1535 lines
52 KiB
Rust
1535 lines
52 KiB
Rust
use alga::general::{ClosedAdd, ClosedMul, ComplexField};
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#[cfg(feature = "std")]
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use matrixmultiply;
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use num::{One, Signed, Zero};
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#[cfg(feature = "std")]
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use std::mem;
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use crate::base::allocator::Allocator;
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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, Dynamic, U1, U2, U3, U4};
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use crate::base::storage::{Storage, StorageMut};
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use crate::base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector, DVectorSlice, VectorSliceN};
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// FIXME: find a way to avoid code duplication just for complex number support.
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impl<N: ComplexField, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
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/// Computes the index of the vector component with the largest complex or real absolute value.
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///
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/// # Examples:
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///
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/// ```
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/// # extern crate num_complex;
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/// # extern crate nalgebra;
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/// # use num_complex::Complex;
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(Complex::new(11.0, 3.0), Complex::new(-15.0, 0.0), Complex::new(13.0, 5.0));
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/// assert_eq!(vec.icamax(), 2);
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/// ```
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#[inline]
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pub fn icamax(&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).norm1() };
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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).norm1() };
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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, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
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/// Computes the index and value of the vector component with the largest value.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(11, -15, 13);
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/// assert_eq!(vec.argmax(), (2, 13));
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/// ```
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#[inline]
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pub fn argmax(&self) -> (usize, N) {
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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) };
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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) };
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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, *the_max)
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}
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/// Computes the index of the vector component with the largest value.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(11, -15, 13);
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/// assert_eq!(vec.imax(), 2);
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/// ```
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#[inline]
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pub fn imax(&self) -> usize {
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self.argmax().0
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}
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/// Computes the index of the vector component with the largest absolute value.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(11, -15, 13);
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/// assert_eq!(vec.iamax(), 1);
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/// ```
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#[inline]
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pub fn iamax(&self) -> usize
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where N: Signed {
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assert!(!self.is_empty(), "The input vector must not be empty.");
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let mut the_max = unsafe { self.vget_unchecked(0).abs() };
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let mut the_i = 0;
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for i in 1..self.nrows() {
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let val = unsafe { self.vget_unchecked(i).abs() };
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if val > the_max {
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the_max = val;
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the_i = i;
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}
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}
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the_i
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}
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/// Computes the index and value of the vector component with the smallest value.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(11, -15, 13);
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/// assert_eq!(vec.argmin(), (1, -15));
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/// ```
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#[inline]
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pub fn argmin(&self) -> (usize, N) {
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assert!(!self.is_empty(), "The input vector must not be empty.");
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let mut the_min = unsafe { self.vget_unchecked(0) };
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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) };
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if val < the_min {
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the_min = val;
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the_i = i;
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}
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}
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(the_i, *the_min)
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}
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/// Computes the index of the vector component with the smallest value.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(11, -15, 13);
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/// assert_eq!(vec.imin(), 1);
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/// ```
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#[inline]
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pub fn imin(&self) -> usize {
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self.argmin().0
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}
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/// Computes the index of the vector component with the smallest absolute value.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Vector3;
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/// let vec = Vector3::new(11, -15, 13);
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/// assert_eq!(vec.iamin(), 0);
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/// ```
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#[inline]
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pub fn iamin(&self) -> usize
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where N: Signed {
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assert!(!self.is_empty(), "The input vector must not be empty.");
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let mut the_min = 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_min {
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the_min = 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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// FIXME: find a way to avoid code duplication just for complex number support.
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impl<N: ComplexField, 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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///
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/// # Examples:
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///
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/// ```
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/// # extern crate num_complex;
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/// # extern crate nalgebra;
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/// # use num_complex::Complex;
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/// # use nalgebra::Matrix2x3;
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/// let mat = Matrix2x3::new(Complex::new(11.0, 1.0), Complex::new(-12.0, 2.0), Complex::new(13.0, 3.0),
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/// Complex::new(21.0, 43.0), Complex::new(22.0, 5.0), Complex::new(-23.0, 0.0));
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/// assert_eq!(mat.icamax_full(), (1, 0));
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/// ```
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#[inline]
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pub fn icamax_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)).norm1() };
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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)).norm1() };
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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: 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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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::Matrix2x3;
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/// let mat = Matrix2x3::new(11, -12, 13,
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/// 21, 22, -23);
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/// assert_eq!(mat.iamax_full(), (1, 2));
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/// ```
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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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{
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#[inline(always)]
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fn dotx<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>, conjugate: impl Fn(N) -> N) -> N
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where
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SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
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{
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assert!(
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self.nrows() == rhs.nrows(),
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"Dot product dimensions mismatch."
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);
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// So we do some special cases for common fixed-size vectors of dimension lower than 8
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// because the `for` loop below won't be very efficient on those.
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if (R::is::<U2>() || R2::is::<U2>()) && (C::is::<U1>() || C2::is::<U1>()) {
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unsafe {
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let a = conjugate(*self.get_unchecked((0, 0))) * *rhs.get_unchecked((0, 0));
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let b = conjugate(*self.get_unchecked((1, 0))) * *rhs.get_unchecked((1, 0));
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return a + b;
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}
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}
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if (R::is::<U3>() || R2::is::<U3>()) && (C::is::<U1>() || C2::is::<U1>()) {
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unsafe {
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let a = conjugate(*self.get_unchecked((0, 0))) * *rhs.get_unchecked((0, 0));
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let b = conjugate(*self.get_unchecked((1, 0))) * *rhs.get_unchecked((1, 0));
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let c = conjugate(*self.get_unchecked((2, 0))) * *rhs.get_unchecked((2, 0));
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return a + b + c;
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}
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}
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if (R::is::<U4>() || R2::is::<U4>()) && (C::is::<U1>() || C2::is::<U1>()) {
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unsafe {
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let mut a = conjugate(*self.get_unchecked((0, 0))) * *rhs.get_unchecked((0, 0));
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let mut b = conjugate(*self.get_unchecked((1, 0))) * *rhs.get_unchecked((1, 0));
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let c = conjugate(*self.get_unchecked((2, 0))) * *rhs.get_unchecked((2, 0));
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let d = conjugate(*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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// https://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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// otherwise 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 { conjugate(*self.get_unchecked((i + 0, j))) * *rhs.get_unchecked((i + 0, j)) };
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acc1 += unsafe { conjugate(*self.get_unchecked((i + 1, j))) * *rhs.get_unchecked((i + 1, j)) };
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acc2 += unsafe { conjugate(*self.get_unchecked((i + 2, j))) * *rhs.get_unchecked((i + 2, j)) };
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acc3 += unsafe { conjugate(*self.get_unchecked((i + 3, j))) * *rhs.get_unchecked((i + 3, j)) };
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acc4 += unsafe { conjugate(*self.get_unchecked((i + 4, j))) * *rhs.get_unchecked((i + 4, j)) };
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acc5 += unsafe { conjugate(*self.get_unchecked((i + 5, j))) * *rhs.get_unchecked((i + 5, j)) };
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acc6 += unsafe { conjugate(*self.get_unchecked((i + 6, j))) * *rhs.get_unchecked((i + 6, j)) };
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acc7 += unsafe { conjugate(*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 { conjugate(*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 two vectors or matrices (seen as vectors).
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///
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/// This is equal to `self.transpose() * rhs`. For the sesquilinear complex dot product, use
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/// `self.dotc(rhs)`.
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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`, the `*` operator.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::{Vector3, Matrix2x3};
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/// let vec1 = Vector3::new(1.0, 2.0, 3.0);
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/// let vec2 = Vector3::new(0.1, 0.2, 0.3);
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/// assert_eq!(vec1.dot(&vec2), 1.4);
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///
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/// let mat1 = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// let mat2 = Matrix2x3::new(0.1, 0.2, 0.3,
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/// 0.4, 0.5, 0.6);
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/// assert_eq!(mat1.dot(&mat2), 9.1);
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/// ```
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///
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#[inline]
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pub fn dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
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where
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SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
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{
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self.dotx(rhs, |e| e)
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}
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/// The conjugate-linear dot product between two vectors or matrices (seen as vectors).
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///
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/// This is equal to `self.adjoint() * rhs`.
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/// For real vectors, this is identical to `self.dot(&rhs)`.
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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`, the `*` operator.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::{Vector2, Complex};
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/// let vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
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/// let vec2 = Vector2::new(Complex::new(0.4, 0.3), Complex::new(0.2, 0.1));
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/// assert_eq!(vec1.dotc(&vec2), Complex::new(2.0, -1.0));
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///
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/// // Note that for complex vectors, we generally have:
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/// // vec1.dotc(&vec2) != vec2.dot(&vec2)
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/// assert_ne!(vec1.dotc(&vec2), vec1.dot(&vec2));
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/// ```
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#[inline]
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pub fn dotc<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
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where
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N: ComplexField,
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SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
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{
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self.dotx(rhs, ComplexField::conjugate)
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}
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/// The dot product between the transpose of `self` and `rhs`.
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///
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/// # Examples:
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///
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/// ```
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/// # use nalgebra::{Vector3, RowVector3, Matrix2x3, Matrix3x2};
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/// let vec1 = Vector3::new(1.0, 2.0, 3.0);
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/// let vec2 = RowVector3::new(0.1, 0.2, 0.3);
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/// assert_eq!(vec1.tr_dot(&vec2), 1.4);
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///
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/// let mat1 = Matrix2x3::new(1.0, 2.0, 3.0,
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/// 4.0, 5.0, 6.0);
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/// let mat2 = Matrix3x2::new(0.1, 0.4,
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/// 0.2, 0.5,
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/// 0.3, 0.6);
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/// assert_eq!(mat1.tr_dot(&mat2), 9.1);
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/// ```
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#[inline]
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pub fn tr_dot<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
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where
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SB: Storage<N, R2, C2>,
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ShapeConstraint: DimEq<C, R2> + DimEq<R, C2>,
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{
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let (nrows, ncols) = self.shape();
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assert!(
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(ncols, nrows) == rhs.shape(),
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"Transposed dot product dimension mismatch."
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);
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let mut res = N::zero();
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for j in 0..self.nrows() {
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for i in 0..self.ncols() {
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res += unsafe { *self.get_unchecked((j, i)) * *rhs.get_unchecked((i, j)) }
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}
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}
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res
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}
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}
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|
|
fn array_axpy<N>(y: &mut [N], a: N, x: &[N], beta: N, stride1: usize, stride2: usize, len: usize)
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|
where N: Scalar + Zero + ClosedAdd + ClosedMul {
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for i in 0..len {
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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 `b` is zero, `self` is never read from.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::Vector3;
|
|
/// let mut vec1 = Vector3::new(1.0, 2.0, 3.0);
|
|
/// let vec2 = Vector3::new(0.1, 0.2, 0.3);
|
|
/// vec1.axpy(10.0, &vec2, 5.0);
|
|
/// assert_eq!(vec1, Vector3::new(6.0, 12.0, 18.0));
|
|
/// ```
|
|
#[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.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2};
|
|
/// let mut vec1 = Vector2::new(1.0, 2.0);
|
|
/// let vec2 = Vector2::new(0.1, 0.2);
|
|
/// let mat = Matrix2::new(1.0, 2.0,
|
|
/// 3.0, 4.0);
|
|
/// vec1.gemv(10.0, &mat, &vec2, 5.0);
|
|
/// assert_eq!(vec1, Vector2::new(10.0, 21.0));
|
|
/// ```
|
|
#[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());
|
|
}
|
|
}
|
|
|
|
|
|
#[inline(always)]
|
|
fn xxgemv<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
a: &SquareMatrix<N, D2, SB>,
|
|
x: &Vector<N, D3, SC>,
|
|
beta: N,
|
|
dot: impl Fn(&DVectorSlice<N, SB::RStride, SB::CStride>, &DVectorSlice<N, SC::RStride, SC::CStride>) -> 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(),
|
|
"Symmetric cgemv: the input matrix must be square."
|
|
);
|
|
assert!(
|
|
dim2 == dim3 && dim1 == dim2,
|
|
"Symmetric cgemv: 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 * dot(&a.slice_range(1.., 0), &x.rows_range(1..));
|
|
|
|
for j in 1..dim2 {
|
|
let col2 = a.column(j);
|
|
let dot = dot(&col2.rows_range(j..), &x.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());
|
|
}
|
|
}
|
|
|
|
/// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** matrix, `x` a
|
|
/// vector, and `alpha, beta` two scalars. DEPRECATED: use `sygemv` instead.
|
|
#[inline]
|
|
#[deprecated(note = "This is renamed `sygemv` to match the original BLAS terminology.")]
|
|
pub fn gemv_symm<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
a: &SquareMatrix<N, D2, SB>,
|
|
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>,
|
|
{
|
|
self.sygemv(alpha, a, x, beta)
|
|
}
|
|
|
|
/// Computes `self = alpha * a * x + beta * self`, where `a` is a **symmetric** matrix, `x` a
|
|
/// vector, and `alpha, beta` two scalars.
|
|
///
|
|
/// For hermitian matrices, use `.hegemv` instead.
|
|
/// If `beta` is zero, `self` is never read. If `self` is read, only its lower-triangular part
|
|
/// (including the diagonal) is actually read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2};
|
|
/// let mat = Matrix2::new(1.0, 2.0,
|
|
/// 2.0, 4.0);
|
|
/// let mut vec1 = Vector2::new(1.0, 2.0);
|
|
/// let vec2 = Vector2::new(0.1, 0.2);
|
|
/// vec1.sygemv(10.0, &mat, &vec2, 5.0);
|
|
/// assert_eq!(vec1, Vector2::new(10.0, 20.0));
|
|
///
|
|
///
|
|
/// // The matrix upper-triangular elements can be garbage because it is never
|
|
/// // read by this method. Therefore, it is not necessary for the caller to
|
|
/// // fill the matrix struct upper-triangle.
|
|
/// let mat = Matrix2::new(1.0, 9999999.9999999,
|
|
/// 2.0, 4.0);
|
|
/// let mut vec1 = Vector2::new(1.0, 2.0);
|
|
/// vec1.sygemv(10.0, &mat, &vec2, 5.0);
|
|
/// assert_eq!(vec1, Vector2::new(10.0, 20.0));
|
|
/// ```
|
|
#[inline]
|
|
pub fn sygemv<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
a: &SquareMatrix<N, D2, SB>,
|
|
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>,
|
|
{
|
|
self.xxgemv(alpha, a, x, beta, |a, b| a.dot(b))
|
|
}
|
|
|
|
/// Computes `self = alpha * a * x + beta * self`, where `a` is an **hermitian** 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.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2, Complex};
|
|
/// let mat = Matrix2::new(Complex::new(1.0, 0.0), Complex::new(2.0, -0.1),
|
|
/// Complex::new(2.0, 1.0), Complex::new(4.0, 0.0));
|
|
/// let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
|
|
/// let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
|
|
/// vec1.sygemv(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
|
|
/// assert_eq!(vec1, Vector2::new(Complex::new(-48.0, 44.0), Complex::new(-75.0, 110.0)));
|
|
///
|
|
///
|
|
/// // The matrix upper-triangular elements can be garbage because it is never
|
|
/// // read by this method. Therefore, it is not necessary for the caller to
|
|
/// // fill the matrix struct upper-triangle.
|
|
///
|
|
/// let mat = Matrix2::new(Complex::new(1.0, 0.0), Complex::new(99999999.9, 999999999.9),
|
|
/// Complex::new(2.0, 1.0), Complex::new(4.0, 0.0));
|
|
/// let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
|
|
/// let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
|
|
/// vec1.sygemv(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
|
|
/// assert_eq!(vec1, Vector2::new(Complex::new(-48.0, 44.0), Complex::new(-75.0, 110.0)));
|
|
/// ```
|
|
#[inline]
|
|
pub fn hegemv<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
a: &SquareMatrix<N, D2, SB>,
|
|
x: &Vector<N, D3, SC>,
|
|
beta: N,
|
|
) where
|
|
N: ComplexField,
|
|
SB: Storage<N, D2, D2>,
|
|
SC: Storage<N, D3>,
|
|
ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,
|
|
{
|
|
self.xxgemv(alpha, a, x, beta, |a, b| a.dotc(b))
|
|
}
|
|
|
|
|
|
#[inline(always)]
|
|
fn gemv_xx<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,
|
|
dot: impl Fn(&VectorSliceN<N, R2, SB::RStride, SB::CStride>, &Vector<N, D3, SC>) -> N,
|
|
) where
|
|
N: One,
|
|
SB: Storage<N, R2, C2>,
|
|
SC: Storage<N, D3>,
|
|
ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
|
|
{
|
|
let dim1 = self.nrows();
|
|
let (nrows2, ncols2) = a.shape();
|
|
let dim3 = x.nrows();
|
|
|
|
assert!(
|
|
nrows2 == dim3 && dim1 == ncols2,
|
|
"Gemv: dimensions mismatch."
|
|
);
|
|
|
|
if ncols2 == 0 {
|
|
return;
|
|
}
|
|
|
|
if beta.is_zero() {
|
|
for j in 0..ncols2 {
|
|
let val = unsafe { self.vget_unchecked_mut(j) };
|
|
*val = alpha * dot(&a.column(j), x)
|
|
}
|
|
} else {
|
|
for j in 0..ncols2 {
|
|
let val = unsafe { self.vget_unchecked_mut(j) };
|
|
*val = alpha * dot(&a.column(j), x) + beta * *val;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/// Computes `self = alpha * a.transpose() * x + beta * self`, where `a` is a matrix, `x` a vector, and
|
|
/// `alpha, beta` two scalars.
|
|
///
|
|
/// If `beta` is zero, `self` is never read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2};
|
|
/// let mat = Matrix2::new(1.0, 3.0,
|
|
/// 2.0, 4.0);
|
|
/// let mut vec1 = Vector2::new(1.0, 2.0);
|
|
/// let vec2 = Vector2::new(0.1, 0.2);
|
|
/// let expected = mat.transpose() * vec2 * 10.0 + vec1 * 5.0;
|
|
///
|
|
/// vec1.gemv_tr(10.0, &mat, &vec2, 5.0);
|
|
/// assert_eq!(vec1, expected);
|
|
/// ```
|
|
#[inline]
|
|
pub fn gemv_tr<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, C2> + AreMultipliable<C2, R2, D3, U1>,
|
|
{
|
|
self.gemv_xx(alpha, a, x, beta, |a, b| a.dot(b))
|
|
}
|
|
|
|
/// Computes `self = alpha * a.adjoint() * x + beta * self`, where `a` is a matrix, `x` a vector, and
|
|
/// `alpha, beta` two scalars.
|
|
///
|
|
/// For real matrices, this is the same as `.gemv_tr`.
|
|
/// If `beta` is zero, `self` is never read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2, Complex};
|
|
/// let mat = Matrix2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0),
|
|
/// Complex::new(5.0, 6.0), Complex::new(7.0, 8.0));
|
|
/// let mut vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
|
|
/// let vec2 = Vector2::new(Complex::new(0.1, 0.2), Complex::new(0.3, 0.4));
|
|
/// let expected = mat.adjoint() * vec2 * Complex::new(10.0, 20.0) + vec1 * Complex::new(5.0, 15.0);
|
|
///
|
|
/// vec1.gemv_ad(Complex::new(10.0, 20.0), &mat, &vec2, Complex::new(5.0, 15.0));
|
|
/// assert_eq!(vec1, expected);
|
|
/// ```
|
|
#[inline]
|
|
pub fn gemv_ad<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: ComplexField,
|
|
SB: Storage<N, R2, C2>,
|
|
SC: Storage<N, D3>,
|
|
ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
|
|
{
|
|
self.gemv_xx(alpha, a, x, beta, |a, b| a.dotc(b))
|
|
}
|
|
}
|
|
|
|
impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
|
|
where N: Scalar + Zero + ClosedAdd + ClosedMul
|
|
{
|
|
#[inline(always)]
|
|
fn gerx<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
x: &Vector<N, D2, SB>,
|
|
y: &Vector<N, D3, SC>,
|
|
beta: N,
|
|
conjugate: impl Fn(N) -> 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 { conjugate(*y.vget_unchecked(j)) };
|
|
self.column_mut(j).axpy(alpha * val, x, beta);
|
|
}
|
|
}
|
|
|
|
/// Computes `self = alpha * x * y.transpose() + beta * self`.
|
|
///
|
|
/// If `beta` is zero, `self` is never read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2x3, Vector2, Vector3};
|
|
/// let mut mat = Matrix2x3::repeat(4.0);
|
|
/// let vec1 = Vector2::new(1.0, 2.0);
|
|
/// let vec2 = Vector3::new(0.1, 0.2, 0.3);
|
|
/// let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
|
|
///
|
|
/// mat.ger(10.0, &vec1, &vec2, 5.0);
|
|
/// assert_eq!(mat, expected);
|
|
/// ```
|
|
#[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>,
|
|
{
|
|
self.gerx(alpha, x, y, beta, |e| e)
|
|
}
|
|
|
|
/// Computes `self = alpha * x * y.adjoint() + beta * self`.
|
|
///
|
|
/// If `beta` is zero, `self` is never read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{Matrix2x3, Vector2, Vector3, Complex};
|
|
/// let mut mat = Matrix2x3::repeat(Complex::new(4.0, 5.0));
|
|
/// let vec1 = Vector2::new(Complex::new(1.0, 2.0), Complex::new(3.0, 4.0));
|
|
/// let vec2 = Vector3::new(Complex::new(0.6, 0.5), Complex::new(0.4, 0.5), Complex::new(0.2, 0.1));
|
|
/// let expected = vec1 * vec2.adjoint() * Complex::new(10.0, 20.0) + mat * Complex::new(5.0, 15.0);
|
|
///
|
|
/// mat.gerc(Complex::new(10.0, 20.0), &vec1, &vec2, Complex::new(5.0, 15.0));
|
|
/// assert_eq!(mat, expected);
|
|
/// ```
|
|
#[inline]
|
|
pub fn gerc<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
x: &Vector<N, D2, SB>,
|
|
y: &Vector<N, D3, SC>,
|
|
beta: N,
|
|
) where
|
|
N: ComplexField,
|
|
SB: Storage<N, D2>,
|
|
SC: Storage<N, D3>,
|
|
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
|
|
{
|
|
self.gerx(alpha, x, y, beta, ComplexField::conjugate)
|
|
}
|
|
|
|
/// 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.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{Matrix2x3, Matrix3x4, Matrix2x4};
|
|
/// let mut mat1 = Matrix2x4::identity();
|
|
/// let mat2 = Matrix2x3::new(1.0, 2.0, 3.0,
|
|
/// 4.0, 5.0, 6.0);
|
|
/// let mat3 = Matrix3x4::new(0.1, 0.2, 0.3, 0.4,
|
|
/// 0.5, 0.6, 0.7, 0.8,
|
|
/// 0.9, 1.0, 1.1, 1.2);
|
|
/// let expected = mat2 * mat3 * 10.0 + mat1 * 5.0;
|
|
///
|
|
/// mat1.gemm(10.0, &mat2, &mat3, 5.0);
|
|
/// assert_relative_eq!(mat1, expected);
|
|
/// ```
|
|
#[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 ncols1 = self.ncols();
|
|
|
|
#[cfg(feature = "std")]
|
|
{
|
|
// matrixmultiply can be used only if the std feature is available.
|
|
let nrows1 = self.nrows();
|
|
let (nrows2, ncols2) = a.shape();
|
|
let (nrows3, ncols3) = b.shape();
|
|
|
|
assert_eq!(
|
|
ncols2, nrows3,
|
|
"gemm: dimensions mismatch for multiplication."
|
|
);
|
|
assert_eq!(
|
|
(nrows1, ncols1),
|
|
(nrows2, ncols3),
|
|
"gemm: dimensions mismatch for addition."
|
|
);
|
|
|
|
// We assume large matrices will be Dynamic but small matrices static.
|
|
// We could use matrixmultiply for large statically-sized matrices but the performance
|
|
// threshold to activate it would be different from SMALL_DIM because our code optimizes
|
|
// better for statically-sized matrices.
|
|
let is_dynamic = R1::is::<Dynamic>()
|
|
|| C1::is::<Dynamic>()
|
|
|| R2::is::<Dynamic>()
|
|
|| C2::is::<Dynamic>()
|
|
|| R3::is::<Dynamic>()
|
|
|| C3::is::<Dynamic>();
|
|
// Threshold determined empirically.
|
|
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,
|
|
);
|
|
}
|
|
return;
|
|
} else if N::is::<f64>() {
|
|
let (rsa, csa) = a.strides();
|
|
let (rsb, csb) = b.strides();
|
|
let (rsc, csc) = self.strides();
|
|
|
|
unsafe {
|
|
matrixmultiply::dgemm(
|
|
nrows2,
|
|
ncols2,
|
|
ncols3,
|
|
mem::transmute_copy(&alpha),
|
|
a.data.ptr() as *const f64,
|
|
rsa as isize,
|
|
csa as isize,
|
|
b.data.ptr() as *const f64,
|
|
rsb as isize,
|
|
csb as isize,
|
|
mem::transmute_copy(&beta),
|
|
self.data.ptr_mut() as *mut f64,
|
|
rsc as isize,
|
|
csc as isize,
|
|
);
|
|
}
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
|
|
for j1 in 0..ncols1 {
|
|
// FIXME: avoid bound checks.
|
|
self.column_mut(j1).gemv(alpha, a, &b.column(j1), beta);
|
|
}
|
|
}
|
|
|
|
/// Computes `self = alpha * a.transpose() * b + beta * self`, where `a, b, self` are matrices.
|
|
/// `alpha` and `beta` are scalar.
|
|
///
|
|
/// If `beta` is zero, `self` is never read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{Matrix3x2, Matrix3x4, Matrix2x4};
|
|
/// let mut mat1 = Matrix2x4::identity();
|
|
/// let mat2 = Matrix3x2::new(1.0, 4.0,
|
|
/// 2.0, 5.0,
|
|
/// 3.0, 6.0);
|
|
/// let mat3 = Matrix3x4::new(0.1, 0.2, 0.3, 0.4,
|
|
/// 0.5, 0.6, 0.7, 0.8,
|
|
/// 0.9, 1.0, 1.1, 1.2);
|
|
/// let expected = mat2.transpose() * mat3 * 10.0 + mat1 * 5.0;
|
|
///
|
|
/// mat1.gemm_tr(10.0, &mat2, &mat3, 5.0);
|
|
/// assert_eq!(mat1, expected);
|
|
/// ```
|
|
#[inline]
|
|
pub fn gemm_tr<R2: Dim, C2: Dim, R3: Dim, C3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
a: &Matrix<N, R2, C2, SB>,
|
|
b: &Matrix<N, R3, C3, SC>,
|
|
beta: N,
|
|
) where
|
|
N: One,
|
|
SB: Storage<N, R2, C2>,
|
|
SC: Storage<N, R3, C3>,
|
|
ShapeConstraint: SameNumberOfRows<R1, C2>
|
|
+ SameNumberOfColumns<C1, C3>
|
|
+ AreMultipliable<C2, R2, R3, C3>,
|
|
{
|
|
let (nrows1, ncols1) = self.shape();
|
|
let (nrows2, ncols2) = a.shape();
|
|
let (nrows3, ncols3) = b.shape();
|
|
|
|
assert_eq!(
|
|
nrows2, nrows3,
|
|
"gemm: dimensions mismatch for multiplication."
|
|
);
|
|
assert_eq!(
|
|
(nrows1, ncols1),
|
|
(ncols2, ncols3),
|
|
"gemm: dimensions mismatch for addition."
|
|
);
|
|
|
|
for j1 in 0..ncols1 {
|
|
// FIXME: avoid bound checks.
|
|
self.column_mut(j1).gemv_tr(alpha, a, &b.column(j1), beta);
|
|
}
|
|
}
|
|
|
|
|
|
/// Computes `self = alpha * a.adjoint() * b + beta * self`, where `a, b, self` are matrices.
|
|
/// `alpha` and `beta` are scalar.
|
|
///
|
|
/// If `beta` is zero, `self` is never read.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{Matrix3x2, Matrix3x4, Matrix2x4, Complex};
|
|
/// let mut mat1 = Matrix2x4::identity();
|
|
/// let mat2 = Matrix3x2::new(Complex::new(1.0, 4.0), Complex::new(7.0, 8.0),
|
|
/// Complex::new(2.0, 5.0), Complex::new(9.0, 10.0),
|
|
/// Complex::new(3.0, 6.0), Complex::new(11.0, 12.0));
|
|
/// let mat3 = Matrix3x4::new(Complex::new(0.1, 1.3), Complex::new(0.2, 1.4), Complex::new(0.3, 1.5), Complex::new(0.4, 1.6),
|
|
/// Complex::new(0.5, 1.7), Complex::new(0.6, 1.8), Complex::new(0.7, 1.9), Complex::new(0.8, 2.0),
|
|
/// Complex::new(0.9, 2.1), Complex::new(1.0, 2.2), Complex::new(1.1, 2.3), Complex::new(1.2, 2.4));
|
|
/// let expected = mat2.adjoint() * mat3 * Complex::new(10.0, 20.0) + mat1 * Complex::new(5.0, 15.0);
|
|
///
|
|
/// mat1.gemm_ad(Complex::new(10.0, 20.0), &mat2, &mat3, Complex::new(5.0, 15.0));
|
|
/// assert_eq!(mat1, expected);
|
|
/// ```
|
|
#[inline]
|
|
pub fn gemm_ad<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: ComplexField,
|
|
SB: Storage<N, R2, C2>,
|
|
SC: Storage<N, R3, C3>,
|
|
ShapeConstraint: SameNumberOfRows<R1, C2>
|
|
+ SameNumberOfColumns<C1, C3>
|
|
+ AreMultipliable<C2, R2, R3, C3>,
|
|
{
|
|
let (nrows1, ncols1) = self.shape();
|
|
let (nrows2, ncols2) = a.shape();
|
|
let (nrows3, ncols3) = b.shape();
|
|
|
|
assert_eq!(
|
|
nrows2, nrows3,
|
|
"gemm: dimensions mismatch for multiplication."
|
|
);
|
|
assert_eq!(
|
|
(nrows1, ncols1),
|
|
(ncols2, ncols3),
|
|
"gemm: dimensions mismatch for addition."
|
|
);
|
|
|
|
for j1 in 0..ncols1 {
|
|
// FIXME: avoid bound checks.
|
|
self.column_mut(j1).gemv_ad(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
|
|
{
|
|
#[inline(always)]
|
|
fn xxgerx<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
x: &Vector<N, D2, SB>,
|
|
y: &Vector<N, D3, SC>,
|
|
beta: N,
|
|
conjugate: impl Fn(N) -> 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 { conjugate(*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,
|
|
);
|
|
}
|
|
}
|
|
|
|
/// 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.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2};
|
|
/// let mut mat = Matrix2::identity();
|
|
/// let vec1 = Vector2::new(1.0, 2.0);
|
|
/// let vec2 = Vector2::new(0.1, 0.2);
|
|
/// let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
|
|
/// mat.m12 = 99999.99999; // This component is on the upper-triangular part and will not be read/written.
|
|
///
|
|
/// mat.ger_symm(10.0, &vec1, &vec2, 5.0);
|
|
/// assert_eq!(mat.lower_triangle(), expected.lower_triangle());
|
|
/// assert_eq!(mat.m12, 99999.99999); // This was untouched.
|
|
#[inline]
|
|
#[deprecated(note = "This is renamed `syger` to match the original BLAS terminology.")]
|
|
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>,
|
|
{
|
|
self.syger(alpha, x, y, beta)
|
|
}
|
|
|
|
/// Computes `self = alpha * x * y.transpose() + beta * self`, where `self` is a **symmetric**
|
|
/// matrix.
|
|
///
|
|
/// For hermitian complex matrices, use `.hegerc` instead.
|
|
/// 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.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2};
|
|
/// let mut mat = Matrix2::identity();
|
|
/// let vec1 = Vector2::new(1.0, 2.0);
|
|
/// let vec2 = Vector2::new(0.1, 0.2);
|
|
/// let expected = vec1 * vec2.transpose() * 10.0 + mat * 5.0;
|
|
/// mat.m12 = 99999.99999; // This component is on the upper-triangular part and will not be read/written.
|
|
///
|
|
/// mat.syger(10.0, &vec1, &vec2, 5.0);
|
|
/// assert_eq!(mat.lower_triangle(), expected.lower_triangle());
|
|
/// assert_eq!(mat.m12, 99999.99999); // This was untouched.
|
|
#[inline]
|
|
pub fn syger<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>,
|
|
{
|
|
self.xxgerx(alpha, x, y, beta, |e| e)
|
|
}
|
|
|
|
/// Computes `self = alpha * x * y.adjoint() + beta * self`, where `self` is an **hermitian**
|
|
/// 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.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # use nalgebra::{Matrix2, Vector2, Complex};
|
|
/// let mut mat = Matrix2::identity();
|
|
/// let vec1 = Vector2::new(Complex::new(1.0, 3.0), Complex::new(2.0, 4.0));
|
|
/// let vec2 = Vector2::new(Complex::new(0.2, 0.4), Complex::new(0.1, 0.3));
|
|
/// let expected = vec1 * vec2.adjoint() * Complex::new(10.0, 20.0) + mat * Complex::new(5.0, 15.0);
|
|
/// mat.m12 = Complex::new(99999.99999, 88888.88888); // This component is on the upper-triangular part and will not be read/written.
|
|
///
|
|
/// mat.hegerc(Complex::new(10.0, 20.0), &vec1, &vec2, Complex::new(5.0, 15.0));
|
|
/// assert_eq!(mat.lower_triangle(), expected.lower_triangle());
|
|
/// assert_eq!(mat.m12, Complex::new(99999.99999, 88888.88888)); // This was untouched.
|
|
#[inline]
|
|
pub fn hegerc<D2: Dim, D3: Dim, SB, SC>(
|
|
&mut self,
|
|
alpha: N,
|
|
x: &Vector<N, D2, SB>,
|
|
y: &Vector<N, D3, SC>,
|
|
beta: N,
|
|
) where
|
|
N: ComplexField,
|
|
SB: Storage<N, D2>,
|
|
SC: Storage<N, D3>,
|
|
ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
|
|
{
|
|
self.xxgerx(alpha, x, y, beta, ComplexField::conjugate)
|
|
}
|
|
}
|
|
|
|
impl<N, D1: Dim, S: StorageMut<N, D1, D1>> SquareMatrix<N, D1, S>
|
|
where N: Scalar + Zero + One + ClosedAdd + ClosedMul
|
|
{
|
|
/// Computes the quadratic form `self = alpha * lhs * mid * lhs.transpose() + beta * self`.
|
|
///
|
|
/// This uses the provided workspace `work` to avoid allocations for intermediate results.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{DMatrix, DVector};
|
|
/// // Note that all those would also work with statically-sized matrices.
|
|
/// // We use DMatrix/DVector since that's the only case where pre-allocating the
|
|
/// // workspace is actually useful (assuming the same workspace is re-used for
|
|
/// // several computations) because it avoids repeated dynamic allocations.
|
|
/// let mut mat = DMatrix::identity(2, 2);
|
|
/// let lhs = DMatrix::from_row_slice(2, 3, &[1.0, 2.0, 3.0,
|
|
/// 4.0, 5.0, 6.0]);
|
|
/// let mid = DMatrix::from_row_slice(3, 3, &[0.1, 0.2, 0.3,
|
|
/// 0.5, 0.6, 0.7,
|
|
/// 0.9, 1.0, 1.1]);
|
|
/// // The random shows that values on the workspace do not
|
|
/// // matter as they will be overwritten.
|
|
/// let mut workspace = DVector::new_random(2);
|
|
/// let expected = &lhs * &mid * lhs.transpose() * 10.0 + &mat * 5.0;
|
|
///
|
|
/// mat.quadform_tr_with_workspace(&mut workspace, 10.0, &lhs, &mid, 5.0);
|
|
/// assert_relative_eq!(mat, expected);
|
|
pub fn quadform_tr_with_workspace<D2, S2, R3, C3, S3, D4, S4>(
|
|
&mut self,
|
|
work: &mut Vector<N, D2, S2>,
|
|
alpha: N,
|
|
lhs: &Matrix<N, R3, C3, S3>,
|
|
mid: &SquareMatrix<N, D4, S4>,
|
|
beta: N,
|
|
) where
|
|
D2: Dim,
|
|
R3: Dim,
|
|
C3: Dim,
|
|
D4: Dim,
|
|
S2: StorageMut<N, D2>,
|
|
S3: Storage<N, R3, C3>,
|
|
S4: Storage<N, D4, D4>,
|
|
ShapeConstraint: DimEq<D1, D2> + DimEq<D1, R3> + DimEq<D2, R3> + DimEq<C3, D4>,
|
|
{
|
|
work.gemv(N::one(), lhs, &mid.column(0), N::zero());
|
|
self.ger(alpha, work, &lhs.column(0), beta);
|
|
|
|
for j in 1..mid.ncols() {
|
|
work.gemv(N::one(), lhs, &mid.column(j), N::zero());
|
|
self.ger(alpha, work, &lhs.column(j), N::one());
|
|
}
|
|
}
|
|
|
|
/// Computes the quadratic form `self = alpha * lhs * mid * lhs.transpose() + beta * self`.
|
|
///
|
|
/// This allocates a workspace vector of dimension D1 for intermediate results.
|
|
/// If `D1` is a type-level integer, then the allocation is performed on the stack.
|
|
/// Use `.quadform_tr_with_workspace(...)` instead to avoid allocations.
|
|
///
|
|
/// # Examples:
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{Matrix2, Matrix3, Matrix2x3, Vector2};
|
|
/// let mut mat = Matrix2::identity();
|
|
/// let lhs = Matrix2x3::new(1.0, 2.0, 3.0,
|
|
/// 4.0, 5.0, 6.0);
|
|
/// let mid = Matrix3::new(0.1, 0.2, 0.3,
|
|
/// 0.5, 0.6, 0.7,
|
|
/// 0.9, 1.0, 1.1);
|
|
/// let expected = lhs * mid * lhs.transpose() * 10.0 + mat * 5.0;
|
|
///
|
|
/// mat.quadform_tr(10.0, &lhs, &mid, 5.0);
|
|
/// assert_relative_eq!(mat, expected);
|
|
pub fn quadform_tr<R3, C3, S3, D4, S4>(
|
|
&mut self,
|
|
alpha: N,
|
|
lhs: &Matrix<N, R3, C3, S3>,
|
|
mid: &SquareMatrix<N, D4, S4>,
|
|
beta: N,
|
|
) where
|
|
R3: Dim,
|
|
C3: Dim,
|
|
D4: Dim,
|
|
S3: Storage<N, R3, C3>,
|
|
S4: Storage<N, D4, D4>,
|
|
ShapeConstraint: DimEq<D1, D1> + DimEq<D1, R3> + DimEq<C3, D4>,
|
|
DefaultAllocator: Allocator<N, D1>,
|
|
{
|
|
let mut work = unsafe { Vector::new_uninitialized_generic(self.data.shape().0, U1) };
|
|
self.quadform_tr_with_workspace(&mut work, alpha, lhs, mid, beta)
|
|
}
|
|
|
|
/// Computes the quadratic form `self = alpha * rhs.transpose() * mid * rhs + beta * self`.
|
|
///
|
|
/// This uses the provided workspace `work` to avoid allocations for intermediate results.
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{DMatrix, DVector};
|
|
/// // Note that all those would also work with statically-sized matrices.
|
|
/// // We use DMatrix/DVector since that's the only case where pre-allocating the
|
|
/// // workspace is actually useful (assuming the same workspace is re-used for
|
|
/// // several computations) because it avoids repeated dynamic allocations.
|
|
/// let mut mat = DMatrix::identity(2, 2);
|
|
/// let rhs = DMatrix::from_row_slice(3, 2, &[1.0, 2.0,
|
|
/// 3.0, 4.0,
|
|
/// 5.0, 6.0]);
|
|
/// let mid = DMatrix::from_row_slice(3, 3, &[0.1, 0.2, 0.3,
|
|
/// 0.5, 0.6, 0.7,
|
|
/// 0.9, 1.0, 1.1]);
|
|
/// // The random shows that values on the workspace do not
|
|
/// // matter as they will be overwritten.
|
|
/// let mut workspace = DVector::new_random(3);
|
|
/// let expected = rhs.transpose() * &mid * &rhs * 10.0 + &mat * 5.0;
|
|
///
|
|
/// mat.quadform_with_workspace(&mut workspace, 10.0, &mid, &rhs, 5.0);
|
|
/// assert_relative_eq!(mat, expected);
|
|
pub fn quadform_with_workspace<D2, S2, D3, S3, R4, C4, S4>(
|
|
&mut self,
|
|
work: &mut Vector<N, D2, S2>,
|
|
alpha: N,
|
|
mid: &SquareMatrix<N, D3, S3>,
|
|
rhs: &Matrix<N, R4, C4, S4>,
|
|
beta: N,
|
|
) where
|
|
D2: Dim,
|
|
D3: Dim,
|
|
R4: Dim,
|
|
C4: Dim,
|
|
S2: StorageMut<N, D2>,
|
|
S3: Storage<N, D3, D3>,
|
|
S4: Storage<N, R4, C4>,
|
|
ShapeConstraint:
|
|
DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,
|
|
{
|
|
work.gemv(N::one(), mid, &rhs.column(0), N::zero());
|
|
self.column_mut(0).gemv_tr(alpha, &rhs, work, beta);
|
|
|
|
for j in 1..rhs.ncols() {
|
|
work.gemv(N::one(), mid, &rhs.column(j), N::zero());
|
|
self.column_mut(j).gemv_tr(alpha, &rhs, work, beta);
|
|
}
|
|
}
|
|
|
|
/// Computes the quadratic form `self = alpha * rhs.transpose() * mid * rhs + beta * self`.
|
|
///
|
|
/// This allocates a workspace vector of dimension D2 for intermediate results.
|
|
/// If `D2` is a type-level integer, then the allocation is performed on the stack.
|
|
/// Use `.quadform_with_workspace(...)` instead to avoid allocations.
|
|
///
|
|
/// ```
|
|
/// # #[macro_use] extern crate approx;
|
|
/// # use nalgebra::{Matrix2, Matrix3x2, Matrix3};
|
|
/// let mut mat = Matrix2::identity();
|
|
/// let rhs = Matrix3x2::new(1.0, 2.0,
|
|
/// 3.0, 4.0,
|
|
/// 5.0, 6.0);
|
|
/// let mid = Matrix3::new(0.1, 0.2, 0.3,
|
|
/// 0.5, 0.6, 0.7,
|
|
/// 0.9, 1.0, 1.1);
|
|
/// let expected = rhs.transpose() * mid * rhs * 10.0 + mat * 5.0;
|
|
///
|
|
/// mat.quadform(10.0, &mid, &rhs, 5.0);
|
|
/// assert_relative_eq!(mat, expected);
|
|
pub fn quadform<D2, S2, R3, C3, S3>(
|
|
&mut self,
|
|
alpha: N,
|
|
mid: &SquareMatrix<N, D2, S2>,
|
|
rhs: &Matrix<N, R3, C3, S3>,
|
|
beta: N,
|
|
) where
|
|
D2: Dim,
|
|
R3: Dim,
|
|
C3: Dim,
|
|
S2: Storage<N, D2, D2>,
|
|
S3: Storage<N, R3, C3>,
|
|
ShapeConstraint: DimEq<D2, R3> + DimEq<D1, C3> + AreMultipliable<C3, R3, D2, U1>,
|
|
DefaultAllocator: Allocator<N, D2>,
|
|
{
|
|
let mut work = unsafe { Vector::new_uninitialized_generic(mid.data.shape().0, U1) };
|
|
self.quadform_with_workspace(&mut work, alpha, mid, rhs, beta)
|
|
}
|
|
}
|