746 lines
24 KiB
Rust
746 lines
24 KiB
Rust
use alga::general::{ClosedAdd, ClosedMul};
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#[cfg(feature = "std")]
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use matrixmultiply;
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use num::{One, Signed, Zero};
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use std::mem;
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use base::allocator::Allocator;
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use base::constraint::{
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AreMultipliable, DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
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};
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use base::dimension::{Dim, Dynamic, U1, U2, U3, U4};
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use base::storage::{Storage, StorageMut};
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use base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector};
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impl<N: Scalar + PartialOrd + Signed, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
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/// Computes the index of the vector component with the largest absolute value.
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#[inline]
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pub fn iamax(&self) -> usize {
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assert!(!self.is_empty(), "The input vector must not be empty.");
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let mut the_max = unsafe { self.vget_unchecked(0).abs() };
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let mut the_i = 0;
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for i in 1..self.nrows() {
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let val = unsafe { self.vget_unchecked(i).abs() };
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if val > the_max {
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the_max = val;
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the_i = i;
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}
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}
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the_i
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}
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/// Computes the index of the vector component with the smallest absolute value.
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#[inline]
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pub fn iamin(&self) -> usize {
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assert!(!self.is_empty(), "The input vector must not be empty.");
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let mut the_max = unsafe { self.vget_unchecked(0).abs() };
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let mut the_i = 0;
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for i in 1..self.nrows() {
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let val = unsafe { self.vget_unchecked(i).abs() };
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if val < the_max {
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the_max = val;
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the_i = i;
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}
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}
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the_i
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}
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}
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impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
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/// Computes the index of the matrix component with the largest absolute value.
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#[inline]
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pub fn iamax_full(&self) -> (usize, usize) {
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assert!(!self.is_empty(), "The input matrix must not be empty.");
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let mut the_max = unsafe { self.get_unchecked(0, 0).abs() };
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let mut the_ij = (0, 0);
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for j in 0..self.ncols() {
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for i in 0..self.nrows() {
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let val = unsafe { self.get_unchecked(i, j).abs() };
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if val > the_max {
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the_max = val;
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the_ij = (i, j);
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}
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}
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}
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the_ij
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}
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}
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impl<N, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
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where
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N: Scalar + Zero + ClosedAdd + ClosedMul,
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{
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/// The dot product between two matrices (seen as vectors).
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///
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/// Note that this is **not** the matrix multiplication as in, e.g., numpy. For matrix
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/// multiplication, use one of: `.gemm`, `mul_to`, `.mul`, `*`.
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#[inline]
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pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
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where
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SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
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{
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assert!(
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self.nrows() == rhs.nrows(),
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"Dot product dimensions mismatch."
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);
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// So we do some special cases for common fixed-size vectors of dimension lower than 8
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// because the `for` loop below won't be very efficient on those.
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if (R::is::<U2>() || R2::is::<U2>()) && (C::is::<U1>() || C2::is::<U1>()) {
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unsafe {
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let a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
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let b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
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return a + b;
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}
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}
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if (R::is::<U3>() || R2::is::<U3>()) && (C::is::<U1>() || C2::is::<U1>()) {
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unsafe {
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let a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
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let b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
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let c = *self.get_unchecked(2, 0) * *rhs.get_unchecked(2, 0);
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return a + b + c;
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}
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}
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if (R::is::<U4>() || R2::is::<U4>()) && (C::is::<U1>() || C2::is::<U1>()) {
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unsafe {
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let mut a = *self.get_unchecked(0, 0) * *rhs.get_unchecked(0, 0);
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let mut b = *self.get_unchecked(1, 0) * *rhs.get_unchecked(1, 0);
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let c = *self.get_unchecked(2, 0) * *rhs.get_unchecked(2, 0);
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let d = *self.get_unchecked(3, 0) * *rhs.get_unchecked(3, 0);
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a += c;
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b += d;
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return a + b;
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}
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}
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// All this is inspired from the "unrolled version" discussed in:
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// http://blog.theincredibleholk.org/blog/2012/12/10/optimizing-dot-product/
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//
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// And this comment from bluss:
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// https://users.rust-lang.org/t/how-to-zip-two-slices-efficiently/2048/12
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let mut res = N::zero();
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// We have to define them outside of the loop (and not inside at first assignment)
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// otherwize vectorization won't kick in for some reason.
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let mut acc0;
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let mut acc1;
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let mut acc2;
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let mut acc3;
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let mut acc4;
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let mut acc5;
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let mut acc6;
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let mut acc7;
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for j in 0..self.ncols() {
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let mut i = 0;
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acc0 = N::zero();
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acc1 = N::zero();
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acc2 = N::zero();
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acc3 = N::zero();
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acc4 = N::zero();
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acc5 = N::zero();
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acc6 = N::zero();
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acc7 = N::zero();
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while self.nrows() - i >= 8 {
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acc0 += unsafe { *self.get_unchecked(i + 0, j) * *rhs.get_unchecked(i + 0, j) };
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acc1 += unsafe { *self.get_unchecked(i + 1, j) * *rhs.get_unchecked(i + 1, j) };
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acc2 += unsafe { *self.get_unchecked(i + 2, j) * *rhs.get_unchecked(i + 2, j) };
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acc3 += unsafe { *self.get_unchecked(i + 3, j) * *rhs.get_unchecked(i + 3, j) };
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acc4 += unsafe { *self.get_unchecked(i + 4, j) * *rhs.get_unchecked(i + 4, j) };
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acc5 += unsafe { *self.get_unchecked(i + 5, j) * *rhs.get_unchecked(i + 5, j) };
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acc6 += unsafe { *self.get_unchecked(i + 6, j) * *rhs.get_unchecked(i + 6, j) };
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acc7 += unsafe { *self.get_unchecked(i + 7, j) * *rhs.get_unchecked(i + 7, j) };
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i += 8;
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}
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res += acc0 + acc4;
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res += acc1 + acc5;
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res += acc2 + acc6;
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res += acc3 + acc7;
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for k in i..self.nrows() {
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res += unsafe { *self.get_unchecked(k, j) * *rhs.get_unchecked(k, j) }
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}
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}
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res
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}
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/// The dot product between the transpose of `self` and `rhs`.
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#[inline]
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pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
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where
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SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>,
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{
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let (nrows, ncols) = self.shape();
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assert!(
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(ncols, nrows) == rhs.shape(),
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"Transposed dot product dimension mismatch."
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);
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let mut res = N::zero();
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for j in 0..self.nrows() {
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for i in 0..self.ncols() {
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res += unsafe { *self.get_unchecked(j, i) * *rhs.get_unchecked(i, j) }
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}
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}
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res
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}
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}
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fn array_axpy<N>(y: &mut [N], a: N, x: &[N], beta: N, stride1: usize, stride2: usize, len: usize)
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where
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N: Scalar + Zero + ClosedAdd + ClosedMul,
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{
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for i in 0..len {
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unsafe {
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let y = y.get_unchecked_mut(i * stride1);
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*y = a * *x.get_unchecked(i * stride2) + beta * *y;
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}
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}
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}
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fn array_ax<N>(y: &mut [N], a: N, x: &[N], stride1: usize, stride2: usize, len: usize)
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where
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N: Scalar + Zero + ClosedAdd + ClosedMul,
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{
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for i in 0..len {
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unsafe {
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*y.get_unchecked_mut(i * stride1) = a * *x.get_unchecked(i * stride2);
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}
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}
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}
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impl<N, D: Dim, S> Vector<N, D, S>
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where
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N: Scalar + Zero + ClosedAdd + ClosedMul,
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S: StorageMut<N, D>,
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{
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/// Computes `self = a * x + b * self`.
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///
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/// If be is zero, `self` is never read from.
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#[inline]
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pub fn axpy<D2: Dim, SB>(&mut self, a: N, x: &Vector<N, D2, SB>, b: N)
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where
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SB: Storage<N, D2>,
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ShapeConstraint: DimEq<D, D2>,
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{
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assert_eq!(self.nrows(), x.nrows(), "Axpy: mismatched vector shapes.");
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let rstride1 = self.strides().0;
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let rstride2 = x.strides().0;
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let y = self.data.as_mut_slice();
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let x = x.data.as_slice();
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if !b.is_zero() {
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array_axpy(y, a, x, b, rstride1, rstride2, x.len());
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} else {
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array_ax(y, a, x, rstride1, rstride2, x.len());
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}
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}
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/// Computes `self = alpha * a * x + beta * self`, where `a` is a matrix, `x` a vector, and
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/// `alpha, beta` two scalars.
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///
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/// If `beta` is zero, `self` is never read.
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#[inline]
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pub fn gemv<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
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&mut self,
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alpha: N,
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a: &Matrix<N, R2, C2, SB>,
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x: &Vector<N, D3, SC>,
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beta: N,
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) where
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N: One,
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SB: Storage<N, R2, C2>,
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SC: Storage<N, D3>,
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ShapeConstraint: DimEq<D, R2> + AreMultipliable<R2, C2, D3, U1>,
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{
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let dim1 = self.nrows();
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let (nrows2, ncols2) = a.shape();
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let dim3 = x.nrows();
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assert!(
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ncols2 == dim3 && dim1 == nrows2,
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"Gemv: dimensions mismatch."
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);
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if ncols2 == 0 {
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return;
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}
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// FIXME: avoid bound checks.
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let col2 = a.column(0);
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let val = unsafe { *x.vget_unchecked(0) };
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self.axpy(alpha * val, &col2, beta);
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for j in 1..ncols2 {
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let col2 = a.column(j);
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let val = unsafe { *x.vget_unchecked(j) };
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self.axpy(alpha * val, &col2, N::one());
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}
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}
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/// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** matrix, `x` a
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/// vector, and `alpha, beta` two scalars.
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///
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/// If `beta` is zero, `self` is never read. If `self` is read, only its lower-triangular part
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/// (including the diagonal) is actually read.
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#[inline]
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pub fn gemv_symm<D2: Dim, D3: Dim, SB, SC>(
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&mut self,
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alpha: N,
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a: &SquareMatrix<N, D2, SB>,
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x: &Vector<N, D3, SC>,
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beta: N,
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) where
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N: One,
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SB: Storage<N, D2, D2>,
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SC: Storage<N, D3>,
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ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,
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{
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let dim1 = self.nrows();
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let dim2 = a.nrows();
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let dim3 = x.nrows();
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assert!(
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a.is_square(),
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"Syetric gemv: the input matrix must be square."
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);
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assert!(
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dim2 == dim3 && dim1 == dim2,
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"Symmetric gemv: dimensions mismatch."
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);
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if dim2 == 0 {
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return;
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}
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// FIXME: avoid bound checks.
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let col2 = a.column(0);
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let val = unsafe { *x.vget_unchecked(0) };
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self.axpy(alpha * val, &col2, beta);
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self[0] += alpha * x.rows_range(1..).dot(&a.slice_range(1.., 0));
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for j in 1..dim2 {
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let col2 = a.column(j);
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let dot = x.rows_range(j..).dot(&col2.rows_range(j..));
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let val;
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unsafe {
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val = *x.vget_unchecked(j);
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*self.vget_unchecked_mut(j) += alpha * dot;
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}
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self.rows_range_mut(j + 1..)
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.axpy(alpha * val, &col2.rows_range(j + 1..), N::one());
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}
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}
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/// Computes `self = alpha * a.transpose() * x + beta * self`, where `a` is a matrix, `x` a vector, and
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/// `alpha, beta` two scalars.
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///
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/// If `beta` is zero, `self` is never read.
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#[inline]
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pub fn gemv_tr<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
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&mut self,
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alpha: N,
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a: &Matrix<N, R2, C2, SB>,
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x: &Vector<N, D3, SC>,
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beta: N,
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) where
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N: One,
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SB: Storage<N, R2, C2>,
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SC: Storage<N, D3>,
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ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
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{
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let dim1 = self.nrows();
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let (nrows2, ncols2) = a.shape();
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let dim3 = x.nrows();
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assert!(
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nrows2 == dim3 && dim1 == ncols2,
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"Gemv: dimensions mismatch."
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);
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if ncols2 == 0 {
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return;
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}
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if beta.is_zero() {
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for j in 0..ncols2 {
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let val = unsafe { self.vget_unchecked_mut(j) };
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*val = alpha * a.column(j).dot(x)
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}
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} else {
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for j in 0..ncols2 {
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let val = unsafe { self.vget_unchecked_mut(j) };
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*val = alpha * a.column(j).dot(x) + beta * *val;
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}
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}
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}
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}
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|
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impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
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where
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N: Scalar + Zero + ClosedAdd + ClosedMul,
|
|
{
|
|
/// Computes `self = alpha * x * y.transpose() + beta * self`.
|
|
///
|
|
/// If `beta` is zero, `self` is never read.
|
|
#[inline]
|
|
pub fn ger<D2: Dim, D3: Dim, SB, SC>(
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&mut self,
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alpha: N,
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x: &Vector<N, D2, SB>,
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y: &Vector<N, D3, SC>,
|
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beta: N,
|
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) where
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N: One,
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SB: Storage<N, D2>,
|
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SC: Storage<N, D3>,
|
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ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
|
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{
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let (nrows1, ncols1) = self.shape();
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let dim2 = x.nrows();
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let dim3 = y.nrows();
|
|
|
|
assert!(
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nrows1 == dim2 && ncols1 == dim3,
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|
"ger: dimensions mismatch."
|
|
);
|
|
|
|
for j in 0..ncols1 {
|
|
// FIXME: avoid bound checks.
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|
let val = unsafe { *y.vget_unchecked(j) };
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self.column_mut(j).axpy(alpha * val, x, beta);
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}
|
|
}
|
|
|
|
/// 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.
|
|
#[inline]
|
|
pub fn gemm<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
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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>();
|
|
// Thershold determined ampirically.
|
|
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,
|
|
);
|
|
}
|
|
} 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.
|
|
#[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.
|
|
#[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.
|
|
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.
|
|
/// Use `.quadform_tr_with_workspace(...)` instead to avoid allocations.
|
|
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.
|
|
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.
|
|
/// Use `.quadform_with_workspace(...)` instead to avoid allocations.
|
|
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)
|
|
}
|
|
}
|