Solve Hermite/Symmetric linear problems

examples/solveh.rs

@@ -0,0 +1,33 @@
+
+extern crate ndarray;
+extern crate ndarray_linalg;
+
+use ndarray::*;
+use ndarray_linalg::*;
+
+// Solve `Ax=b` for Hermite matrix A
+fn solve() -> Result<(), error::LinalgError> {
+    let a: Array2<c64> = random_hermite(3); // complex Hermite positive definite matrix
+    let b: Array1<c64> = random(3);
+    println!("b = {:?}", &b);
+    let x = a.solveh(&b)?;
+    println!("Ax = {:?}", a.dot(&x));;
+    Ok(())
+}
+
+// Solve `Ax=b` for many b with fixed A
+fn factorize() -> Result<(), error::LinalgError> {
+    let a: Array2<f64> = random_hpd(3);
+    let f = a.factorizeh_into()?;
+    // once factorized, you can use it several times:
+    for _ in 0..10 {
+        let b: Array1<f64> = random(3);
+        let _x = f.solveh_into(b)?;
+    }
+    Ok(())
+}
+
+fn main() {
+    solve().unwrap();
+    factorize().unwrap();
+}

src/lapack_traits/mod.rs

@@ -4,6 +4,7 @@ pub mod opnorm;
 pub mod qr;
 pub mod svd;
 pub mod solve;
+pub mod solveh;
 pub mod cholesky;
 pub mod eigh;
 pub mod triangular;
@@ -13,14 +14,18 @@ pub use self::eigh::*;
 pub use self::opnorm::*;
 pub use self::qr::*;
 pub use self::solve::*;
+pub use self::solveh::*;
 pub use self::svd::*;
 pub use self::triangular::*;
 
 use super::error::*;
 use super::types::*;
 
+pub type Pivot = Vec<i32>;
+
 pub trait LapackScalar
-    : OperatorNorm_ + QR_ + SVD_ + Solve_ + Cholesky_ + Eigh_ + Triangular_ {
+    : OperatorNorm_ + QR_ + SVD_ + Solve_ + Solveh_ + Cholesky_ + Eigh_ + Triangular_
+    {
 }
 
 impl LapackScalar for f32 {}

src/lapack_traits/solve.rs

@@ -6,9 +6,7 @@ use error::*;
 use layout::MatrixLayout;
 use types::*;
 
-use super::{Transpose, into_result};
-
-pub type Pivot = Vec<i32>;
+use super::{Pivot, Transpose, into_result};
 
 /// Wraps `*getrf`, `*getri`, and `*getrs`
 pub trait Solve_: Sized {

src/lapack_traits/solveh.rs

@@ -0,0 +1,53 @@
+//! Solve symmetric linear problem using the Bunch-Kaufman diagonal pivoting method.
+//!
+//! See also [the manual of dsytrf](http://www.netlib.org/lapack/lapack-3.1.1/html/dsytrf.f.html)
+
+use lapack::c;
+
+use error::*;
+use layout::MatrixLayout;
+use types::*;
+
+use super::{Pivot, UPLO, into_result};
+
+pub trait Solveh_: Sized {
+    /// Bunch-Kaufman: wrapper of `*sytrf` and `*hetrf`
+    unsafe fn bk(MatrixLayout, UPLO, a: &mut [Self]) -> Result<Pivot>;
+    /// Wrapper of `*sytri` and `*hetri`
+    unsafe fn invh(MatrixLayout, UPLO, a: &mut [Self], &Pivot) -> Result<()>;
+    /// Wrapper of `*sytrs` and `*hetrs`
+    unsafe fn solveh(MatrixLayout, UPLO, a: &[Self], &Pivot, b: &mut [Self]) -> Result<()>;
+}
+
+macro_rules! impl_solveh {
+    ($scalar:ty, $trf:path, $tri:path, $trs:path) => {
+
+impl Solveh_ for $scalar {
+    unsafe fn bk(l: MatrixLayout, uplo: UPLO, a: &mut [Self]) -> Result<Pivot> {
+        let (n, _) = l.size();
+        let mut ipiv = vec![0; n as usize];
+        let info = $trf(l.lapacke_layout(), uplo as u8, n, a, l.lda(), &mut ipiv);
+        into_result(info, ipiv)
+    }
+
+    unsafe fn invh(l: MatrixLayout, uplo: UPLO, a: &mut [Self], ipiv: &Pivot) -> Result<()> {
+        let (n, _) = l.size();
+        let info = $tri(l.lapacke_layout(), uplo as u8, n, a, l.lda(), ipiv);
+        into_result(info, ())
+    }
+
+    unsafe fn solveh(l: MatrixLayout, uplo: UPLO, a: &[Self], ipiv: &Pivot, b: &mut [Self]) -> Result<()> {
+        let (n, _) = l.size();
+        let nrhs = 1;
+        let ldb = 1;
+        let info = $trs(l.lapacke_layout(), uplo as u8, n, nrhs, a, l.lda(), ipiv, b, ldb);
+        into_result(info, ())
+    }
+}
+
+}} // impl_solveh!
+
+impl_solveh!(f64, c::dsytrf, c::dsytri, c::dsytrs);
+impl_solveh!(f32, c::ssytrf, c::ssytri, c::ssytrs);
+impl_solveh!(c64, c::zhetrf, c::zhetri, c::zhetrs);
+impl_solveh!(c32, c::chetrf, c::chetri, c::chetrs);

src/lib.rs

@@ -42,6 +42,7 @@ pub mod operator;
 pub mod opnorm;
 pub mod qr;
 pub mod solve;
+pub mod solveh;
 pub mod svd;
 pub mod trace;
 pub mod triangular;
@@ -59,6 +60,7 @@ pub use operator::*;
 pub use opnorm::*;
 pub use qr::*;
 pub use solve::*;
+pub use solveh::*;
 pub use svd::*;
 pub use trace::*;
 pub use triangular::*;

src/solveh.rs

@@ -0,0 +1,153 @@
+//! Solve Hermite/Symmetric linear problems
+
+use ndarray::*;
+
+use super::convert::*;
+use super::error::*;
+use super::layout::*;
+use super::types::*;
+
+pub use lapack_traits::{Pivot, UPLO};
+
+pub trait SolveH<A: Scalar> {
+    fn solveh<S: Data<Elem = A>>(&self, a: &ArrayBase<S, Ix1>) -> Result<Array1<A>> {
+        let mut a = replicate(a);
+        self.solveh_mut(&mut a)?;
+        Ok(a)
+    }
+    fn solveh_into<S: DataMut<Elem = A>>(&self, mut a: ArrayBase<S, Ix1>) -> Result<ArrayBase<S, Ix1>> {
+        self.solveh_mut(&mut a)?;
+        Ok(a)
+    }
+    fn solveh_mut<'a, S: DataMut<Elem = A>>(&self, &'a mut ArrayBase<S, Ix1>) -> Result<&'a mut ArrayBase<S, Ix1>>;
+}
+
+pub struct FactorizedH<S: Data> {
+    pub a: ArrayBase<S, Ix2>,
+    pub ipiv: Pivot,
+}
+
+impl<A, S> SolveH<A> for FactorizedH<S>
+where
+    A: Scalar,
+    S: Data<Elem = A>,
+{
+    fn solveh_mut<'a, Sb>(&self, rhs: &'a mut ArrayBase<Sb, Ix1>) -> Result<&'a mut ArrayBase<Sb, Ix1>>
+    where
+        Sb: DataMut<Elem = A>,
+    {
+        unsafe {
+            A::solveh(
+                self.a.square_layout()?,
+                UPLO::Upper,
+                self.a.as_allocated()?,
+                &self.ipiv,
+                rhs.as_slice_mut().unwrap(),
+            )?
+        };
+        Ok(rhs)
+    }
+}
+
+impl<A, S> SolveH<A> for ArrayBase<S, Ix2>
+where
+    A: Scalar,
+    S: Data<Elem = A>,
+{
+    fn solveh_mut<'a, Sb>(&self, mut rhs: &'a mut ArrayBase<Sb, Ix1>) -> Result<&'a mut ArrayBase<Sb, Ix1>>
+    where
+        Sb: DataMut<Elem = A>,
+    {
+        let f = self.factorizeh()?;
+        f.solveh_mut(rhs)
+    }
+}
+
+
+impl<A, S> FactorizedH<S>
+where
+    A: Scalar,
+    S: DataMut<Elem = A>,
+{
+    pub fn into_inverseh(mut self) -> Result<ArrayBase<S, Ix2>> {
+        unsafe {
+            A::invh(
+                self.a.square_layout()?,
+                UPLO::Upper,
+                self.a.as_allocated_mut()?,
+                &self.ipiv,
+            )?
+        };
+        Ok(self.a)
+    }
+}
+
+pub trait FactorizeH<S: Data> {
+    fn factorizeh(&self) -> Result<FactorizedH<S>>;
+}
+
+pub trait FactorizeHInto<S: Data> {
+    fn factorizeh_into(self) -> Result<FactorizedH<S>>;
+}
+
+impl<A, S> FactorizeHInto<S> for ArrayBase<S, Ix2>
+where
+    A: Scalar,
+    S: DataMut<Elem = A>,
+{
+    fn factorizeh_into(mut self) -> Result<FactorizedH<S>> {
+        let ipiv = unsafe { A::bk(self.layout()?, UPLO::Upper, self.as_allocated_mut()?)? };
+        Ok(FactorizedH {
+            a: self,
+            ipiv: ipiv,
+        })
+    }
+}
+
+impl<A, Si> FactorizeH<OwnedRepr<A>> for ArrayBase<Si, Ix2>
+where
+    A: Scalar,
+    Si: Data<Elem = A>,
+{
+    fn factorizeh(&self) -> Result<FactorizedH<OwnedRepr<A>>> {
+        let mut a: Array2<A> = replicate(self);
+        let ipiv = unsafe { A::bk(a.layout()?, UPLO::Upper, a.as_allocated_mut()?)? };
+        Ok(FactorizedH { a: a, ipiv: ipiv })
+    }
+}
+
+pub trait InverseH {
+    type Output;
+    fn invh(&self) -> Result<Self::Output>;
+}
+
+pub trait InverseHInto {
+    type Output;
+    fn invh_into(self) -> Result<Self::Output>;
+}
+
+impl<A, S> InverseHInto for ArrayBase<S, Ix2>
+where
+    A: Scalar,
+    S: DataMut<Elem = A>,
+{
+    type Output = Self;
+
+    fn invh_into(self) -> Result<Self::Output> {
+        let f = self.factorizeh_into()?;
+        f.into_inverseh()
+    }
+}
+
+impl<A, Si> InverseH for ArrayBase<Si, Ix2>
+where
+    A: Scalar,
+    Si: Data<Elem = A>,
+{
+    type Output = Array2<A>;
+
+    fn invh(&self) -> Result<Self::Output> {
+        let f = self.factorizeh()?;
+        f.into_inverseh()
+    }
+}