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use alga::general::ComplexField;
use crate::base::allocator::Allocator;
use crate::base::dimension::Dim;
use crate::base::storage::{Storage, StorageMut};
use crate::base::{DefaultAllocator, MatrixN, SquareMatrix};
use crate::linalg::lu;
impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
#[inline]
pub fn try_inverse(self) -> Option<MatrixN<N, D>>
where DefaultAllocator: Allocator<N, D, D> {
let mut me = self.into_owned();
if me.try_inverse_mut() {
Some(me)
} else {
None
}
}
}
impl<N: ComplexField, D: Dim, S: StorageMut<N, D, D>> SquareMatrix<N, D, S> {
#[inline]
pub fn try_inverse_mut(&mut self) -> bool
where DefaultAllocator: Allocator<N, D, D> {
assert!(self.is_square(), "Unable to invert a non-square matrix.");
let dim = self.shape().0;
unsafe {
match dim {
0 => true,
1 => {
let determinant = self.get_unchecked((0, 0)).clone();
if determinant.is_zero() {
false
} else {
*self.get_unchecked_mut((0, 0)) = N::one() / determinant;
true
}
}
2 => {
let m11 = *self.get_unchecked((0, 0));
let m12 = *self.get_unchecked((0, 1));
let m21 = *self.get_unchecked((1, 0));
let m22 = *self.get_unchecked((1, 1));
let determinant = m11 * m22 - m21 * m12;
if determinant.is_zero() {
false
} else {
*self.get_unchecked_mut((0, 0)) = m22 / determinant;
*self.get_unchecked_mut((0, 1)) = -m12 / determinant;
*self.get_unchecked_mut((1, 0)) = -m21 / determinant;
*self.get_unchecked_mut((1, 1)) = m11 / determinant;
true
}
}
3 => {
let m11 = *self.get_unchecked((0, 0));
let m12 = *self.get_unchecked((0, 1));
let m13 = *self.get_unchecked((0, 2));
let m21 = *self.get_unchecked((1, 0));
let m22 = *self.get_unchecked((1, 1));
let m23 = *self.get_unchecked((1, 2));
let m31 = *self.get_unchecked((2, 0));
let m32 = *self.get_unchecked((2, 1));
let m33 = *self.get_unchecked((2, 2));
let minor_m12_m23 = m22 * m33 - m32 * m23;
let minor_m11_m23 = m21 * m33 - m31 * m23;
let minor_m11_m22 = m21 * m32 - m31 * m22;
let determinant =
m11 * minor_m12_m23 - m12 * minor_m11_m23 + m13 * minor_m11_m22;
if determinant.is_zero() {
false
} else {
*self.get_unchecked_mut((0, 0)) = minor_m12_m23 / determinant;
*self.get_unchecked_mut((0, 1)) = (m13 * m32 - m33 * m12) / determinant;
*self.get_unchecked_mut((0, 2)) = (m12 * m23 - m22 * m13) / determinant;
*self.get_unchecked_mut((1, 0)) = -minor_m11_m23 / determinant;
*self.get_unchecked_mut((1, 1)) = (m11 * m33 - m31 * m13) / determinant;
*self.get_unchecked_mut((1, 2)) = (m13 * m21 - m23 * m11) / determinant;
*self.get_unchecked_mut((2, 0)) = minor_m11_m22 / determinant;
*self.get_unchecked_mut((2, 1)) = (m12 * m31 - m32 * m11) / determinant;
*self.get_unchecked_mut((2, 2)) = (m11 * m22 - m21 * m12) / determinant;
true
}
}
4 => {
let oself = self.clone_owned();
do_inverse4(&oself, self)
}
_ => {
let oself = self.clone_owned();
lu::try_invert_to(oself, self)
}
}
}
}
}
fn do_inverse4<N: ComplexField, D: Dim, S: StorageMut<N, D, D>>(
m: &MatrixN<N, D>,
out: &mut SquareMatrix<N, D, S>,
) -> bool
where
DefaultAllocator: Allocator<N, D, D>,
{
let m = m.data.as_slice();
out[(0, 0)] = m[5] * m[10] * m[15] - m[5] * m[11] * m[14] - m[9] * m[6] * m[15]
+ m[9] * m[7] * m[14]
+ m[13] * m[6] * m[11]
- m[13] * m[7] * m[10];
out[(1, 0)] = -m[1] * m[10] * m[15] + m[1] * m[11] * m[14] + m[9] * m[2] * m[15]
- m[9] * m[3] * m[14]
- m[13] * m[2] * m[11]
+ m[13] * m[3] * m[10];
out[(2, 0)] = m[1] * m[6] * m[15] - m[1] * m[7] * m[14] - m[5] * m[2] * m[15]
+ m[5] * m[3] * m[14]
+ m[13] * m[2] * m[7]
- m[13] * m[3] * m[6];
out[(3, 0)] = -m[1] * m[6] * m[11] + m[1] * m[7] * m[10] + m[5] * m[2] * m[11]
- m[5] * m[3] * m[10]
- m[9] * m[2] * m[7]
+ m[9] * m[3] * m[6];
out[(0, 1)] = -m[4] * m[10] * m[15] + m[4] * m[11] * m[14] + m[8] * m[6] * m[15]
- m[8] * m[7] * m[14]
- m[12] * m[6] * m[11]
+ m[12] * m[7] * m[10];
out[(1, 1)] = m[0] * m[10] * m[15] - m[0] * m[11] * m[14] - m[8] * m[2] * m[15]
+ m[8] * m[3] * m[14]
+ m[12] * m[2] * m[11]
- m[12] * m[3] * m[10];
out[(2, 1)] = -m[0] * m[6] * m[15] + m[0] * m[7] * m[14] + m[4] * m[2] * m[15]
- m[4] * m[3] * m[14]
- m[12] * m[2] * m[7]
+ m[12] * m[3] * m[6];
out[(3, 1)] = m[0] * m[6] * m[11] - m[0] * m[7] * m[10] - m[4] * m[2] * m[11]
+ m[4] * m[3] * m[10]
+ m[8] * m[2] * m[7]
- m[8] * m[3] * m[6];
out[(0, 2)] = m[4] * m[9] * m[15] - m[4] * m[11] * m[13] - m[8] * m[5] * m[15]
+ m[8] * m[7] * m[13]
+ m[12] * m[5] * m[11]
- m[12] * m[7] * m[9];
out[(1, 2)] = -m[0] * m[9] * m[15] + m[0] * m[11] * m[13] + m[8] * m[1] * m[15]
- m[8] * m[3] * m[13]
- m[12] * m[1] * m[11]
+ m[12] * m[3] * m[9];
out[(2, 2)] = m[0] * m[5] * m[15] - m[0] * m[7] * m[13] - m[4] * m[1] * m[15]
+ m[4] * m[3] * m[13]
+ m[12] * m[1] * m[7]
- m[12] * m[3] * m[5];
out[(0, 3)] = -m[4] * m[9] * m[14] + m[4] * m[10] * m[13] + m[8] * m[5] * m[14]
- m[8] * m[6] * m[13]
- m[12] * m[5] * m[10]
+ m[12] * m[6] * m[9];
out[(3, 2)] = -m[0] * m[5] * m[11] + m[0] * m[7] * m[9] + m[4] * m[1] * m[11]
- m[4] * m[3] * m[9]
- m[8] * m[1] * m[7]
+ m[8] * m[3] * m[5];
out[(1, 3)] = m[0] * m[9] * m[14] - m[0] * m[10] * m[13] - m[8] * m[1] * m[14]
+ m[8] * m[2] * m[13]
+ m[12] * m[1] * m[10]
- m[12] * m[2] * m[9];
out[(2, 3)] = -m[0] * m[5] * m[14] + m[0] * m[6] * m[13] + m[4] * m[1] * m[14]
- m[4] * m[2] * m[13]
- m[12] * m[1] * m[6]
+ m[12] * m[2] * m[5];
out[(3, 3)] = m[0] * m[5] * m[10] - m[0] * m[6] * m[9] - m[4] * m[1] * m[10]
+ m[4] * m[2] * m[9]
+ m[8] * m[1] * m[6]
- m[8] * m[2] * m[5];
let det = m[0] * out[(0, 0)] + m[1] * out[(0, 1)] + m[2] * out[(0, 2)] + m[3] * out[(0, 3)];
if !det.is_zero() {
let inv_det = N::one() / det;
for j in 0..4 {
for i in 0..4 {
out[(i, j)] *= inv_det;
}
}
true
} else {
false
}
}