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use num::Zero;
#[cfg(feature = "serde-serialize-no-std")]
use serde::{Deserialize, Serialize};
use crate::allocator::{Allocator, Reallocator};
use crate::base::{Const, DefaultAllocator, Matrix, OMatrix, OVector, Unit};
use crate::constraint::{SameNumberOfRows, ShapeConstraint};
use crate::dimension::{Dim, DimMin, DimMinimum};
use crate::storage::StorageMut;
use crate::ComplexField;
use crate::geometry::Reflection;
use crate::linalg::{householder, PermutationSequence};
use std::mem::MaybeUninit;
#[cfg_attr(feature = "serde-serialize-no-std", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize-no-std",
serde(bound(serialize = "DefaultAllocator: Allocator<T, R, C> +
Allocator<T, DimMinimum<R, C>>,
OMatrix<T, R, C>: Serialize,
PermutationSequence<DimMinimum<R, C>>: Serialize,
OVector<T, DimMinimum<R, C>>: Serialize"))
)]
#[cfg_attr(
feature = "serde-serialize-no-std",
serde(bound(deserialize = "DefaultAllocator: Allocator<T, R, C> +
Allocator<T, DimMinimum<R, C>>,
OMatrix<T, R, C>: Deserialize<'de>,
PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>,
OVector<T, DimMinimum<R, C>>: Deserialize<'de>"))
)]
#[derive(Clone, Debug)]
pub struct ColPivQR<T: ComplexField, R: DimMin<C>, C: Dim>
where
DefaultAllocator: Allocator<T, R, C>
+ Allocator<T, DimMinimum<R, C>>
+ Allocator<(usize, usize), DimMinimum<R, C>>,
{
col_piv_qr: OMatrix<T, R, C>,
p: PermutationSequence<DimMinimum<R, C>>,
diag: OVector<T, DimMinimum<R, C>>,
}
impl<T: ComplexField, R: DimMin<C>, C: Dim> Copy for ColPivQR<T, R, C>
where
DefaultAllocator: Allocator<T, R, C>
+ Allocator<T, DimMinimum<R, C>>
+ Allocator<(usize, usize), DimMinimum<R, C>>,
OMatrix<T, R, C>: Copy,
PermutationSequence<DimMinimum<R, C>>: Copy,
OVector<T, DimMinimum<R, C>>: Copy,
{
}
impl<T: ComplexField, R: DimMin<C>, C: Dim> ColPivQR<T, R, C>
where
DefaultAllocator: Allocator<T, R, C>
+ Allocator<T, R>
+ Allocator<T, DimMinimum<R, C>>
+ Allocator<(usize, usize), DimMinimum<R, C>>,
{
pub fn new(mut matrix: OMatrix<T, R, C>) -> Self {
let (nrows, ncols) = matrix.shape_generic();
let min_nrows_ncols = nrows.min(ncols);
let mut p = PermutationSequence::identity_generic(min_nrows_ncols);
if min_nrows_ncols.value() == 0 {
return ColPivQR {
col_piv_qr: matrix,
p,
diag: Matrix::zeros_generic(min_nrows_ncols, Const::<1>),
};
}
let mut diag = Matrix::uninit(min_nrows_ncols, Const::<1>);
for i in 0..min_nrows_ncols.value() {
let piv = matrix.slice_range(i.., i..).icamax_full();
let col_piv = piv.1 + i;
matrix.swap_columns(i, col_piv);
p.append_permutation(i, col_piv);
diag[i] =
MaybeUninit::new(householder::clear_column_unchecked(&mut matrix, i, 0, None));
}
let diag = unsafe { diag.assume_init() };
ColPivQR {
col_piv_qr: matrix,
p,
diag,
}
}
#[inline]
#[must_use]
pub fn r(&self) -> OMatrix<T, DimMinimum<R, C>, C>
where
DefaultAllocator: Allocator<T, DimMinimum<R, C>, C>,
{
let (nrows, ncols) = self.col_piv_qr.shape_generic();
let mut res = self
.col_piv_qr
.rows_generic(0, nrows.min(ncols))
.upper_triangle();
res.set_partial_diagonal(self.diag.iter().map(|e| T::from_real(e.clone().modulus())));
res
}
#[inline]
pub fn unpack_r(self) -> OMatrix<T, DimMinimum<R, C>, C>
where
DefaultAllocator: Reallocator<T, R, C, DimMinimum<R, C>, C>,
{
let (nrows, ncols) = self.col_piv_qr.shape_generic();
let mut res = self
.col_piv_qr
.resize_generic(nrows.min(ncols), ncols, T::zero());
res.fill_lower_triangle(T::zero(), 1);
res.set_partial_diagonal(self.diag.iter().map(|e| T::from_real(e.clone().modulus())));
res
}
#[must_use]
pub fn q(&self) -> OMatrix<T, R, DimMinimum<R, C>>
where
DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>,
{
let (nrows, ncols) = self.col_piv_qr.shape_generic();
let mut res = Matrix::identity_generic(nrows, nrows.min(ncols));
let dim = self.diag.len();
for i in (0..dim).rev() {
let axis = self.col_piv_qr.slice_range(i.., i);
let refl = Reflection::new(Unit::new_unchecked(axis), T::zero());
let mut res_rows = res.slice_range_mut(i.., i..);
refl.reflect_with_sign(&mut res_rows, self.diag[i].clone().signum());
}
res
}
#[inline]
#[must_use]
pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>> {
&self.p
}
pub fn unpack(
self,
) -> (
OMatrix<T, R, DimMinimum<R, C>>,
OMatrix<T, DimMinimum<R, C>, C>,
PermutationSequence<DimMinimum<R, C>>,
)
where
DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
DefaultAllocator: Allocator<T, R, DimMinimum<R, C>>
+ Reallocator<T, R, C, DimMinimum<R, C>, C>
+ Allocator<(usize, usize), DimMinimum<R, C>>,
{
(self.q(), self.r(), self.p)
}
#[doc(hidden)]
pub fn col_piv_qr_internal(&self) -> &OMatrix<T, R, C> {
&self.col_piv_qr
}
pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<T, R2, C2, S2>)
where
S2: StorageMut<T, R2, C2>,
{
let dim = self.diag.len();
for i in 0..dim {
let axis = self.col_piv_qr.slice_range(i.., i);
let refl = Reflection::new(Unit::new_unchecked(axis), T::zero());
let mut rhs_rows = rhs.rows_range_mut(i..);
refl.reflect_with_sign(&mut rhs_rows, self.diag[i].clone().signum().conjugate());
}
}
}
impl<T: ComplexField, D: DimMin<D, Output = D>> ColPivQR<T, D, D>
where
DefaultAllocator:
Allocator<T, D, D> + Allocator<T, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
{
#[must_use = "Did you mean to use solve_mut()?"]
pub fn solve<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<T, R2, C2, S2>,
) -> Option<OMatrix<T, R2, C2>>
where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
DefaultAllocator: Allocator<T, R2, C2>,
{
let mut res = b.clone_owned();
if self.solve_mut(&mut res) {
Some(res)
} else {
None
}
}
pub fn solve_mut<R2: Dim, C2: Dim, S2>(&self, b: &mut Matrix<T, R2, C2, S2>) -> bool
where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
assert_eq!(
self.col_piv_qr.nrows(),
b.nrows(),
"ColPivQR solve matrix dimension mismatch."
);
assert!(
self.col_piv_qr.is_square(),
"ColPivQR solve: unable to solve a non-square system."
);
self.q_tr_mul(b);
let solved = self.solve_upper_triangular_mut(b);
self.p.inv_permute_rows(b);
solved
}
fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<T, R2, C2, S2>,
) -> bool
where
S2: StorageMut<T, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let dim = self.col_piv_qr.nrows();
for k in 0..b.ncols() {
let mut b = b.column_mut(k);
for i in (0..dim).rev() {
let coeff;
unsafe {
let diag = self.diag.vget_unchecked(i).clone().modulus();
if diag.is_zero() {
return false;
}
coeff = b.vget_unchecked(i).clone().unscale(diag);
*b.vget_unchecked_mut(i) = coeff.clone();
}
b.rows_range_mut(..i)
.axpy(-coeff, &self.col_piv_qr.slice_range(..i, i), T::one());
}
}
true
}
#[must_use]
pub fn try_inverse(&self) -> Option<OMatrix<T, D, D>> {
assert!(
self.col_piv_qr.is_square(),
"ColPivQR inverse: unable to compute the inverse of a non-square matrix."
);
let (nrows, ncols) = self.col_piv_qr.shape_generic();
let mut res = OMatrix::identity_generic(nrows, ncols);
if self.solve_mut(&mut res) {
Some(res)
} else {
None
}
}
#[must_use]
pub fn is_invertible(&self) -> bool {
assert!(
self.col_piv_qr.is_square(),
"ColPivQR: unable to test the invertibility of a non-square matrix."
);
for i in 0..self.diag.len() {
if self.diag[i].is_zero() {
return false;
}
}
true
}
#[must_use]
pub fn determinant(&self) -> T {
let dim = self.col_piv_qr.nrows();
assert!(
self.col_piv_qr.is_square(),
"ColPivQR determinant: unable to compute the determinant of a non-square matrix."
);
let mut res = T::one();
for i in 0..dim {
res *= unsafe { self.diag.vget_unchecked(i).clone() };
}
res * self.p.determinant()
}
}