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Added test for QR factorization and fixed unpack issue

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russellb23 2019-06-24 12:20:14 +05:30 committed by Crozet Sébastien
parent 1316133625
commit 63a34528e0
2 changed files with 178 additions and 16 deletions
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38
src/linalg/qrp.rs
View File

@ -11,10 +11,7 @@ use crate::storage::{Storage, StorageMut};
use crate::geometry::Reflection;
use crate::linalg::householder;
//=============================================================================
use crate::linalg::PermutationSequence;
//=============================================================================
/// The QRP decomposition of a general matrix.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
@ -65,7 +62,9 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
let (nrows, ncols) = matrix.data.shape();
let min_nrows_ncols = nrows.min(ncols);
let mut p = PermutationSequence::identity_generic(min_nrows_ncols);
let mut diag = unsafe { MatrixMN::new_uninitialized_generic(min_nrows_ncols, U1) };
println!("diag: {:?}", &diag);
if min_nrows_ncols.value() == 0 {
return QRP {
@ -76,12 +75,18 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
}
for ite in 0..min_nrows_ncols.value() {
let mut col_norm = Vec::new();
for column in matrix.column_iter() {
col_norm.push(column.norm_squared());
}
let piv = matrix.slice_range(ite.., ite..).icamax_full();
let col_piv = piv.1 + ite;
matrix.swap_columns(ite, col_piv);
p.append_permutation(ite, col_piv);
householder::clear_column_unchecked(&mut matrix, &mut diag[ite], ite, 0, None);
println!("matrix: {:?}", &matrix.data);
}
QRP {
@ -139,7 +144,7 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
res
}
/// The column permutations of this decomposition.
/// Retrieves the column permutation of this decomposition.
#[inline]
pub fn p(&self) -> &PermutationSequence<DimMinimum<R, C>> {
&self.p
@ -151,13 +156,14 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
) -> (
MatrixMN<N, R, DimMinimum<R, C>>,
MatrixMN<N, DimMinimum<R, C>, C>,
PermutationSequence<DimMinimum<R, 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>,
Allocator<N, R, DimMinimum<R, C>> + Reallocator<N, R, C, DimMinimum<R, C>, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
{
(self.q(), self.unpack_r())
(self.q(), self.r(), self.p)
}
#[doc(hidden)]
@ -300,18 +306,18 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> +
true
}
// /// Computes the determinant of the decomposed matrix.
// pub fn determinant(&self) -> N {
// let dim = self.qrp.nrows();
// assert!(self.qrp.is_square(), "QRP determinant: unable to compute the determinant of a non-square matrix.");
/// Computes the determinant of the decomposed matrix.
pub fn determinant(&self) -> N {
let dim = self.qrp.nrows();
assert!(self.qrp.is_square(), "QRP determinant: unable to compute the determinant of a non-square matrix.");
// let mut res = N::one();
// for i in 0 .. dim {
// res *= unsafe { *self.diag.vget_unchecked(i) };
// }
let mut res = N::one();
for i in 0 .. dim {
res *= unsafe { *self.diag.vget_unchecked(i) };
}
// res self.q_determinant()
// }
res * self.p.determinant()
}
}
impl<N: ComplexField, R: DimMin<C>, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>

156
tests/linalg/qrp.rs Normal file
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@ -0,0 +1,156 @@
#[cfg_attr(rustfmt, rustfmt_skip)]
use na::Matrix4;
#[test]
fn qrp() {
let m = Matrix4::new (
1.0, -1.0, 2.0, 1.0,
-1.0, 3.0, -1.0, -1.0,
3.0, -5.0, 5.0, 3.0,
1.0, 2.0, 1.0, -2.0);
let qrp = m.qrp();
assert!(relative_eq!(qrp.determinant(), 0.0, epsilon = 1.0e-7));
let (q, r, p) = qrp.unpack();
let mut qr = q * r;
p.inv_permute_columns(& mut qr);
assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
}
#[cfg(feature = "arbitrary")]
mod quickcheck_tests {
macro_rules! gen_tests(
($module: ident, $scalar: ty) => {
mod $module {
use na::{DMatrix, DVector, Matrix3x5, Matrix4, Matrix4x3, Matrix5x3, Vector4};
use std::cmp;
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
quickcheck! {
fn qrp(m: DMatrix<$scalar>) -> bool {
let m = m.map(|e| e.0);
let qrp = m.clone().qrp();
let q = qrp.q();
let r = qrp.r();
println!("m: {}", m);
println!("qrp: {}", &q * &r);
relative_eq!(m, &q * r, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
fn qrp_static_5_3(m: Matrix5x3<$scalar>) -> bool {
let m = m.map(|e| e.0);
let qrp = m.qrp();
let q = qrp.q();
let r = qrp.r();
relative_eq!(m, q * r, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
fn qrp_static_3_5(m: Matrix3x5<$scalar>) -> bool {
let m = m.map(|e| e.0);
let qrp = m.qrp();
let q = qrp.q();
let r = qrp.r();
relative_eq!(m, q * r, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
fn qrp_static_square(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let qrp = m.qrp();
let q = qrp.q();
let r = qrp.r();
println!("{}{}{}{}", q, r, q * r, m);
relative_eq!(m, q * r, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
fn qrp_solve(n: usize, nb: usize) -> bool {
if n != 0 && nb != 0 {
let n = cmp::min(n, 50); // To avoid slowing down the test too much.
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
let qrp = m.clone().qrp();
let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
if qrp.is_invertible() {
let sol1 = qrp.solve(&b1).unwrap();
let sol2 = qrp.solve(&b2).unwrap();
return relative_eq!(&m * sol1, b1, epsilon = 1.0e-6) &&
relative_eq!(&m * sol2, b2, epsilon = 1.0e-6)
}
}
return true;
}
fn qrp_solve_static(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let qrp = m.qrp();
let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);
if qrp.is_invertible() {
let sol1 = qrp.solve(&b1).unwrap();
let sol2 = qrp.solve(&b2).unwrap();
relative_eq!(m * sol1, b1, epsilon = 1.0e-6) &&
relative_eq!(m * sol2, b2, epsilon = 1.0e-6)
}
else {
false
}
}
fn qrp_inverse(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
if let Some(m1) = m.clone().qrp().try_inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
}
else {
true
}
}
fn qrp_inverse_static(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
let qrp = m.qrp();
if let Some(m1) = qrp.try_inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
}
else {
true
}
}
}
}
}
);
gen_tests!(complex, RandComplex<f64>);
gen_tests!(f64, RandScalar<f64>);
}