M-Labs
/
nalgebra
3
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
nalgebra/src/core/blas.rs

498 lines
18 KiB
Rust
Raw Normal View History

Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
use std::mem;
use num::{Zero, One, Signed};
use matrixmultiply;
use alga::general::{ClosedMul, ClosedAdd};
Add symmetric quadratic form computation.
2018-02-02 19:26:07 +08:00
use core::{DefaultAllocator, Scalar, Matrix, SquareMatrix, Vector};
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
use core::dimension::{Dim, U1, U2, U3, U4, Dynamic};
use core::constraint::{ShapeConstraint, SameNumberOfRows, SameNumberOfColumns, AreMultipliable, DimEq};
use core::storage::{Storage, StorageMut};
Add symmetric quadratic form computation.
2018-02-02 19:26:07 +08:00
use core::allocator::Allocator;
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
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 absolute value.
#[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
}
}
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.
#[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 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`, `*`.
#[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
Fix spelling of "below"
2017-10-27 12:13:35 +08:00
// because the `for` loop below won't be very efficient on those.
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
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)
// otherwize 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`.
#[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.
#[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.
#[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.
#[inline]
pub fn gemv_symm<D2: Dim, D3: Dim, SB, SC>(&mut self,
alpha: N,
Add symmetric quadratic form computation.
2018-02-02 19:26:07 +08:00
a: &SquareMatrix<N, D2, SB>,
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
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());
}
}
}
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.
#[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.
#[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 (nrows1, ncols1) = self.shape();
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);
}
}
}
else {
for j1 in 0 .. ncols1 {
// FIXME: avoid bound checks.
self.column_mut(j1).gemv(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);
Add symmetric quadratic form computation.
2018-02-02 19:26:07 +08:00
// FIXME: avoid bound checks.
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
self.generic_slice_mut((j, j), (subdim, U1)).axpy(alpha * val, &x.rows_range(j ..), beta);
}
}
}
Add symmetric quadratic form computation.
2018-02-02 19:26:07 +08:00
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());
}
}
}