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nalgebra/src/base/blas.rs

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use alga::general::{ClosedAdd, ClosedMul};
#[cfg(feature = "std")]
use matrixmultiply;
use num::{One, Signed, Zero};
#[cfg(feature = "std")]
use std::mem;
use base::allocator::Allocator;
use base::constraint::{
AreMultipliable, DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
};
use base::dimension::{Dim, Dynamic, U1, U2, U3, U4};
use base::storage::{Storage, StorageMut};
use base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector};
impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
/// Computes the index of the vector component with the largest value.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Vector3;
/// let vec = Vector3::new(11, -15, 13);
/// assert_eq!(vec.imax(), 2);
/// ```
#[inline]
pub fn imax(&self) -> usize {
assert!(!self.is_empty(), "The input vector must not be empty.");
let mut the_max = unsafe { self.vget_unchecked(0) };
let mut the_i = 0;
for i in 1..self.nrows() {
let val = unsafe { self.vget_unchecked(i) };
if val > the_max {
the_max = val;
the_i = i;
}
}
the_i
}
/// Computes the index of the vector component with the largest absolute value.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Vector3;
/// let vec = Vector3::new(11, -15, 13);
/// assert_eq!(vec.iamax(), 1);
/// ```
#[inline]
pub fn iamax(&self) -> usize {
assert!(!self.is_empty(), "The input vector must not be empty.");
let mut the_max = unsafe { self.vget_unchecked(0).abs() };
let mut the_i = 0;
for i in 1..self.nrows() {
let val = unsafe { self.vget_unchecked(i).abs() };
if val > the_max {
the_max = val;
the_i = i;
}
}
the_i
}
/// Computes the index of the vector component with the smallest value.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Vector3;
/// let vec = Vector3::new(11, -15, 13);
/// assert_eq!(vec.imin(), 1);
/// ```
#[inline]
pub fn imin(&self) -> usize {
assert!(!self.is_empty(), "The input vector must not be empty.");
let mut the_max = unsafe { self.vget_unchecked(0) };
let mut the_i = 0;
for i in 1..self.nrows() {
let val = unsafe { self.vget_unchecked(i) };
if val < the_max {
the_max = val;
the_i = i;
}
}
the_i
}
/// Computes the index of the vector component with the smallest absolute value.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Vector3;
/// let vec = Vector3::new(11, -15, 13);
/// assert_eq!(vec.iamin(), 0);
/// ```
#[inline]
pub fn iamin(&self) -> usize {
assert!(!self.is_empty(), "The input vector must not be empty.");
let mut the_max = unsafe { self.vget_unchecked(0).abs() };
let mut the_i = 0;
for i in 1..self.nrows() {
let val = unsafe { self.vget_unchecked(i).abs() };
if val < the_max {
the_max = val;
the_i = i;
}
}
the_i
}
}
impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
/// Computes the index of the matrix component with the largest absolute value.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Matrix2x3;
/// let mat = Matrix2x3::new(11, -12, 13,
/// 21, 22, -23);
/// assert_eq!(mat.iamax_full(), (1, 2));
/// ```
#[inline]
pub fn iamax_full(&self) -> (usize, usize) {
assert!(!self.is_empty(), "The input matrix must not be empty.");
let mut the_max = unsafe { self.get_unchecked((0, 0)).abs() };
let mut the_ij = (0, 0);
for j in 0..self.ncols() {
for i in 0..self.nrows() {
let val = unsafe { self.get_unchecked((i, j)).abs() };
if val > the_max {
the_max = val;
the_ij = (i, j);
}
}
}
the_ij
}
}
impl<N, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
where N: Scalar + Zero + ClosedAdd + ClosedMul
{
/// The dot product between two vectors or matrices (seen as vectors).
///
/// 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:
///
/// ```
/// # 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]
pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
where
SB: Storage<N, R2, C2>,
ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
{
assert!(
self.nrows() == rhs.nrows(),
"Dot product dimensions mismatch."
);
// 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 = *self.get_unchecked((0, 0)) * *rhs.get_unchecked((0, 0));
let b = *self.get_unchecked((1, 0)) * *rhs.get_unchecked((1, 0));
return a + b;
}
}
if (R::is::<U3>() || R2::is::<U3>()) && (C::is::<U1>() || C2::is::<U1>()) {
unsafe {
let a = *self.get_unchecked((0, 0)) * *rhs.get_unchecked((0, 0));
let b = *self.get_unchecked((1, 0)) * *rhs.get_unchecked((1, 0));
let c = *self.get_unchecked((2, 0)) * *rhs.get_unchecked((2, 0));
return a + b + c;
}
}
if (R::is::<U4>() || R2::is::<U4>()) && (C::is::<U1>() || C2::is::<U1>()) {
unsafe {
let mut a = *self.get_unchecked((0, 0)) * *rhs.get_unchecked((0, 0));
let mut b = *self.get_unchecked((1, 0)) * *rhs.get_unchecked((1, 0));
let c = *self.get_unchecked((2, 0)) * *rhs.get_unchecked((2, 0));
let d = *self.get_unchecked((3, 0)) * *rhs.get_unchecked((3, 0));
a += c;
b += d;
return a + b;
}
}
// All this is inspired from the "unrolled version" discussed in:
// http://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 = N::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 = N::zero();
acc1 = N::zero();
acc2 = N::zero();
acc3 = N::zero();
acc4 = N::zero();
acc5 = N::zero();
acc6 = N::zero();
acc7 = N::zero();
while self.nrows() - i >= 8 {
acc0 += unsafe { *self.get_unchecked((i + 0, j)) * *rhs.get_unchecked((i + 0, j)) };
acc1 += unsafe { *self.get_unchecked((i + 1, j)) * *rhs.get_unchecked((i + 1, j)) };
acc2 += unsafe { *self.get_unchecked((i + 2, j)) * *rhs.get_unchecked((i + 2, j)) };
acc3 += unsafe { *self.get_unchecked((i + 3, j)) * *rhs.get_unchecked((i + 3, j)) };
acc4 += unsafe { *self.get_unchecked((i + 4, j)) * *rhs.get_unchecked((i + 4, j)) };
acc5 += unsafe { *self.get_unchecked((i + 5, j)) * *rhs.get_unchecked((i + 5, j)) };
acc6 += unsafe { *self.get_unchecked((i + 6, j)) * *rhs.get_unchecked((i + 6, j)) };
acc7 += unsafe { *self.get_unchecked((i + 7, j)) * *rhs.get_unchecked((i + 7, j)) };
i += 8;
}
res += acc0 + acc4;
res += acc1 + acc5;
res += acc2 + acc6;
res += acc3 + acc7;
for k in i..self.nrows() {
res += unsafe { *self.get_unchecked((k, j)) * *rhs.get_unchecked((k, j)) }
}
}
res
}
/// The dot product between the transpose of `self` and `rhs`.
///
/// # Examples:
///
/// ```
/// # 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]
pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
where
SB: Storage<N, R2, C2>,
ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>,
{
let (nrows, ncols) = self.shape();
assert!(
(ncols, nrows) == rhs.shape(),
"Transposed dot product dimension mismatch."
);
let mut res = N::zero();
for j in 0..self.nrows() {
for i in 0..self.ncols() {
res += unsafe { *self.get_unchecked((j, i)) * *rhs.get_unchecked((i, j)) }
}
}
res
}
}
fn array_axpy<N>(y: &mut [N], a: N, x: &[N], beta: N, stride1: usize, stride2: usize, len: usize)
where N: Scalar + Zero + ClosedAdd + ClosedMul {
for i in 0..len {
unsafe {
let y = y.get_unchecked_mut(i * stride1);
*y = a * *x.get_unchecked(i * stride2) + beta * *y;
}
}
}
fn array_ax<N>(y: &mut [N], a: N, x: &[N], stride1: usize, stride2: usize, len: usize)
where N: Scalar + Zero + ClosedAdd + ClosedMul {
for i in 0..len {
unsafe {
*y.get_unchecked_mut(i * stride1) = a * *x.get_unchecked(i * stride2);
}
}
}
impl<N, D: Dim, S> Vector<N, D, S>
where
N: Scalar + Zero + ClosedAdd + ClosedMul,
S: StorageMut<N, D>,
{
/// Computes `self = a * x + b * self`.
///
/// If be is zero, `self` is never read from.
///
/// # Examples:
///
/// ```
/// # 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: N, x: &Vector<N, D2, SB>, b: N)
where
SB: Storage<N, D2>,
ShapeConstraint: DimEq<D, D2>,
{
assert_eq!(self.nrows(), x.nrows(), "Axpy: mismatched vector shapes.");
let rstride1 = self.strides().0;
let rstride2 = x.strides().0;
let y = self.data.as_mut_slice();
let x = x.data.as_slice();
if !b.is_zero() {
array_axpy(y, a, x, b, rstride1, rstride2, x.len());
} else {
array_ax(y, a, x, rstride1, rstride2, x.len());
}
}
/// 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:
///
/// ```
/// # 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: N,
a: &Matrix<N, R2, C2, SB>,
x: &Vector<N, D3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, R2, C2>,
SC: Storage<N, D3>,
ShapeConstraint: DimEq<D, R2> + AreMultipliable<R2, C2, D3, U1>,
{
let dim1 = self.nrows();
let (nrows2, ncols2) = a.shape();
let dim3 = x.nrows();
assert!(
ncols2 == dim3 && dim1 == nrows2,
"Gemv: dimensions mismatch."
);
if ncols2 == 0 {
return;
}
// FIXME: avoid bound checks.
let col2 = a.column(0);
let val = unsafe { *x.vget_unchecked(0) };
self.axpy(alpha * val, &col2, beta);
for j in 1..ncols2 {
let col2 = a.column(j);
let val = unsafe { *x.vget_unchecked(j) };
self.axpy(alpha * val, &col2, N::one());
}
}
/// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** 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};
/// 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.gemv_symm(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.gemv_symm(10.0, &mat, &vec2, 5.0);
/// assert_eq!(vec1, Vector2::new(10.0, 20.0));
/// ```
#[inline]
pub fn gemv_symm<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: N,
a: &SquareMatrix<N, D2, SB>,
x: &Vector<N, D3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, D2, D2>,
SC: Storage<N, 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(),
"Syetric gemv: the input matrix must be square."
);
assert!(
dim2 == dim3 && dim1 == dim2,
"Symmetric gemv: dimensions mismatch."
);
if dim2 == 0 {
return;
}
// FIXME: avoid bound checks.
let col2 = a.column(0);
let val = unsafe { *x.vget_unchecked(0) };
self.axpy(alpha * val, &col2, beta);
self[0] += alpha * x.rows_range(1..).dot(&a.slice_range(1.., 0));
for j in 1..dim2 {
let col2 = a.column(j);
let dot = x.rows_range(j..).dot(&col2.rows_range(j..));
let val;
unsafe {
val = *x.vget_unchecked(j);
*self.vget_unchecked_mut(j) += alpha * dot;
}
self.rows_range_mut(j + 1..)
.axpy(alpha * val, &col2.rows_range(j + 1..), N::one());
}
}
/// 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:
///
/// ```
/// # 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: N,
a: &Matrix<N, R2, C2, SB>,
x: &Vector<N, D3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, R2, C2>,
SC: Storage<N, 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 * a.column(j).dot(x)
}
} else {
for j in 0..ncols2 {
let val = unsafe { self.vget_unchecked_mut(j) };
*val = alpha * a.column(j).dot(x) + beta * *val;
}
}
}
}
impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
where N: Scalar + Zero + ClosedAdd + ClosedMul
{
/// Computes `self = alpha * x * y.transpose() + beta * self`.
///
/// If `beta` is zero, `self` is never read.
///
/// # Examples:
///
/// ```
/// # 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: N,
x: &Vector<N, D2, SB>,
y: &Vector<N, D3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, D2>,
SC: Storage<N, 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 {
// FIXME: avoid bound checks.
let val = unsafe { *y.vget_unchecked(j) };
self.column_mut(j).axpy(alpha * val, x, beta);
}
}
/// 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:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # extern crate nalgebra;
/// # 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: N,
a: &Matrix<N, R2, C2, SB>,
b: &Matrix<N, R3, C3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, R2, C2>,
SC: Storage<N, R3, C3>,
ShapeConstraint: SameNumberOfRows<R1, R2>
+ SameNumberOfColumns<C1, C3>
+ AreMultipliable<R2, C2, R3, C3>,
{
let ncols1 = self.ncols();
#[cfg(feature = "std")]
{
// matrixmultiply can be used only if the std feature is available.
let nrows1 = self.nrows();
let (nrows2, ncols2) = a.shape();
let (nrows3, ncols3) = b.shape();
assert_eq!(
ncols2, nrows3,
"gemm: dimensions mismatch for multiplication."
);
assert_eq!(
(nrows1, ncols1),
(nrows2, ncols3),
"gemm: dimensions mismatch for addition."
);
// We assume large matrices will be Dynamic but small matrices static.
// We could use matrixmultiply for large statically-sized matrices but the performance
// threshold to activate it would be different from SMALL_DIM because our code optimizes
// better for statically-sized matrices.
let is_dynamic = R1::is::<Dynamic>()
|| C1::is::<Dynamic>()
|| R2::is::<Dynamic>()
|| C2::is::<Dynamic>()
|| R3::is::<Dynamic>()
|| C3::is::<Dynamic>();
// Threshold determined empirically.
const SMALL_DIM: usize = 5;
if is_dynamic
&& nrows1 > SMALL_DIM
&& ncols1 > SMALL_DIM
&& nrows2 > SMALL_DIM
&& ncols2 > SMALL_DIM
{
if N::is::<f32>() {
let (rsa, csa) = a.strides();
let (rsb, csb) = b.strides();
let (rsc, csc) = self.strides();
unsafe {
matrixmultiply::sgemm(
nrows2,
ncols2,
ncols3,
mem::transmute_copy(&alpha),
a.data.ptr() as *const f32,
rsa as isize,
csa as isize,
b.data.ptr() as *const f32,
rsb as isize,
csb as isize,
mem::transmute_copy(&beta),
self.data.ptr_mut() as *mut f32,
rsc as isize,
csc as isize,
);
}
return;
} else if N::is::<f64>() {
let (rsa, csa) = a.strides();
let (rsb, csb) = b.strides();
let (rsc, csc) = self.strides();
unsafe {
matrixmultiply::dgemm(
nrows2,
ncols2,
ncols3,
mem::transmute_copy(&alpha),
a.data.ptr() as *const f64,
rsa as isize,
csa as isize,
b.data.ptr() as *const f64,
rsb as isize,
csb as isize,
mem::transmute_copy(&beta),
self.data.ptr_mut() as *mut f64,
rsc as isize,
csc as isize,
);
}
return;
}
}
}
for j1 in 0..ncols1 {
// FIXME: avoid bound checks.
self.column_mut(j1).gemv(alpha, a, &b.column(j1), 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.
///
/// # Examples:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # extern crate nalgebra;
/// # 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_relative_eq!(mat1, expected);
/// ```
#[inline]
pub fn gemm_tr<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
&mut self,
alpha: N,
a: &Matrix<N, R2, C2, SB>,
b: &Matrix<N, R3, C3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, R2, C2>,
SC: Storage<N, 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 {
// FIXME: avoid bound checks.
self.column_mut(j1).gemv_tr(alpha, a, &b.column(j1), beta);
}
}
}
impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
where N: Scalar + Zero + ClosedAdd + ClosedMul
{
/// 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:
///
/// ```
/// # 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]
pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>(
&mut self,
alpha: N,
x: &Vector<N, D2, SB>,
y: &Vector<N, D3, SC>,
beta: N,
) where
N: One,
SB: Storage<N, D2>,
SC: Storage<N, 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 { *y.vget_unchecked(j) };
let subdim = Dynamic::new(dim1 - j);
// FIXME: avoid bound checks.
self.generic_slice_mut((j, j), (subdim, U1)).axpy(
alpha * val,
&x.rows_range(j..),
beta,
);
}
}
}
impl<N, D1: Dim, S: StorageMut<N, D1, D1>> SquareMatrix<N, D1, S>
where N: 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.
///
/// # Examples:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # extern crate nalgebra;
/// # 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<N, D2, S2>,
alpha: N,
lhs: &Matrix<N, R3, C3, S3>,
mid: &SquareMatrix<N, D4, S4>,
beta: N,
) where
D2: Dim,
R3: Dim,
C3: Dim,
D4: Dim,
S2: StorageMut<N, D2>,
S3: Storage<N, R3, C3>,
S4: Storage<N, D4, D4>,
ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,
{
work.gemv(N::one(), lhs, &mid.column(0), N::zero());
self.ger(alpha, work, &lhs.column(0), beta);
for j in 1..mid.ncols() {
work.gemv(N::one(), lhs, &mid.column(j), N::zero());
self.ger(alpha, work, &lhs.column(j), N::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.
///
/// # Examples:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # extern crate nalgebra;
/// # 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: N,
lhs: &Matrix<N, R3, C3, S3>,
mid: &SquareMatrix<N, D4, S4>,
beta: N,
) where
R3: Dim,
C3: Dim,
D4: Dim,
S3: Storage<N, R3, C3>,
S4: Storage<N, D4, D4>,
ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>,
DefaultAllocator: Allocator<N, D1>,
{
let mut work = unsafe { Vector::new_uninitialized_generic(self.data.shape().0, U1) };
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.
///
/// ```
/// # #[macro_use] extern crate approx;
/// # extern crate nalgebra;
/// # 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<N, D2, S2>,
alpha: N,
mid: &SquareMatrix<N, D3, S3>,
rhs: &Matrix<N, R4, C4, S4>,
beta: N,
) where
D2: Dim,
D3: Dim,
R4: Dim,
C4: Dim,
S2: StorageMut<N, D2>,
S3: Storage<N, D3, D3>,
S4: Storage<N, R4, C4>,
ShapeConstraint:
DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,
{
work.gemv(N::one(), mid, &rhs.column(0), N::zero());
self.column_mut(0).gemv_tr(alpha, &rhs, work, beta);
for j in 1..rhs.ncols() {
work.gemv(N::one(), mid, &rhs.column(j), N::zero());
self.column_mut(j).gemv_tr(alpha, &rhs, work, beta);
}
}
/// 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.
///
/// ```
/// # #[macro_use] extern crate approx;
/// # extern crate nalgebra;
/// # 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: N,
mid: &SquareMatrix<N, D2, S2>,
rhs: &Matrix<N, R3, C3, S3>,
beta: N,
) where
D2: Dim,
R3: Dim,
C3: Dim,
S2: Storage<N, D2, D2>,
S3: Storage<N, R3, C3>,
ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, U1>,
DefaultAllocator: Allocator<N, D2>,
{
let mut work = unsafe { Vector::new_uninitialized_generic(mid.data.shape().0, U1) };
self.quadform_with_workspace(&mut work, alpha, mid, rhs, beta)
}
}
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