4 files changed, 129 insertions, 2 deletions

diff --git a/packages/base/src/Internal/Algorithms.hs b/packages/base/src/Internal/Algorithms.hs
index 70d65d7..23a5e13 100644
--- a/packages/base/src/Internal/Algorithms.hs
+++ b/packages/base/src/Internal/Algorithms.hs
@@ -20,13 +20,16 @@ imported from "Numeric.LinearAlgebra.LAPACK".
 -}
 -----------------------------------------------------------------------------
 
-module Internal.Algorithms where
+module Internal.Algorithms (
+  module Internal.Algorithms,
+  UpLo(..)
+) where
 
 import Internal.Vector
 import Internal.Matrix
 import Internal.Element
 import Internal.Conversion
-import Internal.LAPACK as LAPACK
+import Internal.LAPACK
 import Internal.Numeric
 import Data.List(foldl1')
 import qualified Data.Array as A
@@ -58,6 +61,7 @@ class (Numeric t,
     mbLinearSolve' :: Matrix t -> Matrix t -> Maybe (Matrix t)
     linearSolve' :: Matrix t -> Matrix t -> Matrix t
     cholSolve'   :: Matrix t -> Matrix t -> Matrix t
+    triSolve'   :: UpLo -> Matrix t -> Matrix t -> Matrix t
     ldlPacked'   :: Matrix t -> (Matrix t, [Int])
     ldlSolve'    :: (Matrix t, [Int]) -> Matrix t -> Matrix t
     linearSolveSVD' :: Matrix t -> Matrix t -> Matrix t
@@ -83,6 +87,7 @@ instance Field Double where
     linearSolve' = linearSolveR                 -- (luSolve . luPacked) ??
     mbLinearSolve' = mbLinearSolveR
     cholSolve' = cholSolveR
+    triSolve' = triSolveR
     linearSolveLS' = linearSolveLSR
     linearSolveSVD' = linearSolveSVDR Nothing
     eig' = eigR
@@ -112,6 +117,7 @@ instance Field (Complex Double) where
     linearSolve' = linearSolveC
     mbLinearSolve' = mbLinearSolveC
     cholSolve' = cholSolveC
+    triSolve' = triSolveC
     linearSolveLS' = linearSolveLSC
     linearSolveSVD' = linearSolveSVDC Nothing
     eig' = eigC
@@ -350,6 +356,10 @@ cholSolve
     -> Matrix t -- ^ solution
 cholSolve = {-# SCC "cholSolve" #-} cholSolve'
 
+-- | Solve a triangular linear system.
+triSolve :: Field t => UpLo -> Matrix t -> Matrix t -> Matrix t
+triSolve = {-# SCC "triSolve" #-} triSolve'
+
 -- | Minimum norm solution of a general linear least squares problem Ax=B using the SVD. Admits rank-deficient systems but it is slower than 'linearSolveLS'. The effective rank of A is determined by treating as zero those singular valures which are less than 'eps' times the largest singular value.
 linearSolveSVD :: Field t => Matrix t -> Matrix t -> Matrix t
 linearSolveSVD = {-# SCC "linearSolveSVD" #-} linearSolveSVD'
diff --git a/packages/base/src/Internal/C/lapack-aux.c b/packages/base/src/Internal/C/lapack-aux.c
index ff7ad92..4a8129c 100644
--- a/packages/base/src/Internal/C/lapack-aux.c
+++ b/packages/base/src/Internal/C/lapack-aux.c
@@ -584,6 +584,90 @@ int cholSolveC_l(KOCMAT(a),OCMAT(b)) {
     OK
 }
 
+//////// triangular real linear system ////////////
+
+int dtrtrs_(char *uplo, char *trans, char *diag, integer *n, integer *nrhs,
+        doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
+        info);
+
+int triSolveR_l_u(KODMAT(a),ODMAT(b)) {
+    integer n = ar;
+    integer lda = aXc;
+    integer nhrs = bc;
+    REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE);
+    DEBUGMSG("triSolveR_l_u");
+    integer res;
+    dtrtrs_ ("U",
+             "N",
+             "N",
+             &n,&nhrs,
+             (double*)ap, &lda,
+             bp, &n,
+             &res);
+    CHECK(res,res);
+    OK
+}
+
+int triSolveR_l_l(KODMAT(a),ODMAT(b)) {
+    integer n = ar;
+    integer lda = aXc;
+    integer nhrs = bc;
+    REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE);
+    DEBUGMSG("triSolveR_l_l");
+    integer res;
+    dtrtrs_ ("L",
+             "N",
+             "N",
+             &n,&nhrs,
+             (double*)ap, &lda,
+             bp, &n,
+             &res);
+    CHECK(res,res);
+    OK
+}
+
+//////// triangular complex linear system ////////////
+
+int ztrtrs_(char *uplo, char *trans, char *diag, integer *n, integer *nrhs,
+        doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb,
+        integer *info);
+
+int triSolveC_l_u(KOCMAT(a),OCMAT(b)) {
+    integer n = ar;
+    integer lda = aXc;
+    integer nhrs = bc;
+    REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE);
+    DEBUGMSG("triSolveC_l_u");
+    integer res;
+    ztrtrs_ ("U",
+             "N",
+             "N",
+             &n,&nhrs,
+             (doublecomplex*)ap, &lda,
+             bp, &n,
+             &res);
+    CHECK(res,res);
+    OK
+}
+
+int triSolveC_l_l(KOCMAT(a),OCMAT(b)) {
+    integer n = ar;
+    integer lda = aXc;
+    integer nhrs = bc;
+    REQUIRES(n>=1 && ar==ac && ar==br,BAD_SIZE);
+    DEBUGMSG("triSolveC_l_u");
+    integer res;
+    ztrtrs_ ("L",
+             "N",
+             "N",
+             &n,&nhrs,
+             (doublecomplex*)ap, &lda,
+             bp, &n,
+             &res);
+    CHECK(res,res);
+    OK
+}
+
 //////////////////// least squares real linear system ////////////
 
 int dgels_(char *trans, integer *m, integer *n, integer *
diff --git a/packages/base/src/Internal/LAPACK.hs b/packages/base/src/Internal/LAPACK.hs
index 231109a..b4dd5cf 100644
--- a/packages/base/src/Internal/LAPACK.hs
+++ b/packages/base/src/Internal/LAPACK.hs
@@ -406,6 +406,36 @@ cholSolveR a b = linearSolveSQAux2 id dpotrs "cholSolveR" (fmat a) b
 cholSolveC :: Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)
 cholSolveC a b = linearSolveSQAux2 id zpotrs "cholSolveC" (fmat a) b
 
+--------------------------------------------------------------------------------
+foreign import ccall unsafe "triSolveR_l_u" dtrtrs_u  :: R ::> R ::> Ok
+foreign import ccall unsafe "triSolveC_l_u" ztrtrs_u  :: C ::> C ::> Ok
+foreign import ccall unsafe "triSolveR_l_l" dtrtrs_l  :: R ::> R ::> Ok
+foreign import ccall unsafe "triSolveC_l_l" ztrtrs_l  :: C ::> C ::> Ok
+
+
+linearSolveTRAux2 g f st a b
+    | n1==n2 && n1==r = unsafePerformIO . g $ do
+        s <- copy ColumnMajor b
+        (a #! s) f #| st
+        return s
+    | otherwise = error $ st ++ " of nonsquare matrix"
+  where
+    n1 = rows a
+    n2 = cols a
+    r  = rows b
+
+data UpLo = Lower | Upper
+
+-- | Solves a triangular system of linear equations.
+triSolveR :: UpLo -> Matrix Double -> Matrix Double -> Matrix Double
+triSolveR Lower a b = linearSolveTRAux2 id dtrtrs_l "triSolveR" (fmat a) b
+triSolveR Upper a b = linearSolveTRAux2 id dtrtrs_u "triSolveR" (fmat a) b
+
+-- | Solves a triangular system of linear equations.
+triSolveC :: UpLo -> Matrix (Complex Double) -> Matrix (Complex Double) -> Matrix (Complex Double)
+triSolveC Lower a b = linearSolveTRAux2 id ztrtrs_l "triSolveC" (fmat a) b
+triSolveC Upper a b = linearSolveTRAux2 id ztrtrs_u "triSolveC" (fmat a) b
+
 -----------------------------------------------------------------------------------
 
 foreign import ccall unsafe "linearSolveLSR_l"   dgels ::           R ::> R ::> Ok
diff --git a/packages/base/src/Numeric/LinearAlgebra.hs b/packages/base/src/Numeric/LinearAlgebra.hs
index badf8f9..869330c 100644
--- a/packages/base/src/Numeric/LinearAlgebra.hs
+++ b/packages/base/src/Numeric/LinearAlgebra.hs
@@ -94,6 +94,9 @@ module Numeric.LinearAlgebra (
     ldlSolve, ldlPacked,
     -- ** Positive definite
     cholSolve,
+    -- ** Triangular
+    UpLo(..),
+    triSolve,
     -- ** Sparse
     cgSolve,
     cgSolve',