nalgebra/src/base/ops.rs

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use num::{One, Signed, Zero};
use std::cmp::{PartialOrd, Ordering};
use std::iter;
use std::ops::{
Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
};
use alga::general::{ComplexField, ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
use crate::base::constraint::{
AreMultipliable, DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
};
use crate::base::dimension::{Dim, DimMul, DimName, DimProd, Dynamic};
use crate::base::storage::{ContiguousStorageMut, Storage, StorageMut};
use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, MatrixSum, Scalar, VectorSliceN};
/*
*
* Indexing.
*
*/
impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Index<usize> for Matrix<N, R, C, S> {
type Output = N;
#[inline]
fn index(&self, i: usize) -> &Self::Output {
let ij = self.vector_to_matrix_index(i);
&self[ij]
}
}
impl<N, R: Dim, C: Dim, S> Index<(usize, usize)> for Matrix<N, R, C, S>
where
N: Scalar,
S: Storage<N, R, C>,
{
type Output = N;
#[inline]
fn index(&self, ij: (usize, usize)) -> &Self::Output {
let shape = self.shape();
assert!(
ij.0 < shape.0 && ij.1 < shape.1,
"Matrix index out of bounds."
);
unsafe { self.get_unchecked((ij.0, ij.1)) }
}
}
// Mutable versions.
impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> IndexMut<usize> for Matrix<N, R, C, S> {
#[inline]
fn index_mut(&mut self, i: usize) -> &mut N {
let ij = self.vector_to_matrix_index(i);
&mut self[ij]
}
}
impl<N, R: Dim, C: Dim, S> IndexMut<(usize, usize)> for Matrix<N, R, C, S>
where
N: Scalar,
S: StorageMut<N, R, C>,
{
#[inline]
fn index_mut(&mut self, ij: (usize, usize)) -> &mut N {
let shape = self.shape();
assert!(
ij.0 < shape.0 && ij.1 < shape.1,
"Matrix index out of bounds."
);
unsafe { self.get_unchecked_mut((ij.0, ij.1)) }
}
}
/*
*
* Neg
*
*/
impl<N, R: Dim, C: Dim, S> Neg for Matrix<N, R, C, S>
where
N: Scalar + ClosedNeg,
S: Storage<N, R, C>,
DefaultAllocator: Allocator<N, R, C>,
{
type Output = MatrixMN<N, R, C>;
#[inline]
fn neg(self) -> Self::Output {
let mut res = self.into_owned();
res.neg_mut();
res
}
}
impl<'a, N, R: Dim, C: Dim, S> Neg for &'a Matrix<N, R, C, S>
where
N: Scalar + ClosedNeg,
S: Storage<N, R, C>,
DefaultAllocator: Allocator<N, R, C>,
{
type Output = MatrixMN<N, R, C>;
#[inline]
fn neg(self) -> Self::Output {
-self.clone_owned()
}
}
impl<N, R: Dim, C: Dim, S> Matrix<N, R, C, S>
where
N: Scalar + ClosedNeg,
S: StorageMut<N, R, C>,
{
/// Negates `self` in-place.
#[inline]
pub fn neg_mut(&mut self) {
for e in self.iter_mut() {
*e = -*e
}
}
}
/*
*
* Addition & Subtraction
*
*/
macro_rules! componentwise_binop_impl(
($Trait: ident, $method: ident, $bound: ident;
$TraitAssign: ident, $method_assign: ident, $method_assign_statically_unchecked: ident,
$method_assign_statically_unchecked_rhs: ident;
$method_to: ident, $method_to_statically_unchecked: ident) => {
impl<N, R1: Dim, C1: Dim, SA: Storage<N, R1, C1>> Matrix<N, R1, C1, SA>
where N: Scalar + $bound {
/*
*
* Methods without dimension checking at compile-time.
* This is useful for code reuse because the sum representative system does not plays
* easily with static checks.
*
*/
#[inline]
fn $method_to_statically_unchecked<R2: Dim, C2: Dim, SB,
R3: Dim, C3: Dim, SC>(&self,
rhs: &Matrix<N, R2, C2, SB>,
out: &mut Matrix<N, R3, C3, SC>)
where SB: Storage<N, R2, C2>,
SC: StorageMut<N, R3, C3> {
assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
assert!(self.shape() == out.shape(), "Matrix addition/subtraction output dimensions mismatch.");
// This is the most common case and should be deduced at compile-time.
// FIXME: use specialization instead?
if self.data.is_contiguous() && rhs.data.is_contiguous() && out.data.is_contiguous() {
let arr1 = self.data.as_slice();
let arr2 = rhs.data.as_slice();
let out = out.data.as_mut_slice();
for i in 0 .. arr1.len() {
unsafe {
*out.get_unchecked_mut(i) = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
}
}
}
else {
for j in 0 .. self.ncols() {
for i in 0 .. self.nrows() {
unsafe {
let val = self.get_unchecked((i, j)).$method(*rhs.get_unchecked((i, j)));
*out.get_unchecked_mut((i, j)) = val;
}
}
}
}
}
#[inline]
fn $method_assign_statically_unchecked<R2, C2, SB>(&mut self, rhs: &Matrix<N, R2, C2, SB>)
where R2: Dim,
C2: Dim,
SA: StorageMut<N, R1, C1>,
SB: Storage<N, R2, C2> {
assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
// This is the most common case and should be deduced at compile-time.
// FIXME: use specialization instead?
if self.data.is_contiguous() && rhs.data.is_contiguous() {
let arr1 = self.data.as_mut_slice();
let arr2 = rhs.data.as_slice();
for i in 0 .. arr2.len() {
unsafe {
arr1.get_unchecked_mut(i).$method_assign(*arr2.get_unchecked(i));
}
}
}
else {
for j in 0 .. rhs.ncols() {
for i in 0 .. rhs.nrows() {
unsafe {
self.get_unchecked_mut((i, j)).$method_assign(*rhs.get_unchecked((i, j)))
}
}
}
}
}
#[inline]
fn $method_assign_statically_unchecked_rhs<R2, C2, SB>(&self, rhs: &mut Matrix<N, R2, C2, SB>)
where R2: Dim,
C2: Dim,
SB: StorageMut<N, R2, C2> {
assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
// This is the most common case and should be deduced at compile-time.
// FIXME: use specialization instead?
if self.data.is_contiguous() && rhs.data.is_contiguous() {
let arr1 = self.data.as_slice();
let arr2 = rhs.data.as_mut_slice();
for i in 0 .. arr1.len() {
unsafe {
let res = arr1.get_unchecked(i).$method(*arr2.get_unchecked(i));
*arr2.get_unchecked_mut(i) = res;
}
}
}
else {
for j in 0 .. self.ncols() {
for i in 0 .. self.nrows() {
unsafe {
let r = rhs.get_unchecked_mut((i, j));
*r = self.get_unchecked((i, j)).$method(*r)
}
}
}
}
}
/*
*
* Methods without dimension checking at compile-time.
* This is useful for code reuse because the sum representative system does not plays
* easily with static checks.
*
*/
/// Equivalent to `self + rhs` but stores the result into `out` to avoid allocations.
#[inline]
pub fn $method_to<R2: Dim, C2: Dim, SB,
R3: Dim, C3: Dim, SC>(&self,
rhs: &Matrix<N, R2, C2, SB>,
out: &mut Matrix<N, R3, C3, SC>)
where SB: Storage<N, R2, C2>,
SC: StorageMut<N, R3, C3>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> +
SameNumberOfRows<R1, R3> + SameNumberOfColumns<C1, C3> {
self.$method_to_statically_unchecked(rhs, out)
}
}
impl<'b, N, R1, C1, R2, C2, SA, SB> $Trait<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
N: Scalar + $bound,
SA: Storage<N, R1, C1>,
SB: Storage<N, R2, C2>,
DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
type Output = MatrixSum<N, R1, C1, R2, C2>;
#[inline]
fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
let mut res = self.into_owned_sum::<R2, C2>();
res.$method_assign_statically_unchecked(rhs);
res
}
}
impl<'a, N, R1, C1, R2, C2, SA, SB> $Trait<Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA>
where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
N: Scalar + $bound,
SA: Storage<N, R1, C1>,
SB: Storage<N, R2, C2>,
DefaultAllocator: SameShapeAllocator<N, R2, C2, R1, C1>,
ShapeConstraint: SameNumberOfRows<R2, R1> + SameNumberOfColumns<C2, C1> {
type Output = MatrixSum<N, R2, C2, R1, C1>;
#[inline]
fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
let mut rhs = rhs.into_owned_sum::<R1, C1>();
assert!(self.shape() == rhs.shape(), "Matrix addition/subtraction dimensions mismatch.");
self.$method_assign_statically_unchecked_rhs(&mut rhs);
rhs
}
}
impl<N, R1, C1, R2, C2, SA, SB> $Trait<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
N: Scalar + $bound,
SA: Storage<N, R1, C1>,
SB: Storage<N, R2, C2>,
DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
type Output = MatrixSum<N, R1, C1, R2, C2>;
#[inline]
fn $method(self, rhs: Matrix<N, R2, C2, SB>) -> Self::Output {
self.$method(&rhs)
}
}
impl<'a, 'b, N, R1, C1, R2, C2, SA, SB> $Trait<&'b Matrix<N, R2, C2, SB>> for &'a Matrix<N, R1, C1, SA>
where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
N: Scalar + $bound,
SA: Storage<N, R1, C1>,
SB: Storage<N, R2, C2>,
DefaultAllocator: SameShapeAllocator<N, R1, C1, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
type Output = MatrixSum<N, R1, C1, R2, C2>;
#[inline]
fn $method(self, rhs: &'b Matrix<N, R2, C2, SB>) -> Self::Output {
let mut res = unsafe {
let (nrows, ncols) = self.shape();
let nrows: SameShapeR<R1, R2> = Dim::from_usize(nrows);
let ncols: SameShapeC<C1, C2> = Dim::from_usize(ncols);
Matrix::new_uninitialized_generic(nrows, ncols)
};
self.$method_to_statically_unchecked(rhs, &mut res);
res
}
}
impl<'b, N, R1, C1, R2, C2, SA, SB> $TraitAssign<&'b Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
N: Scalar + $bound,
SA: StorageMut<N, R1, C1>,
SB: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
#[inline]
fn $method_assign(&mut self, rhs: &'b Matrix<N, R2, C2, SB>) {
self.$method_assign_statically_unchecked(rhs)
}
}
impl<N, R1, C1, R2, C2, SA, SB> $TraitAssign<Matrix<N, R2, C2, SB>> for Matrix<N, R1, C1, SA>
where R1: Dim, C1: Dim, R2: Dim, C2: Dim,
N: Scalar + $bound,
SA: StorageMut<N, R1, C1>,
SB: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
#[inline]
fn $method_assign(&mut self, rhs: Matrix<N, R2, C2, SB>) {
self.$method_assign(&rhs)
}
}
}
);
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<N, C: Dim> iter::Sum for MatrixMN<N, Dynamic, C>
where
N: Scalar + ClosedAdd + Zero,
DefaultAllocator: Allocator<N, Dynamic, C>,
{
/// # Example
/// ```
/// # use nalgebra::DVector;
/// assert_eq!(vec![DVector::repeat(3, 1.0f64),
/// DVector::repeat(3, 1.0f64),
/// DVector::repeat(3, 1.0f64)].into_iter().sum::<DVector<f64>>(),
/// DVector::repeat(3, 1.0f64) + DVector::repeat(3, 1.0f64) + DVector::repeat(3, 1.0f64));
/// ```
///
/// # Panics
/// Panics if the iterator is empty:
/// ```should_panic
/// # use std::iter;
/// # use nalgebra::DMatrix;
/// iter::empty::<DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!
/// ```
fn sum<I: Iterator<Item = MatrixMN<N, Dynamic, C>>>(mut iter: I) -> MatrixMN<N, Dynamic, C> {
if let Some(first) = iter.next() {
iter.fold(first, |acc, x| acc + x)
} else {
panic!("Cannot compute `sum` of empty iterator.")
}
}
}
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)
}
}
impl<'a, N, C: Dim> iter::Sum<&'a MatrixMN<N, Dynamic, C>> for MatrixMN<N, Dynamic, C>
where
N: Scalar + ClosedAdd + Zero,
DefaultAllocator: Allocator<N, Dynamic, C>,
{
/// # Example
/// ```
/// # use nalgebra::DVector;
/// let v = &DVector::repeat(3, 1.0f64);
///
/// assert_eq!(vec![v, v, v].into_iter().sum::<DVector<f64>>(),
/// v + v + v);
/// ```
///
/// # Panics
/// Panics if the iterator is empty:
/// ```should_panic
/// # use std::iter;
/// # use nalgebra::DMatrix;
/// iter::empty::<&DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!
/// ```
fn sum<I: Iterator<Item = &'a MatrixMN<N, Dynamic, C>>>(mut iter: I) -> MatrixMN<N, Dynamic, C> {
if let Some(first) = iter.next() {
iter.fold(first.clone(), |acc, x| acc + x)
} else {
panic!("Cannot compute `sum` of empty iterator.")
}
}
}
/*
*
* 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, ordering: Ordering) -> N2
where N2: Scalar + PartialOrd + Zero {
let mut iter = self.iter();
let mut max = match iter.next() {
Some(first) => abs(*first),
None => { return N2::zero(); }
};
for e in iter {
let ae = abs(*e);
if let Some(ae_ordering) = ae.partial_cmp(&max) {
if ae_ordering == ordering {
max = ae;
}
}
}
max
}
/// Returns the absolute value of the component with the largest absolute value.
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// assert_eq!(Vector3::new(-1.0, 2.0, 3.0).amax(), 3.0);
/// assert_eq!(Vector3::new(-1.0, -2.0, -3.0).amax(), 3.0);
/// ```
#[inline]
pub fn amax(&self) -> N
where N: PartialOrd + Signed {
self.xcmp(|e| e.abs(), Ordering::Greater)
}
/// Returns the the 1-norm of the complex component with the largest 1-norm.
/// # Example
/// ```
/// # use nalgebra::{Vector3, Complex};
/// assert_eq!(Vector3::new(
/// Complex::new(-3.0, -2.0),
/// Complex::new(1.0, 2.0),
/// Complex::new(1.0, 3.0)).camax(), 5.0);
/// ```
#[inline]
pub fn camax(&self) -> N::RealField
where N: ComplexField {
self.xcmp(|e| e.norm1(), Ordering::Greater)
}
/// Returns the component with the largest value.
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// assert_eq!(Vector3::new(-1.0, 2.0, 3.0).max(), 3.0);
/// assert_eq!(Vector3::new(-1.0, -2.0, -3.0).max(), -1.0);
/// ```
#[inline]
pub fn max(&self) -> N
where N: PartialOrd + Signed {
self.xcmp(|e| e, Ordering::Greater)
}
/// Returns the absolute value of the component with the smallest absolute value.
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// assert_eq!(Vector3::new(-1.0, 2.0, -3.0).amin(), 1.0);
/// assert_eq!(Vector3::new(10.0, 2.0, 30.0).amin(), 2.0);
/// ```
#[inline]
pub fn amin(&self) -> N
where N: PartialOrd + Signed {
self.xcmp(|e| e.abs(), Ordering::Less)
}
/// Returns the the 1-norm of the complex component with the smallest 1-norm.
/// # Example
/// ```
/// # use nalgebra::{Vector3, Complex};
/// assert_eq!(Vector3::new(
/// Complex::new(-3.0, -2.0),
/// Complex::new(1.0, 2.0),
/// Complex::new(1.0, 3.0)).camin(), 3.0);
/// ```
#[inline]
pub fn camin(&self) -> N::RealField
where N: ComplexField {
self.xcmp(|e| e.norm1(), Ordering::Less)
}
/// Returns the component with the smallest value.
/// # Example
/// ```
/// # use nalgebra::Vector3;
/// assert_eq!(Vector3::new(-1.0, 2.0, 3.0).min(), -1.0);
/// assert_eq!(Vector3::new(1.0, 2.0, 3.0).min(), 1.0);
/// ```
#[inline]
pub fn min(&self) -> N
where N: PartialOrd + Signed {
self.xcmp(|e| e, Ordering::Less)
}
}