498 lines
18 KiB
Rust
498 lines
18 KiB
Rust
use std::mem;
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use num::{Zero, One, Signed};
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use matrixmultiply;
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use alga::general::{ClosedMul, ClosedAdd};
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use core::{DefaultAllocator, Scalar, Matrix, SquareMatrix, Vector};
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use core::dimension::{Dim, U1, U2, U3, U4, Dynamic};
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use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable, DimEq};
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use core::storage::{Storage, StorageMut};
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use core::allocator::Allocator;
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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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}
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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 N: Scalar + Zero + ClosedAdd + ClosedMul {
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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 SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<R, R2> + DimEq<C, C2> {
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assert!(self.nrows() == rhs.nrows(), "Dot product dimensions mismatch.");
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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>()) &&
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(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>()) &&
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(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>()) &&
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(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 SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<C, R2> + DimEq<R, C2> {
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let (nrows, ncols) = self.shape();
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assert!((ncols, nrows) == rhs.shape(), "Transposed dot product dimension mismatch.");
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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 N: Scalar + Zero + ClosedAdd + ClosedMul {
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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 N: Scalar + Zero + ClosedAdd + ClosedMul {
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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 N: Scalar + Zero + ClosedAdd + ClosedMul,
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S: StorageMut<N, D> {
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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 SB: Storage<N, D2>,
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ShapeConstraint: DimEq<D, D2> {
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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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}
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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>(&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 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> +
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AreMultipliable<R2, C2, D3, U1> {
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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!(ncols2 == dim3 && dim1 == nrows2, "Gemv: dimensions mismatch.");
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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>(&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 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> +
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AreMultipliable<D2, D2, D3, U1> {
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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!(a.is_square(), "Syetric gemv: the input matrix must be square.");
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assert!(dim2 == dim3 && dim1 == dim2, "Symmetric gemv: dimensions mismatch.");
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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 ..).axpy(alpha * val, &col2.rows_range(j + 1 ..), N::one());
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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 N: Scalar + Zero + ClosedAdd + ClosedMul {
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/// Computes `self = alpha * x * y.transpose() + beta * self`.
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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 ger<D2: Dim, D3: Dim, SB, SC>(&mut self, alpha: N, x: &Vector<N, D2, SB>, y: &Vector<N, D3, SC>, beta: N)
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where 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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let (nrows1, ncols1) = self.shape();
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let dim2 = x.nrows();
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let dim3 = y.nrows();
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assert!(nrows1 == dim2 && ncols1 == dim3, "ger: dimensions mismatch.");
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for j in 0 .. ncols1 {
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// 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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}
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}
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/// Computes `self = alpha * a * b + beta * self`, where `a, b, self` are matrices.
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/// `alpha` and `beta` are scalar.
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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 gemm<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(&mut self,
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alpha: N,
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a: &Matrix<N, R2, C2, SB>,
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b: &Matrix<N, R3, C3, SC>,
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beta: N)
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where N: One,
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SB: Storage<N, R2, C2>,
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SC: Storage<N, R3, C3>,
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ShapeConstraint: SameNumberOfRows<R1, R2> +
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SameNumberOfColumns<C1, C3> +
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AreMultipliable<R2, C2, R3, C3> {
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let (nrows1, ncols1) = self.shape();
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let (nrows2, ncols2) = a.shape();
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let (nrows3, ncols3) = b.shape();
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assert_eq!(ncols2, nrows3, "gemm: dimensions mismatch for multiplication.");
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assert_eq!((nrows1, ncols1), (nrows2, ncols3), "gemm: dimensions mismatch for addition.");
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// We assume large matrices will be Dynamic but small matrices static.
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// We could use matrixmultiply for large statically-sized matrices but the performance
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// threshold to activate it would be different from SMALL_DIM because our code optimizes
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// better for statically-sized matrices.
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let is_dynamic = R1::is::<Dynamic>() || C1::is::<Dynamic>() ||
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R2::is::<Dynamic>() || C2::is::<Dynamic>() ||
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R3::is::<Dynamic>() || C3::is::<Dynamic>();
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// Thershold determined ampirically.
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const SMALL_DIM: usize = 5;
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if is_dynamic &&
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nrows1 > SMALL_DIM && ncols1 > SMALL_DIM &&
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nrows2 > SMALL_DIM && ncols2 > SMALL_DIM {
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if N::is::<f32>() {
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let (rsa, csa) = a.strides();
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let (rsb, csb) = b.strides();
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let (rsc, csc) = self.strides();
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unsafe {
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matrixmultiply::sgemm(
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nrows2,
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ncols2,
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ncols3,
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mem::transmute_copy(&alpha),
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a.data.ptr() as *const f32,
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rsa as isize, csa as isize,
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b.data.ptr() as *const f32,
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rsb as isize, csb as isize,
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mem::transmute_copy(&beta),
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self.data.ptr_mut() as *mut f32,
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rsc as isize, csc as isize);
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}
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}
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else if N::is::<f64>() {
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let (rsa, csa) = a.strides();
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let (rsb, csb) = b.strides();
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let (rsc, csc) = self.strides();
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unsafe {
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matrixmultiply::dgemm(
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nrows2,
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ncols2,
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ncols3,
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mem::transmute_copy(&alpha),
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a.data.ptr() as *const f64,
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rsa as isize, csa as isize,
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b.data.ptr() as *const f64,
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rsb as isize, csb as isize,
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mem::transmute_copy(&beta),
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self.data.ptr_mut() as *mut f64,
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rsc as isize, csc as isize);
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}
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}
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}
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else {
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for j1 in 0 .. ncols1 {
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// FIXME: avoid bound checks.
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self.column_mut(j1).gemv(alpha, a, &b.column(j1), beta);
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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 N: Scalar + Zero + ClosedAdd + ClosedMul {
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/// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
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/// matrix.
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///
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/// If `beta` is zero, `self` is never read. The result is symmetric. Only the lower-triangular
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/// (including the diagonal) part of `self` is read/written.
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#[inline]
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pub fn ger_symm<D2: Dim, D3: Dim, SB, SC>(&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 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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let dim1 = self.nrows();
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let dim2 = x.nrows();
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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 * lrs * mid * lhs.transpose() + beta * self`.
|
||
pub fn quadform_symm<D2, S2, R3, C3, S3, S4>(&mut self,
|
||
scratch: &mut Vector<N, D1, S2>,
|
||
alpha: N,
|
||
mid: &SquareMatrix<N, D2, S3>,
|
||
rhs: &Matrix<N, R3, C3, S4>,
|
||
beta: N)
|
||
where D2: Dim, R3: Dim, C3: Dim,
|
||
S2: StorageMut<N, D1>,
|
||
S3: Storage<N, D2, D2>,
|
||
S4: Storage<N, R3, C3>,
|
||
ShapeConstraint: DimEq<D1, D2> + DimEq<D2, R3> + DimEq<D1, C3>, // FIXME: why is this one necessary?
|
||
DefaultAllocator: Allocator<N, D1> {
|
||
|
||
|
||
/*
|
||
scratch.gemv(N::one(), lhs, &mid.column(0), N::zero());
|
||
self.ger_symm(alpha, &scratch, &lhs.column(0), beta);
|
||
|
||
for j in 1 .. mid.ncols() {
|
||
scratch.gemv(N::one(), lhs, &mid.column(j), N::zero());
|
||
self.ger_symm(alpha, &scratch, &lhs.column(j), N::one());
|
||
}
|
||
*/
|
||
|
||
scratch.gemv_symm(N::one(), mid, &rhs.column(0), N::zero());
|
||
self.column_mut(0).gemv(alpha, rhs, &scratch, beta);
|
||
|
||
for j in 1 .. mid.ncols() {
|
||
scratch.gemv_symm(N::one(), mid, &rhs.column(j), N::zero());
|
||
self.slice_range_mut(j .., j).gemv(alpha, &rhs.rows_range(j ..), &scratch, N::one());
|
||
}
|
||
}
|
||
}
|