diff liboctave/SparseCmplxQR.cc @ 5610:9761b7d24e9e

[project @ 2006-02-09 09:12:02 by dbateman]
author dbateman
date Thu, 09 Feb 2006 09:12:03 +0000
parents
children 69a4f320d95a
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new file mode 100644
--- /dev/null
+++ b/liboctave/SparseCmplxQR.cc
@@ -0,0 +1,676 @@
+/*
+
+Copyright (C) 2005 David Bateman
+
+Octave is free software; you can redistribute it and/or modify it
+under the terms of the GNU General Public License as published by the
+Free Software Foundation; either version 2, or (at your option) any
+later version.
+
+Octave is distributed in the hope that it will be useful, but WITHOUT
+ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program; see the file COPYING.  If not, write to the
+Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+Boston, MA 02110-1301, USA.
+
+*/
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+#include <vector>
+
+#include "lo-error.h"
+#include "SparseCmplxQR.h"
+
+SparseComplexQR::SparseComplexQR_rep::SparseComplexQR_rep 
+(const SparseComplexMatrix& a, int order)
+{
+#ifdef HAVE_CXSPARSE
+  // cast away const on A, with full knowledge that CSparse won't touch it
+  CXSPARSE_ZNAME (cs) A;
+  A.nzmax = a.nnz ();
+  A.m = a.rows ();
+  A.n = a.cols ();
+  nrows = A.m;
+  // Cast away const on A, with full knowledge that CSparse won't touch it
+  // Prevents the methods below making a copy of the data.
+  A.p = const_cast<octave_idx_type *>(a.cidx ());
+  A.i = const_cast<octave_idx_type *>(a.ridx ());
+  A.x = const_cast<double _Complex *>(reinterpret_cast<const double _Complex *> 
+				      (a.data ()));
+  A.nz = -1;
+  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+  S = CXSPARSE_ZNAME (cs_sqr) (&A, order, 1);
+  N = CXSPARSE_ZNAME (cs_qr) (&A, S);
+  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+  if (!N)
+    (*current_liboctave_error_handler)
+      ("SparseComplexQR: sparse matrix QR factorization filled");
+  count = 1;
+#else
+  (*current_liboctave_error_handler)
+    ("SparseComplexQR: sparse matrix QR factorization not implemented");
+#endif
+}
+
+SparseComplexQR::SparseComplexQR_rep::~SparseComplexQR_rep (void)
+{
+#ifdef HAVE_CXSPARSE
+  CXSPARSE_ZNAME (cs_sfree) (S);
+  CXSPARSE_ZNAME (cs_nfree) (N);
+#endif
+}
+
+SparseComplexMatrix 
+SparseComplexQR::SparseComplexQR_rep::V (void) const
+{
+#ifdef HAVE_CXSPARSE
+  // Drop zeros from V and sort
+  // XXX FIXME XXX Is the double transpose to sort necessary?
+  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+  CXSPARSE_ZNAME (cs_dropzeros) (N->L);
+  CXSPARSE_ZNAME (cs) *D = CXSPARSE_ZNAME (cs_transpose) (N->L, 1);
+  CXSPARSE_ZNAME (cs_spfree) (N->L);
+  N->L = CXSPARSE_ZNAME (cs_transpose) (D, 1);
+  CXSPARSE_ZNAME (cs_spfree) (D);
+  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+  octave_idx_type nc = N->L->n;
+  octave_idx_type nz = N->L->nzmax;
+  SparseComplexMatrix ret (N->L->m, nc, nz);
+  for (octave_idx_type j = 0; j < nc+1; j++)
+    ret.xcidx (j) = N->L->p[j];
+  for (octave_idx_type j = 0; j < nz; j++)
+    {
+      ret.xridx (j) = N->L->i[j];
+      ret.xdata (j) = reinterpret_cast<Complex *>(N->L->x)[j];
+    }
+  return ret;
+#else
+  return SparseComplexMatrix ();
+#endif
+}
+
+ColumnVector 
+SparseComplexQR::SparseComplexQR_rep::Pinv (void) const
+{
+#ifdef HAVE_CXSPARSE
+  ColumnVector ret(N->L->m);
+  for (octave_idx_type i = 0; i < N->L->m; i++)
+    ret.xelem(i) = S->Pinv[i];
+  return ret;
+#else
+  return ColumnVector ();
+#endif
+}
+
+ColumnVector 
+SparseComplexQR::SparseComplexQR_rep::P (void) const
+{
+#ifdef HAVE_CXSPARSE
+  ColumnVector ret(N->L->m);
+  for (octave_idx_type i = 0; i < N->L->m; i++)
+    ret.xelem(S->Pinv[i]) = i;
+  return ret;
+#else
+  return ColumnVector ();
+#endif
+}
+
+SparseComplexMatrix 
+SparseComplexQR::SparseComplexQR_rep::R (const bool econ) const
+{
+#ifdef HAVE_CXSPARSE
+  // Drop zeros from R and sort
+  // XXX FIXME XXX Is the double transpose to sort necessary?
+  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+  CXSPARSE_ZNAME (cs_dropzeros) (N->U);
+  CXSPARSE_ZNAME (cs) *D = CXSPARSE_ZNAME (cs_transpose) (N->U, 1);
+  CXSPARSE_ZNAME (cs_spfree) (N->U);
+  N->U = CXSPARSE_ZNAME (cs_transpose) (D, 1);
+  CXSPARSE_ZNAME (cs_spfree) (D);
+  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+  octave_idx_type nc = N->U->n;
+  octave_idx_type nz = N->U->nzmax;
+  SparseComplexMatrix ret ((econ ? (nc > nrows ? nrows : nc) : nrows), nc, nz);
+  for (octave_idx_type j = 0; j < nc+1; j++)
+    ret.xcidx (j) = N->U->p[j];
+  for (octave_idx_type j = 0; j < nz; j++)
+    {
+      ret.xridx (j) = N->U->i[j];
+      ret.xdata (j) = reinterpret_cast<Complex *>(N->U->x)[j];
+    }
+  return ret;
+#else
+  return SparseComplexMatrix ();
+#endif
+}
+
+ComplexMatrix
+SparseComplexQR::SparseComplexQR_rep::C (const ComplexMatrix &b) const
+{
+#ifdef HAVE_CXSPARSE
+  octave_idx_type b_nr = b.rows();
+  octave_idx_type b_nc = b.cols();
+  octave_idx_type nc = N->L->n;
+  octave_idx_type nr = nrows;
+  const double _Complex *bvec = 
+    reinterpret_cast<const double _Complex *>(b.fortran_vec());
+  ComplexMatrix ret(b_nr,b_nc);
+  Complex *vec = ret.fortran_vec();
+  if (nr < 1 || nc < 1 || nr != b_nr)
+    (*current_liboctave_error_handler) ("matrix dimension mismatch");
+  else
+    {
+      OCTAVE_LOCAL_BUFFER (Complex, buf, S->m2);
+      for (volatile octave_idx_type j = 0, idx = 0; j < b_nc; j++, idx+=b_nr)
+	{
+	  OCTAVE_QUIT;
+	  volatile octave_idx_type nm = (nr < nc ? nr : nc);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_ipvec) (b_nr, S->Pinv, bvec + idx,
+				     reinterpret_cast<double _Complex *>(buf));
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type i = 0; i < nm; i++)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) 
+		(N->L, i, N->B[i], reinterpret_cast<double _Complex *>(buf));
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  for (octave_idx_type i = 0; i < b_nr; i++)
+	    vec[i+idx] = buf[i];
+	}
+    }
+  return ret;
+#else
+  return ComplexMatrix ();
+#endif
+}
+
+ComplexMatrix
+qrsolve(const SparseComplexMatrix&a, const Matrix &b, octave_idx_type &info)
+{
+#ifdef HAVE_CXSPARSE
+  octave_idx_type nr = a.rows();
+  octave_idx_type nc = a.cols();
+  octave_idx_type b_nc = b.cols();
+  octave_idx_type b_nr = b.rows();
+  ComplexMatrix x;
+  info = 0;
+
+  if (nr < 1 || nc < 1 || nr != b_nr)
+    (*current_liboctave_error_handler)
+      ("matrix dimension mismatch in solution of minimum norm problem");
+  else if (nr >= nc)
+    {
+      SparseComplexQR q (a, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return ComplexMatrix();
+	}
+      x.resize(nc, b_nc);
+      double _Complex *vec = reinterpret_cast<double _Complex *>
+	(x.fortran_vec());
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf, q.S()->m2);
+      OCTAVE_LOCAL_BUFFER (Complex, Xx, b_nr);
+      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
+	{
+	  OCTAVE_QUIT;
+	  for (octave_idx_type j = 0; j < b_nr; j++)
+	    Xx[j] = b.xelem(j,i);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_ipvec) 
+	    (nr, q.S()->Pinv, reinterpret_cast<double _Complex *>(Xx), buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = 0; j < nc; j++)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) (q.N()->L, j, q.N()->B[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_usolve) (q.N()->U, buf);
+	  CXSPARSE_ZNAME (cs_ipvec) (nc, q.S()->Q, buf, vec + idx);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	}
+    }
+  else
+    {
+      SparseComplexMatrix at = a.hermitian();
+      SparseComplexQR q (at, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return ComplexMatrix();
+	}
+      x.resize(nc, b_nc);
+      double _Complex *vec = reinterpret_cast<double _Complex *>
+	(x.fortran_vec());
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf, 
+			   nc > q.S()->m2 ? nc : q.S()->m2);
+      OCTAVE_LOCAL_BUFFER (Complex, Xx, b_nr);
+      OCTAVE_LOCAL_BUFFER (Complex, B, nr);
+      for (octave_idx_type i = 0; i < nr; i++)
+	B[i] = conj (reinterpret_cast<Complex *>(q.N()->B) [i]);
+      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
+	{
+	  OCTAVE_QUIT;
+	  for (octave_idx_type j = 0; j < b_nr; j++)
+	    Xx[j] = b.xelem(j,i);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec)
+	    (nr, q.S()->Q, reinterpret_cast<double _Complex *>(Xx), buf);
+	  CXSPARSE_ZNAME (cs_utsolve) (q.N()->U, buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = nr-1; j >= 0; j--)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+	      CXSPARSE_ZNAME (cs_happly) 
+		(q.N()->L, j, reinterpret_cast<double _Complex *>(B)[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec) (nc, q.S()->Pinv, buf, vec + idx);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	}
+    }
+
+  return x;
+#else
+  return ComplexMatrix ();
+#endif
+}
+
+SparseComplexMatrix
+qrsolve(const SparseComplexMatrix&a, const SparseMatrix &b, octave_idx_type &info)
+{
+#ifdef HAVE_CXSPARSE
+  octave_idx_type nr = a.rows();
+  octave_idx_type nc = a.cols();
+  octave_idx_type b_nc = b.cols();
+  octave_idx_type b_nr = b.rows();
+  SparseComplexMatrix x;
+  volatile octave_idx_type ii, x_nz;
+  info = 0;
+
+  if (nr < 1 || nc < 1 || nr != b_nr)
+    (*current_liboctave_error_handler)
+      ("matrix dimension mismatch in solution of minimum norm problem");
+  else if (nr >= nc)
+    {
+      SparseComplexQR q (a, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return SparseComplexMatrix();
+	}
+      x = SparseComplexMatrix (nc, b_nc, b.nzmax());
+      x.xcidx(0) = 0;
+      x_nz = b.nzmax();
+      ii = 0;
+      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf, q.S()->m2);
+      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
+	{
+	  OCTAVE_QUIT;
+	  for (octave_idx_type j = 0; j < b_nr; j++)
+	    Xx[j] = b.xelem(j,i);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_ipvec) 
+	    (nr, q.S()->Pinv, reinterpret_cast<double _Complex *>(Xx), buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = 0; j < nc; j++)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) (q.N()->L, j, q.N()->B[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_usolve) (q.N()->U, buf);
+	  CXSPARSE_ZNAME (cs_ipvec) (nc, q.S()->Q, buf, 
+				     reinterpret_cast<double _Complex *>(Xx));
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+	  for (octave_idx_type j = 0; j < nc; j++)
+	    {
+	      Complex tmp = Xx[j];
+	      if (tmp != 0.0)
+		{
+		  if (ii == x_nz)
+		    {
+		      // Resize the sparse matrix
+		      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
+		      sz = (sz > 10 ? sz : 10) + x_nz;
+		      x.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  x.xdata(ii) = tmp;
+		  x.xridx(ii++) = j;
+		}
+	    }
+	  x.xcidx(i+1) = ii;
+	}
+    }
+  else
+    {
+      SparseComplexMatrix at = a.hermitian();
+      SparseComplexQR q (at, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return SparseComplexMatrix();
+	}
+      x = SparseComplexMatrix (nc, b_nc, b.nzmax());
+      x.xcidx(0) = 0;
+      x_nz = b.nzmax();
+      ii = 0;
+      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf,
+			   nc > q.S()->m2 ? nc : q.S()->m2);
+      OCTAVE_LOCAL_BUFFER (Complex, B, nr);
+      for (octave_idx_type i = 0; i < nr; i++)
+	B[i] = conj (reinterpret_cast<Complex *>(q.N()->B) [i]);
+      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
+	{
+	  OCTAVE_QUIT;
+	  for (octave_idx_type j = 0; j < b_nr; j++)
+	    Xx[j] = b.xelem(j,i);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec)
+	    (nr, q.S()->Q, reinterpret_cast<double _Complex *>(Xx), buf);
+	  CXSPARSE_ZNAME (cs_utsolve) (q.N()->U, buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = nr-1; j >= 0; j--)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) 
+		(q.N()->L, j, reinterpret_cast<double _Complex *>(B)[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec) (nc, q.S()->Pinv, buf, 
+				     reinterpret_cast<double _Complex *>(Xx));
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+	  for (octave_idx_type j = 0; j < nc; j++)
+	    {
+	      Complex tmp = Xx[j];
+	      if (tmp != 0.0)
+		{
+		  if (ii == x_nz)
+		    {
+		      // Resize the sparse matrix
+		      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
+		      sz = (sz > 10 ? sz : 10) + x_nz;
+		      x.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  x.xdata(ii) = tmp;
+		  x.xridx(ii++) = j;
+		}
+	    }
+	  x.xcidx(i+1) = ii;
+	}
+    }
+
+  x.maybe_compress ();
+  return x;
+#else
+  return SparseComplexMatrix ();
+#endif
+}
+
+ComplexMatrix
+qrsolve(const SparseComplexMatrix&a, const ComplexMatrix &b, octave_idx_type &info)
+{
+#ifdef HAVE_CXSPARSE
+  octave_idx_type nr = a.rows();
+  octave_idx_type nc = a.cols();
+  octave_idx_type b_nc = b.cols();
+  octave_idx_type b_nr = b.rows();
+  const double _Complex *bvec = 
+    reinterpret_cast<const double _Complex *>(b.fortran_vec());
+  ComplexMatrix x;
+  info = 0;
+
+  if (nr < 1 || nc < 1 || nr != b_nr)
+    (*current_liboctave_error_handler)
+      ("matrix dimension mismatch in solution of minimum norm problem");
+  else if (nr >= nc)
+    {
+      SparseComplexQR q (a, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return ComplexMatrix();
+	}
+      x.resize(nc, b_nc);
+      double _Complex *vec = reinterpret_cast<double _Complex *>
+	(x.fortran_vec());
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf, q.S()->m2);
+      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc; 
+	   i++, idx+=nc, bidx+=b_nr)
+	{
+	  OCTAVE_QUIT;
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_ipvec) (nr, q.S()->Pinv, bvec + bidx, buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = 0; j < nc; j++)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) (q.N()->L, j, q.N()->B[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_usolve) (q.N()->U, buf);
+	  CXSPARSE_ZNAME (cs_ipvec) (nc, q.S()->Q, buf, vec + idx);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	}
+    }
+  else
+    {
+      SparseComplexMatrix at = a.hermitian();
+      SparseComplexQR q (at, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return ComplexMatrix();
+	}
+      x.resize(nc, b_nc);
+      double _Complex *vec = reinterpret_cast<double _Complex *>
+	(x.fortran_vec());
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf,
+			   nc > q.S()->m2 ? nc : q.S()->m2);
+      OCTAVE_LOCAL_BUFFER (Complex, B, nr);
+      for (octave_idx_type i = 0; i < nr; i++)
+	B[i] = conj (reinterpret_cast<Complex *>(q.N()->B) [i]);
+      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc; 
+	   i++, idx+=nc, bidx+=b_nr)
+	{
+	  OCTAVE_QUIT;
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec) (nr, q.S()->Q, bvec + bidx, buf);
+	  CXSPARSE_ZNAME (cs_utsolve) (q.N()->U, buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = nr-1; j >= 0; j--)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) 
+		(q.N()->L, j, reinterpret_cast<double _Complex *>(B)[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec) (nc, q.S()->Pinv, buf, vec + idx);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	}
+    }
+
+  return x;
+#else
+  return ComplexMatrix ();
+#endif
+}
+
+SparseComplexMatrix
+qrsolve(const SparseComplexMatrix&a, const SparseComplexMatrix &b, octave_idx_type &info)
+{
+#ifdef HAVE_CXSPARSE
+  octave_idx_type nr = a.rows();
+  octave_idx_type nc = a.cols();
+  octave_idx_type b_nc = b.cols();
+  octave_idx_type b_nr = b.rows();
+  SparseComplexMatrix x;
+  volatile octave_idx_type ii, x_nz;
+  info = 0;
+
+  if (nr < 1 || nc < 1 || nr != b_nr)
+    (*current_liboctave_error_handler)
+      ("matrix dimension mismatch in solution of minimum norm problem");
+  else if (nr >= nc)
+    {
+      SparseComplexQR q (a, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return SparseComplexMatrix();
+	}
+      x = SparseComplexMatrix (nc, b_nc, b.nzmax());
+      x.xcidx(0) = 0;
+      x_nz = b.nzmax();
+      ii = 0;
+      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf, q.S()->m2);
+      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
+	{
+	  OCTAVE_QUIT;
+	  for (octave_idx_type j = 0; j < b_nr; j++)
+	    Xx[j] = b.xelem(j,i);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_ipvec) 
+	    (nr, q.S()->Pinv, reinterpret_cast<double _Complex *>(Xx), buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = 0; j < nc; j++)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) (q.N()->L, j, q.N()->B[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_usolve) (q.N()->U, buf);
+	  CXSPARSE_ZNAME (cs_ipvec) (nc, q.S()->Q, buf, 
+				     reinterpret_cast<double _Complex *>(Xx));
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+	  for (octave_idx_type j = 0; j < nc; j++)
+	    {
+	      Complex tmp = Xx[j];
+	      if (tmp != 0.0)
+		{
+		  if (ii == x_nz)
+		    {
+		      // Resize the sparse matrix
+		      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
+		      sz = (sz > 10 ? sz : 10) + x_nz;
+		      x.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  x.xdata(ii) = tmp;
+		  x.xridx(ii++) = j;
+		}
+	    }
+	  x.xcidx(i+1) = ii;
+	}
+    }
+  else
+    {
+      SparseComplexMatrix at = a.hermitian();
+      SparseComplexQR q (at, 2);
+      if (! q.ok ())
+	{
+	  info = -1;
+	  return SparseComplexMatrix();
+	}
+      x = SparseComplexMatrix (nc, b_nc, b.nzmax());
+      x.xcidx(0) = 0;
+      x_nz = b.nzmax();
+      ii = 0;
+      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
+      OCTAVE_LOCAL_BUFFER (double _Complex, buf,
+			   nc > q.S()->m2 ? nc : q.S()->m2);
+      OCTAVE_LOCAL_BUFFER (Complex, B, nr);
+      for (octave_idx_type i = 0; i < nr; i++)
+	B[i] = conj (reinterpret_cast<Complex *>(q.N()->B) [i]);
+      for (volatile octave_idx_type i = 0, idx = 0; i < b_nc; i++, idx+=nc)
+	{
+	  OCTAVE_QUIT;
+	  for (octave_idx_type j = 0; j < b_nr; j++)
+	    Xx[j] = b.xelem(j,i);
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec)
+	    (nr, q.S()->Q, reinterpret_cast<double _Complex *>(Xx), buf);
+	  CXSPARSE_ZNAME (cs_utsolve) (q.N()->U, buf);
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  for (volatile octave_idx_type j = nr-1; j >= 0; j--)
+	    {
+	      OCTAVE_QUIT;
+	      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	      CXSPARSE_ZNAME (cs_happly) 
+		(q.N()->L, j, reinterpret_cast<double _Complex *>(B)[j], buf);
+	      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	    }
+	  BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+	  CXSPARSE_ZNAME (cs_pvec) (nc, q.S()->Pinv, buf, 
+				     reinterpret_cast<double _Complex *>(Xx));
+	  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
+
+	  for (octave_idx_type j = 0; j < nc; j++)
+	    {
+	      Complex tmp = Xx[j];
+	      if (tmp != 0.0)
+		{
+		  if (ii == x_nz)
+		    {
+		      // Resize the sparse matrix
+		      octave_idx_type sz = x_nz * (b_nc - i) / b_nc;
+		      sz = (sz > 10 ? sz : 10) + x_nz;
+		      x.change_capacity (sz);
+		      x_nz = sz;
+		    }
+		  x.xdata(ii) = tmp;
+		  x.xridx(ii++) = j;
+		}
+	    }
+	  x.xcidx(i+1) = ii;
+	}
+    }
+
+  x.maybe_compress ();
+  return x;
+#else
+  return SparseComplexMatrix ();
+#endif
+}
+
+/*
+;;; Local Variables: ***
+;;; mode: C++ ***
+;;; End: ***
+*/
+