use crate::{RawStorage, SimdComplexField};
use num::{One, Zero};
use simba::scalar::{ClosedAdd, ClosedMul};
use crate::base::allocator::Allocator;
use crate::base::blas_uninit::{axcpy_uninit, gemm_uninit, gemv_uninit};
use crate::base::constraint::{
AreMultipliable, DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
};
use crate::base::dimension::{Const, Dim, Dyn, U1, U2, U3, U4};
use crate::base::storage::{Storage, StorageMut};
use crate::base::uninit::Init;
use crate::base::{
DVectorView, DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector, VectorView,
};
/// # Dot/scalar product
impl<T, R: Dim, C: Dim, S: RawStorage<T, R, C>> Matrix<T, R, C, S>
where
T: Scalar + Zero + ClosedAdd + ClosedMul,
{
#[inline(always)]
fn dotx<R2: Dim, C2: Dim, SB>(
&self,
rhs: &Matrix<T, R2, C2, SB>,
conjugate: impl Fn(T) -> T,
) -> T
where
SB: RawStorage<T, R2, C2>,
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
{
assert!(
self.nrows() == rhs.nrows(),
"Dot product dimensions mismatch for shapes {:?} and {:?}: left rows != right rows.",
self.shape(),
rhs.shape(),
);
assert!(
self.ncols() == rhs.ncols(),
"Dot product dimensions mismatch for shapes {:?} and {:?}: left cols != right cols.",
self.shape(),
rhs.shape(),
);
// So we do some special cases for common fixed-size vectors of dimension lower than 8
// because the `for` loop below won't be very efficient on those.
if (R::is::<U2>() || R2::is::<U2>()) && (C::is::<U1>() || C2::is::<U1>()) {
unsafe {
let a = conjugate(self.get_unchecked((0, 0)).clone())
* rhs.get_unchecked((0, 0)).clone();
let b = conjugate(self.get_unchecked((1, 0)).clone())
* rhs.get_unchecked((1, 0)).clone();
return a + b;
}
}
if (R::is::<U3>() || R2::is::<U3>()) && (C::is::<U1>() || C2::is::<U1>()) {
unsafe {
let a = conjugate(self.get_unchecked((0, 0)).clone())
* rhs.get_unchecked((0, 0)).clone();
let b = conjugate(self.get_unchecked((1, 0)).clone())
* rhs.get_unchecked((1, 0)).clone();
let c = conjugate(self.get_unchecked((2, 0)).clone())
* rhs.get_unchecked((2, 0)).clone();
return a + b + c;
}
}
if (R::is::<U4>() || R2::is::<U4>()) && (C::is::<U1>() || C2::is::<U1>()) {
unsafe {
let mut a = conjugate(self.get_unchecked((0, 0)).clone())
* rhs.get_unchecked((0, 0)).clone();
let mut b = conjugate(self.get_unchecked((1, 0)).clone())
* rhs.get_unchecked((1, 0)).clone();
let c = conjugate(self.get_unchecked((2, 0)).clone())
* rhs.get_unchecked((2, 0)).clone();
let d = conjugate(self.get_unchecked((3, 0)).clone())
* rhs.get_unchecked((3, 0)).clone();
a += c;
b += d;
return a + b;
}
}
// All this is inspired from the "unrolled version" discussed in:
// https://blog.theincredibleholk.org/blog/2012/12/10/optimizing-dot-product/
//
// And this comment from bluss:
// https://users.rust-lang.org/t/how-to-zip-two-slices-efficiently/2048/12
let mut res = T::zero();
// We have to define them outside of the loop (and not inside at first assignment)
// otherwise vectorization won't kick in for some reason.
let mut acc0;
let mut acc1;
let mut acc2;
let mut acc3;
let mut acc4;
let mut acc5;
let mut acc6;
let mut acc7;
for j in 0..self.ncols() {
let mut i = 0;
acc0 = T::zero();
acc1 = T::zero();
acc2 = T::zero();
acc3 = T::zero();
acc4 = T::zero();
acc5 = T::zero();
acc6 = T::zero();
acc7 = T::zero();
while self.nrows() - i >= 8 {
acc0 += unsafe {
conjugate(self.get_unchecked((i, j)).clone())
* rhs.get_unchecked((i, j)).clone()
};
acc1 += unsafe {
conjugate(self.get_unchecked((i + 1, j)).clone())
* rhs.get_unchecked((i + 1, j)).clone()
};
acc2 += unsafe {
conjugate(self.get_unchecked((i + 2, j)).clone())
* rhs.get_unchecked((i + 2, j)).clone()
};
acc3 += unsafe {
conjugate(self.get_unchecked((i + 3, j)).clone())
* rhs.get_unchecked((i + 3, j)).clone()
};
acc4 += unsafe {
conjugate(self.get_unchecked((i + 4, j)).clone())
* rhs.get_unchecked((i + 4, j)).clone()
};
acc5 += unsafe {
conjugate(self.get_unchecked((i + 5, j)).clone())
* rhs.get_unchecked((i + 5, j)).clone()
};
acc6 += unsafe {
conjugate(self.get_unchecked((i + 6, j)).clone())
* rhs.get_unchecked((i + 6, j)).clone()
};
acc7 += unsafe {
conjugate(self.get_unchecked((i + 7, j)).clone())
* rhs.get_unchecked((i + 7, j)).clone()
};
i += 8;
}
res += acc0 + acc4;
res += acc1 + acc5;
res += acc2 + acc6;
res += acc3 + acc7;
for k in i..self.nrows() {
res += unsafe {
conjugate(self.get_unchecked((k, j)).clone())
* rhs.get_unchecked((k, j)).clone()
}
}
}
res
}
/// 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.
///
/// # Example
/// ```
/// # use nalgebra::{Vector3, Matrix2x3};
/// 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);
/// ```
///
#[inline]
#[must_use]
pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> T
where
SB: RawStorage<T, R2, C2>,
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
{
self.dotx(rhs, |e| e)
}
/// 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.
///
/// # Example
/// ```
/// # use nalgebra::{Vector2, Complex};
/// 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));
/// ```
#[inline]
#[must_use]
pub fn dotc<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> T
where
T: SimdComplexField,
SB: RawStorage<T, R2, C2>,
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
{
self.dotx(rhs, T::simd_conjugate)
}
/// The dot product between the transpose of `self` and `rhs`.
///
/// # Example
/// ```
/// # use nalgebra::{Vector3, RowVector3, Matrix2x3, Matrix3x2};
/// 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);
/// ```
#[inline]
#[must_use]
pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<T, R2, C2, SB>) -> T
where
SB: RawStorage<T, R2, C2>,
ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>,
{
let (nrows, ncols) = self.shape();
assert_eq!(
(ncols, nrows),
rhs.shape(),
"Transposed dot product dimension mismatch."
);
let mut res = T::zero();
for j in 0..self.nrows() {
for i in 0..self.ncols() {
res += unsafe {
self.get_unchecked((j, i)).clone() * rhs.get_unchecked((i, j)).clone()
}
}
}
res
}
}
/// # BLAS functions
impl<T, D: Dim, S> Vector<T, D, S>
where
T: Scalar + Zero + ClosedAdd + ClosedMul,
S: StorageMut<T, D>,
{
/// Computes `self = a * x * c + b * self`.
///
/// If `b` is zero, `self` is never read from.
///
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// 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));
/// ```
#[inline]
#[allow(clippy::many_single_char_names)]
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>,
{
unsafe { axcpy_uninit(Init, self, a, x, c, b) };
}
/// Computes `self = a * x + b * self`.
///
/// If `b` is zero, `self` is never read from.
///
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// 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));
/// ```
#[inline]
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>,
{
assert_eq!(self.nrows(), x.nrows(), "Axpy: mismatched vector shapes.");
self.axcpy(a, x, T::one(), b)
}
/// 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
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// 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));
/// ```
#[inline]
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>,
{
// Safety: this is safe because we are passing Status == Init.
unsafe { gemv_uninit(Init, self, alpha, a, x, beta) }
}
#[inline(always)]
fn xxgemv<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
a: &SquareMatrix<T, D2, SB>,
x: &Vector<T, D3, SC>,
beta: T,
dot: impl Fn(
&DVectorView<'_, T, SB::RStride, SB::CStride>,
&DVectorView<'_, T, SC::RStride, SC::CStride>,
) -> T,
) where
T: One,
SB: Storage<T, D2, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,
{
let dim1 = self.nrows();
let dim2 = a.nrows();
let dim3 = x.nrows();
assert!(
a.is_square(),
"Symmetric cgemv: the input matrix must be square."
);
assert!(
dim2 == dim3 && dim1 == dim2,
"Symmetric cgemv: dimensions mismatch."
);
if dim2 == 0 {
return;
}
// TODO: avoid bound checks.
let col2 = a.column(0);
let val = unsafe { x.vget_unchecked(0).clone() };
self.axpy(alpha.clone() * val, &col2, beta);
self[0] += alpha.clone() * dot(&a.view_range(1.., 0), &x.rows_range(1..));
for j in 1..dim2 {
let col2 = a.column(j);
let dot = dot(&col2.rows_range(j..), &x.rows_range(j..));
let val;
unsafe {
val = x.vget_unchecked(j).clone();
*self.vget_unchecked_mut(j) += alpha.clone() * dot;
}
self.rows_range_mut(j + 1..).axpy(
alpha.clone() * val,
&col2.rows_range(j + 1..),
T::one(),
);
}
}
/// 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
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// 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));
/// ```
#[inline]
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>,
{
self.xxgemv(alpha, a, x, beta, |a, b| a.dot(b))
}
/// 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
/// ```
/// # use nalgebra::{Matrix2, Vector2, Complex};
/// 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)));
/// ```
#[inline]
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>,
{
self.xxgemv(alpha, a, x, beta, |a, b| a.dotc(b))
}
#[inline(always)]
fn gemv_xx<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,
dot: impl Fn(&VectorView<'_, T, R2, SB::RStride, SB::CStride>, &Vector<T, D3, SC>) -> T,
) where
T: One,
SB: Storage<T, R2, C2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
{
let dim1 = self.nrows();
let (nrows2, ncols2) = a.shape();
let dim3 = x.nrows();
assert!(
nrows2 == dim3 && dim1 == ncols2,
"Gemv: dimensions mismatch."
);
if ncols2 == 0 {
return;
}
if beta.is_zero() {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha.clone() * dot(&a.column(j), x)
}
} else {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha.clone() * dot(&a.column(j), x) + beta.clone() * val.clone();
}
}
}
/// 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
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// 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);
/// ```
#[inline]
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>,
{
self.gemv_xx(alpha, a, x, beta, |a, b| a.dot(b))
}
/// 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
/// ```
/// # use nalgebra::{Matrix2, Vector2, Complex};
/// 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);
/// ```
#[inline]
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>,
{
self.gemv_xx(alpha, a, x, beta, |a, b| a.dotc(b))
}
}
impl<T, R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>> Matrix<T, R1, C1, S>
where
T: Scalar + Zero + ClosedAdd + ClosedMul,
{
#[inline(always)]
fn gerx<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
conjugate: impl Fn(T) -> T,
) where
T: One,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
let (nrows1, ncols1) = self.shape();
let dim2 = x.nrows();
let dim3 = y.nrows();
assert!(
nrows1 == dim2 && ncols1 == dim3,
"ger: dimensions mismatch."
);
for j in 0..ncols1 {
// TODO: avoid bound checks.
let val = unsafe { conjugate(y.vget_unchecked(j).clone()) };
self.column_mut(j)
.axpy(alpha.clone() * val, x, beta.clone());
}
}
/// Computes `self = alpha * x * y.transpose() + beta * self`.
///
/// If `beta` is zero, `self` is never read.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2x3, Vector2, Vector3};
/// 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);
/// ```
#[inline]
pub fn ger<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
) where
T: One,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.gerx(alpha, x, y, beta, |e| e)
}
/// Computes `self = alpha * x * y.adjoint() + beta * self`.
///
/// If `beta` is zero, `self` is never read.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix2x3, Vector2, Vector3, Complex};
/// 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);
/// ```
#[inline]
pub fn gerc<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
) where
T: SimdComplexField,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.gerx(alpha, x, y, beta, SimdComplexField::simd_conjugate)
}
/// 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.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix2x3, Matrix3x4, Matrix2x4};
/// 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);
/// ```
#[inline]
pub fn gemm<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
&mut self,
alpha: T,
a: &Matrix<T, R2, C2, SB>,
b: &Matrix<T, R3, C3, SC>,
beta: T,
) where
T: One,
SB: Storage<T, R2, C2>,
SC: Storage<T, R3, C3>,
ShapeConstraint: SameNumberOfRows<R1, R2>
+ SameNumberOfColumns<C1, C3>
+ AreMultipliable<R2, C2, R3, C3>,
{
// SAFETY: this is valid because our matrices are initialized and
// we are using status = Init.
unsafe { gemm_uninit(Init, self, alpha, a, b, beta) }
}
/// 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.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix3x2, Matrix3x4, Matrix2x4};
/// 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);
/// ```
#[inline]
pub fn gemm_tr<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
&mut self,
alpha: T,
a: &Matrix<T, R2, C2, SB>,
b: &Matrix<T, R3, C3, SC>,
beta: T,
) where
T: One,
SB: Storage<T, R2, C2>,
SC: Storage<T, R3, C3>,
ShapeConstraint: SameNumberOfRows<R1, C2>
+ SameNumberOfColumns<C1, C3>
+ AreMultipliable<C2, R2, R3, C3>,
{
let (nrows1, ncols1) = self.shape();
let (nrows2, ncols2) = a.shape();
let (nrows3, ncols3) = b.shape();
assert_eq!(
nrows2, nrows3,
"gemm: dimensions mismatch for multiplication."
);
assert_eq!(
(nrows1, ncols1),
(ncols2, ncols3),
"gemm: dimensions mismatch for addition."
);
for j1 in 0..ncols1 {
// TODO: avoid bound checks.
self.column_mut(j1)
.gemv_tr(alpha.clone(), a, &b.column(j1), beta.clone());
}
}
/// 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.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix3x2, Matrix3x4, Matrix2x4, Complex};
/// 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);
/// ```
#[inline]
pub fn gemm_ad<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
&mut self,
alpha: T,
a: &Matrix<T, R2, C2, SB>,
b: &Matrix<T, R3, C3, SC>,
beta: T,
) where
T: SimdComplexField,
SB: Storage<T, R2, C2>,
SC: Storage<T, R3, C3>,
ShapeConstraint: SameNumberOfRows<R1, C2>
+ SameNumberOfColumns<C1, C3>
+ AreMultipliable<C2, R2, R3, C3>,
{
let (nrows1, ncols1) = self.shape();
let (nrows2, ncols2) = a.shape();
let (nrows3, ncols3) = b.shape();
assert_eq!(
nrows2, nrows3,
"gemm: dimensions mismatch for multiplication."
);
assert_eq!(
(nrows1, ncols1),
(ncols2, ncols3),
"gemm: dimensions mismatch for addition."
);
for j1 in 0..ncols1 {
// TODO: avoid bound checks.
self.column_mut(j1)
.gemv_ad(alpha.clone(), a, &b.column(j1), beta.clone());
}
}
}
impl<T, R1: Dim, C1: Dim, S: StorageMut<T, R1, C1>> Matrix<T, R1, C1, S>
where
T: Scalar + Zero + ClosedAdd + ClosedMul,
{
#[inline(always)]
fn xxgerx<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
conjugate: impl Fn(T) -> T,
) where
T: One,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
let dim1 = self.nrows();
let dim2 = x.nrows();
let dim3 = y.nrows();
assert!(
self.is_square(),
"Symmetric ger: the input matrix must be square."
);
assert!(dim1 == dim2 && dim1 == dim3, "ger: dimensions mismatch.");
for j in 0..dim1 {
let val = unsafe { conjugate(y.vget_unchecked(j).clone()) };
let subdim = Dyn(dim1 - j);
// TODO: avoid bound checks.
self.generic_view_mut((j, j), (subdim, Const::<1>)).axpy(
alpha.clone() * val,
&x.rows_range(j..),
beta.clone(),
);
}
}
/// 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.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// 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.
/// ```
#[inline]
#[deprecated(note = "This is renamed `syger` to match the original BLAS terminology.")]
pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
) where
T: One,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.syger(alpha, x, y, beta)
}
/// 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.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2, Vector2};
/// 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.
/// ```
#[inline]
pub fn syger<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
) where
T: One,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.xxgerx(alpha, x, y, beta, |e| e)
}
/// 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.
///
/// # Example
/// ```
/// # use nalgebra::{Matrix2, Vector2, Complex};
/// 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.
/// ```
#[inline]
pub fn hegerc<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: T,
x: &Vector<T, D2, SB>,
y: &Vector<T, D3, SC>,
beta: T,
) where
T: SimdComplexField,
SB: Storage<T, D2>,
SC: Storage<T, D3>,
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
{
self.xxgerx(alpha, x, y, beta, SimdComplexField::simd_conjugate)
}
}
impl<T, D1: Dim, S: StorageMut<T, D1, D1>> SquareMatrix<T, D1, S>
where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
{
/// Computes the quadratic form `self = alpha * lhs * mid * lhs.transpose() + beta * self`.
///
/// This uses the provided workspace `work` to avoid allocations for intermediate results.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{DMatrix, DVector};
/// // 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_with_workspace<D2, S2, R3, C3, S3, D4, S4>(
&mut self,
work: &mut Vector<T, D2, S2>,
alpha: T,
lhs: &Matrix<T, R3, C3, S3>,
mid: &SquareMatrix<T, D4, S4>,
beta: T,
) where
D2: Dim,
R3: Dim,
C3: Dim,
D4: Dim,
S2: StorageMut<T, D2>,
S3: Storage<T, R3, C3>,
S4: Storage<T, D4, D4>,
ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,
{
work.gemv(T::one(), lhs, &mid.column(0), T::zero());
self.ger(alpha.clone(), work, &lhs.column(0), beta);
for j in 1..mid.ncols() {
work.gemv(T::one(), lhs, &mid.column(j), T::zero());
self.ger(alpha.clone(), work, &lhs.column(j), T::one());
}
}
/// 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.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix2, Matrix3, Matrix2x3, Vector2};
/// 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_tr<R3, C3, S3, D4, S4>(
&mut self,
alpha: T,
lhs: &Matrix<T, R3, C3, S3>,
mid: &SquareMatrix<T, D4, S4>,
beta: T,
) where
R3: Dim,
C3: Dim,
D4: Dim,
S3: Storage<T, R3, C3>,
S4: Storage<T, D4, D4>,
ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>,
DefaultAllocator: Allocator<T, D1>,
{
// TODO: would it be useful to avoid the zero-initialization of the workspace data?
let mut work = Matrix::zeros_generic(self.shape_generic().0, Const::<1>);
self.quadform_tr_with_workspace(&mut work, alpha, lhs, mid, beta)
}
/// Computes the quadratic form `self = alpha * rhs.transpose() * mid * rhs + beta * self`.
///
/// This uses the provided workspace `work` to avoid allocations for intermediate results.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{DMatrix, DVector};
/// // 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_with_workspace<D2, S2, D3, S3, R4, C4, S4>(
&mut self,
work: &mut Vector<T, D2, S2>,
alpha: T,
mid: &SquareMatrix<T, D3, S3>,
rhs: &Matrix<T, R4, C4, S4>,
beta: T,
) where
D2: Dim,
D3: Dim,
R4: Dim,
C4: Dim,
S2: StorageMut<T, D2>,
S3: Storage<T, D3, D3>,
S4: Storage<T, R4, C4>,
ShapeConstraint:
DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,
{
work.gemv(T::one(), mid, &rhs.column(0), T::zero());
self.column_mut(0)
.gemv_tr(alpha.clone(), rhs, work, beta.clone());
for j in 1..rhs.ncols() {
work.gemv(T::one(), mid, &rhs.column(j), T::zero());
self.column_mut(j)
.gemv_tr(alpha.clone(), rhs, work, beta.clone());
}
}
/// 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.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Matrix2, Matrix3x2, Matrix3};
/// 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 quadform<D2, S2, R3, C3, S3>(
&mut self,
alpha: T,
mid: &SquareMatrix<T, D2, S2>,
rhs: &Matrix<T, R3, C3, S3>,
beta: T,
) where
D2: Dim,
R3: Dim,
C3: Dim,
S2: Storage<T, D2, D2>,
S3: Storage<T, R3, C3>,
ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, U1>,
DefaultAllocator: Allocator<T, D2>,
{
// TODO: would it be useful to avoid the zero-initialization of the workspace data?
let mut work = Vector::zeros_generic(mid.shape_generic().0, Const::<1>);
self.quadform_with_workspace(&mut work, alpha, mid, rhs, beta)
}
}