/*

Copyright (C) 2005-2020 The Octave Project Developers

See the file COPYRIGHT.md in the top-level directory of this distribution
or <https://octave.org/COPYRIGHT.html/>.


This file is part of Octave.

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 3 of the License, 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 Octave; see the file COPYING.  If not, see
<https://www.gnu.org/licenses/>.

*/

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include "CMatrix.h"
#include "CSparse.h"
#include "MArray.h"
#include "dColVector.h"
#include "dMatrix.h"
#include "dSparse.h"
#include "lo-error.h"
#include "oct-locbuf.h"
#include "oct-refcount.h"
#include "oct-sparse.h"
#include "quit.h"
#include "sparse-qr.h"

namespace octave
{
  namespace math
  {
    template <typename SPARSE_T>
    class
    cxsparse_types
    {
    };

    template <>
    class
    cxsparse_types<SparseMatrix>
    {
    public:
#if defined (HAVE_CXSPARSE)
      typedef CXSPARSE_DNAME (s) symbolic_type;
      typedef CXSPARSE_DNAME (n) numeric_type;
#else
      typedef void symbolic_type;
      typedef void numeric_type;
#endif
    };

    template <>
    class
    cxsparse_types<SparseComplexMatrix>
    {
    public:
#if defined (HAVE_CXSPARSE)
      typedef CXSPARSE_ZNAME (s) symbolic_type;
      typedef CXSPARSE_ZNAME (n) numeric_type;
#else
      typedef void symbolic_type;
      typedef void numeric_type;
#endif
    };

    template <typename SPARSE_T>
    class sparse_qr<SPARSE_T>::sparse_qr_rep
    {
    public:

      sparse_qr_rep (const SPARSE_T& a, int order);

      // No copying!

      sparse_qr_rep (const sparse_qr_rep&) = delete;

      sparse_qr_rep& operator = (const sparse_qr_rep&) = delete;

      ~sparse_qr_rep (void);

      bool ok (void) const
      {
#if defined (HAVE_CXSPARSE)
        return (N && S);
#else
        return false;
#endif
      }

      SPARSE_T V (void) const;

      ColumnVector Pinv (void) const;

      ColumnVector P (void) const;

      SPARSE_T R (bool econ) const;

      typename SPARSE_T::dense_matrix_type
      C (const typename SPARSE_T::dense_matrix_type& b) const;

      typename SPARSE_T::dense_matrix_type
      Q (void) const;

      refcount<octave_idx_type> count;

      octave_idx_type nrows;
      octave_idx_type ncols;

      typename cxsparse_types<SPARSE_T>::symbolic_type *S;
      typename cxsparse_types<SPARSE_T>::numeric_type *N;

      template <typename RHS_T, typename RET_T>
      RET_T
      tall_solve (const RHS_T& b, octave_idx_type& info) const;

      template <typename RHS_T, typename RET_T>
      RET_T
      wide_solve (const RHS_T& b, octave_idx_type& info) const;
    };

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::sparse_qr_rep::Pinv (void) const
    {
#if defined (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
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::sparse_qr_rep::P (void) const
    {
#if defined (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
    }

    // Specializations.

    // Real-valued matrices.

    template <>
    sparse_qr<SparseMatrix>::sparse_qr_rep::sparse_qr_rep
    (const SparseMatrix& a, int order)
      : count (1), nrows (a.rows ()), ncols (a.columns ())
#if defined (HAVE_CXSPARSE)
      , S (nullptr), N (nullptr)
#endif
    {
#if defined (HAVE_CXSPARSE)

      CXSPARSE_DNAME () A;

      A.nzmax = a.nnz ();
      A.m = nrows;
      A.n = ncols;
      // 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<suitesparse_integer *>
              (to_suitesparse_intptr (a.cidx ()));
      A.i = const_cast<suitesparse_integer *>
              (to_suitesparse_intptr (a.ridx ()));
      A.x = const_cast<double *> (a.data ());
      A.nz = -1;

      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
      S = CXSPARSE_DNAME (_sqr) (order, &A, 1);
      N = CXSPARSE_DNAME (_qr) (&A, S);
      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

      if (! N)
        (*current_liboctave_error_handler)
          ("sparse_qr: sparse matrix QR factorization filled");

#else

      octave_unused_parameter (order);

      (*current_liboctave_error_handler)
        ("sparse_qr: support for CXSparse was unavailable or disabled when liboctave was built");

#endif
    }

    template <>
    sparse_qr<SparseMatrix>::sparse_qr_rep::~sparse_qr_rep (void)
    {
#if defined (HAVE_CXSPARSE)
      CXSPARSE_DNAME (_sfree) (S);
      CXSPARSE_DNAME (_nfree) (N);
#endif
    }

    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::V (void) const
    {
#if defined (HAVE_CXSPARSE)

      // Drop zeros from V and sort
      // FIXME: Is the double transpose to sort necessary?

      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
      CXSPARSE_DNAME (_dropzeros) (N->L);
      CXSPARSE_DNAME () *D = CXSPARSE_DNAME (_transpose) (N->L, 1);
      CXSPARSE_DNAME (_spfree) (N->L);
      N->L = CXSPARSE_DNAME (_transpose) (D, 1);
      CXSPARSE_DNAME (_spfree) (D);
      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

      octave_idx_type nc = N->L->n;
      octave_idx_type nz = N->L->nzmax;
      SparseMatrix 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) = N->L->x[j];
        }

      return ret;

#else

      return SparseMatrix ();

#endif
    }

    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::R (bool econ) const
    {
#if defined (HAVE_CXSPARSE)

      // Drop zeros from R and sort
      // FIXME: Is the double transpose to sort necessary?

      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
      CXSPARSE_DNAME (_dropzeros) (N->U);
      CXSPARSE_DNAME () *D = CXSPARSE_DNAME (_transpose) (N->U, 1);
      CXSPARSE_DNAME (_spfree) (N->U);
      N->U = CXSPARSE_DNAME (_transpose) (D, 1);
      CXSPARSE_DNAME (_spfree) (D);
      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

      octave_idx_type nc = N->U->n;
      octave_idx_type nz = N->U->nzmax;

      SparseMatrix 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) = N->U->x[j];
        }

      return ret;

#else

      octave_unused_parameter (econ);

      return SparseMatrix ();

#endif
    }

    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::C (const Matrix& b) const
    {
#if defined (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 *bvec = b.fortran_vec ();

      Matrix ret (b_nr, b_nc);
      double *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0 || nr != b_nr)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0 || b_nc == 0)
        ret = Matrix (nc, b_nc, 0.0);
      else
        {
          OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0;
               j < b_nc;
               j++, idx += b_nr)
            {
              octave_quit ();

              for (octave_idx_type i = nr; i < S->m2; i++)
                buf[i] = 0.;

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
              CXSPARSE_DNAME (_ipvec) (S->pinv, bvec + idx, buf, b_nr);
              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_DNAME (_happly) (N->L, i, N->B[i], 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

      octave_unused_parameter (b);

      return Matrix ();

#endif
    }

    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::Q (void) const
    {
#if defined (HAVE_CXSPARSE)
      octave_idx_type nc = N->L->n;
      octave_idx_type nr = nrows;
      Matrix ret (nr, nr);
      double *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0)
        ret = Matrix (nc, nr, 0.0);
      else
        {
          OCTAVE_LOCAL_BUFFER (double, bvec, nr + 1);

          for (octave_idx_type i = 0; i < nr; i++)
            bvec[i] = 0.;

          OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0; j < nr; j++, idx+=nr)
            {
              octave_quit ();

              bvec[j] = 1.0;
              for (octave_idx_type i = nr; i < S->m2; i++)
                buf[i] = 0.;

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
              CXSPARSE_DNAME (_ipvec) (S->pinv, bvec, buf, nr);
              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_DNAME (_happly) (N->L, i, N->B[i], buf);
                  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
                }

              for (octave_idx_type i = 0; i < nr; i++)
                vec[i+idx] = buf[i];

              bvec[j] = 0.0;
            }
        }

      return ret.transpose ();

#else

      return Matrix ();

#endif
    }

    template <>
    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<MArray<double>, Matrix>
    (const MArray<double>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const double *bvec = b.data ();

      Matrix x (nc, b_nc);
      double *vec = x.fortran_vec ();

      OCTAVE_LOCAL_BUFFER (double, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_ipvec) (S->pinv, bvec + bidx, buf, nr);
          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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, vec + idx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return Matrix ();

#endif
    }

    template <>
    template <>
    Matrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<MArray<double>, Matrix>
    (const MArray<double>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const double *bvec = b.data ();

      Matrix x (nc, b_nc);
      double *vec = x.fortran_vec ();

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->q, bvec + bidx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->pinv, buf, vec + idx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return Matrix ();

#endif
    }

    template <>
    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<SparseMatrix, SparseMatrix>
    (const SparseMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, 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);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_ipvec) (S->pinv, Xx, buf, nr);
          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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = 0; j < nc; j++)
            {
              double 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;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return SparseMatrix ();

#endif
    }

    template <>
    template <>
    SparseMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<SparseMatrix, SparseMatrix>
    (const SparseMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      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);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->q, Xx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = 0; j < nc; j++)
            {
              double 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;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<MArray<Complex>, ComplexMatrix>
    (const MArray<Complex>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      Complex *vec = x.fortran_vec ();

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, 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++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_ipvec) (S->pinv, Xx, buf, nr);
          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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xx, nc);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          CXSPARSE_DNAME (_ipvec) (S->pinv, Xz, buf, nr);
          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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xz, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = 0; j < nc; j++)
            vec[j+idx] = Complex (Xx[j], Xz[j]);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<MArray<Complex>, ComplexMatrix>
    (const MArray<Complex>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      Complex *vec = x.fortran_vec ();

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      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++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->q, Xx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->q, Xz, buf, nr);
          CXSPARSE_DNAME (_utsolve) (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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xz, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = 0; j < nc; j++)
            vec[j+idx] = Complex (Xx[j], Xz[j]);
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    // Complex-valued matrices.

    template <>
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::sparse_qr_rep
    (const SparseComplexMatrix& a, int order)
      : count (1), nrows (a.rows ()), ncols (a.columns ())
#if defined (HAVE_CXSPARSE)
      , S (nullptr), N (nullptr)
#endif
    {
#if defined (HAVE_CXSPARSE)

      CXSPARSE_ZNAME () A;

      A.nzmax = a.nnz ();
      A.m = nrows;
      A.n = ncols;
      // 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<suitesparse_integer *>
              (to_suitesparse_intptr (a.cidx ()));
      A.i = const_cast<suitesparse_integer *>
              (to_suitesparse_intptr (a.ridx ()));
      A.x = const_cast<cs_complex_t *>
              (reinterpret_cast<const cs_complex_t *> (a.data ()));
      A.nz = -1;

      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
      S = CXSPARSE_ZNAME (_sqr) (order, &A, 1);
      N = CXSPARSE_ZNAME (_qr) (&A, S);
      END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

      if (! N)
        (*current_liboctave_error_handler)
          ("sparse_qr: sparse matrix QR factorization filled");

#else

      octave_unused_parameter (order);

      (*current_liboctave_error_handler)
        ("sparse_qr: support for CXSparse was unavailable or disabled when liboctave was built");

#endif
    }

    template <>
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::~sparse_qr_rep (void)
    {
#if defined (HAVE_CXSPARSE)
      CXSPARSE_ZNAME (_sfree) (S);
      CXSPARSE_ZNAME (_nfree) (N);
#endif
    }

    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::V (void) const
    {
#if defined (HAVE_CXSPARSE)
      // Drop zeros from V and sort
      // FIXME: Is the double transpose to sort necessary?

      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
      CXSPARSE_ZNAME (_dropzeros) (N->L);
      CXSPARSE_ZNAME () *D = CXSPARSE_ZNAME (_transpose) (N->L, 1);
      CXSPARSE_ZNAME (_spfree) (N->L);
      N->L = CXSPARSE_ZNAME (_transpose) (D, 1);
      CXSPARSE_ZNAME (_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
    }

    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::R (bool econ) const
    {
#if defined (HAVE_CXSPARSE)
      // Drop zeros from R and sort
      // FIXME: Is the double transpose to sort necessary?

      BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
      CXSPARSE_ZNAME (_dropzeros) (N->U);
      CXSPARSE_ZNAME () *D = CXSPARSE_ZNAME (_transpose) (N->U, 1);
      CXSPARSE_ZNAME (_spfree) (N->U);
      N->U = CXSPARSE_ZNAME (_transpose) (D, 1);
      CXSPARSE_ZNAME (_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

      octave_unused_parameter (econ);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::C (const ComplexMatrix& b) const
    {
#if defined (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 cs_complex_t *bvec
        = reinterpret_cast<const cs_complex_t *> (b.fortran_vec ());
      ComplexMatrix ret (b_nr, b_nc);
      Complex *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0 || nr != b_nr)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0 || b_nc == 0)
        ret = ComplexMatrix (nc, b_nc, Complex (0.0, 0.0));
      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 (_ipvec) (S->pinv, bvec + idx,
                                       reinterpret_cast<cs_complex_t *> (buf),
                                       b_nr);
              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 (_happly) (N->L, i, N->B[i],
                                            reinterpret_cast<cs_complex_t *> (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

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::Q (void) const
    {
#if defined (HAVE_CXSPARSE)
      octave_idx_type nc = N->L->n;
      octave_idx_type nr = nrows;
      ComplexMatrix ret (nr, nr);
      Complex *vec = ret.fortran_vec ();

      if (nr < 0 || nc < 0)
        (*current_liboctave_error_handler) ("matrix dimension mismatch");

      if (nr == 0 || nc == 0)
        ret = ComplexMatrix (nc, nr, Complex (0.0, 0.0));
      else
        {
          OCTAVE_LOCAL_BUFFER (cs_complex_t, bvec, nr);

          for (octave_idx_type i = 0; i < nr; i++)
            bvec[i] = cs_complex_t (0.0, 0.0);

          OCTAVE_LOCAL_BUFFER (Complex, buf, S->m2);

          for (volatile octave_idx_type j = 0, idx = 0; j < nr; j++, idx+=nr)
            {
              octave_quit ();

              bvec[j] = cs_complex_t (1.0, 0.0);

              volatile octave_idx_type nm = (nr < nc ? nr : nc);

              BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
              CXSPARSE_ZNAME (_ipvec) (S->pinv, bvec,
                                       reinterpret_cast<cs_complex_t *> (buf),
                                       nr);
              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 (_happly) (N->L, i, N->B[i],
                                            reinterpret_cast<cs_complex_t *> (buf));
                  END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
                }

              for (octave_idx_type i = 0; i < nr; i++)
                vec[i+idx] = buf[i];

              bvec[j] = cs_complex_t (0.0, 0.0);
            }
        }

      return ret.hermitian ();

#else

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::tall_solve<SparseComplexMatrix,
                                                       SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, 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++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_ipvec) (S->pinv, Xx, buf, nr);
          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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_ipvec) (S->pinv, Xz, buf, nr);
          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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_usolve) (N->U, buf);
          CXSPARSE_DNAME (_ipvec) (S->q, buf, Xz, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Complex (Xx[j], Xz[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;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseMatrix>::sparse_qr_rep::wide_solve<SparseComplexMatrix,
                                                       SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nr = b.rows ();
      octave_idx_type b_nc = b.cols ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (double, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, Xz, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (double, buf, nbuf);

      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++)
            {
              Complex c = b.xelem (j,i);
              Xx[j] = c.real ();
              Xz[j] = c.imag ();
            }

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->q, Xx, buf, nr);
          CXSPARSE_DNAME (_utsolve) (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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = 0.;

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->q, Xz, buf, nr);
          CXSPARSE_DNAME (_utsolve) (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_DNAME (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_DNAME (_pvec) (S->pinv, buf, Xz, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;

          for (octave_idx_type j = 0; j < nc; j++)
            {
              Complex tmp = Complex (Xx[j], Xz[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;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<MArray<double>,
                                                              ComplexMatrix>
      (const MArray<double>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *> (x.fortran_vec ());

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, 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);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_ipvec) (S->pinv,
                                   reinterpret_cast<cs_complex_t *>(Xx),
                                   buf, nr);
          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 (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf, vec + idx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<MArray<double>,
                                                              ComplexMatrix>
      (const MArray<double>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *> (x.fortran_vec ());

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (Complex, Xx, b_nr);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = 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);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->q, reinterpret_cast<cs_complex_t *>(Xx),
                                  buf, nr);
          CXSPARSE_ZNAME (_utsolve) (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 (_happly) (N->L, j, B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->pinv, buf, vec + idx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<SparseMatrix,
                                                              SparseComplexMatrix>
      (const SparseMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, 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);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_ipvec) (S->pinv,
                                   reinterpret_cast<cs_complex_t *>(Xx),
                                   buf, nr);
          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 (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf,
                                   reinterpret_cast<cs_complex_t *> (Xx),
                                   nc);
          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;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<SparseMatrix,
                                                              SparseComplexMatrix>
      (const SparseMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = 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);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->q,
                                  reinterpret_cast<cs_complex_t *>(Xx),
                                  buf, nr);
          CXSPARSE_ZNAME (_utsolve) (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 (_happly) (N->L, j, B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->pinv, buf,
                                  reinterpret_cast<cs_complex_t *> (Xx),
                                  nc);
          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;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<MArray<Complex>,
                                                              ComplexMatrix>
      (const MArray<Complex>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const cs_complex_t *bvec = reinterpret_cast<const cs_complex_t *>
                                 (b.fortran_vec ());

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *>
                          (x.fortran_vec ());

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, S->m2);

      for (volatile octave_idx_type i = 0, idx = 0, bidx = 0; i < b_nc;
           i++, idx+=nc, bidx+=b_nr)
        {
          octave_quit ();

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_ipvec) (S->pinv, bvec + bidx, buf, nr);
          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 (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf, vec + idx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    ComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<MArray<Complex>,
                                                              ComplexMatrix>
      (const MArray<Complex>& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      const cs_complex_t *bvec = reinterpret_cast<const cs_complex_t *>
                                 (b.fortran_vec ());

      ComplexMatrix x (nc, b_nc);
      cs_complex_t *vec = reinterpret_cast<cs_complex_t *> (x.fortran_vec ());

      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = 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 ();

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->q, bvec + bidx, buf, nr);
          CXSPARSE_ZNAME (_utsolve) (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 (_happly) (N->L, j, B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->pinv, buf, vec + idx, nc);
          END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
        }

      info = 0;

      return x;

#else

      octave_unused_parameter (b);

      return ComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::tall_solve<SparseComplexMatrix, SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      octave_idx_type nr = nrows;
      octave_idx_type nc = ncols;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, 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);

          for (octave_idx_type j = nr; j < S->m2; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_ipvec) (S->pinv,
                                   reinterpret_cast<cs_complex_t *>(Xx),
                                   buf, nr);
          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 (_happly) (N->L, j, N->B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_usolve) (N->U, buf);
          CXSPARSE_ZNAME (_ipvec) (S->q, buf,
                                   reinterpret_cast<cs_complex_t *> (Xx),
                                   nc);
          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;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <>
    template <>
    SparseComplexMatrix
    sparse_qr<SparseComplexMatrix>::sparse_qr_rep::wide_solve<SparseComplexMatrix, SparseComplexMatrix>
      (const SparseComplexMatrix& b, octave_idx_type& info) const
    {
      info = -1;

#if defined (HAVE_CXSPARSE)

      // These are swapped because the original matrix was transposed in
      // sparse_qr<SparseComplexMatrix>::solve.

      octave_idx_type nr = ncols;
      octave_idx_type nc = nrows;

      octave_idx_type b_nc = b.cols ();
      octave_idx_type b_nr = b.rows ();

      SparseComplexMatrix x (nc, b_nc, b.nnz ());
      x.xcidx (0) = 0;

      volatile octave_idx_type x_nz = b.nnz ();
      volatile octave_idx_type ii = 0;
      volatile octave_idx_type nbuf = (nc > S->m2 ? nc : S->m2);

      OCTAVE_LOCAL_BUFFER (Complex, Xx, (b_nr > nc ? b_nr : nc));
      OCTAVE_LOCAL_BUFFER (cs_complex_t, buf, nbuf);
      OCTAVE_LOCAL_BUFFER (double, B, nr);

      for (octave_idx_type i = 0; i < nr; i++)
        B[i] = 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);

          for (octave_idx_type j = nr; j < nbuf; j++)
            buf[j] = cs_complex_t (0.0, 0.0);

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->q, reinterpret_cast<cs_complex_t *>(Xx),
                                  buf, nr);
          CXSPARSE_ZNAME (_utsolve) (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 (_happly) (N->L, j, B[j], buf);
              END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
            }

          BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
          CXSPARSE_ZNAME (_pvec) (S->pinv, buf,
                                  reinterpret_cast<cs_complex_t *>(Xx), nc);
          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;
        }

      info = 0;

      x.maybe_compress ();

      return x;

#else

      octave_unused_parameter (b);

      return SparseComplexMatrix ();

#endif
    }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>::sparse_qr (void)
      : rep (new sparse_qr_rep (SPARSE_T (), 0))
    { }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>::sparse_qr (const SPARSE_T& a, int order)
      : rep (new sparse_qr_rep (a, order))
    { }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>::sparse_qr (const sparse_qr<SPARSE_T>& a)
      : rep (a.rep)
    {
      rep->count++;
    }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>::~sparse_qr (void)
    {
      if (--rep->count == 0)
        delete rep;
    }

    template <typename SPARSE_T>
    sparse_qr<SPARSE_T>&
    sparse_qr<SPARSE_T>::operator = (const sparse_qr<SPARSE_T>& a)
    {
      if (this != &a)
        {
          if (--rep->count == 0)
            delete rep;

          rep = a.rep;
          rep->count++;
        }

      return *this;
    }

    template <typename SPARSE_T>
    bool
    sparse_qr<SPARSE_T>::ok (void) const
    {
      return rep->ok ();
    }

    template <typename SPARSE_T>
    SPARSE_T
    sparse_qr<SPARSE_T>::V (void) const
    {
      return rep->V ();
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::Pinv (void) const
    {
      return rep->P ();
    }

    template <typename SPARSE_T>
    ColumnVector
    sparse_qr<SPARSE_T>::P (void) const
    {
      return rep->P ();
    }

    template <typename SPARSE_T>
    SPARSE_T
    sparse_qr<SPARSE_T>::R (bool econ) const
    {
      return rep->R (econ);
    }

    template <typename SPARSE_T>
    typename SPARSE_T::dense_matrix_type
    sparse_qr<SPARSE_T>::C (const typename SPARSE_T::dense_matrix_type& b) const
    {
      return rep->C (b);
    }

    template <typename SPARSE_T>
    typename SPARSE_T::dense_matrix_type
    sparse_qr<SPARSE_T>::Q (void) const
    {
      return rep->Q ();
    }

    // FIXME: Why is the "order" of the QR calculation as used in the
    // CXSparse function sqr 3 for real matrices and 2 for complex?  These
    // values seem to be required but there was no explanation in David
    // Bateman's original code.

    template <typename SPARSE_T>
    class
    cxsparse_defaults
    {
    public:
      enum { order = -1 };
    };

    template <>
    class
    cxsparse_defaults<SparseMatrix>
    {
    public:
      enum { order = 3 };
    };

    template <>
    class
    cxsparse_defaults<SparseComplexMatrix>
    {
    public:
      enum { order = 2 };
    };

    template <typename SPARSE_T>
    template <typename RHS_T, typename RET_T>
    RET_T
    sparse_qr<SPARSE_T>::solve (const SPARSE_T& a, const RHS_T& b,
                                octave_idx_type& info)
    {
      info = -1;

      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 ();

      int order = cxsparse_defaults<SPARSE_T>::order;

      if (nr < 0 || nc < 0 || nr != b_nr)
        (*current_liboctave_error_handler)
          ("matrix dimension mismatch in solution of minimum norm problem");

      if (nr == 0 || nc == 0 || b_nc == 0)
        {
          info = 0;

          return RET_T (nc, b_nc, 0.0);
        }
      else if (nr >= nc)
        {
          sparse_qr<SPARSE_T> q (a, order);

          return q.ok () ? q.tall_solve<RHS_T, RET_T> (b, info) : RET_T ();
        }
      else
        {
          sparse_qr<SPARSE_T> q (a.hermitian (), order);

          return q.ok () ? q.wide_solve<RHS_T, RET_T> (b, info) : RET_T ();
        }
    }

    template <typename SPARSE_T>
    template <typename RHS_T, typename RET_T>
    RET_T
    sparse_qr<SPARSE_T>::tall_solve (const RHS_T& b, octave_idx_type& info) const
    {
      return rep->template tall_solve<RHS_T, RET_T> (b, info);
    }

    template <typename SPARSE_T>
    template <typename RHS_T, typename RET_T>
    RET_T
    sparse_qr<SPARSE_T>::wide_solve (const RHS_T& b, octave_idx_type& info) const
    {
      return rep->template wide_solve<RHS_T, RET_T> (b, info);
    }

    Matrix
    qrsolve (const SparseMatrix& a, const MArray<double>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<MArray<double>, Matrix> (a, b,
                                                                     info);
    }

    SparseMatrix
    qrsolve (const SparseMatrix& a, const SparseMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<SparseMatrix, SparseMatrix> (a, b,
                                                                         info);
    }

    ComplexMatrix
    qrsolve (const SparseMatrix& a, const MArray<Complex>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<MArray<Complex>,
                                            ComplexMatrix> (a, b, info);
    }

    SparseComplexMatrix
    qrsolve (const SparseMatrix& a, const SparseComplexMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseMatrix>::solve<SparseComplexMatrix,
                                            SparseComplexMatrix> (a, b, info);
    }

    ComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const MArray<double>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<MArray<double>,
                                                   ComplexMatrix> (a, b, info);
    }

    SparseComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const SparseMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<SparseMatrix,
                                                   SparseComplexMatrix>
                                             (a, b, info);
    }

    ComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const MArray<Complex>& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<MArray<Complex>,
                                                   ComplexMatrix> (a, b, info);
    }

    SparseComplexMatrix
    qrsolve (const SparseComplexMatrix& a, const SparseComplexMatrix& b,
             octave_idx_type& info)
    {
      return sparse_qr<SparseComplexMatrix>::solve<SparseComplexMatrix,
                                                   SparseComplexMatrix>
                                             (a, b, info);
    }

    // Instantiations we need.

    template class sparse_qr<SparseMatrix>;

    template class sparse_qr<SparseComplexMatrix>;
  }
}