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Re: 2.9.5 and 2.1.73


From: David Bateman
Subject: Re: 2.9.5 and 2.1.73
Date: Tue, 14 Mar 2006 18:12:32 +0100
User-agent: Mozilla Thunderbird 1.0.6-7.5.20060mdk (X11/20050322)

With the mentioned attachment this time..

D.

David Bateman wrote:

>John W. Eaton wrote:
>
>  
>
>>I'd like to make a new set of snapshots soon (this week, if
>>possible).  Are there any outstanding bugs that you think must be
>>fixed before I do that?
>>
>>Thanks,
>>
>>jwe
>>
>>
>> 
>>
>>    
>>
>Yes. I have quite a few changes, in particular to the sparse rectangular
>solver code I recently introduced. In fact in is partially disabled in
>the current CVS. I have a couple of issues (ie seg-faults) with the code
>at the moment but will send it hopefully before the end of the week.
>
>There are also three features I have patches for I'd like to add for 2.9.5
>
>* Disable the calculation of the condition number for the diagonal and
>triangular sparse solvers. Given the manner in which these solvers work,
>its generally not possible to pass these singular matrices. You have to
>force the matrix type to be able to. The calculation of the condition
>number can often take orders of magnitude longer than the calculation of
>the solution for these two cases, and so disabling the makes the speed
>comparable (or slightly faster) than matlab.
>* Special case sparse permutations like A = B(p,q) where p and q are
>strict permutations (ie the elements of p and q are unique). This gives
>several orders of magnitude is speedup of the above indexing operation
>* Sparse Dulmange-Mendelsohn solver. I'd like to have this in 2.9.5 so
>that my Octave 2006 paper can refer to 2.9.5 as the version the
>benchmarks are created against. However I have a question on how to use
>C++ template functions in octave. My problem is I need to write
>"dmsolve<SparseMatrix,SparseMatrix,SparseMatrix>(...)" rather than
>"dmsolve(....)" to call the specific version of a template function. I
>can find no instances of the use of such calls to specific template
>functions in octave and so I'm not sure of the best way to include the
>code. I attach my current version of the code as a separate function
>dmsol, so if you can comment on the best way to include this I'd
>appreciate it..
>
>Cheers
>David
>
>
>  
>


-- 
David Bateman                                address@hidden
Motorola Labs - Paris                        +33 1 69 35 48 04 (Ph) 
Parc Les Algorithmes, Commune de St Aubin    +33 6 72 01 06 33 (Mob) 
91193 Gif-Sur-Yvette FRANCE                  +33 1 69 35 77 01 (Fax) 

The information contained in this communication has been classified as: 

[x] General Business Information 
[ ] Motorola Internal Use Only 
[ ] Motorola Confidential Proprietary

/*

Copyright (C) 2006 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 "defun-dld.h"
#include "error.h"
#include "gripes.h"
#include "oct-obj.h"
#include "utils.h"

#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"
#include "MArray2.h"
#include "MSparse.h"
#include "SparseQR.h"
#include "SparseCmplxQR.h"
#include "SparseType.h"
#include "oct-sort.h"

template <class T>
static MSparse<T>
dmsolve_extract (const MSparse<T> &A, const octave_idx_type *Pinv, 
                const octave_idx_type *Q, octave_idx_type rst, 
                octave_idx_type rend, octave_idx_type cst, 
                octave_idx_type cend, octave_idx_type maxnz = -1,
                bool lazy = false)
{
  octave_idx_type nz = (rend - rst) * (cend - cst);
  maxnz = (maxnz < 0 ? A.nnz () : maxnz);
  MSparse<T> B (rend - rst, cend - cst, (nz < maxnz ? nz : maxnz));
  // Some sparse functions can support lazy indexing (where elements
  // in the row are in no particular order), even though octave in 
  // general can't. For those functions that can using it is a big 
  // win here in terms of speed.
  if (lazy)
    {
      nz = 0;
      for (octave_idx_type j = cst ; j < cend ; j++)
        {
          octave_idx_type qq = (Q ? Q [j] : j);
          B.xcidx (j - cst) = nz;
          for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++)
            {
              OCTAVE_QUIT;
              octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p));
              if (r >= rst && r < rend)
                {
                  B.xdata (nz) = A.data (p);
                  B.xridx (nz++) =  r - rst ;
                }
            }
        }
      B.xcidx (cend - cst) = nz ;
    }
  else
    {
      OCTAVE_LOCAL_BUFFER (T, X, rend - rst);
      octave_sort<octave_idx_type> sort;
      octave_idx_type *ri = B.xridx();
      nz = 0;
      for (octave_idx_type j = cst ; j < cend ; j++)
        {
          octave_idx_type qq = (Q ? Q [j] : j);
          B.xcidx (j - cst) = nz;
          for (octave_idx_type p = A.cidx(qq) ; p < A.cidx (qq+1) ; p++)
            {
              OCTAVE_QUIT;
              octave_idx_type r = (Pinv ? Pinv [A.ridx (p)] : A.ridx (p));
              if (r >= rst && r < rend)
                {
                  X [r-rst] = A.data (p);
                  B.xridx (nz++) =  r - rst ;
                }
            }
          sort.sort (ri + B.xcidx (j - cst), nz - B.xcidx (j - cst));
          for (octave_idx_type p = B.cidx (j - cst); p < nz; p++)
            B.xdata (p) = X [B.xridx (p)]; 
        }
      B.xcidx (cend - cst) = nz ;
    }
  return B;
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
static MSparse<double>
dmsolve_extract (const MSparse<double> &A, const octave_idx_type *Pinv, 
                const octave_idx_type *Q, octave_idx_type rst, 
                octave_idx_type rend, octave_idx_type cst, 
                octave_idx_type cend, octave_idx_type maxnz,
                bool lazy);

static MSparse<Complex>
dmsolve_extract (const MSparse<Complex> &A, const octave_idx_type *Pinv, 
                const octave_idx_type *Q, octave_idx_type rst, 
                octave_idx_type rend, octave_idx_type cst, 
                octave_idx_type cend, octave_idx_type maxnz,
                bool lazy);
#endif

template <class T>
static MArray2<T>
dmsolve_extract (const MArray2<T> &m, const octave_idx_type *, 
                 const octave_idx_type *, octave_idx_type r1, 
                 octave_idx_type r2, octave_idx_type c1, 
                 octave_idx_type c2)
{
  r2 -= 1;
  c2 -= 1;
  if (r1 > r2) { octave_idx_type tmp = r1; r1 = r2; r2 = tmp; }
  if (c1 > c2) { octave_idx_type tmp = c1; c1 = c2; c2 = tmp; }

  octave_idx_type new_r = r2 - r1 + 1;
  octave_idx_type new_c = c2 - c1 + 1;

  MArray2<T> result (new_r, new_c);

  for (octave_idx_type j = 0; j < new_c; j++)
    for (octave_idx_type i = 0; i < new_r; i++)
      result.xelem (i, j) = m.elem (r1+i, c1+j);

  return result;
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
static MArray2<double>
dmsolve_extract (const MArray2<double> &m, const octave_idx_type *, 
                 const octave_idx_type *, octave_idx_type r1, 
                 octave_idx_type r2, octave_idx_type c1, 
                 octave_idx_type c2)

static MArray2<Complex>
dmsolve_extract (const MArray2<Complex> &m, const octave_idx_type *, 
                 const octave_idx_type *, octave_idx_type r1, 
                 octave_idx_type r2, octave_idx_type c1, 
                 octave_idx_type c2)
#endif

template <class T>
static void
dmsolve_insert (MArray2<T> &a, const MArray2<T> &b, const octave_idx_type *Q,
               octave_idx_type r, octave_idx_type c)
{
  T *ax = a.fortran_vec();
  const T *bx = b.fortran_vec();
  octave_idx_type anr = a.rows();
  octave_idx_type nr = b.rows();
  octave_idx_type nc = b.cols();
  for (octave_idx_type j = 0; j < nc; j++)
    {
      octave_idx_type aoff = (c + j) * anr;
      octave_idx_type boff = j * nr;
      for (octave_idx_type i = 0; i < nr; i++)
        {
          OCTAVE_QUIT;
          ax [Q [r + i] + aoff] = bx [i + boff];
        }
    }
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
static void
dmsolve_insert (MArray2<double> &a, const MArray2<double> &b, 
               const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);

static void
dmsolve_insert (MArray2<Complex> &a, const MArray2<Complex> &b,
               const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);
#endif

template <class T>
static void
dmsolve_insert (MSparse<T> &a, const MSparse<T> &b, const octave_idx_type *Q,
               octave_idx_type r, octave_idx_type c)
{
  octave_idx_type b_rows = b.rows ();
  octave_idx_type b_cols = b.cols ();
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();

  OCTAVE_LOCAL_BUFFER (octave_idx_type, Qinv, nr);
  for (octave_idx_type i = 0; i < nr; i++)
    Qinv [Q [i]] = i;

  // First count the number of elements in the final array
  octave_idx_type nel = a.xcidx(c) + b.nnz ();

  if (c + b_cols < nc)
    nel += a.xcidx(nc) - a.xcidx(c + b_cols);

  for (octave_idx_type i = c; i < c + b_cols; i++)
    for (octave_idx_type j = a.xcidx(i); j < a.xcidx(i+1); j++)
      if (Qinv [a.xridx(j)] < r || Qinv [a.xridx(j)] >= r + b_rows)
        nel++;

  OCTAVE_LOCAL_BUFFER (T, X, nr);
  octave_sort<octave_idx_type> sort;
  MSparse<T> tmp (a);
  a = MSparse<T> (nr, nc, nel);
  octave_idx_type *ri = a.xridx();

  for (octave_idx_type i = 0; i < tmp.cidx(c); i++)
    {
      a.xdata(i) = tmp.xdata(i);
      a.xridx(i) = tmp.xridx(i);
    }
  for (octave_idx_type i = 0; i < c + 1; i++)
    a.xcidx(i) = tmp.xcidx(i);

  octave_idx_type ii = a.xcidx(c);

  for (octave_idx_type i = c; i < c + b_cols; i++)
    {
      OCTAVE_QUIT;

      for (octave_idx_type j = tmp.xcidx(i); j < tmp.xcidx(i+1); j++)
        if (Qinv [tmp.xridx(j)] < r ||  Qinv [tmp.xridx(j)] >= r + b_rows)
          {
            X [tmp.xridx(j)] = tmp.xdata(j);
            a.xridx(ii++) = tmp.xridx(j);
          }

      OCTAVE_QUIT;

      for (octave_idx_type j = b.cidx(i-c); j < b.cidx(i-c+1); j++)
        {
          X [Q [r + b.ridx(j)]] = b.data(j);
          a.xridx(ii++) = Q [r + b.ridx(j)];
        }

      sort.sort (ri + a.xcidx (i), ii - a.xcidx (i));
      for (octave_idx_type p = a.xcidx (i); p < ii; p++)
        a.xdata (p) = X [a.xridx (p)]; 
      a.xcidx(i+1) = ii;
    }

  for (octave_idx_type i = c + b_cols; i < nc; i++)
    {
      for (octave_idx_type j = tmp.xcidx(i); j < tmp.cidx(i+1); j++)
        {
          a.xdata(ii) = tmp.xdata(j);
          a.xridx(ii++) = tmp.xridx(j);
        }
      a.xcidx(i+1) = ii;
    }
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
static void
dmsolve_insert (MSparse<double> &a, const SparseMatrix &b, 
               const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);

static void
dmsolve_insert (MSparse<Complex> &a, const MSparse<Complex> &b,
               const octave_idx_type *Q, octave_idx_type r, octave_idx_type c);
#endif

template <class T, class RT>
static void
dmsolve_permute (MArray2<RT> &a, const MArray2<T>& b, const octave_idx_type *p)
{
  octave_idx_type b_nr = b.rows ();
  octave_idx_type b_nc = b.cols ();
  const T *Bx = b.fortran_vec();
  a.resize(b_nr, b_nc);
  RT *Btx = a.fortran_vec();
  for (octave_idx_type j = 0; j < b_nc; j++)
    {
      octave_idx_type off = j * b_nr;
      for (octave_idx_type i = 0; i < b_nr; i++)
        {
          OCTAVE_QUIT;
          Btx [p [i] + off] = Bx [ i + off];
        }
    }
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
static void
dmsolve_permute (MArray2<double> &a, const MArray2<double>& b,
                 const octave_idx_type *p);

static void
dmsolve_permute (MArray2<Complex> &a, const MArray2<double>& b,
                 const octave_idx_type *p);

static void
dmsolve_permute (MArray2<Complex> &a, const MArray2<Complex>& b,
                 const octave_idx_type *p);
#endif

template <class T, class RT>
static void
dmsolve_permute (MSparse<RT> &a, const MSparse<T>& b, const octave_idx_type *p)
{
  octave_idx_type b_nr = b.rows ();
  octave_idx_type b_nc = b.cols ();
  octave_idx_type b_nz = b.nnz ();
  octave_idx_type nz = 0;
  a = MSparse<RT> (b_nr, b_nc, b_nz);
  octave_sort<octave_idx_type> sort;
  octave_idx_type *ri = a.xridx();
  OCTAVE_LOCAL_BUFFER (RT, X, b_nr);
  a.xcidx(0) = 0;
  for (octave_idx_type j = 0; j < b_nc; j++)
    {
      for (octave_idx_type i = b.cidx(j); i < b.cidx(j+1); i++)
        {
          OCTAVE_QUIT;
          octave_idx_type r = p [b.ridx (i)];
          X [r] = b.data (i);
          a.xridx(nz++) = p [b.ridx (i)];
        }
      sort.sort (ri + a.xcidx (j), nz - a.xcidx (j));
      for (octave_idx_type i = a.cidx (j); i < nz; i++)
        {
          OCTAVE_QUIT;
          a.xdata (i) = X [a.xridx (i)]; 
        }
      a.xcidx(j+1) = nz;
    }
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
static void
dmsolve_permute (MSparse<double> &a, const MSparse<double>& b, 
                 const octave_idx_type *p);

static void
dmsolve_permute (MSparse<Complex> &a, const MSparse<double>& b,
                 const octave_idx_type *p);

static void
dmsolve_permute (MSparse<Complex> &a, const MSparse<Complex>& b,
                 const octave_idx_type *p);
#endif

static void
solve_singularity_warning (double rcond)
{
  // Dummy singularity handler so that LU solver doesn't flag
  // an error for numerically rank defficient matrices
}

template <class RT, class ST, class T>
RT
dmsolve (const ST &a, const T &b, octave_idx_type &info)
{
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();
  octave_idx_type nz = a.nnz ();
  octave_idx_type b_nr = b.rows ();
  octave_idx_type b_nc = b.cols ();
  RT retval;

  if (nr < 1 || nc < 1 || nr != b_nr)
    (*current_liboctave_error_handler)
      ("matrix dimension mismatch in solution of minimum norm problem");
  else
    {
      octave_idx_type nnz_remaining = a.nnz ();
      CXSPARSE_DNAME () csm;
      csm.m = nr;
      csm.n = nc;
      csm.x = NULL;
      csm.nz = -1;
      csm.nzmax = a.nnz ();
      // Cast away const on A, with full knowledge that CSparse won't touch it.
      // Prevents the methods below making a copy of the data.
      csm.p = const_cast<octave_idx_type *>(a.cidx ());
      csm.i = const_cast<octave_idx_type *>(a.ridx ());

      CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm);
      octave_idx_type *p = dm->P;
      octave_idx_type *q = dm->Q;
      OCTAVE_LOCAL_BUFFER (octave_idx_type, pinv, nr);
      for (octave_idx_type i = 0; i < nr; i++)
        pinv [p [i]] = i;
      RT btmp;
      dmsolve_permute (btmp, b, pinv);
      SparseType mtyp (SparseType::Full);
      info = 0;
      double rcond = 0.0;
      retval.resize (nc, b_nc);

      // Leading over-determined block
      if (dm->rr [2] < nr && dm->cc [3] < nc)
        {
          ST m = dmsolve_extract (a, pinv, q, dm->rr [2], nr, dm->cc [3], nc, 
                                  nnz_remaining, true);
          nnz_remaining -= m.nnz();
          RT mtmp = 
            qrsolve (m, dmsolve_extract (btmp, NULL, NULL, dm->rr[2], b_nr, 0,
                                         b_nc), info);
          dmsolve_insert (retval, mtmp, q, dm->cc [3], 0);
          if (dm->rr [2] > 0 && !info && !error_state)
            {
              m = dmsolve_extract (a, pinv, q, 0, dm->rr [2], 
                                   dm->cc [3], nc, nnz_remaining, true);
              nnz_remaining -= m.nnz();
              RT ctmp = dmsolve_extract (btmp, NULL, NULL, 0, 
                                         dm->rr[2], 0, b_nc);
              btmp.insert (ctmp - m * mtmp, 0, 0);
            }
        }
      
      // Structurally non-singular blocks
      // XXX FIXME XXX Should use fine Dulmange-Mendelsohn decomposition here.
      if (dm->rr [1] < dm->rr [2] && dm->cc [2] < dm->cc [3] && 
          !info && !error_state)
        {
          ST m = dmsolve_extract (a, pinv, q, dm->rr [1], dm->rr [2], 
                                  dm->cc [2], dm->cc [3], nnz_remaining, false);
          nnz_remaining -= m.nnz();
          RT btmp2 = dmsolve_extract (btmp, NULL, NULL, dm->rr [1], dm->rr [2], 
                                      0, b_nc);
          RT mtmp = m.solve (mtyp, btmp2, info, rcond, 
                             solve_singularity_warning);        
          if (info != 0)
            {
              info = 0;
              mtmp = qrsolve (m, btmp2, info);
            }

          dmsolve_insert (retval, mtmp, q, dm->cc [2], 0);
          if (dm->rr [1] > 0 && !info && !error_state)
            {
              m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], dm->cc [2],
                                   dm->cc [3], nnz_remaining, true);
              nnz_remaining -= m.nnz();
              RT ctmp = dmsolve_extract (btmp, NULL, NULL, 0,
                                         dm->rr[1], 0, b_nc);
              btmp.insert (ctmp - m * mtmp, 0, 0);
            }
        }

      // Trailing under-determined block
      if (dm->rr [1] > 0 && dm->cc [2] > 0 && !info && !error_state)
        {
          ST m = dmsolve_extract (a, pinv, q, 0, dm->rr [1], 0, 
                                  dm->cc [2], nnz_remaining, true);
          RT mtmp = 
            qrsolve (m, dmsolve_extract(btmp, NULL, NULL, 0, dm->rr [1] , 0, 
                                        b_nc), info);
          dmsolve_insert (retval, mtmp, q, 0, 0);
        }

      CXSPARSE_DNAME (_dfree) (dm);
    }
  return retval;
}

#if !defined (CXX_NEW_FRIEND_TEMPLATE_DECL)
extern Matrix
dmsolve (const SparseMatrix &a, const Matrix &b, 
         octave_idx_type &info);

extern ComplexMatrix
dmsolve (const SparseMatrix &a, const ComplexMatrix &b, 
         octave_idx_type &info);

extern ComplexMatrix
dmsolve (const SparseComplexMatrix &a, const Matrix &b, 
         octave_idx_type &info);

extern ComplexMatrix
dmsolve (const SparseComplexMatrix &a, const ComplexMatrix &b, 
         octave_idx_type &info);

extern SparseMatrix
dmsolve (const SparseMatrix &a, const SparseMatrix &b, 
         octave_idx_type &info);

extern SparseComplexMatrix
dmsolve (const SparseMatrix &a, const SparseComplexMatrix &b, 
         octave_idx_type &info);

extern SparseComplexMatrix
dmsolve (const SparseComplexMatrix &a, const SparseMatrix &b, 
         octave_idx_type &info);

extern SparseComplexMatrix
dmsolve (const SparseComplexMatrix &a, const SparseComplexMatrix &b, 
         octave_idx_type &info);
#endif

DEFUN_DLD (dmsol, args, , "x = dmsol (A, b)")
{
  octave_value retval;
  int nargin = args.length();
  octave_idx_type info;

  if (nargin !=2)
    {
      print_usage ("dmsol");
      return retval;
    }

  if (args(0).is_real_type ())
    {
      const SparseMatrix m = args(0).sparse_matrix_value ();

      if (args(1).is_real_type  ())
        {
          if (args(1).class_name () == "sparse")
            {
              const SparseMatrix b = args(1).sparse_matrix_value();
              if (!error_state)
                retval = dmsolve <SparseMatrix, SparseMatrix,
                  SparseMatrix> (m, b, info);
            }
          else
            {
              const Matrix b = args(1).matrix_value();
              if (!error_state)
                retval = dmsolve <Matrix, SparseMatrix, Matrix>(m, b, info);
            }
        }
      else
        {
          if (args(1).class_name () == "sparse")
            {
              const SparseComplexMatrix b = 
                args(1).sparse_complex_matrix_value();
              if (!error_state)
                retval = dmsolve <SparseComplexMatrix, SparseMatrix, 
                  SparseComplexMatrix> (m, b, info);
            }
          else
            {
              const ComplexMatrix b = args(1).complex_matrix_value();
              if (!error_state)
                retval = dmsolve <ComplexMatrix, SparseMatrix,
                  ComplexMatrix> (m, b, info);
            }
        }
    }
  else
    {
      const SparseComplexMatrix m = args(0).sparse_complex_matrix_value ();

      if (args(1).is_real_type  ())
        {
          if (args(1).class_name () == "sparse")
            {
              const SparseMatrix b = args(1).sparse_matrix_value();
              if (!error_state)
                retval = dmsolve <SparseComplexMatrix, SparseComplexMatrix,
                  SparseMatrix> (m, b, info);
            }
          else
            {
              const Matrix b = args(1).matrix_value();
              if (!error_state)
                retval = dmsolve <ComplexMatrix, SparseComplexMatrix,
                  Matrix> (m, b, info);
            }
        }
      else
        {
          if (args(1).class_name () == "sparse")
            {
              const SparseComplexMatrix b = 
                args(1).sparse_complex_matrix_value();
              if (!error_state)
                retval = dmsolve <SparseComplexMatrix, SparseComplexMatrix,
                  SparseComplexMatrix> (m, b, info);
            }
          else
            {
              const ComplexMatrix b = args(1).complex_matrix_value();
              if (!error_state)
                retval = dmsolve <ComplexMatrix, SparseComplexMatrix, 
                  ComplexMatrix> (m, b, info);
            }
        }
    }

  return retval;
}

/*

%!function f(a, sz, feps)
%! b = randn(sz); x = dmsol(a,b); 
%! assert (a * x, b, feps);
%! b = randn(sz)+1i*randn(sz); x = dmsol(a,b);  
%! assert (a * x, b, feps);
%! b = sprandn(sz(1),sz(2),0.2); x = dmsol(a,b);
%! assert (sparse(a * x), b, feps);
%! b = sprandn(sz(1),sz(2),0.2)+1i*sprandn(sz(1),sz(2),0.2); x = dmsol(a,b); 
%! assert (sparse(a * x), b, feps);
%!test
%! a = sprandn(10,11,0.2)+speye(10,11); f(a,[10,2],1e-10);
%! ## Test this by forcing matrix_type
%! a = sprandn(10,10,0.2)+speye(10,10); f(a,[10,2],1e-10);
%!test
%! a = 1i*sprandn(10,11,0.2)+speye(10,11); f(a,[10,2],1e-10);
%! ## Test this by forcing matrix_type
%! a = 1i*sprandn(10,10,0.2)+speye(10,10); f(a,[10,2],1e-10);

*/

DEFUN_DLD (qrsol, args, nargout, "x = qrsol (A, b)")
{
  octave_value retval;
  int nargin = args.length();
  octave_idx_type info;

  if (nargin !=2)
    {
      print_usage ("qrsol");
      return retval;
    }

  if (args(0).is_real_type ())
    {
      SparseMatrix m = args(0).sparse_matrix_value ();

      if (args(1).is_real_type  ())
        {
          if (args(1).class_name () == "sparse")
            retval = qrsolve (m, args(1).sparse_matrix_value(), info);
          else
            retval = qrsolve (m, args(1).matrix_value(), info);
        }
      else
        {
          if (args(1).class_name () == "sparse")
            retval = qrsolve (m, args(1).sparse_complex_matrix_value(), info);
          else
            retval = qrsolve (m, args(1).complex_matrix_value(), info);
        }
    }
  else
    {
      SparseComplexMatrix m = args(0).sparse_complex_matrix_value ();

      if (args(1).is_real_type  ())
        {
          if (args(1).class_name () == "sparse")
            retval = qrsolve (m, args(1).sparse_matrix_value(), info);
          else
            retval = qrsolve (m, args(1).matrix_value(), info);
        }
      else
        {
          if (args(1).class_name () == "sparse")
            retval = qrsolve (m, args(1).sparse_complex_matrix_value(), info);
          else
            retval = qrsolve (m, args(1).complex_matrix_value(), info);
        }
    }

  return retval;
}

/*

%!function f(a, sz, feps)
%! b = randn(sz); x = qrsol(a,b); 
%! assert (a * x, b, feps);
%! b = randn(sz)+1i*randn(sz); x = qrsol(a,b);  
%! assert (a * x, b, feps);
%! b = sprandn(sz(1),sz(2),0.2); x = qrsol(a,b);
%! assert (sparse(a * x), b, feps);
%! b = sprandn(sz(1),sz(2),0.2)+1i*sprandn(sz(1),sz(2),0.2); x = qrsol(a,b); 
%! assert (sparse(a * x), b, feps);
%!test
%! a = sprandn(10,11,0.2)+speye(10,11); f(a,[10,2],1e-10);
%! ## Test this by forcing matrix_type
%! a = sprandn(10,10,0.2)+speye(10,10); f(a,[10,2],1e-10);
%!test
%! a = 1i*sprandn(10,11,0.2)+speye(10,11); f(a,[10,2],1e-10);
%! ## Test this by forcing matrix_type
%! a = 1i*sprandn(10,10,0.2)+speye(10,10); f(a,[10,2],1e-10);

*/

/*
;;; Local Variables: ***
;;; mode: C++ ***
;;; End: ***
*/

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