Merge pull request #1055 from dimforge/fix-pow
Fix Matrix::pow and make it work with integer matrices
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c0f8530d5e
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@ -1,83 +1,71 @@
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//! This module provides the matrix exponential (pow) function to square matrices.
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//! This module provides the matrix exponential (pow) function to square matrices.
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use std::ops::DivAssign;
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use crate::{
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use crate::{
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allocator::Allocator,
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allocator::Allocator,
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storage::{Storage, StorageMut},
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storage::{Storage, StorageMut},
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DefaultAllocator, DimMin, Matrix, OMatrix,
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DefaultAllocator, DimMin, Matrix, OMatrix, Scalar,
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};
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};
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use num::PrimInt;
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use num::{One, Zero};
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use simba::scalar::ComplexField;
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use simba::scalar::{ClosedAdd, ClosedMul};
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impl<T: ComplexField, D, S> Matrix<T, D, D, S>
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impl<T, D, S> Matrix<T, D, D, S>
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where
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where
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T: Scalar + Zero + One + ClosedAdd + ClosedMul,
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D: DimMin<D, Output = D>,
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D: DimMin<D, Output = D>,
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S: StorageMut<T, D, D>,
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S: StorageMut<T, D, D>,
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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{
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{
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/// Attempts to raise this matrix to an integral power `e` in-place. If this
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/// Raises this matrix to an integral power `exp` in-place.
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/// matrix is non-invertible and `e` is negative, it leaves this matrix
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pub fn pow_mut(&mut self, mut exp: u32) {
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/// untouched and returns `false`. Otherwise, it returns `true` and
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/// overwrites this matrix with the result.
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pub fn pow_mut<I: PrimInt + DivAssign>(&mut self, mut e: I) -> bool {
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let zero = I::zero();
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// A matrix raised to the zeroth power is just the identity.
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// A matrix raised to the zeroth power is just the identity.
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if e == zero {
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if exp == 0 {
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self.fill_with_identity();
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self.fill_with_identity();
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return true;
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} else if exp > 1 {
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}
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// We use the buffer to hold the result of multiplier^2, thus avoiding
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// extra allocations.
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let mut x = self.clone_owned();
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let mut workspace = self.clone_owned();
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// If e is negative, we compute the inverse matrix, then raise it to the
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if exp % 2 == 0 {
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// power of -e.
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self.fill_with_identity();
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if e < zero && !self.try_inverse_mut() {
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} else {
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return false;
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// Avoid an useless multiplication by the identity
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}
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// if the exponent is odd.
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exp -= 1;
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let one = I::one();
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let two = I::from(2u8).unwrap();
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// We use the buffer to hold the result of multiplier ^ 2, thus avoiding
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// extra allocations.
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let mut multiplier = self.clone_owned();
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let mut buf = self.clone_owned();
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// Exponentiation by squares.
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loop {
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if e % two == one {
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self.mul_to(&multiplier, &mut buf);
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self.copy_from(&buf);
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}
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}
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e /= two;
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// Exponentiation by squares.
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multiplier.mul_to(&multiplier, &mut buf);
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loop {
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multiplier.copy_from(&buf);
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if exp % 2 == 1 {
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self.mul_to(&x, &mut workspace);
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self.copy_from(&workspace);
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}
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if e == zero {
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exp /= 2;
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return true;
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if exp == 0 {
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break;
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}
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x.mul_to(&x, &mut workspace);
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x.copy_from(&workspace);
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}
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}
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}
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}
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}
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}
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}
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}
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impl<T: ComplexField, D, S: Storage<T, D, D>> Matrix<T, D, D, S>
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impl<T, D, S: Storage<T, D, D>> Matrix<T, D, D, S>
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where
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where
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T: Scalar + Zero + One + ClosedAdd + ClosedMul,
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D: DimMin<D, Output = D>,
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D: DimMin<D, Output = D>,
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S: StorageMut<T, D, D>,
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S: StorageMut<T, D, D>,
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
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{
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{
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/// Attempts to raise this matrix to an integral power `e`. If this matrix
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/// Raise this matrix to an integral power `exp`.
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/// is non-invertible and `e` is negative, it returns `None`. Otherwise, it
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/// returns the result as a new matrix. Uses exponentiation by squares.
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#[must_use]
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#[must_use]
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pub fn pow<I: PrimInt + DivAssign>(&self, e: I) -> Option<OMatrix<T, D, D>> {
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pub fn pow(&self, exp: u32) -> OMatrix<T, D, D> {
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let mut clone = self.clone_owned();
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let mut result = self.clone_owned();
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result.pow_mut(exp);
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if clone.pow_mut(e) {
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result
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Some(clone)
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} else {
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None
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}
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}
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}
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}
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}
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@ -9,6 +9,7 @@ mod full_piv_lu;
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mod hessenberg;
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mod hessenberg;
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mod inverse;
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mod inverse;
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mod lu;
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mod lu;
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mod pow;
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mod qr;
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mod qr;
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mod schur;
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mod schur;
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mod solve;
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mod solve;
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@ -0,0 +1,49 @@
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#[cfg(feature = "proptest-support")]
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mod proptest_tests {
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macro_rules! gen_tests(
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($module: ident, $scalar: expr, $scalar_type: ty) => {
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mod $module {
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use na::DMatrix;
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#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
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use std::cmp;
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use crate::proptest::*;
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use proptest::{prop_assert, proptest};
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proptest! {
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#[test]
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fn pow(n in PROPTEST_MATRIX_DIM, p in 0u32..=4) {
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let n = cmp::max(1, cmp::min(n, 10));
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let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
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let m_pow = m.pow(p);
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let mut expected = m.clone();
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expected.fill_with_identity();
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for _ in 0..p {
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expected = &m * &expected;
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}
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prop_assert!(relative_eq!(m_pow, expected, epsilon = 1.0e-5))
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}
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#[test]
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fn pow_static_square_4x4(m in matrix4_($scalar), p in 0u32..=4) {
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let mut expected = m.clone();
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let m_pow = m.pow(p);
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expected.fill_with_identity();
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for _ in 0..p {
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expected = &m * &expected;
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}
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prop_assert!(relative_eq!(m_pow, expected, epsilon = 1.0e-5))
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}
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}
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}
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}
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);
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gen_tests!(complex, complex_f64(), RandComplex<f64>);
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gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
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}
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