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118 changes: 84 additions & 34 deletions lax/src/svddc.rs
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
use super::*;
use crate::{error::*, layout::MatrixLayout};
use cauchy::*;
use num_traits::Zero;
use num_traits::{ToPrimitive, Zero};

/// Specifies how many of the columns of *U* and rows of *V*ᵀ are computed and returned.
///
Expand All @@ -21,56 +21,106 @@ pub trait SVDDC_: Scalar {
unsafe fn svddc(l: MatrixLayout, jobz: UVTFlag, a: &mut [Self]) -> Result<SVDOutput<Self>>;
}

macro_rules! impl_svdd {
($scalar:ty, $gesdd:path) => {
macro_rules! impl_svddc {
(@real, $scalar:ty, $gesdd:path) => {
impl_svddc!(@body, $scalar, $gesdd, );
};
(@complex, $scalar:ty, $gesdd:path) => {
impl_svddc!(@body, $scalar, $gesdd, rwork);
};
(@body, $scalar:ty, $gesdd:path, $($rwork_ident:ident),*) => {
impl SVDDC_ for $scalar {
unsafe fn svddc(
l: MatrixLayout,
jobz: UVTFlag,
mut a: &mut [Self],
) -> Result<SVDOutput<Self>> {
let (m, n) = l.size();
let m = l.lda();
let n = l.len();
let k = m.min(n);
let lda = l.lda();
let (ucol, vtrow) = match jobz {
UVTFlag::Full => (m, n),
let mut s = vec![Self::Real::zero(); k as usize];

let (u_col, vt_row) = match jobz {
UVTFlag::Full | UVTFlag::None => (m, n),
UVTFlag::Some => (k, k),
UVTFlag::None => (1, 1),
};
let mut s = vec![Self::Real::zero(); k.max(1) as usize];
let mut u = vec![Self::zero(); (m * ucol).max(1) as usize];
let ldu = l.resized(m, ucol).lda();
let mut vt = vec![Self::zero(); (vtrow * n).max(1) as usize];
let ldvt = l.resized(vtrow, n).lda();
let (mut u, mut vt) = match jobz {
UVTFlag::Full => (
Some(vec![Self::zero(); (m * m) as usize]),
Some(vec![Self::zero(); (n * n) as usize]),
),
UVTFlag::Some => (
Some(vec![Self::zero(); (m * u_col) as usize]),
Some(vec![Self::zero(); (n * vt_row) as usize]),
),
UVTFlag::None => (None, None),
};

$( // for complex only
let mx = n.max(m) as usize;
let mn = n.min(m) as usize;
let lrwork = match jobz {
UVTFlag::None => 7 * mn,
_ => std::cmp::max(5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn),
};
let mut $rwork_ident = vec![Self::Real::zero(); lrwork];
)*

// eval work size
let mut info = 0;
let mut iwork = vec![0; 8 * k as usize];
let mut work_size = [Self::zero()];
$gesdd(
l.lapacke_layout(),
jobz as u8,
m,
n,
&mut a,
lda,
m,
&mut s,
&mut u,
ldu,
&mut vt,
ldvt,
)
.as_lapack_result()?;
Ok(SVDOutput {
s,
u: if jobz == UVTFlag::None { None } else { Some(u) },
vt: if jobz == UVTFlag::None {
None
} else {
Some(vt)
},
})
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 []),
vt_row,
&mut work_size,
-1,
$(&mut $rwork_ident,)*
&mut iwork,
&mut info,
);
info.as_lapack_result()?;

// do svd
let lwork = work_size[0].to_usize().unwrap();
let mut work = vec![Self::zero(); lwork];
$gesdd(
jobz 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 []),
vt_row,
&mut work,
lwork as i32,
$(&mut $rwork_ident,)*
&mut iwork,
&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_svdd!(f32, lapacke::sgesdd);
impl_svdd!(f64, lapacke::dgesdd);
impl_svdd!(c32, lapacke::cgesdd);
impl_svdd!(c64, lapacke::zgesdd);
impl_svddc!(@real, f32, lapack::sgesdd);
impl_svddc!(@real, f64, lapack::dgesdd);
impl_svddc!(@complex, c32, lapack::cgesdd);
impl_svddc!(@complex, c64, lapack::zgesdd);
22 changes: 11 additions & 11 deletions ndarray-linalg/src/svddc.rs
Original file line number Diff line number Diff line change
@@ -1,12 +1,8 @@
//! Singular-value decomposition (SVD) by divide-and-conquer (?gesdd)

use super::{convert::*, error::*, layout::*, types::*};
use ndarray::*;

use super::convert::*;
use super::error::*;
use super::layout::*;
use super::types::*;

pub use lapack::svddc::UVTFlag;

/// Singular-value decomposition of matrix (copying) by divide-and-conquer
Expand Down Expand Up @@ -87,17 +83,21 @@ where
let svd_res = unsafe { A::svddc(l, uvt_flag, self.as_allocated_mut()?)? };
let (m, n) = l.size();
let k = m.min(n);
let (ldu, tdu, ldvt, tdvt) = match uvt_flag {
UVTFlag::Full => (m, m, n, n),
UVTFlag::Some => (m, k, k, n),
UVTFlag::None => (1, 1, 1, 1),

let (u_col, vt_row) = match uvt_flag {
UVTFlag::Full => (m, n),
UVTFlag::Some => (k, k),
UVTFlag::None => (0, 0),
};

let u = svd_res
.u
.map(|u| into_matrix(l.resized(ldu, tdu), u).expect("Size of U mismatches"));
.map(|u| into_matrix(l.resized(m, u_col), u).unwrap());

let vt = svd_res
.vt
.map(|vt| into_matrix(l.resized(ldvt, tdvt), vt).expect("Size of VT mismatches"));
.map(|vt| into_matrix(l.resized(vt_row, n), vt).unwrap());

let s = ArrayBase::from(svd_res.s);
Ok((u, s, vt))
}
Expand Down
43 changes: 23 additions & 20 deletions ndarray-linalg/tests/svddc.rs
Original file line number Diff line number Diff line change
@@ -1,13 +1,13 @@
use ndarray::*;
use ndarray_linalg::*;

fn test(a: &Array2<f64>, flag: UVTFlag) {
fn test<T: Scalar + Lapack>(a: &Array2<T>, flag: UVTFlag) {
let (n, m) = a.dim();
let k = n.min(m);
let answer = a.clone();
println!("a = \n{:?}", a);
let (u, s, vt): (_, Array1<_>, _) = a.svddc(flag).unwrap();
let mut sm = match flag {
let mut sm: Array2<T> = match flag {
UVTFlag::Full => Array::zeros((n, m)),
UVTFlag::Some => Array::zeros((k, k)),
UVTFlag::None => {
Expand All @@ -22,53 +22,56 @@ fn test(a: &Array2<f64>, flag: UVTFlag) {
println!("s = \n{:?}", &s);
println!("v = \n{:?}", &vt);
for i in 0..k {
sm[(i, i)] = s[i];
sm[(i, i)] = T::from_real(s[i]);
}
assert_close_l2!(&u.dot(&sm).dot(&vt), &answer, 1e-7);
assert_close_l2!(&u.dot(&sm).dot(&vt), &answer, T::real(1e-7));
}

macro_rules! test_svd_impl {
($n:expr, $m:expr) => {
($scalar:ty, $n:expr, $m:expr) => {
paste::item! {
#[test]
fn [<svddc_full_ $n x $m>]() {
fn [<svddc_ $scalar _full_ $n x $m>]() {
let a = random(($n, $m));
test(&a, UVTFlag::Full);
test::<$scalar>(&a, UVTFlag::Full);
}

#[test]
fn [<svddc_some_ $n x $m>]() {
fn [<svddc_ $scalar _some_ $n x $m>]() {
let a = random(($n, $m));
test(&a, UVTFlag::Some);
test::<$scalar>(&a, UVTFlag::Some);
}

#[test]
fn [<svddc_none_ $n x $m>]() {
fn [<svddc_ $scalar _none_ $n x $m>]() {
let a = random(($n, $m));
test(&a, UVTFlag::None);
test::<$scalar>(&a, UVTFlag::None);
}

#[test]
fn [<svddc_full_ $n x $m _t>]() {
fn [<svddc_ $scalar _full_ $n x $m _t>]() {
let a = random(($n, $m).f());
test(&a, UVTFlag::Full);
test::<$scalar>(&a, UVTFlag::Full);
}

#[test]
fn [<svddc_some_ $n x $m _t>]() {
fn [<svddc_ $scalar _some_ $n x $m _t>]() {
let a = random(($n, $m).f());
test(&a, UVTFlag::Some);
test::<$scalar>(&a, UVTFlag::Some);
}

#[test]
fn [<svddc_none_ $n x $m _t>]() {
fn [<svddc_ $scalar _none_ $n x $m _t>]() {
let a = random(($n, $m).f());
test(&a, UVTFlag::None);
test::<$scalar>(&a, UVTFlag::None);
}
}
};
}

test_svd_impl!(3, 3);
test_svd_impl!(4, 3);
test_svd_impl!(3, 4);
test_svd_impl!(f64, 3, 3);
test_svd_impl!(f64, 4, 3);
test_svd_impl!(f64, 3, 4);
test_svd_impl!(c64, 3, 3);
test_svd_impl!(c64, 4, 3);
test_svd_impl!(c64, 3, 4);