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#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Serialize};
use alga::general::ComplexField;
use crate::allocator::Allocator;
use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, SquareMatrix};
use crate::constraint::{SameNumberOfRows, ShapeConstraint};
use crate::dimension::{Dim, DimSub, Dynamic};
use crate::storage::{Storage, StorageMut};
/// The Cholesky decomposition of a symmetric-definite-positive matrix.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(
serialize = "DefaultAllocator: Allocator<N, D>,
MatrixN<N, D>: Serialize"
))
)]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(
deserialize = "DefaultAllocator: Allocator<N, D>,
MatrixN<N, D>: Deserialize<'de>"
))
)]
#[derive(Clone, Debug)]
pub struct Cholesky<N: ComplexField, D: Dim>
where DefaultAllocator: Allocator<N, D, D>
{
chol: MatrixN<N, D>,
}
impl<N: ComplexField, D: Dim> Copy for Cholesky<N, D>
where
DefaultAllocator: Allocator<N, D, D>,
MatrixN<N, D>: Copy,
{}
impl<N: ComplexField, D: DimSub<Dynamic>> Cholesky<N, D>
where DefaultAllocator: Allocator<N, D, D>
{
/// Attempts to compute the Cholesky decomposition of `matrix`.
///
/// Returns `None` if the input matrix is not definite-positive. The input matrix is assumed
/// to be symmetric and only the lower-triangular part is read.
pub fn new(mut matrix: MatrixN<N, D>) -> Option<Self> {
assert!(matrix.is_square(), "The input matrix must be square.");
let n = matrix.nrows();
for j in 0..n {
for k in 0..j {
let factor = unsafe { -*matrix.get_unchecked((j, k)) };
let (mut col_j, col_k) = matrix.columns_range_pair_mut(j, k);
let mut col_j = col_j.rows_range_mut(j..);
let col_k = col_k.rows_range(j..);
col_j.axpy(factor.conjugate(), &col_k, N::one());
}
let diag = unsafe { *matrix.get_unchecked((j, j)) };
if !diag.is_zero() {
if let Some(denom) = diag.try_sqrt() {
unsafe {
*matrix.get_unchecked_mut((j, j)) = denom;
}
let mut col = matrix.slice_range_mut(j + 1.., j);
col /= denom;
continue;
}
}
// The diagonal element is either zero or its square root could not
// be taken (e.g. for negative real numbers).
return None;
}
Some(Cholesky { chol: matrix })
}
/// Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly
/// upper-triangular part filled with zeros.
pub fn unpack(mut self) -> MatrixN<N, D> {
self.chol.fill_upper_triangle(N::zero(), 1);
self.chol
}
/// Retrieves the lower-triangular factor of the Cholesky decomposition, without zeroing-out
/// its strict upper-triangular part.
///
/// The values of the strict upper-triangular part are garbage and should be ignored by further
/// computations.
pub fn unpack_dirty(self) -> MatrixN<N, D> {
self.chol
}
/// Retrieves the lower-triangular factor of the Cholesky decomposition with its strictly
/// uppen-triangular part filled with zeros.
pub fn l(&self) -> MatrixN<N, D> {
self.chol.lower_triangle()
}
/// Retrieves the lower-triangular factor of the Cholesky decomposition, without zeroing-out
/// its strict upper-triangular part.
///
/// This is an allocation-less version of `self.l()`. The values of the strict upper-triangular
/// part are garbage and should be ignored by further computations.
pub fn l_dirty(&self) -> &MatrixN<N, D> {
&self.chol
}
/// Solves the system `self * x = b` where `self` is the decomposed matrix and `x` the unknown.
///
/// The result is stored on `b`.
pub fn solve_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<N, R2, C2, S2>)
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let _ = self.chol.solve_lower_triangular_mut(b);
let _ = self.chol.ad_solve_lower_triangular_mut(b);
}
/// Returns the solution of the system `self * x = b` where `self` is the decomposed matrix and
/// `x` the unknown.
pub fn solve<R2: Dim, C2: Dim, S2>(&self, b: &Matrix<N, R2, C2, S2>) -> MatrixMN<N, R2, C2>
where
S2: StorageMut<N, R2, C2>,
DefaultAllocator: Allocator<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let mut res = b.clone_owned();
self.solve_mut(&mut res);
res
}
/// Computes the inverse of the decomposed matrix.
pub fn inverse(&self) -> MatrixN<N, D> {
let shape = self.chol.data.shape();
let mut res = MatrixN::identity_generic(shape.0, shape.1);
self.solve_mut(&mut res);
res
}
}
impl<N: ComplexField, D: DimSub<Dynamic>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
where DefaultAllocator: Allocator<N, D, D>
{
/// Attempts to compute the Cholesky decomposition of this matrix.
///
/// Returns `None` if the input matrix is not definite-positive. The input matrix is assumed
/// to be symmetric and only the lower-triangular part is read.
pub fn cholesky(self) -> Option<Cholesky<N, D>> {
Cholesky::new(self.into_owned())
}
}