Type Definition nalgebra::base::Vector

pub type Vector<T, D, S> = Matrix<T, D, U1, S>;

A matrix with one column and D rows.

Implementations

impl<T, D: Dim, S> Vector<T, D, S>where
    T: Scalar + Zero + ClosedAdd + ClosedMul,
    S: StorageMut<T, D>,

BLAS functions

pub fn axcpy<D2: Dim, SB>(&mut self, a: T, x: &Vector<T, D2, SB>, c: T, b: T)where
    SB: Storage<T, D2>,
    ShapeConstraint: DimEq<D, D2>,

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

If b is zero, self is never read from.

Example

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

pub fn axpy<D2: Dim, SB>(&mut self, a: T, x: &Vector<T, D2, SB>, b: T)where
    T: One,
    SB: Storage<T, D2>,
    ShapeConstraint: DimEq<D, D2>,

Computes self = a * x + b * self.

If b is zero, self is never read from.

Example

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

pub fn gemv<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: T,
    a: &Matrix<T, R2, C2, SB>,
    x: &Vector<T, D3, SC>,
    beta: T
)where
    T: One,
    SB: Storage<T, R2, C2>,
    SC: Storage<T, D3>,
    ShapeConstraint: DimEq<D, R2> + AreMultipliable<R2, C2, D3, U1>,

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

If beta is zero, self is never read.

Example

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

pub fn sygemv<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: T,
    a: &SquareMatrix<T, D2, SB>,
    x: &Vector<T, D3, SC>,
    beta: T
)where
    T: One,
    SB: Storage<T, D2, D2>,
    SC: Storage<T, D3>,
    ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,

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

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

Examples

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


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

pub fn hegemv<D2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: T,
    a: &SquareMatrix<T, D2, SB>,
    x: &Vector<T, D3, SC>,
    beta: T
)where
    T: SimdComplexField,
    SB: Storage<T, D2, D2>,
    SC: Storage<T, D3>,
    ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,

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

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

Examples

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


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

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

pub fn gemv_tr<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: T,
    a: &Matrix<T, R2, C2, SB>,
    x: &Vector<T, D3, SC>,
    beta: T
)where
    T: One,
    SB: Storage<T, R2, C2>,
    SC: Storage<T, D3>,
    ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,

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

If beta is zero, self is never read.

Example

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

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

pub fn gemv_ad<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
    &mut self,
    alpha: T,
    a: &Matrix<T, R2, C2, SB>,
    x: &Vector<T, D3, SC>,
    beta: T
)where
    T: SimdComplexField,
    SB: Storage<T, R2, C2>,
    SC: Storage<T, D3>,
    ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,

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

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

Example

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

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

impl<T, D: Dim, S: RawStorage<T, D>> Vector<T, D, S>

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

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

impl<T, D: Dim, S: RawStorageMut<T, D>> Vector<T, D, S>

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

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

impl<T: Scalar + Zero, D: DimAdd<U1>, S: RawStorage<T, D>> Vector<T, D, S>

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

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

pub fn from_homogeneous<SB>(
    v: Vector<T, DimSum<D, U1>, SB>
) -> Option<OVector<T, D>>where
    SB: RawStorage<T, DimSum<D, U1>>,
    DefaultAllocator: Allocator<T, D>,

Constructs a vector from coordinates in projective space, i.e., removes a 0 at the end of self. Returns None if this last component is not zero.

impl<T: Scalar, D: DimAdd<U1>, S: RawStorage<T, D>> Vector<T, D, S>

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

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

impl<T: Scalar + Field, S: RawStorage<T, U3>> Vector<T, U3, S>

pub fn cross_matrix(&self) -> OMatrix<T, U3, U3>

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

impl<T: Scalar, D, S: RawStorage<T, D>> Vector<T, D, S>where
    D: DimName + ToTypenum,

Swizzling

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

Builds a new vector from components of self.

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

Builds a new vector from components of self.

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

Builds a new vector from components of self.

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

Builds a new vector from components of self.

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

Builds a new vector from components of self.

pub fn xxy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xyx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xyy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yxx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yxy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yyx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn yyy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U1, Output = Greater>,

Builds a new vector from components of self.

pub fn xz(&self) -> Vector2<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yz(&self) -> Vector2<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zx(&self) -> Vector2<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zy(&self) -> Vector2<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zz(&self) -> Vector2<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xxz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xyz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xzx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xzy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn xzz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yxz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yyz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yzx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yzy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn yzz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zxx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zxy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zxz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zyx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zyy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zyz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zzx(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zzy(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

pub fn zzz(&self) -> Vector3<T>where
    D::Typenum: Cmp<U2, Output = Greater>,

Builds a new vector from components of self.

impl<T: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Storage<T, D>> Vector<T, D, S>

Interpolation

pub fn lerp<S2: Storage<T, D>>(
    &self,
    rhs: &Vector<T, D, S2>,
    t: T
) -> OVector<T, D>where
    DefaultAllocator: Allocator<T, D>,

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

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

Examples:

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

pub fn slerp<S2: Storage<T, D>>(
    &self,
    rhs: &Vector<T, D, S2>,
    t: T
) -> OVector<T, D>where
    T: RealField,
    DefaultAllocator: Allocator<T, D>,

Computes the spherical linear interpolation between two non-zero vectors.

The result is a unit vector.

Examples:

let v1 =Vector2::new(1.0, 2.0);
let v2 = Vector2::new(2.0, -3.0);

let v = v1.slerp(&v2, 1.0);

assert_eq!(v, v2.normalize());

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

Find the min and max components (vector-specific methods)

pub fn icamax(&self) -> usizewhere
    T: ComplexField,

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, T)where
    T: PartialOrd,

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) -> usizewhere
    T: PartialOrd,

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) -> usizewhere
    T: PartialOrd + Signed,

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

Examples:

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

pub fn argmin(&self) -> (usize, T)where
    T: PartialOrd,

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) -> usizewhere
    T: PartialOrd,

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) -> usizewhere
    T: PartialOrd + Signed,

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

Examples:

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

impl<T: RealField, D1: Dim, S1: Storage<T, D1>> Vector<T, D1, S1>

pub fn convolve_full<D2, S2>(
    &self,
    kernel: Vector<T, D2, S2>
) -> OVector<T, DimDiff<DimSum<D1, D2>, U1>>where
    D1: DimAdd<D2>,
    D2: DimAdd<D1, Output = DimSum<D1, D2>>,
    DimSum<D1, D2>: DimSub<U1>,
    S2: Storage<T, D2>,
    DefaultAllocator: Allocator<T, DimDiff<DimSum<D1, D2>, U1>>,

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: Vector<T, D2, S2>
) -> OVector<T, DimDiff<DimSum<D1, U1>, D2>>where
    D1: DimAdd<U1>,
    D2: Dim,
    DimSum<D1, U1>: DimSub<D2>,
    S2: Storage<T, D2>,
    DefaultAllocator: Allocator<T, DimDiff<DimSum<D1, U1>, D2>>,

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: Vector<T, D2, S2>) -> OVector<T, D1>where
    D2: Dim,
    S2: Storage<T, D2>,
    DefaultAllocator: Allocator<T, D1>,

Returns the convolution of the target vector and a kernel.

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

Arguments

• kernel - A Vector with size > 0

Errors

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

impl<T: Scalar + Zero + ClosedAdd + ClosedMul, D: Dim, S: StorageMut<T, D>> Vector<T, D, S>

pub fn axpy_cs<D2: Dim, S2>(&mut self, alpha: T, x: &CsVector<T, D2, S2>, beta: T)where
    S2: CsStorage<T, D2>,
    ShapeConstraint: DimEq<D, D2>,

Perform a sparse axpy operation: self = alpha * x + beta * self operation.