/*

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 <vector>

#include "MArray2.h"
#include "MSparse.h"
#include "SparseQR.h"
#include "SparseCmplxQR.h"
#include "MatrixType.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)
{
  // 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)
{
#ifdef HAVE_CXSPARSE
  octave_idx_type nr = a.rows ();
  octave_idx_type nc = a.cols ();
  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 ());

#if defined(CS_VER) && (CS_VER >= 2)
      CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm, 0);
      octave_idx_type *p = dm->p;
      octave_idx_type *q = dm->q;
#else
      CXSPARSE_DNAME (d) *dm = CXSPARSE_DNAME(_dmperm) (&csm);
      octave_idx_type *p = dm->P;
      octave_idx_type *q = dm->Q;
#endif
      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);
      info = 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)
	    {
	      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
      // FIXME Should use fine Dulmange-Mendelsohn decomposition here.
      if (dm->rr [1] < dm->rr [2] && dm->cc [2] < dm->cc [3] && !info)
	{
	  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);
	  double rcond = 0.0;
	  MatrixType mtyp (MatrixType::Full);
	  RT mtmp = m.solve (mtyp, btmp2, info, rcond, 
			     solve_singularity_warning, false);	
	  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)
	    {
	      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)
	{
	  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;
#else
  return RT ();
#endif
}

#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

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