lax/least_squares.rs
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//! Least squares
use crate::{error::*, layout::*, *};
use cauchy::*;
use num_traits::{ToPrimitive, Zero};
/// Result of LeastSquares
pub struct LeastSquaresOwned<A: Scalar> {
/// singular values
pub singular_values: Vec<A::Real>,
/// The rank of the input matrix A
pub rank: i32,
}
/// Result of LeastSquares
pub struct LeastSquaresRef<'work, A: Scalar> {
/// singular values
pub singular_values: &'work [A::Real],
/// The rank of the input matrix A
pub rank: i32,
}
pub struct LeastSquaresWork<T: Scalar> {
pub a_layout: MatrixLayout,
pub b_layout: MatrixLayout,
pub singular_values: Vec<MaybeUninit<T::Real>>,
pub work: Vec<MaybeUninit<T>>,
pub iwork: Vec<MaybeUninit<i32>>,
pub rwork: Option<Vec<MaybeUninit<T::Real>>>,
}
pub trait LeastSquaresWorkImpl: Sized {
type Elem: Scalar;
fn new(a_layout: MatrixLayout, b_layout: MatrixLayout) -> Result<Self>;
fn calc(
&mut self,
a: &mut [Self::Elem],
b: &mut [Self::Elem],
) -> Result<LeastSquaresRef<Self::Elem>>;
fn eval(
self,
a: &mut [Self::Elem],
b: &mut [Self::Elem],
) -> Result<LeastSquaresOwned<Self::Elem>>;
}
macro_rules! impl_least_squares_work_c {
($c:ty, $lsd:path) => {
impl LeastSquaresWorkImpl for LeastSquaresWork<$c> {
type Elem = $c;
fn new(a_layout: MatrixLayout, b_layout: MatrixLayout) -> Result<Self> {
let (m, n) = a_layout.size();
let (m_, nrhs) = b_layout.size();
let k = m.min(n);
assert!(m_ >= m);
let rcond = -1.;
let mut singular_values = vec_uninit(k as usize);
let mut rank: i32 = 0;
// eval work size
let mut info = 0;
let mut work_size = [Self::Elem::zero()];
let mut iwork_size = [0];
let mut rwork = [<Self::Elem as Scalar>::Real::zero()];
unsafe {
$lsd(
&m,
&n,
&nrhs,
std::ptr::null_mut(),
&m,
std::ptr::null_mut(),
&m_,
AsPtr::as_mut_ptr(&mut singular_values),
&rcond,
&mut rank,
AsPtr::as_mut_ptr(&mut work_size),
&(-1),
AsPtr::as_mut_ptr(&mut rwork),
iwork_size.as_mut_ptr(),
&mut info,
)
};
info.as_lapack_result()?;
let lwork = work_size[0].to_usize().unwrap();
let liwork = iwork_size[0].to_usize().unwrap();
let lrwork = rwork[0].to_usize().unwrap();
let work = vec_uninit(lwork);
let iwork = vec_uninit(liwork);
let rwork = vec_uninit(lrwork);
Ok(LeastSquaresWork {
a_layout,
b_layout,
work,
iwork,
rwork: Some(rwork),
singular_values,
})
}
fn calc(
&mut self,
a: &mut [Self::Elem],
b: &mut [Self::Elem],
) -> Result<LeastSquaresRef<Self::Elem>> {
let (m, n) = self.a_layout.size();
let (m_, nrhs) = self.b_layout.size();
assert!(m_ >= m);
let lwork = self.work.len().to_i32().unwrap();
// Transpose if a is C-continuous
let mut a_t = None;
let _ = match self.a_layout {
MatrixLayout::C { .. } => {
let (layout, t) = transpose(self.a_layout, a);
a_t = Some(t);
layout
}
MatrixLayout::F { .. } => self.a_layout,
};
// Transpose if b is C-continuous
let mut b_t = None;
let b_layout = match self.b_layout {
MatrixLayout::C { .. } => {
let (layout, t) = transpose(self.b_layout, b);
b_t = Some(t);
layout
}
MatrixLayout::F { .. } => self.b_layout,
};
let rcond: <Self::Elem as Scalar>::Real = -1.;
let mut rank: i32 = 0;
let mut info = 0;
unsafe {
$lsd(
&m,
&n,
&nrhs,
AsPtr::as_mut_ptr(a_t.as_mut().map(|v| v.as_mut_slice()).unwrap_or(a)),
&m,
AsPtr::as_mut_ptr(b_t.as_mut().map(|v| v.as_mut_slice()).unwrap_or(b)),
&m_,
AsPtr::as_mut_ptr(&mut self.singular_values),
&rcond,
&mut rank,
AsPtr::as_mut_ptr(&mut self.work),
&lwork,
AsPtr::as_mut_ptr(self.rwork.as_mut().unwrap()),
AsPtr::as_mut_ptr(&mut self.iwork),
&mut info,
);
}
info.as_lapack_result()?;
let singular_values = unsafe { self.singular_values.slice_assume_init_ref() };
// Skip a_t -> a transpose because A has been destroyed
// Re-transpose b
if let Some(b_t) = b_t {
transpose_over(b_layout, &b_t, b);
}
Ok(LeastSquaresRef {
singular_values,
rank,
})
}
fn eval(
mut self,
a: &mut [Self::Elem],
b: &mut [Self::Elem],
) -> Result<LeastSquaresOwned<Self::Elem>> {
let LeastSquaresRef { rank, .. } = self.calc(a, b)?;
let singular_values = unsafe { self.singular_values.assume_init() };
Ok(LeastSquaresOwned {
singular_values,
rank,
})
}
}
};
}
impl_least_squares_work_c!(c64, lapack_sys::zgelsd_);
impl_least_squares_work_c!(c32, lapack_sys::cgelsd_);
macro_rules! impl_least_squares_work_r {
($c:ty, $lsd:path) => {
impl LeastSquaresWorkImpl for LeastSquaresWork<$c> {
type Elem = $c;
fn new(a_layout: MatrixLayout, b_layout: MatrixLayout) -> Result<Self> {
let (m, n) = a_layout.size();
let (m_, nrhs) = b_layout.size();
let k = m.min(n);
assert!(m_ >= m);
let rcond = -1.;
let mut singular_values = vec_uninit(k as usize);
let mut rank: i32 = 0;
// eval work size
let mut info = 0;
let mut work_size = [Self::Elem::zero()];
let mut iwork_size = [0];
unsafe {
$lsd(
&m,
&n,
&nrhs,
std::ptr::null_mut(),
&m,
std::ptr::null_mut(),
&m_,
AsPtr::as_mut_ptr(&mut singular_values),
&rcond,
&mut rank,
AsPtr::as_mut_ptr(&mut work_size),
&(-1),
iwork_size.as_mut_ptr(),
&mut info,
)
};
info.as_lapack_result()?;
let lwork = work_size[0].to_usize().unwrap();
let liwork = iwork_size[0].to_usize().unwrap();
let work = vec_uninit(lwork);
let iwork = vec_uninit(liwork);
Ok(LeastSquaresWork {
a_layout,
b_layout,
work,
iwork,
rwork: None,
singular_values,
})
}
fn calc(
&mut self,
a: &mut [Self::Elem],
b: &mut [Self::Elem],
) -> Result<LeastSquaresRef<Self::Elem>> {
let (m, n) = self.a_layout.size();
let (m_, nrhs) = self.b_layout.size();
assert!(m_ >= m);
let lwork = self.work.len().to_i32().unwrap();
// Transpose if a is C-continuous
let mut a_t = None;
let _ = match self.a_layout {
MatrixLayout::C { .. } => {
let (layout, t) = transpose(self.a_layout, a);
a_t = Some(t);
layout
}
MatrixLayout::F { .. } => self.a_layout,
};
// Transpose if b is C-continuous
let mut b_t = None;
let b_layout = match self.b_layout {
MatrixLayout::C { .. } => {
let (layout, t) = transpose(self.b_layout, b);
b_t = Some(t);
layout
}
MatrixLayout::F { .. } => self.b_layout,
};
let rcond: <Self::Elem as Scalar>::Real = -1.;
let mut rank: i32 = 0;
let mut info = 0;
unsafe {
$lsd(
&m,
&n,
&nrhs,
AsPtr::as_mut_ptr(a_t.as_mut().map(|v| v.as_mut_slice()).unwrap_or(a)),
&m,
AsPtr::as_mut_ptr(b_t.as_mut().map(|v| v.as_mut_slice()).unwrap_or(b)),
&m_,
AsPtr::as_mut_ptr(&mut self.singular_values),
&rcond,
&mut rank,
AsPtr::as_mut_ptr(&mut self.work),
&lwork,
AsPtr::as_mut_ptr(&mut self.iwork),
&mut info,
);
}
info.as_lapack_result()?;
let singular_values = unsafe { self.singular_values.slice_assume_init_ref() };
// Skip a_t -> a transpose because A has been destroyed
// Re-transpose b
if let Some(b_t) = b_t {
transpose_over(b_layout, &b_t, b);
}
Ok(LeastSquaresRef {
singular_values,
rank,
})
}
fn eval(
mut self,
a: &mut [Self::Elem],
b: &mut [Self::Elem],
) -> Result<LeastSquaresOwned<Self::Elem>> {
let LeastSquaresRef { rank, .. } = self.calc(a, b)?;
let singular_values = unsafe { self.singular_values.assume_init() };
Ok(LeastSquaresOwned {
singular_values,
rank,
})
}
}
};
}
impl_least_squares_work_r!(f64, lapack_sys::dgelsd_);
impl_least_squares_work_r!(f32, lapack_sys::sgelsd_);