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@ -19,6 +19,7 @@ pub mod householder;
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mod inverse;
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mod lu;
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mod permutation_sequence;
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mod pow;
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mod qr;
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mod schur;
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mod solve;
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@ -41,6 +42,7 @@ pub use self::full_piv_lu::*;
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pub use self::hessenberg::*;
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pub use self::lu::*;
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pub use self::permutation_sequence::*;
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pub use self::pow::*;
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pub use self::qr::*;
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pub use self::schur::*;
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pub use self::svd::*;
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@ -0,0 +1,72 @@
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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::{allocator::Allocator, DefaultAllocator, DimMin, MatrixN};
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use num::PrimInt;
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use simba::scalar::ComplexField;
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impl<N: ComplexField, D> MatrixN<N, D>
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where
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D: DimMin<D, Output = D>,
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DefaultAllocator: Allocator<N, D, D>,
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DefaultAllocator: Allocator<N, D>,
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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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/// matrix is non-invertible and `e` is negative, it leaves this matrix
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/// untouched and returns `Err(())`. Otherwise, it returns `Ok(())` and
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/// overwrites this matrix with the result.
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#[must_use]
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pub fn pow_mut<T: PrimInt + DivAssign>(&mut self, mut e: T) -> Result<(), ()> {
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let zero = T::zero();
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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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self.fill_with_identity();
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return Ok(());
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}
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// If e is negative, we compute the inverse matrix, then raise it to the
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// power of -e.
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if e < zero {
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if !self.try_inverse_mut() {
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return Err(());
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}
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}
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let one = T::one();
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let two = T::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();
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let mut buf = self.clone();
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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 *= &multiplier;
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}
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e /= two;
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multiplier.mul_to(&multiplier, &mut buf);
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multiplier.copy_from(&buf);
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if e == zero {
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return Ok(());
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}
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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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/// 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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pub fn pow<T: PrimInt + DivAssign>(&self, e: T) -> Option<Self> {
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let mut clone = self.clone();
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match clone.pow_mut(e) {
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Ok(()) => Some(clone),
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Err(()) => None,
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}
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}
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}
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