Fix Matrix::pow and make it work only with positive exponents

This commit is contained in:
Sébastien Crozet 2021-12-30 23:03:43 +01:00
parent fdaf8c0fbe
commit d806669cc7
1 changed files with 40 additions and 52 deletions

View File

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