nalgebra/nalgebra-lapack/src/svd.rs

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use std::cmp;
use num::Signed;
use na::{Scalar, Matrix, VectorN, MatrixN, MatrixMN,
DefaultAllocator};
use na::dimension::{Dim, DimMin, DimMinimum, U1};
use na::storage::Storage;
use na::allocator::Allocator;
use lapack::fortran as interface;
/// The SVD decomposition of a general matrix.
pub struct SVD<N: Scalar, R: DimMin<C>, C: Dim>
where DefaultAllocator: Allocator<N, R, R> +
Allocator<N, DimMinimum<R, C>> +
Allocator<N, C, C> {
/// The left-singular vectors `U` of this SVD.
pub u: MatrixN<N, R>,
/// The right-singular vectors `V^t` of this SVD.
pub vt: MatrixN<N, C>,
/// The singular values of this SVD.
pub singular_values: VectorN<N, DimMinimum<R, C>>
}
/// Trait implemented by floats (`f32`, `f64`) and complex floats (`Complex<f32>`, `Complex<f64>`)
/// supported by the Singular Value Decompotition.
pub trait SVDScalar<R: DimMin<C>, C: Dim>: Scalar
where DefaultAllocator: Allocator<Self, R, R> +
Allocator<Self, R, C> +
Allocator<Self, DimMinimum<R, C>> +
Allocator<Self, C, C> {
/// Computes the SVD decomposition of `m`.
fn compute(m: MatrixMN<Self, R, C>) -> Option<SVD<Self, R, C>>;
}
impl<N: SVDScalar<R, C>, R: DimMin<C>, C: Dim> SVD<N, R, C>
where DefaultAllocator: Allocator<N, R, R> +
Allocator<N, R, C> +
Allocator<N, DimMinimum<R, C>> +
Allocator<N, C, C> {
/// Computes the Singular Value Decomposition of `matrix`.
pub fn new(m: MatrixMN<N, R, C>) -> Option<Self> {
N::compute(m)
}
}
macro_rules! svd_impl(
($t: ty, $lapack_func: path) => (
impl<R: Dim, C: Dim> SVDScalar<R, C> for $t
where R: DimMin<C>,
DefaultAllocator: Allocator<$t, R, C> +
Allocator<$t, R, R> +
Allocator<$t, C, C> +
Allocator<$t, DimMinimum<R, C>> {
fn compute(mut m: MatrixMN<$t, R, C>) -> Option<SVD<$t, R, C>> {
let (nrows, ncols) = m.data.shape();
if nrows.value() == 0 || ncols.value() == 0 {
return None;
}
let job = b'A';
let lda = nrows.value() as i32;
let mut u = unsafe { Matrix::new_uninitialized_generic(nrows, nrows) };
let mut s = unsafe { Matrix::new_uninitialized_generic(nrows.min(ncols), U1) };
let mut vt = unsafe { Matrix::new_uninitialized_generic(ncols, ncols) };
let ldu = nrows.value();
let ldvt = ncols.value();
let mut work = [ 0.0 ];
let mut lwork = -1 as i32;
let mut info = 0;
let mut iwork = unsafe { ::uninitialized_vec(8 * cmp::min(nrows.value(), ncols.value())) };
$lapack_func(job, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
lda, &mut s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
ldvt as i32, &mut work, lwork, &mut iwork, &mut info);
lapack_check!(info);
lwork = work[0] as i32;
let mut work = unsafe { ::uninitialized_vec(lwork as usize) };
$lapack_func(job, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
lda, &mut s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
ldvt as i32, &mut work, lwork, &mut iwork, &mut info);
lapack_check!(info);
Some(SVD { u: u, singular_values: s, vt: vt })
}
}
impl<R: DimMin<C>, C: Dim> SVD<$t, R, C>
// FIXME: All those bounds…
where DefaultAllocator: Allocator<$t, R, C> +
Allocator<$t, C, R> +
Allocator<$t, U1, R> +
Allocator<$t, U1, C> +
Allocator<$t, R, R> +
Allocator<$t, DimMinimum<R, C>> +
Allocator<$t, DimMinimum<R, C>, R> +
Allocator<$t, DimMinimum<R, C>, C> +
Allocator<$t, R, DimMinimum<R, C>> +
Allocator<$t, C, C> {
/// Reconstructs the matrix from its decomposition.
///
/// Useful if some components (e.g. some singular values) of this decomposition have
/// been manually changed by the user.
#[inline]
pub fn recompose(self) -> MatrixMN<$t, R, C> {
let nrows = self.u.data.shape().0;
let ncols = self.vt.data.shape().1;
let min_nrows_ncols = nrows.min(ncols);
let mut res: MatrixMN<_, R, C> = Matrix::zeros_generic(nrows, ncols);
{
let mut sres = res.generic_slice_mut((0, 0), (min_nrows_ncols, ncols));
sres.copy_from(&self.vt.rows_generic(0, min_nrows_ncols));
for i in 0 .. min_nrows_ncols.value() {
let eigval = self.singular_values[i];
let mut row = sres.row_mut(i);
row *= eigval;
}
}
self.u * res
}
/// Computes the pseudo-inverse of the decomposed matrix.
///
/// All singular value bellow epsilon will be set to zero instead of being inverted.
#[inline]
pub fn pseudo_inverse(&self, epsilon: $t) -> MatrixMN<$t, C, R> {
let nrows = self.u.data.shape().0;
let ncols = self.vt.data.shape().1;
let min_nrows_ncols = nrows.min(ncols);
let mut res: MatrixMN<_, C, R> = Matrix::zeros_generic(ncols, nrows);
{
let mut sres = res.generic_slice_mut((0, 0), (min_nrows_ncols, nrows));
self.u.columns_generic(0, min_nrows_ncols).transpose_to(&mut sres);
for i in 0 .. min_nrows_ncols.value() {
let eigval = self.singular_values[i];
let mut row = sres.row_mut(i);
if eigval.abs() > epsilon {
row /= eigval
}
else {
row.fill(0.0);
}
}
}
self.vt.tr_mul(&res)
}
/// The rank of the decomposed matrix.
///
/// This is the number of singular values that are not too small (i.e. greater than
/// the given `epsilon`).
#[inline]
pub fn rank(&self, epsilon: $t) -> usize {
let mut i = 0;
for e in self.singular_values.as_slice().iter() {
if e.abs() > epsilon {
i += 1;
}
}
i
}
// FIXME: add methods to retrieve the null-space and column-space? (Respectively
// corresponding to the zero and non-zero singular values).
}
);
);
/*
macro_rules! svd_complex_impl(
($name: ident, $t: ty, $lapack_func: path) => (
impl SVDScalar for Complex<$t> {
fn compute<R: Dim, C: Dim, S>(mut m: Matrix<$t, R, C, S>) -> Option<SVD<$t, R, C, S::Alloc>>
Option<(MatrixN<Complex<$t>, R, S::Alloc>,
VectorN<$t, DimMinimum<R, C>, S::Alloc>,
MatrixN<Complex<$t>, C, S::Alloc>)>
where R: DimMin<C>,
S: ContiguousStorage<Complex<$t>, R, C>,
S::Alloc: OwnedAllocator<Complex<$t>, R, C, S> +
Allocator<Complex<$t>, R, R> +
Allocator<Complex<$t>, C, C> +
Allocator<$t, DimMinimum<R, C>> {
let (nrows, ncols) = m.data.shape();
if nrows.value() == 0 || ncols.value() == 0 {
return None;
}
let jobu = b'A';
let jobvt = b'A';
let lda = nrows.value() as i32;
let min_nrows_ncols = nrows.min(ncols);
let mut u = unsafe { Matrix::new_uninitialized_generic(nrows, nrows) };
let mut s = unsafe { Matrix::new_uninitialized_generic(min_nrows_ncols, U1) };
let mut vt = unsafe { Matrix::new_uninitialized_generic(ncols, ncols) };
let ldu = nrows.value();
let ldvt = ncols.value();
let mut work = [ Complex::new(0.0, 0.0) ];
let mut lwork = -1 as i32;
let mut rwork = vec![ 0.0; (5 * min_nrows_ncols.value()) ];
let mut info = 0;
$lapack_func(jobu, jobvt, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
lda, s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
ldvt as i32, &mut work, lwork, &mut rwork, &mut info);
lapack_check!(info);
lwork = work[0].re as i32;
let mut work = vec![Complex::new(0.0, 0.0); lwork as usize];
$lapack_func(jobu, jobvt, nrows.value() as i32, ncols.value() as i32, m.as_mut_slice(),
lda, s.as_mut_slice(), u.as_mut_slice(), ldu as i32, vt.as_mut_slice(),
ldvt as i32, &mut work, lwork, &mut rwork, &mut info);
lapack_check!(info);
Some((u, s, vt))
}
);
);
*/
svd_impl!(f32, interface::sgesdd);
svd_impl!(f64, interface::dgesdd);
// svd_complex_impl!(lapack_svd_complex_f32, f32, interface::cgesvd);
// svd_complex_impl!(lapack_svd_complex_f64, f64, interface::zgesvd);