, ShapeConstraint: DimEq<D1, R3>, ShapeConstraint: DimEq<C3, D4>, DefaultAllocator: Allocator<N, D1, U1>,` [src]

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

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 C3: Dim, D2: Dim, R3: Dim, S2: Storage<N, D2, D2>, S3: Storage<N, R3, C3>, ShapeConstraint: DimEq<D2, R3>, ShapeConstraint: DimEq<D1, C3>, ShapeConstraint: AreMultipliable<C3, R3, D2, U1>, DefaultAllocator: Allocator<N, D2, U1>,` [src]

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)`[src]

Negates self in-place.

`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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,` [src]

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 C2: Dim, N: SimdComplexField, R2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>,` [src]

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 C2: Dim, C3: Dim, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: StorageMut<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: DimEq<C1, R3>, ShapeConstraint: DimEq<C2, C3>,` [src]

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 C2: Dim, C3: Dim, N: SimdComplexField, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: StorageMut<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: DimEq<C1, R3>, ShapeConstraint: DimEq<C2, C3>,` [src]

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 C2: Dim, C3: Dim, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: StorageMut<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R3, R1>, ShapeConstraint: SameNumberOfColumns<C3, C2>, ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,` [src]

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 C1: DimMul<C2>, C2: Dim, N: ClosedMul<N>, R1: DimMul<R2>, R2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, <R1 as DimMul<R2>>::Output, <C1 as DimMul<C2>>::Output>,` [src]

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

`#[must_use = "Did you mean to use add_scalar_mut()?"]pub fn add_scalar( &self, rhs: N ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where DefaultAllocator: Allocator<N, R, C>,` [src]

Adds a scalar to self.

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

Adds a scalar to self in-place.

`pub fn amax(&self) -> N where N: Zero + SimdSigned + SimdPartialOrd,` [src]

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,` [src]

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,` [src]

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,` [src]

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,` [src]

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,` [src]

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);

`#[must_use = "Did you mean to use append_scaling_mut()?"]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>,` [src]

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

`#[must_use = "Did you mean to use prepend_scaling_mut()?"]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>,` [src]

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

`#[must_use = "Did you mean to use append_nonuniform_scaling_mut()?"]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, U1>, DefaultAllocator: Allocator<N, D, D>,` [src]

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

`#[must_use = "Did you mean to use prepend_nonuniform_scaling_mut()?"]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, U1>, DefaultAllocator: Allocator<N, D, D>,` [src]

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

`#[must_use = "Did you mean to use append_translation_mut()?"]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, U1>, DefaultAllocator: Allocator<N, D, D>,` [src]

Computes the transformation equal to self followed by a translation.

`#[must_use = "Did you mean to use prepend_translation_mut()?"]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, U1>, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, <D as DimNameSub<U1>>::Output, U1>,` [src]

Computes the transformation equal to a translation followed by self.

`pub fn append_scaling_mut(&mut self, scaling: N) where D: DimNameSub<U1>,` [src]

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>,` [src]

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, U1>,` [src]

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, U1>,` [src]

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, U1>,` [src]

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, U1>, DefaultAllocator: Allocator<N, <D as DimNameSub<U1>>::Output, U1>,` [src]

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, U1>>::Buffer> ) -> Matrix<N, <D as DimNameSub<U1>>::Output, U1, <DefaultAllocator as Allocator<N, <D as DimNameSub<U1>>::Output, U1>>::Buffer>`[src]

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>`[src]

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>,` [src]

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 inf( &self, other: &Matrix<N, R, C, S> ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer>`[src]

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>`[src]

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>)`[src]

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>,` [src]

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>,` [src]

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

`pub fn fill(&mut self, val: N)`[src]

Sets all the elements of this matrix to val.

`pub fn fill_with_identity(&mut self) where N: Zero + One,` [src]

Fills self with the identity matrix.

`pub fn fill_diagonal(&mut self, val: N)`[src]

Sets all the diagonal elements of this matrix to val.

`pub fn fill_row(&mut self, i: usize, val: N)`[src]

Sets all the elements of the selected row to val.

`pub fn fill_column(&mut self, j: usize, val: N)`[src]

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 R: DimMin<C>, R2: Dim, S2: Storage<N, R2, U1>, ShapeConstraint: DimEq<<R as DimMin<C>>::Output, R2>,` [src]

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>)`[src]

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>,` [src]

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, U1>, ShapeConstraint: SameNumberOfRows<R, R2>,` [src]

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)`[src]

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)`[src]

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)`[src]

Swaps two rows in-place.

`pub fn swap_columns(&mut self, icol1: usize, icol2: usize)`[src]

Swaps two columns in-place.

`pub fn fill_lower_triangle_with_upper_triangle(&mut self)`[src]

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)`[src]

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<>::Output> where I: MatrixIndex<'a, N, R, C, S>,` [src]

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<>::OutputMut> where I: MatrixIndexMut<'a, N, R, C, S>, S: StorageMut<N, R, C>,` [src]

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 ) -> >::Output where I: MatrixIndex<'a, N, R, C, S>,` [src]

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 ) -> >::OutputMut where I: MatrixIndexMut<'a, N, R, C, S>, S: StorageMut<N, R, C>,` [src]

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 ) -> >::Output where I: MatrixIndex<'a, N, R, C, S>,` [src]

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 ) -> >::OutputMut where I: MatrixIndexMut<'a, N, R, C, S>, S: StorageMut<N, R, C>,` [src]

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

`pub fn len(&self) -> usize`[src]

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)`[src]

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`[src]

The number of rows of this matrix.

Examples:

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

`pub fn ncols(&self) -> usize`[src]

The number of columns of this matrix.

Examples:

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

`pub fn strides(&self) -> (usize, usize)`[src]

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>`[src]

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>`[src]

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>`[src]

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)`[src]

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`[src]

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<N>>::Epsilon, max_relative: <N as AbsDiffEq<N>>::Epsilon ) -> bool where C2: Dim, N: RelativeEq<N>, R2: Dim, SB: Storage<N, R2, C2>, <N as AbsDiffEq<N>>::Epsilon: Copy, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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 C2: Dim, N: PartialEq<N>, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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>,` [src]

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 C2: Dim, R2: Dim, DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>, [src]

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 F: FnMut(N) -> N2, N2: Scalar, DefaultAllocator: Allocator<N2, R, C>,` [src]

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`[src]

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 F: FnMut(usize, usize, N) -> N2, N2: Scalar, DefaultAllocator: Allocator<N2, R, C>,` [src]

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 F: FnMut(N, N2) -> N3, N2: Scalar, N3: Scalar, S2: Storage<N2, R, C>, DefaultAllocator: Allocator<N3, R, C>,` [src]

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

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`[src]

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 C2: Dim, N2: Scalar, R2: Dim, S2: Storage<N2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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 C2: Dim, R2: Dim, SB: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, C2>, ShapeConstraint: SameNumberOfColumns<C, R2>,` [src]

Transposes self and store the result into out.

`#[must_use = "Did you mean to use transpose_mut()?"]pub fn transpose( &self ) -> Matrix<N, C, R, <DefaultAllocator as Allocator<N, C, R>>::Buffer> where DefaultAllocator: Allocator<N, C, R>,` [src]

Transposes self.

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

Mutably iterates through this matrix coordinates.

`pub fn as_mut_ptr(&mut self) -> *mut N`[src]

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>`[src]

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>`[src]

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) )`[src]

Swaps two entries without bound-checking.

`pub fn swap(&mut self, row_cols1: (usize, usize), row_cols2: (usize, usize))`[src]

Swaps two entries.

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

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, C2>, ShapeConstraint: SameNumberOfColumns<C, R2>,` [src]

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

`pub fn apply<F>(&mut self, f: F) where F: FnMut(N) -> N,` [src]

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 C2: Dim, N2: Scalar, R2: Dim, S2: Storage<N2, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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

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`[src]

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`[src]

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

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

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

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

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

`pub fn transpose_mut(&mut self)`[src]

Transposes the square matrix self in-place.

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

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

`#[must_use = "Did you mean to use adjoint_mut()?"]pub fn adjoint( &self ) -> Matrix<N, C, R, <DefaultAllocator as Allocator<N, C, R>>::Buffer> where DefaultAllocator: Allocator<N, C, R>,` [src]

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

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

👎 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>,` [src]

👎 Deprecated:

Renamed self.adjoint().

The conjugate transposition of self.

`#[must_use = "Did you mean to use conjugate_mut()?"]pub fn conjugate( &self ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where DefaultAllocator: Allocator<N, R, C>,` [src]

The conjugate of self.

`#[must_use = "Did you mean to use unscale_mut()?"]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>,` [src]

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

`#[must_use = "Did you mean to use scale_mut()?"]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>,` [src]

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

`pub fn conjugate_mut(&mut self)`[src]

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

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

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

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

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

`pub fn conjugate_transform_mut(&mut self)`[src]

👎 Deprecated:

Renamed to self.adjoint_mut().

Sets self to its adjoint.

`pub fn adjoint_mut(&mut self)`[src]

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

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

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, U1>>::Buffer> where N2: Scalar, DefaultAllocator: Allocator<N2, D, U1>,` [src]

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<N>,` [src]

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>,` [src]

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>,` [src]

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>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output, U1>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, <D as DimAdd<U1>>::Output, U1>,` [src]

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, U2>, ShapeConstraint: SameNumberOfColumns<C, U1>, ShapeConstraint: SameNumberOfRows<R2, U2>, ShapeConstraint: SameNumberOfColumns<C2, U1>,` [src]

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: SameShapeAllocator<N, R, C, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>, [src]

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>`[src]

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 C2: Dim, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: DimEq<R, R2>, ShapeConstraint: DimEq<C, C2>,` [src]

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, U1>>::Buffer> where S2: Storage<N, D, U1>, DefaultAllocator: Allocator<N, D, U1>,` [src]

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 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 ColRange: SliceRange<C>, RowRange: SliceRange<R>,` [src]

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>,` [src]

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>,` [src]

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 ColRange: SliceRange<C>, RowRange: SliceRange<R>,` [src]

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>,` [src]

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>,` [src]

Slice containing all the columns indexed by the range cols.

`pub fn norm_squared(&self) -> <N as SimdComplexField>::SimdRealField`[src]

The squared L2 norm of this vector.

`pub fn norm(&self) -> <N as SimdComplexField>::SimdRealField`[src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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`[src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R, R2>, ShapeConstraint: SameNumberOfColumns<C, C2>,` [src]

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`[src]

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`[src]

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>,` [src]

Sets the magnitude of this vector.

`#[must_use = "Did you mean to use normalize_mut()?"]pub fn normalize( &self ) -> Matrix<N, R, C, <DefaultAllocator as Allocator<N, R, C>>::Buffer> where DefaultAllocator: Allocator<N, R, C>,` [src]

Returns a normalized version of this matrix.

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

The Lp norm of this matrix.

`#[must_use = "Did you mean to use simd_try_normalize_mut()?"]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>, DefaultAllocator: Allocator<<N as SimdValue>::Element, R, C>,` [src]

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>,` [src]

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.

`#[must_use = "Did you mean to use try_normalize_mut()?"]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>,` [src]

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`[src]

Normalizes this matrix in-place and returns its norm.

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

`#[must_use = "Did you mean to use simd_try_normalize_mut()?"]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>, DefaultAllocator: Allocator<<N as SimdValue>::Element, R, C>,` [src]

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>`[src]

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`[src]

Indicates if this is an empty matrix.

`pub fn is_square(&self) -> bool`[src]

Indicates if this is a square matrix.

`pub fn is_identity(&self, eps: <N as AbsDiffEq<N>>::Epsilon) -> bool where N: Zero + One + RelativeEq<N>, <N as AbsDiffEq<N>>::Epsilon: Copy,` [src]

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<N>>::Epsilon) -> bool where N: Zero + One + ClosedAdd<N> + ClosedMul<N> + RelativeEq<N>, S: Storage<N, R, C>, <N as AbsDiffEq<N>>::Epsilon: Copy, DefaultAllocator: Allocator<N, R, C>, DefaultAllocator: Allocator<N, C, C>,` [src]

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, U1>,` [src]

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

`pub fn is_invertible(&self) -> bool`[src]

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>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, C, U1>,` [src]

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, U1>>::Buffer>, f: impl Fn(&mut Matrix<N, R, U1, <DefaultAllocator as Allocator<N, R, U1>>::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, U1>>::Buffer> where DefaultAllocator: Allocator<N, R, U1>,` [src]

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

`pub fn sum(&self) -> N`[src]

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>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, C, U1>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, R, U1>,` [src]

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`[src]

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>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, C, U1>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, R, U1>,` [src]

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`[src]

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>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, C, U1>,` [src]

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, U1>>::Buffer> where DefaultAllocator: Allocator<N, R, U1>,` [src]

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

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, U1>>::Buffer> where D1: DimAdd<U1>, D2: Dim, S2: Storage<N, D2, U1>, <D1 as DimAdd<U1>>::Output: DimSub<D2>, DefaultAllocator: Allocator<N, <<D1 as DimAdd<U1>>::Output as DimSub<D2>>::Output, U1>,` [src]

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, U1>>::Buffer> where D2: Dim, S2: Storage<N, D2, U1>, DefaultAllocator: Allocator<N, D1, U1>,` [src]

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>, DefaultAllocator: Allocator<(usize, usize), D, U1>,` [src]

Computes the matrix determinant.

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

`pub fn try_inverse_mut(&mut self) -> bool where DefaultAllocator: Allocator<N, D, D>,` [src]

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, U1>>::Buffer>>`[src]

Computes the eigenvalues of this matrix.

`pub fn complex_eigenvalues( &self ) -> Matrix<Complex<N>, D, U1, <DefaultAllocator as Allocator<Complex<N>, D, U1>>::Buffer> where N: RealField, DefaultAllocator: Allocator<Complex<N>, D, U1>,` [src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: Storage<N, R2, C2>, DefaultAllocator: Allocator<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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 C2: Dim, R2: Dim, S2: StorageMut<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R2, D>,` [src]

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, U1>>::Buffer>`[src]

Computes the singular values of this matrix.

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

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, U1>>::Buffer>`[src]

Computes the eigenvalues of this symmetric matrix.

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

`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 C2: Dim, C3: Dim, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: StorageMut<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R3>, ShapeConstraint: SameNumberOfColumns<C1, C3>,` [src]

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 C2: Dim, C3: Dim, R2: Dim, R3: Dim, SB: Storage<N, R2, C2>, SC: StorageMut<N, R3, C3>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>, ShapeConstraint: SameNumberOfRows<R1, R3>, ShapeConstraint: SameNumberOfColumns<C1, C3>,` [src]

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

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 C2: Dim, N: ClosedMul<N>, R2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>, [src]

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

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 C2: Dim, N: ClosedMul<N>, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>,` [src]

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 C2: Dim, N: ClosedMul<N>, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>,` [src]

👎 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 C2: Dim, N: ClosedDiv<N>, R2: Dim, SB: Storage<N, R2, C2>, DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>, [src]

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

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 C2: Dim, N: ClosedDiv<N>, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>,` [src]

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 C2: Dim, N: ClosedDiv<N>, R2: Dim, SB: Storage<N, R2, C2>, ShapeConstraint: SameNumberOfRows<R1, R2>, ShapeConstraint: SameNumberOfColumns<C1, C2>,` [src]

👎 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 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>>`[src]

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>>`[src]

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>>`[src]

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>>`[src]

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,` [src]

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,` [src]

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,` [src]

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,` [src]

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>>`[src]

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>>`[src]

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>>`[src]

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>>`[src]

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,` [src]

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,` [src]

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,` [src]

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,` [src]

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>>`[src]

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>>`[src]

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 CSlice: DimName, RSlice: DimName,` [src]

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 CSlice: DimName, RSlice: DimName,` [src]

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 CSlice: Dim, RSlice: Dim,` [src]

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 CSlice: Dim, RSlice: Dim,` [src]

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>, [src]

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>, [src]

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>>`[src]

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>>`[src]

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>>`[src]

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>>`[src]

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,` [src]

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,` [src]

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,` [src]

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,` [src]

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>>`[src]

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>>`[src]

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>>`[src]

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>>`[src]

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,` [src]

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,` [src]

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,` [src]

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,` [src]

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>>`[src]

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>>`[src]

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 CSlice: DimName, RSlice: DimName,` [src]

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 CSlice: DimName, RSlice: DimName,` [src]

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 CSlice: Dim, RSlice: Dim,` [src]

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 CSlice: Dim, RSlice: Dim,` [src]

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>, [src]

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

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