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Merged
merged 2 commits into from
Jul 11, 2020
Merged

SVD using LAPACK #218

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ea930d0
SVD using LAPACK
termoshtt Jul 11, 2020
2373b43
Add test for complex in SVD
termoshtt Jul 11, 2020
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199 changes: 166 additions & 33 deletions lax/src/svd.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -2,16 +2,27 @@

use crate::{error::*, layout::MatrixLayout};
use cauchy::*;
use num_traits::Zero;
use num_traits::{ToPrimitive, Zero};

#[repr(u8)]
#[derive(Debug, Copy, Clone)]
enum FlagSVD {
All = b'A',
// OverWrite = b'O',
// Separately = b'S',
No = b'N',
}

impl FlagSVD {
fn from_bool(calc_uv: bool) -> Self {
if calc_uv {
FlagSVD::All
} else {
FlagSVD::No
}
}
}

/// Result of SVD
pub struct SVDOutput<A: Scalar> {
/// diagonal values
Expand All @@ -24,6 +35,7 @@ pub struct SVDOutput<A: Scalar> {

/// Wraps `*gesvd`
pub trait SVD_: Scalar {
/// Calculate singular value decomposition $ A = U \Sigma V^T $
unsafe fn svd(
l: MatrixLayout,
calc_u: bool,
Expand All @@ -32,7 +44,7 @@ pub trait SVD_: Scalar {
) -> Result<SVDOutput<Self>>;
}

macro_rules! impl_svd {
macro_rules! impl_svd_real {
($scalar:ty, $gesvd:path) => {
impl SVD_ for $scalar {
unsafe fn svd(
Expand All @@ -41,48 +53,169 @@ macro_rules! impl_svd {
calc_vt: bool,
mut a: &mut [Self],
) -> Result<SVDOutput<Self>> {
let (m, n) = l.size();
let k = ::std::cmp::min(n, m);
let lda = l.lda();
let (ju, ldu, mut u) = if calc_u {
(FlagSVD::All, m, vec![Self::zero(); (m * m) as usize])
} else {
(FlagSVD::No, 1, Vec::new())
let ju = match l {
MatrixLayout::F { .. } => FlagSVD::from_bool(calc_u),
MatrixLayout::C { .. } => FlagSVD::from_bool(calc_vt),
};
let (jvt, ldvt, mut vt) = if calc_vt {
(FlagSVD::All, n, vec![Self::zero(); (n * n) as usize])
} else {
(FlagSVD::No, n, Vec::new())
let jvt = match l {
MatrixLayout::F { .. } => FlagSVD::from_bool(calc_vt),
MatrixLayout::C { .. } => FlagSVD::from_bool(calc_u),
};

let m = l.lda();
let mut u = match ju {
FlagSVD::All => Some(vec![Self::zero(); (m * m) as usize]),
FlagSVD::No => None,
};

let n = l.len();
let mut vt = match jvt {
FlagSVD::All => Some(vec![Self::zero(); (n * n) as usize]),
FlagSVD::No => None,
};

let k = std::cmp::min(m, n);
let mut s = vec![Self::Real::zero(); k as usize];
let mut superb = vec![Self::Real::zero(); (k - 1) as usize];

// eval work size
let mut info = 0;
let mut work_size = [Self::zero()];
$gesvd(
ju as u8,
jvt as u8,
m,
n,
&mut a,
m,
&mut s,
u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
m,
vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
n,
&mut work_size,
-1,
&mut info,
);
info.as_lapack_result()?;

// calc
let lwork = work_size[0].to_usize().unwrap();
let mut work = vec![Self::zero(); lwork];
$gesvd(
l.lapacke_layout(),
ju as u8,
jvt as u8,
m,
n,
&mut a,
lda,
m,
&mut s,
&mut u,
ldu,
&mut vt,
ldvt,
&mut superb,
)
.as_lapack_result()?;
Ok(SVDOutput {
s,
u: if calc_u { Some(u) } else { None },
vt: if calc_vt { Some(vt) } else { None },
})
u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
m,
vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
n,
&mut work,
lwork as i32,
&mut info,
);
info.as_lapack_result()?;
match l {
MatrixLayout::F { .. } => Ok(SVDOutput { s, u, vt }),
MatrixLayout::C { .. } => Ok(SVDOutput { s, u: vt, vt: u }),
}
}
}
};
} // impl_svd_real!

impl_svd_real!(f64, lapack::dgesvd);
impl_svd_real!(f32, lapack::sgesvd);

macro_rules! impl_svd_complex {
($scalar:ty, $gesvd:path) => {
impl SVD_ for $scalar {
unsafe fn svd(
l: MatrixLayout,
calc_u: bool,
calc_vt: bool,
mut a: &mut [Self],
) -> Result<SVDOutput<Self>> {
let ju = match l {
MatrixLayout::F { .. } => FlagSVD::from_bool(calc_u),
MatrixLayout::C { .. } => FlagSVD::from_bool(calc_vt),
};
let jvt = match l {
MatrixLayout::F { .. } => FlagSVD::from_bool(calc_vt),
MatrixLayout::C { .. } => FlagSVD::from_bool(calc_u),
};

let m = l.lda();
let mut u = match ju {
FlagSVD::All => Some(vec![Self::zero(); (m * m) as usize]),
FlagSVD::No => None,
};

let n = l.len();
let mut vt = match jvt {
FlagSVD::All => Some(vec![Self::zero(); (n * n) as usize]),
FlagSVD::No => None,
};

let k = std::cmp::min(m, n);
let mut s = vec![Self::Real::zero(); k as usize];

let mut rwork = vec![Self::Real::zero(); 5 * k as usize];

// eval work size
let mut info = 0;
let mut work_size = [Self::zero()];
$gesvd(
ju as u8,
jvt as u8,
m,
n,
&mut a,
m,
&mut s,
u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
m,
vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
n,
&mut work_size,
-1,
&mut rwork,
&mut info,
);
info.as_lapack_result()?;

// calc
let lwork = work_size[0].to_usize().unwrap();
let mut work = vec![Self::zero(); lwork];
$gesvd(
ju as u8,
jvt as u8,
m,
n,
&mut a,
m,
&mut s,
u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
m,
vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut []),
n,
&mut work,
lwork as i32,
&mut rwork,
&mut info,
);
info.as_lapack_result()?;
match l {
MatrixLayout::F { .. } => Ok(SVDOutput { s, u, vt }),
MatrixLayout::C { .. } => Ok(SVDOutput { s, u: vt, vt: u }),
}
}
}
};
} // impl_svd!
} // impl_svd_real!

impl_svd!(f64, lapacke::dgesvd);
impl_svd!(f32, lapacke::sgesvd);
impl_svd!(c64, lapacke::zgesvd);
impl_svd!(c32, lapacke::cgesvd);
impl_svd_complex!(c64, lapack::zgesvd);
impl_svd_complex!(c32, lapack::cgesvd);
28 changes: 21 additions & 7 deletions ndarray-linalg/src/svd.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,6 @@

use ndarray::*;

use super::convert::*;
use super::error::*;
use super::layout::*;
use super::types::*;
Expand Down Expand Up @@ -99,12 +98,27 @@ where
let l = self.layout()?;
let svd_res = unsafe { A::svd(l, calc_u, calc_vt, self.as_allocated_mut()?)? };
let (n, m) = l.size();
let u = svd_res
.u
.map(|u| into_matrix(l.resized(n, n), u).expect("Size of U mismatches"));
let vt = svd_res
.vt
.map(|vt| into_matrix(l.resized(m, m), vt).expect("Size of VT mismatches"));
let n = n as usize;
let m = m as usize;

let u = svd_res.u.map(|u| {
assert_eq!(u.len(), n * n);
match l {
MatrixLayout::F { .. } => Array::from_shape_vec((n, n).f(), u),
MatrixLayout::C { .. } => Array::from_shape_vec((n, n), u),
}
.unwrap()
});

let vt = svd_res.vt.map(|vt| {
assert_eq!(vt.len(), m * m);
match l {
MatrixLayout::F { .. } => Array::from_shape_vec((m, m).f(), vt),
MatrixLayout::C { .. } => Array::from_shape_vec((m, m), vt),
}
.unwrap()
});

let s = ArrayBase::from(svd_res.s);
Ok((u, s, vt))
}
Expand Down
60 changes: 36 additions & 24 deletions ndarray-linalg/tests/svd.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -2,7 +2,7 @@ use ndarray::*;
use ndarray_linalg::*;
use std::cmp::min;

fn test(a: &Array2<f64>) {
fn test<T: Scalar + Lapack>(a: &Array2<T>) {
let (n, m) = a.dim();
let answer = a.clone();
println!("a = \n{:?}", a);
Expand All @@ -12,14 +12,14 @@ fn test(a: &Array2<f64>) {
println!("u = \n{:?}", &u);
println!("s = \n{:?}", &s);
println!("v = \n{:?}", &vt);
let mut sm = Array::zeros((n, m));
let mut sm = Array::<T, _>::zeros((n, m));
for i in 0..min(n, m) {
sm[(i, i)] = s[i];
sm[(i, i)] = T::from(s[i]).unwrap();
}
assert_close_l2!(&u.dot(&sm).dot(&vt), &answer, 1e-7);
assert_close_l2!(&u.dot(&sm).dot(&vt), &answer, T::real(1e-7));
}

fn test_no_vt(a: &Array2<f64>) {
fn test_no_vt<T: Scalar + Lapack>(a: &Array2<T>) {
let (n, _m) = a.dim();
println!("a = \n{:?}", a);
let (u, _s, vt): (_, Array1<_>, _) = a.svd(true, false).unwrap();
Expand All @@ -30,7 +30,7 @@ fn test_no_vt(a: &Array2<f64>) {
assert_eq!(u.dim().1, n);
}

fn test_no_u(a: &Array2<f64>) {
fn test_no_u<T: Scalar + Lapack>(a: &Array2<T>) {
let (_n, m) = a.dim();
println!("a = \n{:?}", a);
let (u, _s, vt): (_, Array1<_>, _) = a.svd(false, true).unwrap();
Expand All @@ -41,40 +41,52 @@ fn test_no_u(a: &Array2<f64>) {
assert_eq!(vt.dim().1, m);
}

fn test_diag_only(a: &Array2<f64>) {
fn test_diag_only<T: Scalar + Lapack>(a: &Array2<T>) {
println!("a = \n{:?}", a);
let (u, _s, vt): (_, Array1<_>, _) = a.svd(false, false).unwrap();
assert!(u.is_none());
assert!(vt.is_none());
}

macro_rules! test_svd_impl {
($test:ident, $n:expr, $m:expr) => {
($type:ty, $test:ident, $n:expr, $m:expr) => {
paste::item! {
#[test]
fn [<svd_ $test _ $n x $m>]() {
fn [<svd_ $type _ $test _ $n x $m>]() {
let a = random(($n, $m));
$test(&a);
$test::<$type>(&a);
}

#[test]
fn [<svd_ $test _ $n x $m _t>]() {
fn [<svd_ $type _ $test _ $n x $m _t>]() {
let a = random(($n, $m).f());
$test(&a);
$test::<$type>(&a);
}
}
};
}

test_svd_impl!(test, 3, 3);
test_svd_impl!(test_no_vt, 3, 3);
test_svd_impl!(test_no_u, 3, 3);
test_svd_impl!(test_diag_only, 3, 3);
test_svd_impl!(test, 4, 3);
test_svd_impl!(test_no_vt, 4, 3);
test_svd_impl!(test_no_u, 4, 3);
test_svd_impl!(test_diag_only, 4, 3);
test_svd_impl!(test, 3, 4);
test_svd_impl!(test_no_vt, 3, 4);
test_svd_impl!(test_no_u, 3, 4);
test_svd_impl!(test_diag_only, 3, 4);
test_svd_impl!(f64, test, 3, 3);
test_svd_impl!(f64, test_no_vt, 3, 3);
test_svd_impl!(f64, test_no_u, 3, 3);
test_svd_impl!(f64, test_diag_only, 3, 3);
test_svd_impl!(f64, test, 4, 3);
test_svd_impl!(f64, test_no_vt, 4, 3);
test_svd_impl!(f64, test_no_u, 4, 3);
test_svd_impl!(f64, test_diag_only, 4, 3);
test_svd_impl!(f64, test, 3, 4);
test_svd_impl!(f64, test_no_vt, 3, 4);
test_svd_impl!(f64, test_no_u, 3, 4);
test_svd_impl!(f64, test_diag_only, 3, 4);
test_svd_impl!(c64, test, 3, 3);
test_svd_impl!(c64, test_no_vt, 3, 3);
test_svd_impl!(c64, test_no_u, 3, 3);
test_svd_impl!(c64, test_diag_only, 3, 3);
test_svd_impl!(c64, test, 4, 3);
test_svd_impl!(c64, test_no_vt, 4, 3);
test_svd_impl!(c64, test_no_u, 4, 3);
test_svd_impl!(c64, test_diag_only, 4, 3);
test_svd_impl!(c64, test, 3, 4);
test_svd_impl!(c64, test_no_vt, 3, 4);
test_svd_impl!(c64, test_no_u, 3, 4);
test_svd_impl!(c64, test_diag_only, 3, 4);