forked from M-Labs/nalgebra
867 lines
29 KiB
Rust
867 lines
29 KiB
Rust
use num::{One, Signed, Zero};
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use std::cmp::PartialOrd;
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use std::iter;
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use std::ops::{
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Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
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};
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use alga::general::{ComplexField, ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
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use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
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use crate::base::constraint::{
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AreMultipliable, DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
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};
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use crate::base::dimension::{Dim, DimMul, DimName, DimProd};
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use crate::base::storage::{ContiguousStorageMut, Storage, StorageMut};
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use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, MatrixSum, Scalar, VectorSliceN};
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/*
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*
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* Indexing.
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*
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*/
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impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Index<usize> for Matrix<N, R, C, S> {
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type Output = N;
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#[inline]
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fn index(&self, i: usize) -> &Self::Output {
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let ij = self.vector_to_matrix_index(i);
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&self[ij]
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}
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}
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impl<N, R: Dim, C: Dim, S> Index<(usize, usize)> for Matrix<N, R, C, S>
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where
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N: Scalar,
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S: Storage<N, R, C>,
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{
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type Output = N;
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#[inline]
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fn index(&self, ij: (usize, usize)) -> &Self::Output {
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let shape = self.shape();
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assert!(
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ij.0 < shape.0 && ij.1 < shape.1,
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"Matrix index out of bounds."
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);
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unsafe { self.get_unchecked((ij.0, ij.1)) }
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}
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}
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// Mutable versions.
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impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> IndexMut<usize> for Matrix<N, R, C, S> {
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#[inline]
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fn index_mut(&mut self, i: usize) -> &mut N {
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let ij = self.vector_to_matrix_index(i);
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&mut self[ij]
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}
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}
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impl<N, R: Dim, C: Dim, S> IndexMut<(usize, usize)> for Matrix<N, R, C, S>
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where
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N: Scalar,
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S: StorageMut<N, R, C>,
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{
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#[inline]
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fn index_mut(&mut self, ij: (usize, usize)) -> &mut N {
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let shape = self.shape();
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assert!(
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ij.0 < shape.0 && ij.1 < shape.1,
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"Matrix index out of bounds."
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);
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unsafe { self.get_unchecked_mut((ij.0, ij.1)) }
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}
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}
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/*
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*
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* Neg
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*
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*/
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impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S>
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where
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N: Scalar + ClosedNeg,
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S: Storage<N, R, C>,
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DefaultAllocator: Allocator<N, R, C>,
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{
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type Output = MatrixMN<N, R, C>;
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#[inline]
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fn neg(self) -> Self::Output {
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let mut res = self.into_owned();
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res.neg_mut();
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res
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}
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}
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impl<'a, N, R: Dim, C: Dim, S> Neg for &'a Matrix<N, R, C, S>
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where
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N: Scalar + ClosedNeg,
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S: Storage<N, R, C>,
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DefaultAllocator: Allocator<N, R, C>,
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{
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type Output = MatrixMN<N, R, C>;
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#[inline]
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fn neg(self) -> Self::Output {
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-self.clone_owned()
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}
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}
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impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S>
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where
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N: Scalar + ClosedNeg,
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S: StorageMut<N, R, C>,
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{
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/// Negates `self` in-place.
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#[inline]
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pub fn neg_mut(&mut self) {
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for e in self.iter_mut() {
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*e = -*e
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}
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}
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}
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/*
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*
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* Addition & Subtraction
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*
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*/
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macro_rules! componentwise_binop_impl(
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($Trait: ident, $method: ident, $bound: ident;
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$TraitAssign: ident, $method_assign: ident, $method_assign_statically_unchecked: ident,
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$method_assign_statically_unchecked_rhs: ident;
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$method_to: ident, $method_to_statically_unchecked: ident) => {
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impl<N, R1: Dim, C1: Dim, SA: Storage<N, R1, C1>> Matrix<N, R1, C1, SA>
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where N: Scalar + $bound {
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/*
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*
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* Methods without dimension checking at compile-time.
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* This is useful for code reuse because the sum representative system does not plays
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* easily with static checks.
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*
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*/
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#[inline]
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fn $method_to_statically_unchecked<R2: Dim, C2: Dim, SB,
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R3: Dim, C3: Dim, SC>(&self,
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rhs: &Matrix<N, R2, C2, SB>,
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out: &mut Matrix<N, R3, C3, SC>)
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where SB: Storage<N, R2, C2>,
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SC: StorageMut<N, R3, C3> {
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assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
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assert!(self.shape() == out.shape(), "Matrix addition/subtraction output dimensions mismatch.");
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// This is the most common case and should be deduced at compile-time.
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// FIXME: use specialization instead?
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if self.data.is_contiguous() && rhs.data.is_contiguous() && out.data.is_contiguous() {
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let arr1 = self.data.as_slice();
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let arr2 = rhs.data.as_slice();
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let out = out.data.as_mut_slice();
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for i in 0 .. arr1.len() {
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unsafe {
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*out.get_unchecked_mut(i) = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
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}
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}
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}
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else {
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for j in 0 .. self.ncols() {
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for i in 0 .. self.nrows() {
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unsafe {
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let val = self.get_unchecked((i, j)).$method(*rhs.get_unchecked((i, j)));
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*out.get_unchecked_mut((i, j)) = 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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#[inline]
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fn $method_assign_statically_unchecked<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
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where R2: Dim,
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C2: Dim,
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SA: StorageMut<N, R1, C1>,
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SB: Storage<N, R2, C2> {
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assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
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// This is the most common case and should be deduced at compile-time.
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// FIXME: use specialization instead?
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if self.data.is_contiguous() && rhs.data.is_contiguous() {
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let arr1 = self.data.as_mut_slice();
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let arr2 = rhs.data.as_slice();
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for i in 0 .. arr2.len() {
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unsafe {
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arr1.get_unchecked_mut(i).$method_assign(*arr2.get_unchecked(i));
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}
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}
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}
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else {
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for j in 0 .. rhs.ncols() {
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for i in 0 .. rhs.nrows() {
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unsafe {
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self.get_unchecked_mut((i, j)).$method_assign(*rhs.get_unchecked((i, j)))
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}
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}
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}
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}
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}
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#[inline]
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fn $method_assign_statically_unchecked_rhs<R2, C2, SB>(&self, rhs: &mut Matrix<N, R2, C2, SB>)
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where R2: Dim,
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C2: Dim,
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SB: StorageMut<N, R2, C2> {
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assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
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// This is the most common case and should be deduced at compile-time.
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// FIXME: use specialization instead?
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if self.data.is_contiguous() && rhs.data.is_contiguous() {
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let arr1 = self.data.as_slice();
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let arr2 = rhs.data.as_mut_slice();
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for i in 0 .. arr1.len() {
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unsafe {
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let res = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
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*arr2.get_unchecked_mut(i) = res;
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}
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}
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}
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else {
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for j in 0 .. self.ncols() {
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for i in 0 .. self.nrows() {
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unsafe {
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let r = rhs.get_unchecked_mut((i, j));
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*r = self.get_unchecked((i, j)).$method(*r)
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}
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}
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}
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}
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}
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/*
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*
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* Methods without dimension checking at compile-time.
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* This is useful for code reuse because the sum representative system does not plays
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* easily with static checks.
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*
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*/
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/// Equivalent to `self + rhs` but stores the result into `out` to avoid allocations.
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#[inline]
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pub fn $method_to<R2: Dim, C2: Dim, SB,
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R3: Dim, C3: Dim, SC>(&self,
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rhs: &Matrix<N, R2, C2, SB>,
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out: &mut Matrix<N, R3, C3, SC>)
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where SB: Storage<N, R2, C2>,
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SC: StorageMut<N, R3, C3>,
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ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> +
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SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3> {
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self.$method_to_statically_unchecked(rhs, out)
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}
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}
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impl<'b, N, R1, C1, R2, C2, SA, SB> $Trait<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
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where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
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N: Scalar + $bound,
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SA: Storage<N, R1, C1>,
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SB: Storage<N, R2, C2>,
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DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
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type Output = MatrixSum<N, R1, C1, R2, C2>;
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#[inline]
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fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
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assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
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let mut res = self.into_owned_sum::<R2, C2>();
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res.$method_assign_statically_unchecked(rhs);
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res
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}
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}
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impl<'a, N, R1, C1, R2, C2, SA, SB> $Trait<Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA>
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where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
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N: Scalar + $bound,
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SA: Storage<N, R1, C1>,
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SB: Storage<N, R2, C2>,
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DefaultAllocator: SameShapeAllocator<N, R2, C2, R1, C1>,
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ShapeConstraint: SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1> {
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type Output = MatrixSum<N, R2, C2, R1, C1>;
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#[inline]
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fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
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let mut rhs = rhs.into_owned_sum::<R1, C1>();
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assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
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self.$method_assign_statically_unchecked_rhs(&mut rhs);
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rhs
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}
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}
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impl<N, R1, C1, R2, C2, SA, SB> $Trait<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
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where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
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N: Scalar + $bound,
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SA: Storage<N, R1, C1>,
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SB: Storage<N, R2, C2>,
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DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
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type Output = MatrixSum<N, R1, C1, R2, C2>;
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#[inline]
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fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
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self.$method(&rhs)
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}
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}
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impl<'a, 'b, N, R1, C1, R2, C2, SA, SB> $Trait<&'b Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA>
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where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
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N: Scalar + $bound,
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SA: Storage<N, R1, C1>,
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SB: Storage<N, R2, C2>,
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DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
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type Output = MatrixSum<N, R1, C1, R2, C2>;
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#[inline]
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fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
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let mut res = unsafe {
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let (nrows, ncols) = self.shape();
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let nrows: SameShapeR<R1, R2> = Dim::from_usize(nrows);
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let ncols: SameShapeC<C1, C2> = Dim::from_usize(ncols);
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Matrix::new_uninitialized_generic(nrows, ncols)
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};
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self.$method_to_statically_unchecked(rhs, &mut res);
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res
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}
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}
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impl<'b, N, R1, C1, R2, C2, SA, SB> $TraitAssign<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
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where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
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N: Scalar + $bound,
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SA: StorageMut<N, R1, C1>,
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SB: Storage<N, R2, C2>,
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ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
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|
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#[inline]
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fn $method_assign(&mut self, rhs: &'b Matrix<N, R2, C2, SB>) {
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self.$method_assign_statically_unchecked(rhs)
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}
|
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}
|
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|
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impl<N, R1, C1, R2, C2, SA, SB> $TraitAssign<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
|
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where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
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N: Scalar + $bound,
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SA: StorageMut<N, R1, C1>,
|
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SB: Storage<N, R2, C2>,
|
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ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
|
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|
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#[inline]
|
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fn $method_assign(&mut self, rhs: Matrix<N, R2, C2, SB>) {
|
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self.$method_assign(&rhs)
|
||
}
|
||
}
|
||
}
|
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);
|
||
|
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componentwise_binop_impl!(Add, add, ClosedAdd;
|
||
AddAssign, add_assign, add_assign_statically_unchecked, add_assign_statically_unchecked_mut;
|
||
add_to, add_to_statically_unchecked);
|
||
componentwise_binop_impl!(Sub, sub, ClosedSub;
|
||
SubAssign, sub_assign, sub_assign_statically_unchecked, sub_assign_statically_unchecked_mut;
|
||
sub_to, sub_to_statically_unchecked);
|
||
|
||
impl<N, R: DimName, C: DimName> iter::Sum for MatrixMN<N, R, C>
|
||
where
|
||
N: Scalar + ClosedAdd + Zero,
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
fn sum<I: Iterator<Item = MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C> {
|
||
iter.fold(Matrix::zero(), |acc, x| acc + x)
|
||
}
|
||
}
|
||
|
||
impl<'a, N, R: DimName, C: DimName> iter::Sum<&'a MatrixMN<N, R, C>> for MatrixMN<N, R, C>
|
||
where
|
||
N: Scalar + ClosedAdd + Zero,
|
||
DefaultAllocator: Allocator<N, R, C>,
|
||
{
|
||
fn sum<I: Iterator<Item = &'a MatrixMN<N, R, C>>>(iter: I) -> MatrixMN<N, R, C> {
|
||
iter.fold(Matrix::zero(), |acc, x| acc + x)
|
||
}
|
||
}
|
||
|
||
/*
|
||
*
|
||
* Multiplication
|
||
*
|
||
*/
|
||
|
||
// Matrix × Scalar
|
||
// Matrix / Scalar
|
||
macro_rules! componentwise_scalarop_impl(
|
||
($Trait: ident, $method: ident, $bound: ident;
|
||
$TraitAssign: ident, $method_assign: ident) => {
|
||
impl<N, R: Dim, C: Dim, S> $Trait<N> for Matrix<N, R, C, S>
|
||
where N: Scalar + $bound,
|
||
S: Storage<N, R, C>,
|
||
DefaultAllocator: Allocator<N, R, C> {
|
||
type Output = MatrixMN<N, R, C>;
|
||
|
||
#[inline]
|
||
fn $method(self, rhs: N) -> Self::Output {
|
||
let mut res = self.into_owned();
|
||
|
||
// XXX: optimize our iterator!
|
||
//
|
||
// Using our own iterator prevents loop unrolling, which breaks some optimization
|
||
// (like SIMD). On the other hand, using the slice iterator is 4x faster.
|
||
|
||
// for left in res.iter_mut() {
|
||
for left in res.as_mut_slice().iter_mut() {
|
||
*left = left.$method(rhs)
|
||
}
|
||
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<'a, N, R: Dim, C: Dim, S> $Trait<N> for &'a Matrix<N, R, C, S>
|
||
where N: Scalar + $bound,
|
||
S: Storage<N, R, C>,
|
||
DefaultAllocator: Allocator<N, R, C> {
|
||
type Output = MatrixMN<N, R, C>;
|
||
|
||
#[inline]
|
||
fn $method(self, rhs: N) -> Self::Output {
|
||
self.clone_owned().$method(rhs)
|
||
}
|
||
}
|
||
|
||
impl<N, R: Dim, C: Dim, S> $TraitAssign<N> for Matrix<N, R, C, S>
|
||
where N: Scalar + $bound,
|
||
S: StorageMut<N, R, C> {
|
||
#[inline]
|
||
fn $method_assign(&mut self, rhs: N) {
|
||
for j in 0 .. self.ncols() {
|
||
for i in 0 .. self.nrows() {
|
||
unsafe { self.get_unchecked_mut((i, j)).$method_assign(rhs) };
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
);
|
||
|
||
componentwise_scalarop_impl!(Mul, mul, ClosedMul; MulAssign, mul_assign);
|
||
componentwise_scalarop_impl!(Div, div, ClosedDiv; DivAssign, div_assign);
|
||
|
||
macro_rules! left_scalar_mul_impl(
|
||
($($T: ty),* $(,)*) => {$(
|
||
impl<R: Dim, C: Dim, S: Storage<$T, R, C>> Mul<Matrix<$T, R, C, S>> for $T
|
||
where DefaultAllocator: Allocator<$T, R, C> {
|
||
type Output = MatrixMN<$T, R, C>;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: Matrix<$T, R, C, S>) -> Self::Output {
|
||
let mut res = rhs.into_owned();
|
||
|
||
// XXX: optimize our iterator!
|
||
//
|
||
// Using our own iterator prevents loop unrolling, which breaks some optimization
|
||
// (like SIMD). On the other hand, using the slice iterator is 4x faster.
|
||
|
||
// for rhs in res.iter_mut() {
|
||
for rhs in res.as_mut_slice().iter_mut() {
|
||
*rhs = self * *rhs
|
||
}
|
||
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<'b, R: Dim, C: Dim, S: Storage<$T, R, C>> Mul<&'b Matrix<$T, R, C, S>> for $T
|
||
where DefaultAllocator: Allocator<$T, R, C> {
|
||
type Output = MatrixMN<$T, R, C>;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: &'b Matrix<$T, R, C, S>) -> Self::Output {
|
||
self * rhs.clone_owned()
|
||
}
|
||
}
|
||
)*}
|
||
);
|
||
|
||
left_scalar_mul_impl!(u8, u16, u32, u64, usize, i8, i16, i32, i64, isize, f32, f64);
|
||
|
||
// Matrix × Matrix
|
||
impl<'a, 'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>>
|
||
for &'a Matrix<N, R1, C1, SA>
|
||
where
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SA: Storage<N, R1, C1>,
|
||
SB: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, R1, C2>,
|
||
ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,
|
||
{
|
||
type Output = MatrixMN<N, R1, C2>;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
|
||
let mut res =
|
||
unsafe { Matrix::new_uninitialized_generic(self.data.shape().0, rhs.data.shape().1) };
|
||
|
||
self.mul_to(rhs, &mut res);
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<'a, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>>
|
||
for &'a Matrix<N, R1, C1, SA>
|
||
where
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SB: Storage<N, R2, C2>,
|
||
SA: Storage<N, R1, C1>,
|
||
DefaultAllocator: Allocator<N, R1, C2>,
|
||
ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,
|
||
{
|
||
type Output = MatrixMN<N, R1, C2>;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
|
||
self * &rhs
|
||
}
|
||
}
|
||
|
||
impl<'b, N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<&'b Matrix<N, R2, C2, SB>>
|
||
for Matrix<N, R1, C1, SA>
|
||
where
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SB: Storage<N, R2, C2>,
|
||
SA: Storage<N, R1, C1>,
|
||
DefaultAllocator: Allocator<N, R1, C2>,
|
||
ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,
|
||
{
|
||
type Output = MatrixMN<N, R1, C2>;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
|
||
&self * rhs
|
||
}
|
||
}
|
||
|
||
impl<N, R1: Dim, C1: Dim, R2: Dim, C2: Dim, SA, SB> Mul<Matrix<N, R2, C2, SB>>
|
||
for Matrix<N, R1, C1, SA>
|
||
where
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SB: Storage<N, R2, C2>,
|
||
SA: Storage<N, R1, C1>,
|
||
DefaultAllocator: Allocator<N, R1, C2>,
|
||
ShapeConstraint: AreMultipliable<R1, C1, R2, C2>,
|
||
{
|
||
type Output = MatrixMN<N, R1, C2>;
|
||
|
||
#[inline]
|
||
fn mul(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
|
||
&self * &rhs
|
||
}
|
||
}
|
||
|
||
// FIXME: this is too restrictive:
|
||
// − we can't use `a *= b` when `a` is a mutable slice.
|
||
// − we can't use `a *= b` when C2 is not equal to C1.
|
||
impl<N, R1, C1, R2, SA, SB> MulAssign<Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA>
|
||
where
|
||
R1: Dim,
|
||
C1: Dim,
|
||
R2: Dim,
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SB: Storage<N, R2, C1>,
|
||
SA: ContiguousStorageMut<N, R1, C1> + Clone,
|
||
ShapeConstraint: AreMultipliable<R1, C1, R2, C1>,
|
||
DefaultAllocator: Allocator<N, R1, C1, Buffer = SA>,
|
||
{
|
||
#[inline]
|
||
fn mul_assign(&mut self, rhs: Matrix<N, R2, C1, SB>) {
|
||
*self = &*self * rhs
|
||
}
|
||
}
|
||
|
||
impl<'b, N, R1, C1, R2, SA, SB> MulAssign<&'b Matrix<N, R2, C1, SB>> for Matrix<N, R1, C1, SA>
|
||
where
|
||
R1: Dim,
|
||
C1: Dim,
|
||
R2: Dim,
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SB: Storage<N, R2, C1>,
|
||
SA: ContiguousStorageMut<N, R1, C1> + Clone,
|
||
ShapeConstraint: AreMultipliable<R1, C1, R2, C1>,
|
||
// FIXME: this is too restrictive. See comments for the non-ref version.
|
||
DefaultAllocator: Allocator<N, R1, C1, Buffer = SA>,
|
||
{
|
||
#[inline]
|
||
fn mul_assign(&mut self, rhs: &'b Matrix<N, R2, C1, SB>) {
|
||
*self = &*self * rhs
|
||
}
|
||
}
|
||
|
||
// Transpose-multiplication.
|
||
impl<N, R1: Dim, C1: Dim, SA> Matrix<N, R1, C1, SA>
|
||
where
|
||
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
|
||
SA: Storage<N, R1, C1>,
|
||
{
|
||
/// Equivalent to `self.transpose() * rhs`.
|
||
#[inline]
|
||
pub fn tr_mul<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixMN<N, C1, C2>
|
||
where
|
||
SB: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, C1, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R1, R2>,
|
||
{
|
||
let mut res =
|
||
unsafe { Matrix::new_uninitialized_generic(self.data.shape().1, rhs.data.shape().1) };
|
||
|
||
self.tr_mul_to(rhs, &mut res);
|
||
res
|
||
}
|
||
|
||
/// Equivalent to `self.adjoint() * rhs`.
|
||
#[inline]
|
||
pub fn ad_mul<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixMN<N, C1, C2>
|
||
where
|
||
N: ComplexField,
|
||
SB: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, C1, C2>,
|
||
ShapeConstraint: SameNumberOfRows<R1, R2>,
|
||
{
|
||
let mut res =
|
||
unsafe { Matrix::new_uninitialized_generic(self.data.shape().1, rhs.data.shape().1) };
|
||
|
||
self.ad_mul_to(rhs, &mut res);
|
||
res
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn xx_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
|
||
&self,
|
||
rhs: &Matrix<N, R2, C2, SB>,
|
||
out: &mut Matrix<N, R3, C3, SC>,
|
||
dot: impl Fn(&VectorSliceN<N, R1, SA::RStride, SA::CStride>, &VectorSliceN<N, R2, SB::RStride, SB::CStride>) -> N,
|
||
) where
|
||
SB: Storage<N, R2, C2>,
|
||
SC: StorageMut<N, R3, C3>,
|
||
ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>,
|
||
{
|
||
let (nrows1, ncols1) = self.shape();
|
||
let (nrows2, ncols2) = rhs.shape();
|
||
let (nrows3, ncols3) = out.shape();
|
||
|
||
assert!(
|
||
nrows1 == nrows2,
|
||
"Matrix multiplication dimensions mismatch."
|
||
);
|
||
assert!(
|
||
nrows3 == ncols1 && ncols3 == ncols2,
|
||
"Matrix multiplication output dimensions mismatch."
|
||
);
|
||
|
||
for i in 0..ncols1 {
|
||
for j in 0..ncols2 {
|
||
let dot = dot(&self.column(i), &rhs.column(j));
|
||
unsafe { *out.get_unchecked_mut((i, j)) = dot };
|
||
}
|
||
}
|
||
}
|
||
|
||
/// Equivalent to `self.transpose() * rhs` but stores the result into `out` to avoid
|
||
/// allocations.
|
||
#[inline]
|
||
pub fn tr_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
|
||
&self,
|
||
rhs: &Matrix<N, R2, C2, SB>,
|
||
out: &mut Matrix<N, R3, C3, SC>,
|
||
) where
|
||
SB: Storage<N, R2, C2>,
|
||
SC: StorageMut<N, R3, C3>,
|
||
ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>,
|
||
{
|
||
self.xx_mul_to(rhs, out, |a, b| a.dot(b))
|
||
}
|
||
|
||
/// Equivalent to `self.adjoint() * rhs` but stores the result into `out` to avoid
|
||
/// allocations.
|
||
#[inline]
|
||
pub fn ad_mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
|
||
&self,
|
||
rhs: &Matrix<N, R2, C2, SB>,
|
||
out: &mut Matrix<N, R3, C3, SC>,
|
||
) where
|
||
N: ComplexField,
|
||
SB: Storage<N, R2, C2>,
|
||
SC: StorageMut<N, R3, C3>,
|
||
ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>,
|
||
{
|
||
self.xx_mul_to(rhs, out, |a, b| a.dotc(b))
|
||
}
|
||
|
||
/// Equivalent to `self * rhs` but stores the result into `out` to avoid allocations.
|
||
#[inline]
|
||
pub fn mul_to<R2: Dim, C2: Dim, SB, R3: Dim, C3: Dim, SC>(
|
||
&self,
|
||
rhs: &Matrix<N, R2, C2, SB>,
|
||
out: &mut Matrix<N, R3, C3, SC>,
|
||
) where
|
||
SB: Storage<N, R2, C2>,
|
||
SC: StorageMut<N, R3, C3>,
|
||
ShapeConstraint: SameNumberOfRows<R3, R1>
|
||
+ SameNumberOfColumns<C3, C2>
|
||
+ AreMultipliable<R1, C1, R2, C2>,
|
||
{
|
||
out.gemm(N::one(), self, rhs, N::zero());
|
||
}
|
||
|
||
/// The kronecker product of two matrices (aka. tensor product of the corresponding linear
|
||
/// maps).
|
||
pub fn kronecker<R2: Dim, C2: Dim, SB>(
|
||
&self,
|
||
rhs: &Matrix<N, R2, C2, SB>,
|
||
) -> MatrixMN<N, DimProd<R1, R2>, DimProd<C1, C2>>
|
||
where
|
||
N: ClosedMul,
|
||
R1: DimMul<R2>,
|
||
C1: DimMul<C2>,
|
||
SB: Storage<N, R2, C2>,
|
||
DefaultAllocator: Allocator<N, DimProd<R1, R2>, DimProd<C1, C2>>,
|
||
{
|
||
let (nrows1, ncols1) = self.data.shape();
|
||
let (nrows2, ncols2) = rhs.data.shape();
|
||
|
||
let mut res =
|
||
unsafe { Matrix::new_uninitialized_generic(nrows1.mul(nrows2), ncols1.mul(ncols2)) };
|
||
|
||
{
|
||
let mut data_res = res.data.ptr_mut();
|
||
|
||
for j1 in 0..ncols1.value() {
|
||
for j2 in 0..ncols2.value() {
|
||
for i1 in 0..nrows1.value() {
|
||
unsafe {
|
||
let coeff = *self.get_unchecked((i1, j1));
|
||
|
||
for i2 in 0..nrows2.value() {
|
||
*data_res = coeff * *rhs.get_unchecked((i2, j2));
|
||
data_res = data_res.offset(1);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
}
|
||
|
||
res
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar + ClosedAdd, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
|
||
/// Adds a scalar to `self`.
|
||
#[inline]
|
||
pub fn add_scalar(&self, rhs: N) -> MatrixMN<N, R, C>
|
||
where DefaultAllocator: Allocator<N, R, C> {
|
||
let mut res = self.clone_owned();
|
||
res.add_scalar_mut(rhs);
|
||
res
|
||
}
|
||
|
||
/// Adds a scalar to `self` in-place.
|
||
#[inline]
|
||
pub fn add_scalar_mut(&mut self, rhs: N)
|
||
where S: StorageMut<N, R, C> {
|
||
for e in self.iter_mut() {
|
||
*e += rhs
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<N, D: DimName> iter::Product for MatrixN<N, D>
|
||
where
|
||
N: Scalar + Zero + One + ClosedMul + ClosedAdd,
|
||
DefaultAllocator: Allocator<N, D, D>,
|
||
{
|
||
fn product<I: Iterator<Item = MatrixN<N, D>>>(iter: I) -> MatrixN<N, D> {
|
||
iter.fold(Matrix::one(), |acc, x| acc * x)
|
||
}
|
||
}
|
||
|
||
impl<'a, N, D: DimName> iter::Product<&'a MatrixN<N, D>> for MatrixN<N, D>
|
||
where
|
||
N: Scalar + Zero + One + ClosedMul + ClosedAdd,
|
||
DefaultAllocator: Allocator<N, D, D>,
|
||
{
|
||
fn product<I: Iterator<Item = &'a MatrixN<N, D>>>(iter: I) -> MatrixN<N, D> {
|
||
iter.fold(Matrix::one(), |acc, x| acc * x)
|
||
}
|
||
}
|
||
|
||
impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
|
||
#[inline(always)]
|
||
fn xcmp<N2>(&self, abs: impl Fn(N) -> N2, cmp: impl Fn(N2, N2) -> bool) -> N2
|
||
where N2: Scalar + PartialOrd + Zero {
|
||
let mut max = N2::zero();
|
||
|
||
for e in self.iter() {
|
||
let ae = abs(*e);
|
||
|
||
if cmp(ae, max) {
|
||
max = ae;
|
||
}
|
||
}
|
||
|
||
max
|
||
}
|
||
|
||
/// Returns the absolute value of the component with the largest absolute value.
|
||
#[inline]
|
||
pub fn amax(&self) -> N
|
||
where N: PartialOrd + Signed {
|
||
self.xcmp(|e| e.abs(), |a, b| a > b)
|
||
}
|
||
|
||
/// Returns the the 1-norm of the complex component with the largest 1-norm.
|
||
#[inline]
|
||
pub fn camax(&self) -> N::Real
|
||
where N: ComplexField {
|
||
self.xcmp(|e| e.norm1(), |a, b| a > b)
|
||
}
|
||
|
||
/// Returns the component with the largest value.
|
||
#[inline]
|
||
pub fn max(&self) -> N
|
||
where N: PartialOrd + Signed {
|
||
self.xcmp(|e| e, |a, b| a > b)
|
||
}
|
||
|
||
/// Returns the absolute value of the component with the smallest absolute value.
|
||
#[inline]
|
||
pub fn amin(&self) -> N
|
||
where N: PartialOrd + Signed {
|
||
self.xcmp(|e| e.abs(), |a, b| a < b)
|
||
}
|
||
|
||
/// Returns the the 1-norm of the complex component with the smallest 1-norm.
|
||
#[inline]
|
||
pub fn camin(&self) -> N::Real
|
||
where N: ComplexField {
|
||
self.xcmp(|e| e.norm1(), |a, b| a < b)
|
||
}
|
||
|
||
/// Returns the component with the smallest value.
|
||
#[inline]
|
||
pub fn min(&self) -> N
|
||
where N: PartialOrd + Signed {
|
||
self.xcmp(|e| e, |a, b| a < b)
|
||
}
|
||
} |