use num::Zero;
#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Serialize};
use crate::allocator::{Allocator, Reallocator};
use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Unit, VectorN};
use crate::constraint::{SameNumberOfRows, ShapeConstraint};
use crate::dimension::{Dim, DimMin, DimMinimum, U1};
use crate::storage::{Storage, StorageMut};
use simba::scalar::ComplexField;
use crate::geometry::Reflection;
use crate::linalg::householder;
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(serialize = "DefaultAllocator: Allocator<N, R, C> +
Allocator<N, DimMinimum<R, C>>,
MatrixMN<N, R, C>: Serialize,
VectorN<N, DimMinimum<R, C>>: Serialize"))
)]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(deserialize = "DefaultAllocator: Allocator<N, R, C> +
Allocator<N, DimMinimum<R, C>>,
MatrixMN<N, R, C>: Deserialize<'de>,
VectorN<N, DimMinimum<R, C>>: Deserialize<'de>"))
)]
#[derive(Clone, Debug)]
pub struct QR<N: ComplexField, R: DimMin<C>, C: Dim>
where
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>>,
{
qr: MatrixMN<N, R, C>,
diag: VectorN<N, DimMinimum<R, C>>,
}
impl<N: ComplexField, R: DimMin<C>, C: Dim> Copy for QR<N, R, C>
where
DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>>,
MatrixMN<N, R, C>: Copy,
VectorN<N, DimMinimum<R, C>>: Copy,
{
}
impl<N: ComplexField, R: DimMin<C>, C: Dim> QR<N, R, C>
where
DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>>,
{
pub fn new(mut matrix: MatrixMN<N, R, C>) -> Self {
let (nrows, ncols) = matrix.data.shape();
let min_nrows_ncols = nrows.min(ncols);
let mut diag = unsafe { MatrixMN::new_uninitialized_generic(min_nrows_ncols, U1) };
if min_nrows_ncols.value() == 0 {
return QR { qr: matrix, diag };
}
for ite in 0..min_nrows_ncols.value() {
householder::clear_column_unchecked(&mut matrix, &mut diag[ite], ite, 0, None);
}
QR { qr: matrix, diag }
}
#[inline]
pub fn r(&self) -> MatrixMN<N, DimMinimum<R, C>, C>
where
DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>,
{
let (nrows, ncols) = self.qr.data.shape();
let mut res = self.qr.rows_generic(0, nrows.min(ncols)).upper_triangle();
res.set_partial_diagonal(self.diag.iter().map(|e| N::from_real(e.modulus())));
res
}
#[inline]
pub fn unpack_r(self) -> MatrixMN<N, DimMinimum<R, C>, C>
where
DefaultAllocator: Reallocator<N, R, C, DimMinimum<R, C>, C>,
{
let (nrows, ncols) = self.qr.data.shape();
let mut res = self.qr.resize_generic(nrows.min(ncols), ncols, N::zero());
res.fill_lower_triangle(N::zero(), 1);
res.set_partial_diagonal(self.diag.iter().map(|e| N::from_real(e.modulus())));
res
}
pub fn q(&self) -> MatrixMN<N, R, DimMinimum<R, C>>
where
DefaultAllocator: Allocator<N, R, DimMinimum<R, C>>,
{
let (nrows, ncols) = self.qr.data.shape();
let mut res = Matrix::identity_generic(nrows, nrows.min(ncols));
let dim = self.diag.len();
for i in (0..dim).rev() {
let axis = self.qr.slice_range(i.., i);
let refl = Reflection::new(Unit::new_unchecked(axis), N::zero());
let mut res_rows = res.slice_range_mut(i.., i..);
refl.reflect_with_sign(&mut res_rows, self.diag[i].signum());
}
res
}
pub fn unpack(
self,
) -> (
MatrixMN<N, R, DimMinimum<R, C>>,
MatrixMN<N, DimMinimum<R, C>, C>,
)
where
DimMinimum<R, C>: DimMin<C, Output = DimMinimum<R, C>>,
DefaultAllocator:
Allocator<N, R, DimMinimum<R, C>> + Reallocator<N, R, C, DimMinimum<R, C>, C>,
{
(self.q(), self.unpack_r())
}
#[doc(hidden)]
pub fn qr_internal(&self) -> &MatrixMN<N, R, C> {
&self.qr
}
pub fn q_tr_mul<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<N, R2, C2, S2>)
where
S2: StorageMut<N, R2, C2>,
{
let dim = self.diag.len();
for i in 0..dim {
let axis = self.qr.slice_range(i.., i);
let refl = Reflection::new(Unit::new_unchecked(axis), N::zero());
let mut rhs_rows = rhs.rows_range_mut(i..);
refl.reflect_with_sign(&mut rhs_rows, self.diag[i].signum().conjugate());
}
}
}
impl<N: ComplexField, D: DimMin<D, Output = D>> QR<N, D, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
pub fn solve<R2: Dim, C2: Dim, S2>(
&self,
b: &Matrix<N, R2, C2, S2>,
) -> Option<MatrixMN<N, R2, C2>>
where
S2: Storage<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
DefaultAllocator: Allocator<N, 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<N, R2, C2, S2>) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
assert_eq!(
self.qr.nrows(),
b.nrows(),
"QR solve matrix dimension mismatch."
);
assert!(
self.qr.is_square(),
"QR solve: unable to solve a non-square system."
);
self.q_tr_mul(b);
self.solve_upper_triangular_mut(b)
}
fn solve_upper_triangular_mut<R2: Dim, C2: Dim, S2>(
&self,
b: &mut Matrix<N, R2, C2, S2>,
) -> bool
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
let dim = self.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).modulus();
if diag.is_zero() {
return false;
}
coeff = b.vget_unchecked(i).unscale(diag);
*b.vget_unchecked_mut(i) = coeff;
}
b.rows_range_mut(..i)
.axpy(-coeff, &self.qr.slice_range(..i, i), N::one());
}
}
true
}
pub fn try_inverse(&self) -> Option<MatrixN<N, D>> {
assert!(
self.qr.is_square(),
"QR inverse: unable to compute the inverse of a non-square matrix."
);
let (nrows, ncols) = self.qr.data.shape();
let mut res = MatrixN::identity_generic(nrows, ncols);
if self.solve_mut(&mut res) {
Some(res)
} else {
None
}
}
pub fn is_invertible(&self) -> bool {
assert!(
self.qr.is_square(),
"QR: 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
}
}