pass copied slice (qr, hess,schur,lu)

2 files changed, 93 insertions, 115 deletions

diff --git a/packages/base/src/Internal/C/lapack-aux.c b/packages/base/src/Internal/C/lapack-aux.c
index ab78dac..8524962 100644
--- a/packages/base/src/Internal/C/lapack-aux.c
+++ b/packages/base/src/Internal/C/lapack-aux.c
@@ -901,18 +901,17 @@ int chol_l_S(ODMAT(l)) {
 
 //////////////////// QR factorization /////////////////////////
 
-/* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer *
+int dgeqr2_(integer *m, integer *n, doublereal *a, integer *
         lda, doublereal *tau, doublereal *work, integer *info);
 
-int qr_l_R(KODMAT(a), DVEC(tau), ODMAT(r)) {
-    integer m = ar;
-    integer n = ac;
+int qr_l_R(DVEC(tau), ODMAT(r)) {
+    integer m = rr;
+    integer n = rc;
     integer mn = MIN(m,n);
-    REQUIRES(m>=1 && n >=1 && rr== m && rc == n && taun == mn, BAD_SIZE);
+    REQUIRES(m>=1 && n >=1 && taun == mn, BAD_SIZE);
     DEBUGMSG("qr_l_R");
     double *WORK = (double*)malloc(n*sizeof(double));
     CHECK(!WORK,MEM);
-    memcpy(rp,ap,m*n*sizeof(double));
     integer res;
     dgeqr2_ (&m,&n,rp,&m,taup,WORK,&res);
     CHECK(res,res);
@@ -920,18 +919,17 @@ int qr_l_R(KODMAT(a), DVEC(tau), ODMAT(r)) {
     OK
 }
 
-/* Subroutine */ int zgeqr2_(integer *m, integer *n, doublecomplex *a,
+int zgeqr2_(integer *m, integer *n, doublecomplex *a,
         integer *lda, doublecomplex *tau, doublecomplex *work, integer *info);
 
-int qr_l_C(KOCMAT(a), CVEC(tau), OCMAT(r)) {
-    integer m = ar;
-    integer n = ac;
+int qr_l_C(CVEC(tau), OCMAT(r)) {
+    integer m = rr;
+    integer n = rc;
     integer mn = MIN(m,n);
-    REQUIRES(m>=1 && n >=1 && rr== m && rc == n && taun == mn, BAD_SIZE);
+    REQUIRES(m>=1 && n >=1 && taun == mn, BAD_SIZE);
     DEBUGMSG("qr_l_C");
     doublecomplex *WORK = (doublecomplex*)malloc(n*sizeof(doublecomplex));
     CHECK(!WORK,MEM);
-    memcpy(rp,ap,m*n*sizeof(doublecomplex));
     integer res;
     zgeqr2_ (&m,&n,rp,&m,taup,WORK,&res);
     CHECK(res,res);
@@ -939,19 +937,18 @@ int qr_l_C(KOCMAT(a), CVEC(tau), OCMAT(r)) {
     OK
 }
 
-/* Subroutine */ int dorgqr_(integer *m, integer *n, integer *k, doublereal *
+int dorgqr_(integer *m, integer *n, integer *k, doublereal *
         a, integer *lda, doublereal *tau, doublereal *work, integer *lwork,
         integer *info);
 
-int c_dorgqr(KODMAT(a), KDVEC(tau), ODMAT(r)) {
-    integer m = ar;
-    integer n = MIN(ac,ar);
+int c_dorgqr(KDVEC(tau), ODMAT(r)) {
+    integer m = rr;
+    integer n = MIN(rc,rr);
     integer k = taun;
     DEBUGMSG("c_dorgqr");
     integer lwork = 8*n; // FIXME
     double *WORK = (double*)malloc(lwork*sizeof(double));
     CHECK(!WORK,MEM);
-    memcpy(rp,ap,m*k*sizeof(double));
     integer res;
     dorgqr_ (&m,&n,&k,rp,&m,(double*)taup,WORK,&lwork,&res);
     CHECK(res,res);
@@ -959,19 +956,18 @@ int c_dorgqr(KODMAT(a), KDVEC(tau), ODMAT(r)) {
     OK
 }
 
-/* Subroutine */ int zungqr_(integer *m, integer *n, integer *k,
+int zungqr_(integer *m, integer *n, integer *k,
         doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
         work, integer *lwork, integer *info);
 
-int c_zungqr(KOCMAT(a), KCVEC(tau), OCMAT(r)) {
-    integer m = ar;
-    integer n = MIN(ac,ar);
+int c_zungqr(KCVEC(tau), OCMAT(r)) {
+    integer m = rr;
+    integer n = MIN(rc,rr);
     integer k = taun;
     DEBUGMSG("z_ungqr");
     integer lwork = 8*n; // FIXME
     doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex));
     CHECK(!WORK,MEM);
-    memcpy(rp,ap,m*k*sizeof(doublecomplex));
     integer res;
     zungqr_ (&m,&n,&k,rp,&m,(doublecomplex*)taup,WORK,&lwork,&res);
     CHECK(res,res);
@@ -982,20 +978,19 @@ int c_zungqr(KOCMAT(a), KCVEC(tau), OCMAT(r)) {
 
 //////////////////// Hessenberg factorization /////////////////////////
 
-/* Subroutine */ int dgehrd_(integer *n, integer *ilo, integer *ihi,
+int dgehrd_(integer *n, integer *ilo, integer *ihi,
         doublereal *a, integer *lda, doublereal *tau, doublereal *work,
         integer *lwork, integer *info);
 
-int hess_l_R(KODMAT(a), DVEC(tau), ODMAT(r)) {
-    integer m = ar;
-    integer n = ac;
+int hess_l_R(DVEC(tau), ODMAT(r)) {
+    integer m = rr;
+    integer n = rc;
     integer mn = MIN(m,n);
-    REQUIRES(m>=1 && n == m && rr== m && rc == n && taun == mn-1, BAD_SIZE);
+    REQUIRES(m>=1 && n == m && taun == mn-1, BAD_SIZE);
     DEBUGMSG("hess_l_R");
-    integer lwork = 5*n; // fixme
+    integer lwork = 5*n; // FIXME
     double *WORK = (double*)malloc(lwork*sizeof(double));
     CHECK(!WORK,MEM);
-    memcpy(rp,ap,m*n*sizeof(double));
     integer res;
     integer one = 1;
     dgehrd_ (&n,&one,&n,rp,&n,taup,WORK,&lwork,&res);
@@ -1005,20 +1000,19 @@ int hess_l_R(KODMAT(a), DVEC(tau), ODMAT(r)) {
 }
 
 
-/* Subroutine */ int zgehrd_(integer *n, integer *ilo, integer *ihi,
+int zgehrd_(integer *n, integer *ilo, integer *ihi,
         doublecomplex *a, integer *lda, doublecomplex *tau, doublecomplex *
         work, integer *lwork, integer *info);
 
-int hess_l_C(KOCMAT(a), CVEC(tau), OCMAT(r)) {
-    integer m = ar;
-    integer n = ac;
+int hess_l_C(CVEC(tau), OCMAT(r)) {
+    integer m = rr;
+    integer n = rc;
     integer mn = MIN(m,n);
-    REQUIRES(m>=1 && n == m && rr== m && rc == n && taun == mn-1, BAD_SIZE);
+    REQUIRES(m>=1 && n == m && taun == mn-1, BAD_SIZE);
     DEBUGMSG("hess_l_C");
-    integer lwork = 5*n; // fixme
+    integer lwork = 5*n; // FIXME
     doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex));
     CHECK(!WORK,MEM);
-    memcpy(rp,ap,m*n*sizeof(doublecomplex));
     integer res;
     integer one = 1;
     zgehrd_ (&n,&one,&n,rp,&n,taup,WORK,&lwork,&res);
@@ -1029,23 +1023,17 @@ int hess_l_C(KOCMAT(a), CVEC(tau), OCMAT(r)) {
 
 //////////////////// Schur factorization /////////////////////////
 
-/* Subroutine */ int dgees_(char *jobvs, char *sort, L_fp select, integer *n,
+int dgees_(char *jobvs, char *sort, L_fp select, integer *n,
         doublereal *a, integer *lda, integer *sdim, doublereal *wr,
         doublereal *wi, doublereal *vs, integer *ldvs, doublereal *work,
         integer *lwork, logical *bwork, integer *info);
 
-int schur_l_R(KODMAT(a), ODMAT(u), ODMAT(s)) {
-    integer m = ar;
-    integer n = ac;
-    REQUIRES(m>=1 && n==m && ur==n && uc==n && sr==n && sc==n, BAD_SIZE);
+int schur_l_R(ODMAT(u), ODMAT(s)) {
+    integer m = sr;
+    integer n = sc;
+    REQUIRES(m>=1 && n==m && ur==n && uc==n, BAD_SIZE);
     DEBUGMSG("schur_l_R");
-    //int k;
-    //printf("---------------------------\n");
-    //printf("%p: ",ap); for(k=0;k<n*n;k++) printf("%f ",ap[k]); printf("\n");
-    //printf("%p: ",up); for(k=0;k<n*n;k++) printf("%f ",up[k]); printf("\n");
-    //printf("%p: ",sp); for(k=0;k<n*n;k++) printf("%f ",sp[k]); printf("\n");
-    memcpy(sp,ap,n*n*sizeof(double));
-    integer lwork = 6*n; // fixme
+    integer lwork = 6*n; // FIXME
     double *WORK = (double*)malloc(lwork*sizeof(double));
     double *WR = (double*)malloc(n*sizeof(double));
     double *WI = (double*)malloc(n*sizeof(double));
@@ -1054,9 +1042,6 @@ int schur_l_R(KODMAT(a), ODMAT(u), ODMAT(s)) {
     integer res;
     integer sdim;
     dgees_ ("V","N",NULL,&n,sp,&n,&sdim,WR,WI,up,&n,WORK,&lwork,BWORK,&res);
-    //printf("%p: ",ap); for(k=0;k<n*n;k++) printf("%f ",ap[k]); printf("\n");
-    //printf("%p: ",up); for(k=0;k<n*n;k++) printf("%f ",up[k]); printf("\n");
-    //printf("%p: ",sp); for(k=0;k<n*n;k++) printf("%f ",sp[k]); printf("\n");
     if(res>0) {
         return NOCONVER;
     }
@@ -1069,18 +1054,17 @@ int schur_l_R(KODMAT(a), ODMAT(u), ODMAT(s)) {
 }
 
 
-/* Subroutine */ int zgees_(char *jobvs, char *sort, L_fp select, integer *n,
+int zgees_(char *jobvs, char *sort, L_fp select, integer *n,
         doublecomplex *a, integer *lda, integer *sdim, doublecomplex *w,
         doublecomplex *vs, integer *ldvs, doublecomplex *work, integer *lwork,
          doublereal *rwork, logical *bwork, integer *info);
 
-int schur_l_C(KOCMAT(a), OCMAT(u), OCMAT(s)) {
-    integer m = ar;
-    integer n = ac;
-    REQUIRES(m>=1 && n==m && ur==n && uc==n && sr==n && sc==n, BAD_SIZE);
+int schur_l_C(OCMAT(u), OCMAT(s)) {
+    integer m = sr;
+    integer n = sc;
+    REQUIRES(m>=1 && n==m && ur==n && uc==n, BAD_SIZE);
     DEBUGMSG("schur_l_C");
-    memcpy(sp,ap,n*n*sizeof(doublecomplex));
-    integer lwork = 6*n; // fixme
+    integer lwork = 6*n; // FIXME
     doublecomplex *WORK = (doublecomplex*)malloc(lwork*sizeof(doublecomplex));
     doublecomplex *W = (doublecomplex*)malloc(n*sizeof(doublecomplex));
     // W not really required in this call
@@ -1103,21 +1087,20 @@ int schur_l_C(KOCMAT(a), OCMAT(u), OCMAT(s)) {
 
 //////////////////// LU factorization /////////////////////////
 
-/* Subroutine */ int dgetrf_(integer *m, integer *n, doublereal *a, integer *
+int dgetrf_(integer *m, integer *n, doublereal *a, integer *
         lda, integer *ipiv, integer *info);
 
-int lu_l_R(KODMAT(a), DVEC(ipiv), ODMAT(r)) {
-    integer m = ar;
-    integer n = ac;
+int lu_l_R(DVEC(ipiv), ODMAT(r)) {
+    integer m = rr;
+    integer n = rc;
     integer mn = MIN(m,n);
     REQUIRES(m>=1 && n >=1 && ipivn == mn, BAD_SIZE);
     DEBUGMSG("lu_l_R");
     integer* auxipiv = (integer*)malloc(mn*sizeof(integer));
-    memcpy(rp,ap,m*n*sizeof(double));
     integer res;
     dgetrf_ (&m,&n,rp,&m,auxipiv,&res);
     if(res>0) {
-        res = 0; // fixme
+        res = 0; // FIXME
     }
     CHECK(res,res);
     int k;
@@ -1129,21 +1112,20 @@ int lu_l_R(KODMAT(a), DVEC(ipiv), ODMAT(r)) {
 }
 
 
-/* Subroutine */ int zgetrf_(integer *m, integer *n, doublecomplex *a,
+int zgetrf_(integer *m, integer *n, doublecomplex *a,
         integer *lda, integer *ipiv, integer *info);
 
-int lu_l_C(KOCMAT(a), DVEC(ipiv), OCMAT(r)) {
-    integer m = ar;
-    integer n = ac;
+int lu_l_C(DVEC(ipiv), OCMAT(r)) {
+    integer m = rr;
+    integer n = rc;
     integer mn = MIN(m,n);
     REQUIRES(m>=1 && n >=1 && ipivn == mn, BAD_SIZE);
     DEBUGMSG("lu_l_C");
     integer* auxipiv = (integer*)malloc(mn*sizeof(integer));
-    memcpy(rp,ap,m*n*sizeof(doublecomplex));
     integer res;
     zgetrf_ (&m,&n,rp,&m,auxipiv,&res);
     if(res>0) {
-        res = 0; // fixme
+        res = 0; // FIXME
     }
     CHECK(res,res);
     int k;
@@ -1157,11 +1139,11 @@ int lu_l_C(KOCMAT(a), DVEC(ipiv), OCMAT(r)) {
 
 //////////////////// LU substitution /////////////////////////
 
-/* Subroutine */ int dgetrs_(char *trans, integer *n, integer *nrhs,
+int dgetrs_(char *trans, integer *n, integer *nrhs,
         doublereal *a, integer *lda, integer *ipiv, doublereal *b, integer *
         ldb, integer *info);
 
-int luS_l_R(KODMAT(a), KDVEC(ipiv), KODMAT(b), ODMAT(x)) {
+int luS_l_R(KODMAT(a), KDVEC(ipiv), ODMAT(b)) {
   integer m = ar;
   integer n = ac;
   integer mrhs = br;
@@ -1174,19 +1156,18 @@ int luS_l_R(KODMAT(a), KDVEC(ipiv), KODMAT(b), ODMAT(x)) {
     auxipiv[k] = (integer)ipivp[k];
   }
   integer res;
-  memcpy(xp,bp,mrhs*nrhs*sizeof(double));
-  dgetrs_ ("N",&n,&nrhs,(/*no const (!?)*/ double*)ap,&m,auxipiv,xp,&mrhs,&res);
+  dgetrs_ ("N",&n,&nrhs,(/*no const (!?)*/ double*)ap,&m,auxipiv,bp,&mrhs,&res);
   CHECK(res,res);
   free(auxipiv);
   OK
 }
 
 
-/* Subroutine */ int zgetrs_(char *trans, integer *n, integer *nrhs,
+int zgetrs_(char *trans, integer *n, integer *nrhs,
         doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *b,
         integer *ldb, integer *info);
 
-int luS_l_C(KOCMAT(a), KDVEC(ipiv), KOCMAT(b), OCMAT(x)) {
+int luS_l_C(KOCMAT(a), KDVEC(ipiv), OCMAT(b)) {
     integer m = ar;
     integer n = ac;
     integer mrhs = br;
@@ -1199,8 +1180,7 @@ int luS_l_C(KOCMAT(a), KDVEC(ipiv), KOCMAT(b), OCMAT(x)) {
         auxipiv[k] = (integer)ipivp[k];
     }
     integer res;
-    memcpy(xp,bp,mrhs*nrhs*sizeof(doublecomplex));
-    zgetrs_ ("N",&n,&nrhs,(doublecomplex*)ap,&m,auxipiv,xp,&mrhs,&res);
+    zgetrs_ ("N",&n,&nrhs,(doublecomplex*)ap,&m,auxipiv,bp,&mrhs,&res);
     CHECK(res,res);
     free(auxipiv);
     OK
diff --git a/packages/base/src/Internal/LAPACK.hs b/packages/base/src/Internal/LAPACK.hs
index ce00c16..65deceb 100644
--- a/packages/base/src/Internal/LAPACK.hs
+++ b/packages/base/src/Internal/LAPACK.hs
@@ -455,29 +455,29 @@ mbCholS =  unsafePerformIO . mbCatch . cholAux dpotrf "cholS"
 
 type TMVM t = t ::> t :> t ::> Ok
 
-foreign import ccall unsafe "qr_l_R" dgeqr2 :: TMVM R
-foreign import ccall unsafe "qr_l_C" zgeqr2 :: TMVM C
+foreign import ccall unsafe "qr_l_R" dgeqr2 :: R :> R ::> Ok
+foreign import ccall unsafe "qr_l_C" zgeqr2 :: C :> C ::> Ok
 
 -- | QR factorization of a real matrix, using LAPACK's /dgeqr2/.
 qrR :: Matrix Double -> (Matrix Double, Vector Double)
-qrR = qrAux dgeqr2 "qrR" . fmat
+qrR = qrAux dgeqr2 "qrR"
 
 -- | QR factorization of a complex matrix, using LAPACK's /zgeqr2/.
 qrC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double))
-qrC = qrAux zgeqr2 "qrC" . fmat
+qrC = qrAux zgeqr2 "qrC"
 
 qrAux f st a = unsafePerformIO $ do
-    r <- createMatrix ColumnMajor m n
+    r <- copy ColumnMajor a
     tau <- createVector mn
-    f # a # tau # r #| st
+    f # tau # r #| st
     return (r,tau)
   where
     m = rows a
     n = cols a
     mn = min m n
 
-foreign import ccall unsafe "c_dorgqr" dorgqr :: TMVM R
-foreign import ccall unsafe "c_zungqr" zungqr :: TMVM C
+foreign import ccall unsafe "c_dorgqr" dorgqr :: R :> R ::> Ok
+foreign import ccall unsafe "c_zungqr" zungqr :: C :> C ::> Ok
 
 -- | build rotation from reflectors
 qrgrR :: Int -> (Matrix Double, Vector Double) -> Matrix Double
@@ -487,28 +487,28 @@ qrgrC :: Int -> (Matrix (Complex Double), Vector (Complex Double)) -> Matrix (Co
 qrgrC = qrgrAux zungqr "qrgrC"
 
 qrgrAux f st n (a, tau) = unsafePerformIO $ do
-    res <- createMatrix ColumnMajor (rows a) n
-    f # (fmat a) # (subVector 0 n tau') # res #| st
+    res <- copy ColumnMajor (sliceMatrix (0,0) (rows a,n) a)
+    f # (subVector 0 n tau') # res #| st
     return res
   where
     tau' = vjoin [tau, constantD 0 n]
 
 -----------------------------------------------------------------------------------
-foreign import ccall unsafe "hess_l_R" dgehrd :: TMVM R
-foreign import ccall unsafe "hess_l_C" zgehrd :: TMVM C
+foreign import ccall unsafe "hess_l_R" dgehrd :: R :> R ::> Ok
+foreign import ccall unsafe "hess_l_C" zgehrd :: C :> C ::> Ok
 
 -- | Hessenberg factorization of a square real matrix, using LAPACK's /dgehrd/.
 hessR :: Matrix Double -> (Matrix Double, Vector Double)
-hessR = hessAux dgehrd "hessR" . fmat
+hessR = hessAux dgehrd "hessR"
 
 -- | Hessenberg factorization of a square complex matrix, using LAPACK's /zgehrd/.
 hessC :: Matrix (Complex Double) -> (Matrix (Complex Double), Vector (Complex Double))
-hessC = hessAux zgehrd "hessC" . fmat
+hessC = hessAux zgehrd "hessC"
 
 hessAux f st a = unsafePerformIO $ do
-    r <- createMatrix ColumnMajor m n
+    r <- copy ColumnMajor a
     tau <- createVector (mn-1)
-    f # a # tau # r #| st
+    f # tau # r #| st
     return (r,tau)
   where
     m = rows a
@@ -516,28 +516,28 @@ hessAux f st a = unsafePerformIO $ do
     mn = min m n
 
 -----------------------------------------------------------------------------------
-foreign import ccall unsafe "schur_l_R" dgees :: R ::> R ::> R ::> Ok
-foreign import ccall unsafe "schur_l_C" zgees :: C ::> C ::> C ::> Ok
+foreign import ccall unsafe "schur_l_R" dgees :: R ::> R ::> Ok
+foreign import ccall unsafe "schur_l_C" zgees :: C ::> C ::> Ok
 
 -- | Schur factorization of a square real matrix, using LAPACK's /dgees/.
 schurR :: Matrix Double -> (Matrix Double, Matrix Double)
-schurR = schurAux dgees "schurR" . fmat
+schurR = schurAux dgees "schurR"
 
 -- | Schur factorization of a square complex matrix, using LAPACK's /zgees/.
 schurC :: Matrix (Complex Double) -> (Matrix (Complex Double), Matrix (Complex Double))
-schurC = schurAux zgees "schurC" . fmat
+schurC = schurAux zgees "schurC"
 
 schurAux f st a = unsafePerformIO $ do
     u <- createMatrix ColumnMajor n n
-    s <- createMatrix ColumnMajor n n
-    f # a # u # s #| st
+    s <- copy ColumnMajor a
+    f # u # s #| st
     return (u,s)
   where
     n = rows a
 
 -----------------------------------------------------------------------------------
-foreign import ccall unsafe "lu_l_R" dgetrf :: TMVM R
-foreign import ccall unsafe "lu_l_C" zgetrf :: C ::> R :> C ::> Ok
+foreign import ccall unsafe "lu_l_R" dgetrf :: R :> R ::> Ok
+foreign import ccall unsafe "lu_l_C" zgetrf :: R :> C ::> Ok
 
 -- | LU factorization of a general real matrix, using LAPACK's /dgetrf/.
 luR :: Matrix Double -> (Matrix Double, [Int])
@@ -548,9 +548,9 @@ luC :: Matrix (Complex Double) -> (Matrix (Complex Double), [Int])
 luC = luAux zgetrf "luC" . fmat
 
 luAux f st a = unsafePerformIO $ do
-    lu <- createMatrix ColumnMajor n m
+    lu <- copy ColumnMajor a
     piv <- createVector (min n m)
-    f # a # piv # lu #| st
+    f # piv # lu #| st
     return (lu, map (pred.round) (toList piv))
   where
     n = rows a
@@ -558,10 +558,8 @@ luAux f st a = unsafePerformIO $ do
 
 -----------------------------------------------------------------------------------
 
-type Tlus t = t ::> Double :> t ::> t ::> Ok
-
-foreign import ccall unsafe "luS_l_R" dgetrs :: Tlus R
-foreign import ccall unsafe "luS_l_C" zgetrs :: Tlus C
+foreign import ccall unsafe "luS_l_R" dgetrs :: R ::> R :> R ::> Ok
+foreign import ccall unsafe "luS_l_C" zgetrs :: C ::> R :> C ::> Ok
 
 -- | Solve a real linear system from a precomputed LU decomposition ('luR'), using LAPACK's /dgetrs/.
 lusR :: Matrix Double -> [Int] -> Matrix Double -> Matrix Double
@@ -573,13 +571,13 @@ lusC a piv b = lusAux zgetrs "lusC" (fmat a) piv (fmat b)
 
 lusAux f st a piv b
     | n1==n2 && n2==n =unsafePerformIO $ do
-         x <- createMatrix ColumnMajor n m
-         f # a # piv' # b # x #| st
+         x <- copy ColumnMajor b
+         f # a # piv' # x #| st
          return x
     | otherwise = error $ st ++ " on LU factorization of nonsquare matrix"
-  where n1 = rows a
-        n2 = cols a
-        n = rows b
-        m = cols b
-        piv' = fromList (map (fromIntegral.succ) piv) :: Vector Double
+  where
+    n1 = rows a
+    n2 = cols a
+    n = rows b
+    piv' = fromList (map (fromIntegral.succ) piv) :: Vector Double