WIP: LeastSquaresWork

Author: termoshtt

lax/src/least_squares.rs

@@ -12,6 +12,14 @@ pub struct LeastSquaresOwned<A: Scalar> {
     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,
+}
+
 #[cfg_attr(doc, katexit::katexit)]
 /// Solve least square problem
 pub trait LeastSquaresSvdDivideConquer_: Scalar {
@@ -29,7 +37,89 @@ pub trait LeastSquaresSvdDivideConquer_: Scalar {
         a: &mut [Self],
         b_layout: MatrixLayout,
         b: &mut [Self],
-    ) -> Result<LeastSquaresOutput<Self>>;
+    ) -> Result<LeastSquaresOwned<Self>>;
+}
+
+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], b: &mut [Self]) -> Result<LeastSquaresRef<Self::Elem>>;
+    fn eval(self, a: &mut [Self], b: &mut [Self]) -> Result<LeastSquaresOwned<Self::Elem>>;
+}
+
+impl LeastSquaresWorkImpl for LeastSquaresWork<c64> {
+    type Elem = c64;
+
+    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 {
+            lapack_sys::zgelsd_(
+                &m,
+                &n,
+                &nrhs,
+                std::ptr::null_mut(),
+                &a_layout.lda(),
+                std::ptr::null_mut(),
+                &b_layout.lda(),
+                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], b: &mut [Self]) -> Result<LeastSquaresRef<Self::Elem>> {
+        todo!()
+    }
+
+    fn eval(self, a: &mut [Self], b: &mut [Self]) -> Result<LeastSquaresOwned<Self::Elem>> {
+        todo!()
+    }
 }
 
 macro_rules! impl_least_squares {