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//! 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,
};
use num::PrimInt;
use simba::scalar::ComplexField;
impl<T: ComplexField, D, S> Matrix<T, D, D, S>
where
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 `Err(())`. Otherwise, it returns `Ok(())` and
/// overwrites this matrix with the result.
#[must_use]
pub fn pow_mut<I: PrimInt + DivAssign>(&mut self, mut e: I) -> Result<(), ()> {
let zero = I::zero();
// A matrix raised to the zeroth power is just the identity.
if e == zero {
self.fill_with_identity();
return Ok(());
}
// If e is negative, we compute the inverse matrix, then raise it to the
// power of -e.
if e < zero {
if !self.try_inverse_mut() {
return Err(());
}
}
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;
multiplier.mul_to(&multiplier, &mut buf);
multiplier.copy_from(&buf);
if e == zero {
return Ok(());
}
}
}
}
impl<T: ComplexField, D, S: Storage<T, D, D>> Matrix<T, D, D, S>
where
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.
#[must_use]
pub fn pow<I: PrimInt + DivAssign>(&self, e: I) -> Option<OMatrix<T, D, D>> {
let mut clone = self.clone_owned();
match clone.pow_mut(e) {
Ok(()) => Some(clone),
Err(()) => None,
}
}
}