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svddc.rs
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svddc.rs
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use crate::{error::*, layout::MatrixLayout, *};
use cauchy::*;
use num_traits::{ToPrimitive, Zero};
#[cfg_attr(doc, katexit::katexit)]
/// Singular value decomposition with divide-and-conquer method
pub trait SVDDC_: Scalar {
/// Compute singular value decomposition $A = U \Sigma V^T$
///
/// LAPACK correspondance
/// ----------------------
///
/// | f32 | f64 | c32 | c64 |
/// |:-------|:-------|:-------|:-------|
/// | sgesdd | dgesdd | cgesdd | zgesdd |
///
fn svddc(l: MatrixLayout, jobz: JobSvd, a: &mut [Self]) -> Result<SVDOutput<Self>>;
}
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 {
fn svddc(l: MatrixLayout, jobz: JobSvd, a: &mut [Self],) -> Result<SVDOutput<Self>> {
let m = l.lda();
let n = l.len();
let k = m.min(n);
let mut s = unsafe { vec_uninit( k as usize) };
let (u_col, vt_row) = match jobz {
JobSvd::All | JobSvd::None => (m, n),
JobSvd::Some => (k, k),
};
let (mut u, mut vt) = match jobz {
JobSvd::All => (
Some(unsafe { vec_uninit( (m * m) as usize) }),
Some(unsafe { vec_uninit( (n * n) as usize) }),
),
JobSvd::Some => (
Some(unsafe { vec_uninit( (m * u_col) as usize) }),
Some(unsafe { vec_uninit( (n * vt_row) as usize) }),
),
JobSvd::None => (None, None),
};
$( // for complex only
let mx = n.max(m) as usize;
let mn = n.min(m) as usize;
let lrwork = match jobz {
JobSvd::None => 7 * mn,
_ => std::cmp::max(5*mn*mn + 5*mn, 2*mx*mn + 2*mn*mn + mn),
};
let mut $rwork_ident: Vec<MaybeUninit<Self::Real>> = unsafe { vec_uninit( lrwork) };
)*
// eval work size
let mut info = 0;
let mut iwork: Vec<MaybeUninit<i32>> = unsafe { vec_uninit( 8 * k as usize) };
let mut work_size = [Self::zero()];
unsafe {
$gesdd(
jobz.as_ptr(),
&m,
&n,
AsPtr::as_mut_ptr(a),
&m,
AsPtr::as_mut_ptr(&mut s),
AsPtr::as_mut_ptr(u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut [])),
&m,
AsPtr::as_mut_ptr(vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut [])),
&vt_row,
AsPtr::as_mut_ptr(&mut work_size),
&(-1),
$(AsPtr::as_mut_ptr(&mut $rwork_ident),)*
AsPtr::as_mut_ptr(&mut iwork),
&mut info,
);
}
info.as_lapack_result()?;
// do svd
let lwork = work_size[0].to_usize().unwrap();
let mut work: Vec<MaybeUninit<Self>> = unsafe { vec_uninit( lwork) };
unsafe {
$gesdd(
jobz.as_ptr(),
&m,
&n,
AsPtr::as_mut_ptr(a),
&m,
AsPtr::as_mut_ptr(&mut s),
AsPtr::as_mut_ptr(u.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut [])),
&m,
AsPtr::as_mut_ptr(vt.as_mut().map(|x| x.as_mut_slice()).unwrap_or(&mut [])),
&vt_row,
AsPtr::as_mut_ptr(&mut work),
&(lwork as i32),
$(AsPtr::as_mut_ptr(&mut $rwork_ident),)*
AsPtr::as_mut_ptr(&mut iwork),
&mut info,
);
}
info.as_lapack_result()?;
let s = unsafe { s.assume_init() };
let u = u.map(|v| unsafe { v.assume_init() });
let vt = vt.map(|v| unsafe { v.assume_init() });
match l {
MatrixLayout::F { .. } => Ok(SVDOutput { s, u, vt }),
MatrixLayout::C { .. } => Ok(SVDOutput { s, u: vt, vt: u }),
}
}
}
};
}
impl_svddc!(@real, f32, lapack_sys::sgesdd_);
impl_svddc!(@real, f64, lapack_sys::dgesdd_);
impl_svddc!(@complex, c32, lapack_sys::cgesdd_);
impl_svddc!(@complex, c64, lapack_sys::zgesdd_);