First attempt at xgges (qz decomposition), passing tests. Serialization failing across many modules

This commit is contained in:
metric-space 2022-01-18 22:35:11 -05:00 committed by Saurabh
parent d1c72f0686
commit 372152dc31
4 changed files with 318 additions and 0 deletions

View File

@ -86,6 +86,7 @@ mod eigen;
mod hessenberg; mod hessenberg;
mod lu; mod lu;
mod qr; mod qr;
mod qz;
mod schur; mod schur;
mod svd; mod svd;
mod symmetric_eigen; mod symmetric_eigen;
@ -97,6 +98,7 @@ pub use self::eigen::Eigen;
pub use self::hessenberg::Hessenberg; pub use self::hessenberg::Hessenberg;
pub use self::lu::{LUScalar, LU}; pub use self::lu::{LUScalar, LU};
pub use self::qr::QR; pub use self::qr::QR;
pub use self::qz::QZ;
pub use self::schur::Schur; pub use self::schur::Schur;
pub use self::svd::SVD; pub use self::svd::SVD;
pub use self::symmetric_eigen::SymmetricEigen; pub use self::symmetric_eigen::SymmetricEigen;

288
nalgebra-lapack/src/qz.rs Normal file
View File

@ -0,0 +1,288 @@
#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Serialize};
use num::Zero;
use num_complex::Complex;
use simba::scalar::RealField;
use crate::ComplexHelper;
use na::allocator::Allocator;
use na::dimension::{Const, Dim};
use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
use lapack;
/// Eigendecomposition of a real square matrix with complex eigenvalues.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
serde(
bound(serialize = "DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
OVector<T, D>: Serialize,
OMatrix<T, D, D>: Serialize")
)
)]
#[cfg_attr(
feature = "serde-serialize",
serde(
bound(deserialize = "DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
OVector<T, D>: Serialize,
OMatrix<T, D, D>: Deserialize<'de>")
)
)]
#[derive(Clone, Debug)]
pub struct QZ<T: Scalar, D: Dim>
where
DefaultAllocator: Allocator<T, D> + Allocator<T, D, D>,
{
alphar: OVector<T, D>,
alphai: OVector<T, D>,
beta: OVector<T,D>,
vsl: OMatrix<T, D, D>,
s: OMatrix<T, D, D>,
vsr: OMatrix<T, D, D>,
t: OMatrix<T, D, D>
}
impl<T: Scalar + Copy, D: Dim> Copy for QZ<T, D>
where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
OMatrix<T, D, D>: Copy,
OVector<T, D>: Copy,
{
}
impl<T: QZScalar + RealField, D: Dim> QZ<T, D>
where
DefaultAllocator: Allocator<T, D, D> + Allocator<T, D>,
{
/// Computes the eigenvalues and real Schur form of the matrix `m`.
///
/// Panics if the method did not converge.
pub fn new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self {
Self::try_new(a,b).expect("Schur decomposition: convergence failed.")
}
/// Computes the eigenvalues and real Schur form of the matrix `m`.
///
/// Returns `None` if the method did not converge.
pub fn try_new(mut a: OMatrix<T, D, D>, mut b: OMatrix<T, D, D>) -> Option<Self> {
assert!(
a.is_square() && b.is_square(),
"Unable to compute the qz decomposition of non-square matrices."
);
// another assert to compare shape?
let (nrows, ncols) = a.shape_generic();
let n = nrows.value();
let lda = n as i32;
let ldb = lda.clone();
let mut info = 0;
let mut alphar = Matrix::zeros_generic(nrows, Const::<1>);
let mut alphai = Matrix::zeros_generic(nrows, Const::<1>);
let mut beta = Matrix::zeros_generic(nrows, Const::<1>);
let mut vsl = Matrix::zeros_generic(nrows, ncols);
let mut vsr = Matrix::zeros_generic(nrows, ncols);
// Placeholders:
let mut bwork = [0i32];
let mut unused = 0;
let lwork = T::xgges_work_size(
b'V',
b'V',
b'N',
n as i32,
a.as_mut_slice(),
n as i32,
b.as_mut_slice(),
n as i32,
&mut unused,
alphar.as_mut_slice(),
alphai.as_mut_slice(),
beta.as_mut_slice(),
vsl.as_mut_slice(),
n as i32,
vsr.as_mut_slice(),
n as i32,
&mut bwork,
&mut info,
);
lapack_check!(info);
let mut work = vec![T::zero(); lwork as usize];
T::xgges(
b'V',
b'V',
b'N',
n as i32,
a.as_mut_slice(),
n as i32,
b.as_mut_slice(),
n as i32,
&mut unused,
alphar.as_mut_slice(),
alphai.as_mut_slice(),
beta.as_mut_slice(),
vsl.as_mut_slice(),
n as i32,
vsr.as_mut_slice(),
n as i32,
&mut work,
lwork,
&mut bwork,
&mut info,
);
lapack_check!(info);
Some(QZ {alphar, alphai, beta,
vsl, s:a,
vsr, t:b})
}
/// Retrieves the unitary matrix `Q` and the upper-quasitriangular matrix `T` such that the
/// decomposed matrix equals `Q * T * Q.transpose()`.
pub fn unpack(self) -> (OMatrix<T, D, D>, OMatrix<T, D, D>, OMatrix<T, D, D>, OMatrix<T, D, D>){
(self.vsl, self.s, self.t, self.vsr)
}
/// computes the generalized eigenvalues
#[must_use]
pub fn eigenvalues(&self) -> OVector<Complex<T>, D>
where
DefaultAllocator: Allocator<Complex<T>, D>,
{
let mut out = Matrix::zeros_generic(self.t.shape_generic().0, Const::<1>);
for i in 0..out.len() {
out[i] = Complex::new(self.alphar[i].clone()/self.beta[i].clone(),
self.alphai[i].clone()/self.beta[i].clone())
}
out
}
}
/*
*
* Lapack functions dispatch.
*
*/
/// Trait implemented by scalars for which Lapack implements the RealField QZ decomposition.
pub trait QZScalar: Scalar {
#[allow(missing_docs)]
fn xgges(
jobvsl: u8,
jobvsr: u8,
sort: u8,
// select: ???
n: i32,
a: &mut [Self],
lda: i32,
b: &mut [Self],
ldb: i32,
sdim: &mut i32,
alphar: &mut [Self],
alphai: &mut [Self],
beta : &mut [Self],
vsl: &mut [Self],
ldvsl: i32,
vsr: &mut [Self],
ldvsr: i32,
work: &mut [Self],
lwork: i32,
bwork: &mut [i32],
info: &mut i32
);
#[allow(missing_docs)]
fn xgges_work_size(
jobvsl: u8,
jobvsr: u8,
sort: u8,
// select: ???
n: i32,
a: &mut [Self],
lda: i32,
b: &mut [Self],
ldb: i32,
sdim: &mut i32,
alphar: &mut [Self],
alphai: &mut [Self],
beta : &mut [Self],
vsl: &mut [Self],
ldvsl: i32,
vsr: &mut [Self],
ldvsr: i32,
bwork: &mut [i32],
info: &mut i32
) -> i32;
}
macro_rules! real_eigensystem_scalar_impl (
($N: ty, $xgges: path) => (
impl QZScalar for $N {
#[inline]
fn xgges(jobvsl: u8,
jobvsr: u8,
sort: u8,
// select: ???
n: i32,
a: &mut [$N],
lda: i32,
b: &mut [$N],
ldb: i32,
sdim: &mut i32,
alphar: &mut [$N],
alphai: &mut [$N],
beta : &mut [$N],
vsl: &mut [$N],
ldvsl: i32,
vsr: &mut [$N],
ldvsr: i32,
work: &mut [$N],
lwork: i32,
bwork: &mut [i32],
info: &mut i32) {
unsafe { $xgges(jobvsl, jobvsr, sort, None, n, a, lda, b, ldb, sdim, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, bwork, info); }
}
#[inline]
fn xgges_work_size(jobvsl: u8,
jobvsr: u8,
sort: u8,
// select: ???
n: i32,
a: &mut [$N],
lda: i32,
b: &mut [$N],
ldb: i32,
sdim: &mut i32,
alphar: &mut [$N],
alphai: &mut [$N],
beta : &mut [$N],
vsl: &mut [$N],
ldvsl: i32,
vsr: &mut [$N],
ldvsr: i32,
bwork: &mut [i32],
info: &mut i32)
-> i32 {
let mut work = [ Zero::zero() ];
let lwork = -1 as i32;
unsafe { $xgges(jobvsl, jobvsr, sort, None, n, a, lda, b, ldb, sdim, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, &mut work, lwork, bwork, info); }
ComplexHelper::real_part(work[0]) as i32
}
}
)
);
real_eigensystem_scalar_impl!(f32, lapack::sgges);
real_eigensystem_scalar_impl!(f64, lapack::dgges);

View File

@ -1,6 +1,7 @@
mod cholesky; mod cholesky;
mod lu; mod lu;
mod qr; mod qr;
mod qz;
mod real_eigensystem; mod real_eigensystem;
mod schur; mod schur;
mod svd; mod svd;

View File

@ -0,0 +1,27 @@
use na::DMatrix;
use nl::QZ;
use std::cmp;
use crate::proptest::*;
use proptest::{prop_assert, proptest};
proptest! {
#[test]
fn qz(n in PROPTEST_MATRIX_DIM) {
let n = cmp::max(1, cmp::min(n, 10));
let a = DMatrix::<f64>::new_random(n, n);
let b = DMatrix::<f64>::new_random(n, n);
let (vsl,s,t,vsr) = QZ::new(a.clone(), b.clone()).unpack();
prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a, epsilon = 1.0e-7));
prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b, epsilon = 1.0e-7))
}
#[test]
fn qz_static(a in matrix4(), b in matrix4()) {
let (vsl,s,t,vsr) = QZ::new(a.clone(), b.clone()).unpack();
prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a, epsilon = 1.0e-7));
prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b, epsilon = 1.0e-7))
}
}