Merge pull request #1055 from dimforge/fix-pow

Fix Matrix::pow and make it work with integer matrices
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Sébastien Crozet 2021-12-31 09:57:56 +01:00 committed by GitHub
commit c0f8530d5e
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3 changed files with 90 additions and 52 deletions

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@ -1,83 +1,71 @@
//! This module provides the matrix exponential (pow) function to square matrices. //! This module provides the matrix exponential (pow) function to square matrices.
use std::ops::DivAssign;
use crate::{ use crate::{
allocator::Allocator, allocator::Allocator,
storage::{Storage, StorageMut}, storage::{Storage, StorageMut},
DefaultAllocator, DimMin, Matrix, OMatrix, DefaultAllocator, DimMin, Matrix, OMatrix, Scalar,
}; };
use num::PrimInt; use num::{One, Zero};
use simba::scalar::ComplexField; use simba::scalar::{ClosedAdd, ClosedMul};
impl<T: ComplexField, D, S> Matrix<T, D, D, S> impl<T, D, S> Matrix<T, D, D, S>
where where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
D: DimMin<D, Output = D>, D: DimMin<D, Output = D>,
S: StorageMut<T, D, D>, S: StorageMut<T, D, D>,
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
{ {
/// Attempts to raise this matrix to an integral power `e` in-place. If this /// Raises this matrix to an integral power `exp` in-place.
/// matrix is non-invertible and `e` is negative, it leaves this matrix pub fn pow_mut(&mut self, mut exp: u32) {
/// untouched and returns `false`. Otherwise, it returns `true` and
/// overwrites this matrix with the result.
pub fn pow_mut<I: PrimInt + DivAssign>(&mut self, mut e: I) -> bool {
let zero = I::zero();
// A matrix raised to the zeroth power is just the identity. // A matrix raised to the zeroth power is just the identity.
if e == zero { if exp == 0 {
self.fill_with_identity(); self.fill_with_identity();
return true; } else if exp > 1 {
} // We use the buffer to hold the result of multiplier^2, thus avoiding
// extra allocations.
let mut x = self.clone_owned();
let mut workspace = self.clone_owned();
// If e is negative, we compute the inverse matrix, then raise it to the if exp % 2 == 0 {
// power of -e. self.fill_with_identity();
if e < zero && !self.try_inverse_mut() { } else {
return false; // Avoid an useless multiplication by the identity
} // if the exponent is odd.
exp -= 1;
let one = I::one();
let two = I::from(2u8).unwrap();
// We use the buffer to hold the result of multiplier ^ 2, thus avoiding
// extra allocations.
let mut multiplier = self.clone_owned();
let mut buf = self.clone_owned();
// Exponentiation by squares.
loop {
if e % two == one {
self.mul_to(&multiplier, &mut buf);
self.copy_from(&buf);
} }
e /= two; // Exponentiation by squares.
multiplier.mul_to(&multiplier, &mut buf); loop {
multiplier.copy_from(&buf); if exp % 2 == 1 {
self.mul_to(&x, &mut workspace);
self.copy_from(&workspace);
}
if e == zero { exp /= 2;
return true;
if exp == 0 {
break;
}
x.mul_to(&x, &mut workspace);
x.copy_from(&workspace);
} }
} }
} }
} }
impl<T: ComplexField, D, S: Storage<T, D, D>> Matrix<T, D, D, S> impl<T, D, S: Storage<T, D, D>> Matrix<T, D, D, S>
where where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
D: DimMin<D, Output = D>, D: DimMin<D, Output = D>,
S: StorageMut<T, D, D>, S: StorageMut<T, D, D>,
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>, DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
{ {
/// Attempts to raise this matrix to an integral power `e`. If this matrix /// Raise this matrix to an integral power `exp`.
/// is non-invertible and `e` is negative, it returns `None`. Otherwise, it
/// returns the result as a new matrix. Uses exponentiation by squares.
#[must_use] #[must_use]
pub fn pow<I: PrimInt + DivAssign>(&self, e: I) -> Option<OMatrix<T, D, D>> { pub fn pow(&self, exp: u32) -> OMatrix<T, D, D> {
let mut clone = self.clone_owned(); let mut result = self.clone_owned();
result.pow_mut(exp);
if clone.pow_mut(e) { result
Some(clone)
} else {
None
}
} }
} }

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@ -9,6 +9,7 @@ mod full_piv_lu;
mod hessenberg; mod hessenberg;
mod inverse; mod inverse;
mod lu; mod lu;
mod pow;
mod qr; mod qr;
mod schur; mod schur;
mod solve; mod solve;

49
tests/linalg/pow.rs Normal file
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@ -0,0 +1,49 @@
#[cfg(feature = "proptest-support")]
mod proptest_tests {
macro_rules! gen_tests(
($module: ident, $scalar: expr, $scalar_type: ty) => {
mod $module {
use na::DMatrix;
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
use std::cmp;
use crate::proptest::*;
use proptest::{prop_assert, proptest};
proptest! {
#[test]
fn pow(n in PROPTEST_MATRIX_DIM, p in 0u32..=4) {
let n = cmp::max(1, cmp::min(n, 10));
let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
let m_pow = m.pow(p);
let mut expected = m.clone();
expected.fill_with_identity();
for _ in 0..p {
expected = &m * &expected;
}
prop_assert!(relative_eq!(m_pow, expected, epsilon = 1.0e-5))
}
#[test]
fn pow_static_square_4x4(m in matrix4_($scalar), p in 0u32..=4) {
let mut expected = m.clone();
let m_pow = m.pow(p);
expected.fill_with_identity();
for _ in 0..p {
expected = &m * &expected;
}
prop_assert!(relative_eq!(m_pow, expected, epsilon = 1.0e-5))
}
}
}
}
);
gen_tests!(complex, complex_f64(), RandComplex<f64>);
gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
}