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Sparse-op-defs.h

/*

Copyright (C) 2004, 2005, 2006, 2007, 2008 David Bateman
Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004 Andy Adler
Copyright (C) 2008 Jaroslav Hajek

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
<http://www.gnu.org/licenses/>.

*/

#if !defined (octave_sparse_op_defs_h)
#define octave_sparse_op_defs_h 1

#include "Array-util.h"
#include "mx-ops.h"
#include "oct-locbuf.h"

#define SPARSE_BIN_OP_DECL(R, OP, X, Y, API) \
  extern API R OP (const X&, const Y&)

#define SPARSE_CMP_OP_DECL(OP, X, Y, API) \
  extern API SparseBoolMatrix OP (const X&, const Y&)

#define SPARSE_BOOL_OP_DECL(OP, X, Y, API) \
  extern API SparseBoolMatrix OP (const X&, const Y&)

// matrix by scalar operations.

#define SPARSE_SMS_BIN_OP_DECLS(R1, R2, M, S, API)  \
  SPARSE_BIN_OP_DECL (R1, operator +, M, S, API); \
  SPARSE_BIN_OP_DECL (R1, operator -, M, S, API); \
  SPARSE_BIN_OP_DECL (R2, operator *, M, S, API); \
  SPARSE_BIN_OP_DECL (R2, operator /, M, S, API);

#define SPARSE_SMS_BIN_OP_1(R, F, OP, M, S)     \
  R \
  F (const M& m, const S& s) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
 \
    R r (nr, nc, (0.0 OP s)); \
 \
    for (octave_idx_type j = 0; j < nc; j++) \
      for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) \
        r.elem (m.ridx (i), j) = m.data (i) OP s; \
    return r; \
  }

#define SPARSE_SMS_BIN_OP_2(R, F, OP, M, S)     \
  R \
  F (const M& m, const S& s) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
    octave_idx_type nz = m.nnz (); \
 \
    R r (nr, nc, nz); \
 \
    for (octave_idx_type i = 0; i < nz; i++) \
      { \
      r.data(i) = m.data(i) OP s; \
      r.ridx(i) = m.ridx(i); \
      } \
    for (octave_idx_type i = 0; i < nc + 1; i++) \
      r.cidx(i) = m.cidx(i); \
    \
    r.maybe_compress (true); \
    return r; \
  }

#define SPARSE_SMS_BIN_OPS(R1, R2, M, S) \
  SPARSE_SMS_BIN_OP_1 (R1, operator +, +, M, S) \
  SPARSE_SMS_BIN_OP_1 (R1, operator -, -, M, S) \
  SPARSE_SMS_BIN_OP_2 (R2, operator *, *, M, S) \
  SPARSE_SMS_BIN_OP_2 (R2, operator /, /, M, S)

#define SPARSE_SMS_CMP_OP_DECLS(M, S, API) \
  SPARSE_CMP_OP_DECL (mx_el_lt, M, S, API); \
  SPARSE_CMP_OP_DECL (mx_el_le, M, S, API); \
  SPARSE_CMP_OP_DECL (mx_el_ge, M, S, API); \
  SPARSE_CMP_OP_DECL (mx_el_gt, M, S, API); \
  SPARSE_CMP_OP_DECL (mx_el_eq, M, S, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M, S, API);

#define SPARSE_SMS_EQNE_OP_DECLS(M, S, API) \
  SPARSE_CMP_OP_DECL (mx_el_eq, M, S, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M, S, API);

#define SPARSE_SMS_CMP_OP(F, OP, M, MZ, MC, S, SZ, SC)      \
  SparseBoolMatrix \
  F (const M& m, const S& s) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
    SparseBoolMatrix r; \
    \
    if (MC (MZ) OP SC (s)) \
      { \
        r = SparseBoolMatrix (nr, nc, true); \
      for (octave_idx_type j = 0; j < nc; j++) \
        for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
            if (! (MC (m.data (i)) OP SC (s))) \
              r.data (m.ridx (i) + j * nr) = false; \
        r.maybe_compress (true); \
      } \
    else \
      { \
        r = SparseBoolMatrix (nr, nc, m.nnz ()); \
        r.cidx (0) = static_cast<octave_idx_type> (0); \
        octave_idx_type nel = 0; \
      for (octave_idx_type j = 0; j < nc; j++) \
          { \
          for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
              if (MC (m.data (i)) OP SC (s)) \
                { \
                  r.ridx (nel) = m.ridx (i); \
                  r.data (nel++) = true; \
                } \
            r.cidx (j + 1) = nel; \
          } \
        r.maybe_compress (false); \
      } \
    return r; \
  }

#define SPARSE_SMS_CMP_OPS(M, MZ, CM, S, SZ, CS)      \
  SPARSE_SMS_CMP_OP (mx_el_lt, <,  M, MZ, CM, S, SZ, CS)    \
  SPARSE_SMS_CMP_OP (mx_el_le, <=, M, MZ, CM, S, SZ, CS)    \
  SPARSE_SMS_CMP_OP (mx_el_ge, >=, M, MZ, CM, S, SZ, CS)    \
  SPARSE_SMS_CMP_OP (mx_el_gt, >,  M, MZ, CM, S, SZ, CS)    \
  SPARSE_SMS_CMP_OP (mx_el_eq, ==, M, MZ,   , S, SZ,   )    \
  SPARSE_SMS_CMP_OP (mx_el_ne, !=, M, MZ,   , S, SZ,   )

#define SPARSE_SMS_EQNE_OPS(M, MZ, CM, S, SZ, CS)     \
  SPARSE_SMS_CMP_OP (mx_el_eq, ==, M, MZ,   , S, SZ,   )    \
  SPARSE_SMS_CMP_OP (mx_el_ne, !=, M, MZ,   , S, SZ,   )

#define SPARSE_SMS_BOOL_OP_DECLS(M, S, API) \
  SPARSE_BOOL_OP_DECL (mx_el_and, M, S, API); \
  SPARSE_BOOL_OP_DECL (mx_el_or,  M, S, API);

#define SPARSE_SMS_BOOL_OP(F, OP, M, S, LHS_ZERO, RHS_ZERO) \
  SparseBoolMatrix \
  F (const M& m, const S& s) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
    SparseBoolMatrix r; \
    \
    if (nr > 0 && nc > 0) \
      { \
      if (LHS_ZERO OP (s != RHS_ZERO)) \
        { \
            r = SparseBoolMatrix (nr, nc, true); \
          for (octave_idx_type j = 0; j < nc; j++) \
            for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
                if (! ((m.data(i) != LHS_ZERO) OP (s != RHS_ZERO))) \
                  r.data (m.ridx (i) + j * nr) = false; \
            r.maybe_compress (true); \
          } \
      else \
        { \
            r = SparseBoolMatrix (nr, nc, m.nnz ()); \
            r.cidx (0) = static_cast<octave_idx_type> (0); \
            octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < nc; j++) \
              { \
              for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
                  if ((m.data(i) != LHS_ZERO) OP (s != RHS_ZERO)) \
                    { \
                      r.ridx (nel) = m.ridx (i); \
                      r.data (nel++) = true; \
                    } \
                r.cidx (j + 1) = nel; \
              } \
            r.maybe_compress (false); \
          } \
      }     \
    return r; \
  }

#define SPARSE_SMS_BOOL_OPS2(M, S, LHS_ZERO, RHS_ZERO) \
  SPARSE_SMS_BOOL_OP (mx_el_and, &&, M, S, LHS_ZERO, RHS_ZERO) \
  SPARSE_SMS_BOOL_OP (mx_el_or,  ||, M, S, LHS_ZERO, RHS_ZERO)

#define SPARSE_SMS_BOOL_OPS(M, S, ZERO) \
  SPARSE_SMS_BOOL_OPS2(M, S, ZERO, ZERO)

#define SPARSE_SMS_OP_DECLS(R1, R2, M, S, API) \
  SPARSE_SMS_BIN_OP_DECLS (R1, R2, M, S, API)    \
  SPARSE_SMS_CMP_OP_DECLS (M, S, API) \
  SPARSE_SMS_BOOL_OP_DECLS (M, S, API)

// scalar by matrix operations.

#define SPARSE_SSM_BIN_OP_DECLS(R1, R2, S, M, API)    \
  SPARSE_BIN_OP_DECL (R1, operator +, S, M, API); \
  SPARSE_BIN_OP_DECL (R1, operator -, S, M, API); \
  SPARSE_BIN_OP_DECL (R2, operator *, S, M, API); \
  SPARSE_BIN_OP_DECL (R2, operator /, S, M, API);

#define SPARSE_SSM_BIN_OP_1(R, F, OP, S, M) \
  R \
  F (const S& s, const M& m) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
 \
    R r (nr, nc, (s OP 0.0)); \
 \
    for (octave_idx_type j = 0; j < nc; j++) \
      for (octave_idx_type i = m.cidx (j); i < m.cidx (j+1); i++) \
        r.elem (m.ridx (i), j) = s OP m.data (i); \
 \
    return r; \
  }

#define SPARSE_SSM_BIN_OP_2(R, F, OP, S, M) \
  R \
  F (const S& s, const M& m) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
    octave_idx_type nz = m.nnz (); \
 \
    R r (nr, nc, nz); \
 \
    for (octave_idx_type i = 0; i < nz; i++) \
      { \
      r.data(i) = s OP m.data(i); \
      r.ridx(i) = m.ridx(i); \
      } \
    for (octave_idx_type i = 0; i < nc + 1; i++) \
      r.cidx(i) = m.cidx(i); \
 \
    r.maybe_compress(true); \
    return r; \
  }

#define SPARSE_SSM_BIN_OPS(R1, R2, S, M) \
  SPARSE_SSM_BIN_OP_1 (R1, operator +, +, S, M) \
  SPARSE_SSM_BIN_OP_1 (R1, operator -, -, S, M) \
  SPARSE_SSM_BIN_OP_2 (R2, operator *, *, S, M) \
  SPARSE_SSM_BIN_OP_2 (R2, operator /, /, S, M)

#define SPARSE_SSM_CMP_OP_DECLS(S, M, API) \
  SPARSE_CMP_OP_DECL (mx_el_lt, S, M, API); \
  SPARSE_CMP_OP_DECL (mx_el_le, S, M, API); \
  SPARSE_CMP_OP_DECL (mx_el_ge, S, M, API); \
  SPARSE_CMP_OP_DECL (mx_el_gt, S, M, API); \
  SPARSE_CMP_OP_DECL (mx_el_eq, S, M, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, S, M, API);

#define SPARSE_SSM_EQNE_OP_DECLS(S, M, API) \
  SPARSE_CMP_OP_DECL (mx_el_eq, S, M, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, S, M, API);

#define SPARSE_SSM_CMP_OP(F, OP, S, SZ, SC, M, MZ, MC)      \
  SparseBoolMatrix \
  F (const S& s, const M& m) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
    SparseBoolMatrix r; \
    \
    if (SC (s) OP SC (MZ)) \
      { \
        r = SparseBoolMatrix (nr, nc, true); \
      for (octave_idx_type j = 0; j < nc; j++) \
        for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
            if (! (SC (s) OP MC (m.data (i)))) \
              r.data (m.ridx (i) + j * nr) = false; \
        r.maybe_compress (true); \
      } \
    else \
      { \
        r = SparseBoolMatrix (nr, nc, m.nnz ()); \
        r.cidx (0) = static_cast<octave_idx_type> (0); \
        octave_idx_type nel = 0; \
      for (octave_idx_type j = 0; j < nc; j++) \
          { \
          for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
              if (SC (s) OP MC (m.data (i))) \
                { \
                  r.ridx (nel) = m.ridx (i); \
                  r.data (nel++) = true; \
                } \
            r.cidx (j + 1) = nel; \
          } \
        r.maybe_compress (false); \
      } \
    return r; \
  }

#define SPARSE_SSM_CMP_OPS(S, SZ, SC, M, MZ, MC)      \
  SPARSE_SSM_CMP_OP (mx_el_lt, <,  S, SZ, SC, M, MZ, MC)    \
  SPARSE_SSM_CMP_OP (mx_el_le, <=, S, SZ, SC, M, MZ, MC)    \
  SPARSE_SSM_CMP_OP (mx_el_ge, >=, S, SZ, SC, M, MZ, MC)    \
  SPARSE_SSM_CMP_OP (mx_el_gt, >,  S, SZ, SC, M, MZ, MC)    \
  SPARSE_SSM_CMP_OP (mx_el_eq, ==, S, SZ,   , M, MZ,   )    \
  SPARSE_SSM_CMP_OP (mx_el_ne, !=, S, SZ,   , M, MZ,   )

#define SPARSE_SSM_EQNE_OPS(S, SZ, SC, M, MZ, MC)     \
  SPARSE_SSM_CMP_OP (mx_el_eq, ==, S, SZ,   , M, MZ,   )    \
  SPARSE_SSM_CMP_OP (mx_el_ne, !=, S, SZ,   , M, MZ,   )

#define SPARSE_SSM_BOOL_OP_DECLS(S, M, API) \
  SPARSE_BOOL_OP_DECL (mx_el_and, S, M, API); \
  SPARSE_BOOL_OP_DECL (mx_el_or,  S, M, API); \

#define SPARSE_SSM_BOOL_OP(F, OP, S, M, LHS_ZERO, RHS_ZERO) \
  SparseBoolMatrix \
  F (const S& s, const M& m) \
  { \
    octave_idx_type nr = m.rows (); \
    octave_idx_type nc = m.cols (); \
    SparseBoolMatrix r; \
    \
    if (nr > 0 && nc > 0) \
      { \
      if ((s != LHS_ZERO) OP RHS_ZERO) \
        { \
            r = SparseBoolMatrix (nr, nc, true); \
          for (octave_idx_type j = 0; j < nc; j++) \
            for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
                if (! ((s != LHS_ZERO) OP (m.data(i) != RHS_ZERO))) \
                  r.data (m.ridx (i) + j * nr) = false; \
            r.maybe_compress (true); \
          } \
      else \
        { \
            r = SparseBoolMatrix (nr, nc, m.nnz ()); \
            r.cidx (0) = static_cast<octave_idx_type> (0); \
            octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < nc; j++) \
              { \
              for (octave_idx_type i = m.cidx(j); i < m.cidx(j+1); i++) \
                  if ((s != LHS_ZERO) OP (m.data(i) != RHS_ZERO)) \
                    { \
                      r.ridx (nel) = m.ridx (i); \
                      r.data (nel++) = true; \
                    } \
                r.cidx (j + 1) = nel; \
              } \
            r.maybe_compress (false); \
          } \
      }     \
    return r; \
  }

#define SPARSE_SSM_BOOL_OPS2(S, M, LHS_ZERO, RHS_ZERO) \
  SPARSE_SSM_BOOL_OP (mx_el_and, &&, S, M, LHS_ZERO, RHS_ZERO) \
  SPARSE_SSM_BOOL_OP (mx_el_or,  ||, S, M, LHS_ZERO, RHS_ZERO)

#define SPARSE_SSM_BOOL_OPS(S, M, ZERO) \
  SPARSE_SSM_BOOL_OPS2(S, M, ZERO, ZERO)

#define SPARSE_SSM_OP_DECLS(R1, R2, S, M, API) \
  SPARSE_SSM_BIN_OP_DECLS (R1, R2, S, M, API)    \
  SPARSE_SSM_CMP_OP_DECLS (S, M, API) \
  SPARSE_SSM_BOOL_OP_DECLS (S, M, API) \

// matrix by matrix operations.

#define SPARSE_SMSM_BIN_OP_DECLS(R1, R2, M1, M2, API) \
  SPARSE_BIN_OP_DECL (R1, operator +, M1, M2, API); \
  SPARSE_BIN_OP_DECL (R1, operator -, M1, M2, API); \
  SPARSE_BIN_OP_DECL (R2, product,    M1, M2, API); \
  SPARSE_BIN_OP_DECL (R2, quotient,   M1, M2, API);

#define SPARSE_SMSM_BIN_OP_1(R, F, OP, M1, M2)  \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m1_nr == 1 && m1_nc == 1) \
      { \
        if (m1.elem(0,0) == 0.) \
          r = OP R (m2); \
        else \
          { \
          r = R (m2_nr, m2_nc, m1.data(0) OP 0.); \
            \
            for (octave_idx_type j = 0 ; j < m2_nc ; j++) \
              { \
                OCTAVE_QUIT; \
                octave_idx_type idxj = j * m2_nr; \
                for (octave_idx_type i = m2.cidx(j) ; i < m2.cidx(j+1) ; i++) \
                  { \
                    OCTAVE_QUIT; \
                    r.data(idxj + m2.ridx(i)) = m1.data(0) OP m2.data(i); \
              } \
              } \
            r.maybe_compress (); \
          } \
      } \
    else if (m2_nr == 1 && m2_nc == 1) \
      { \
        if (m2.elem(0,0) == 0.) \
          r = R (m1); \
        else \
          { \
          r = R (m1_nr, m1_nc, 0. OP m2.data(0)); \
            \
            for (octave_idx_type j = 0 ; j < m1_nc ; j++) \
              { \
                OCTAVE_QUIT; \
                octave_idx_type idxj = j * m1_nr; \
                for (octave_idx_type i = m1.cidx(j) ; i < m1.cidx(j+1) ; i++) \
                  { \
                    OCTAVE_QUIT; \
                    r.data(idxj + m1.ridx(i)) = m1.data(i) OP m2.data(0); \
              } \
              } \
            r.maybe_compress (); \
          } \
      } \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
      r = R (m1_nr, m1_nc, (m1.nnz () + m2.nnz ())); \
        \
        octave_idx_type jx = 0; \
        r.cidx (0) = 0; \
        for (octave_idx_type i = 0 ; i < m1_nc ; i++) \
          { \
            octave_idx_type  ja = m1.cidx(i); \
            octave_idx_type  ja_max = m1.cidx(i+1); \
            bool ja_lt_max= ja < ja_max; \
            \
            octave_idx_type  jb = m2.cidx(i); \
            octave_idx_type  jb_max = m2.cidx(i+1); \
            bool jb_lt_max = jb < jb_max; \
            \
            while (ja_lt_max || jb_lt_max ) \
              { \
                OCTAVE_QUIT; \
                if ((! jb_lt_max) || \
                      (ja_lt_max && (m1.ridx(ja) < m2.ridx(jb)))) \
                  { \
                    r.ridx(jx) = m1.ridx(ja); \
                    r.data(jx) = m1.data(ja) OP 0.; \
                    jx++; \
                    ja++; \
                    ja_lt_max= ja < ja_max; \
                  } \
                else if (( !ja_lt_max ) || \
                     (jb_lt_max && (m2.ridx(jb) < m1.ridx(ja)) ) ) \
                  { \
                r.ridx(jx) = m2.ridx(jb); \
                r.data(jx) = 0. OP m2.data(jb); \
                jx++; \
                    jb++; \
                    jb_lt_max= jb < jb_max; \
                  } \
                else \
                  { \
                 if ((m1.data(ja) OP m2.data(jb)) != 0.) \
                     { \
                          r.data(jx) = m1.data(ja) OP m2.data(jb); \
                          r.ridx(jx) = m1.ridx(ja); \
                          jx++; \
                       } \
                     ja++; \
                     ja_lt_max= ja < ja_max; \
                     jb++; \
                     jb_lt_max= jb < jb_max; \
                  } \
              } \
            r.cidx(i+1) = jx; \
          } \
        \
      r.maybe_compress (); \
      } \
 \
    return r; \
  }

#define SPARSE_SMSM_BIN_OP_2(R, F, OP, M1, M2)  \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m1_nr == 1 && m1_nc == 1) \
      { \
        if (m1.elem(0,0) == 0.) \
          r = R (m2_nr, m2_nc); \
        else \
          { \
          r = R (m2); \
            octave_idx_type m2_nnz = m2.nnz(); \
            \
            for (octave_idx_type i = 0 ; i < m2_nnz ; i++) \
              { \
                OCTAVE_QUIT; \
                r.data (i) = m1.data(0) OP r.data(i); \
              } \
            r.maybe_compress (); \
          } \
      } \
    else if (m2_nr == 1 && m2_nc == 1) \
      { \
        if (m2.elem(0,0) == 0.) \
          r = R (m1_nr, m1_nc); \
        else \
          { \
          r = R (m1); \
            octave_idx_type m1_nnz = m1.nnz(); \
            \
            for (octave_idx_type i = 0 ; i < m1_nnz ; i++) \
              { \
                OCTAVE_QUIT; \
                r.data (i) = r.data(i) OP m2.data(0); \
              } \
            r.maybe_compress (); \
          } \
      } \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
        r = R (m1_nr, m1_nc, (m1.nnz () > m2.nnz () ? m1.nnz () : m2.nnz ())); \
        \
        octave_idx_type jx = 0; \
      r.cidx (0) = 0; \
        for (octave_idx_type i = 0 ; i < m1_nc ; i++) \
          { \
            octave_idx_type  ja = m1.cidx(i); \
            octave_idx_type  ja_max = m1.cidx(i+1); \
            bool ja_lt_max= ja < ja_max; \
            \
            octave_idx_type  jb = m2.cidx(i); \
            octave_idx_type  jb_max = m2.cidx(i+1); \
            bool jb_lt_max = jb < jb_max; \
            \
            while (ja_lt_max || jb_lt_max ) \
              { \
                OCTAVE_QUIT; \
                if ((! jb_lt_max) || \
                      (ja_lt_max && (m1.ridx(ja) < m2.ridx(jb)))) \
                  { \
                     ja++; ja_lt_max= ja < ja_max; \
                  } \
                else if (( !ja_lt_max ) || \
                     (jb_lt_max && (m2.ridx(jb) < m1.ridx(ja)) ) ) \
                  { \
                     jb++; jb_lt_max= jb < jb_max; \
                  } \
                else \
                  { \
                 if ((m1.data(ja) OP m2.data(jb)) != 0.) \
                     { \
                          r.data(jx) = m1.data(ja) OP m2.data(jb); \
                          r.ridx(jx) = m1.ridx(ja); \
                          jx++; \
                       } \
                     ja++; ja_lt_max= ja < ja_max; \
                     jb++; jb_lt_max= jb < jb_max; \
                  } \
              } \
            r.cidx(i+1) = jx; \
          } \
        \
      r.maybe_compress (); \
      } \
 \
    return r; \
  }

#define SPARSE_SMSM_BIN_OP_3(R, F, OP, M1, M2)  \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m1_nr == 1 && m1_nc == 1) \
      { \
        if ((m1.elem (0,0) OP Complex()) == Complex()) \
          { \
            octave_idx_type m2_nnz = m2.nnz(); \
            r = R (m2); \
            for (octave_idx_type i = 0 ; i < m2_nnz ; i++) \
              r.data (i) = m1.elem(0,0) OP r.data(i); \
            r.maybe_compress (); \
          } \
        else \
          { \
            r = R (m2_nr, m2_nc, m1.elem(0,0) OP Complex ()); \
            for (octave_idx_type j = 0 ; j < m2_nc ; j++) \
              { \
                OCTAVE_QUIT; \
                octave_idx_type idxj = j * m2_nr; \
                for (octave_idx_type i = m2.cidx(j) ; i < m2.cidx(j+1) ; i++) \
                  { \
                    OCTAVE_QUIT; \
                    r.data(idxj + m2.ridx(i)) = m1.elem(0,0) OP m2.data(i); \
              } \
              } \
            r.maybe_compress (); \
          } \
      } \
    else if (m2_nr == 1 && m2_nc == 1) \
      { \
        if ((Complex() OP m1.elem (0,0)) == Complex()) \
          { \
            octave_idx_type m1_nnz = m1.nnz(); \
            r = R (m1); \
            for (octave_idx_type i = 0 ; i < m1_nnz ; i++) \
              r.data (i) = r.data(i) OP m2.elem(0,0); \
            r.maybe_compress (); \
          } \
        else \
          { \
            r = R (m1_nr, m1_nc, Complex() OP m2.elem(0,0)); \
            for (octave_idx_type j = 0 ; j < m1_nc ; j++) \
              { \
                OCTAVE_QUIT; \
                octave_idx_type idxj = j * m1_nr; \
                for (octave_idx_type i = m1.cidx(j) ; i < m1.cidx(j+1) ; i++) \
                  { \
                    OCTAVE_QUIT; \
                    r.data(idxj + m1.ridx(i)) = m1.data(i) OP m2.elem(0,0); \
              } \
              } \
            r.maybe_compress (); \
          } \
      } \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
 \
        /* FIXME Kludge... Always double/Complex, so Complex () */ \
        r = R (m1_nr, m1_nc, (Complex () OP Complex ())); \
        \
        for (octave_idx_type i = 0 ; i < m1_nc ; i++) \
          { \
            octave_idx_type  ja = m1.cidx(i); \
            octave_idx_type  ja_max = m1.cidx(i+1); \
            bool ja_lt_max= ja < ja_max; \
            \
            octave_idx_type  jb = m2.cidx(i); \
            octave_idx_type  jb_max = m2.cidx(i+1); \
            bool jb_lt_max = jb < jb_max; \
            \
            while (ja_lt_max || jb_lt_max ) \
              { \
                OCTAVE_QUIT; \
                if ((! jb_lt_max) || \
                      (ja_lt_max && (m1.ridx(ja) < m2.ridx(jb)))) \
                  { \
                /* keep those kludges coming */ \
                    r.elem(m1.ridx(ja),i) = m1.data(ja) OP Complex (); \
                    ja++; \
                    ja_lt_max= ja < ja_max; \
                  } \
                else if (( !ja_lt_max ) || \
                     (jb_lt_max && (m2.ridx(jb) < m1.ridx(ja)) ) ) \
                  { \
                /* keep those kludges coming */ \
                    r.elem(m2.ridx(jb),i) = Complex () OP m2.data(jb);  \
                    jb++; \
                    jb_lt_max= jb < jb_max; \
                  } \
                else \
                  { \
                    r.elem(m1.ridx(ja),i) = m1.data(ja) OP m2.data(jb); \
                    ja++; \
                    ja_lt_max= ja < ja_max; \
                    jb++; \
                    jb_lt_max= jb < jb_max; \
                  } \
              } \
          } \
      r.maybe_compress (true); \
      } \
 \
    return r; \
  }

// Note that SM ./ SM needs to take into account the NaN and Inf values
// implied by the division by zero.
// FIXME Are the NaNs double(NaN) or Complex(NaN,Nan) in the complex
// case?
#define SPARSE_SMSM_BIN_OPS(R1, R2, M1, M2)  \
  SPARSE_SMSM_BIN_OP_1 (R1, operator +,  +, M1, M2) \
  SPARSE_SMSM_BIN_OP_1 (R1, operator -,  -, M1, M2) \
  SPARSE_SMSM_BIN_OP_2 (R2, product,     *, M1, M2) \
  SPARSE_SMSM_BIN_OP_3 (R2, quotient,    /, M1, M2)

#define SPARSE_SMSM_CMP_OP_DECLS(M1, M2, API) \
  SPARSE_CMP_OP_DECL (mx_el_lt, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_le, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ge, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_gt, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_eq, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M1, M2, API);

#define SPARSE_SMSM_EQNE_OP_DECLS(M1, M2, API) \
  SPARSE_CMP_OP_DECL (mx_el_eq, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M1, M2, API);

// FIXME -- this macro duplicatest the bodies of the template
// functions defined in the SPARSE_SSM_CMP_OP and SPARSE_SMS_CMP_OP
// macros.

#define SPARSE_SMSM_CMP_OP(F, OP, M1, Z1, C1, M2, Z2, C2)   \
  SparseBoolMatrix \
  F (const M1& m1, const M2& m2) \
  { \
    SparseBoolMatrix r; \
    \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
    \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
    \
    if (m1_nr == 1 && m1_nc == 1) \
      { \
    if (C1 (m1.elem(0,0)) OP C2 (Z2)) \
        { \
          r = SparseBoolMatrix (m2_nr, m2_nc, true); \
          for (octave_idx_type j = 0; j < m2_nc; j++) \
            for (octave_idx_type i = m2.cidx(j); i < m2.cidx(j+1); i++) \
            if (! (C1 (m1.elem (0,0)) OP C2 (m2.data(i)))) \
              r.data (m2.ridx (i) + j * m2_nr) = false; \
          r.maybe_compress (true); \
        } \
      else \
        { \
          r = SparseBoolMatrix (m2_nr, m2_nc, m2.nnz ()); \
          r.cidx (0) = static_cast<octave_idx_type> (0); \
          octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m2_nc; j++) \
            { \
            for (octave_idx_type i = m2.cidx(j); i < m2.cidx(j+1); i++) \
              if (C1 (m1.elem (0,0)) OP C2 (m2.data(i))) \
                { \
                  r.ridx (nel) = m2.ridx (i); \
                  r.data (nel++) = true; \
                } \
            r.cidx (j + 1) = nel; \
            }     \
          r.maybe_compress (false); \
        } \
      } \
    else if (m2_nr == 1 && m2_nc == 1) \
      { \
      if (C1 (Z1) OP C2 (m2.elem (0,0))) \
        { \
          r = SparseBoolMatrix (m1_nr, m1_nc, true); \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            for (octave_idx_type i = m1.cidx(j); i < m1.cidx(j+1); i++) \
            if (! (C1 (m1.data (i)) OP C2 (m2.elem(0,0)))) \
              r.data (m1.ridx (i) + j * m1_nr) = false; \
          r.maybe_compress (true); \
        } \
      else \
        { \
          r = SparseBoolMatrix (m1_nr, m1_nc, m1.nnz ()); \
          r.cidx (0) = static_cast<octave_idx_type> (0); \
          octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            { \
            for (octave_idx_type i = m1.cidx(j); i < m1.cidx(j+1); i++) \
              if (C1 (m1.data (i)) OP C2 (m2.elem(0,0))) \
                { \
                  r.ridx (nel) = m1.ridx (i); \
                  r.data (nel++) = true; \
                } \
            r.cidx (j + 1) = nel; \
            }     \
          r.maybe_compress (false); \
        } \
      } \
    else if (m1_nr == m2_nr && m1_nc == m2_nc) \
      { \
      if (m1_nr != 0 || m1_nc != 0) \
        { \
            if (C1 (Z1) OP C2 (Z2)) \
            { \
                r = SparseBoolMatrix (m1_nr, m1_nc, true); \
              for (octave_idx_type j = 0; j < m1_nc; j++) \
                  { \
                     octave_idx_type i1 = m1.cidx (j); \
                     octave_idx_type e1 = m1.cidx (j+1); \
                     octave_idx_type i2 = m2.cidx (j); \
                     octave_idx_type e2 = m2.cidx (j+1); \
                     while (i1 < e1 || i2 < e2) \
                       { \
                         if (i1 == e1 || (i2 < e2 && m1.ridx(i1) > m2.ridx(i2))) \
                           { \
                             if (! (C1 (Z1) OP C2 (m2.data (i2)))) \
                               r.data (m2.ridx (i2) + j * m1_nr) = false; \
                             i2++; \
                           } \
                         else if (i2 == e2 || m1.ridx(i1) < m2.ridx(i2)) \
                           { \
                             if (! (C1 (m1.data (i1)) OP C2 (Z2))) \
                               r.data (m1.ridx (i1) + j * m1_nr) = false; \
                             i1++; \
                           } \
                         else \
                           { \
                             if (! (C1 (m1.data (i1)) OP C2 (m2.data (i2)))) \
                               r.data (m1.ridx (i1) + j * m1_nr) = false; \
                             i1++; \
                             i2++; \
                           } \
                       } \
                  } \
                r.maybe_compress (true); \
              } \
            else \
              { \
                r = SparseBoolMatrix (m1_nr, m1_nc, m1.nnz () + m2.nnz ()); \
                r.cidx (0) = static_cast<octave_idx_type> (0); \
                octave_idx_type nel = 0; \
              for (octave_idx_type j = 0; j < m1_nc; j++) \
                  { \
                     octave_idx_type i1 = m1.cidx (j); \
                     octave_idx_type e1 = m1.cidx (j+1); \
                     octave_idx_type i2 = m2.cidx (j); \
                     octave_idx_type e2 = m2.cidx (j+1); \
                     while (i1 < e1 || i2 < e2) \
                       { \
                         if (i1 == e1 || (i2 < e2 && m1.ridx(i1) > m2.ridx(i2))) \
                           { \
                             if (C1 (Z1) OP C2 (m2.data (i2))) \
                               { \
                                 r.ridx (nel) = m2.ridx (i2); \
                                 r.data (nel++) = true; \
                               } \
                             i2++; \
                           } \
                         else if (i2 == e2 || m1.ridx(i1) < m2.ridx(i2)) \
                           { \
                             if (C1 (m1.data (i1)) OP C2 (Z2)) \
                               { \
                                 r.ridx (nel) = m1.ridx (i1); \
                                 r.data (nel++) = true; \
                               } \
                             i1++; \
                           } \
                         else \
                           { \
                             if (C1 (m1.data (i1)) OP C2 (m2.data (i2))) \
                               { \
                                 r.ridx (nel) = m1.ridx (i1); \
                                 r.data (nel++) = true; \
                               } \
                             i1++; \
                             i2++; \
                           } \
                       } \
                     r.cidx (j + 1) = nel; \
                  } \
                r.maybe_compress (false); \
              } \
        } \
      }           \
    else \
      { \
      if ((m1_nr != 0 || m1_nc != 0) && (m2_nr != 0 || m2_nc != 0)) \
        gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
      } \
    return r; \
  }

#define SPARSE_SMSM_CMP_OPS(M1, Z1, C1, M2, Z2, C2)  \
  SPARSE_SMSM_CMP_OP (mx_el_lt, <,  M1, Z1, C1, M2, Z2, C2) \
  SPARSE_SMSM_CMP_OP (mx_el_le, <=, M1, Z1, C1, M2, Z2, C2) \
  SPARSE_SMSM_CMP_OP (mx_el_ge, >=, M1, Z1, C1, M2, Z2, C2) \
  SPARSE_SMSM_CMP_OP (mx_el_gt, >,  M1, Z1, C1, M2, Z2, C2) \
  SPARSE_SMSM_CMP_OP (mx_el_eq, ==, M1, Z1,   , M2, Z2,   ) \
  SPARSE_SMSM_CMP_OP (mx_el_ne, !=, M1, Z1,   , M2, Z2,   )

#define SPARSE_SMSM_EQNE_OPS(M1, Z1, C1, M2, Z2, C2)  \
  SPARSE_SMSM_CMP_OP (mx_el_eq, ==, M1, Z1,   , M2, Z2,   ) \
  SPARSE_SMSM_CMP_OP (mx_el_ne, !=, M1, Z1,   , M2, Z2,   )

#define SPARSE_SMSM_BOOL_OP_DECLS(M1, M2, API) \
  SPARSE_BOOL_OP_DECL (mx_el_and, M1, M2, API); \
  SPARSE_BOOL_OP_DECL (mx_el_or,  M1, M2, API);

// FIXME -- this macro duplicatest the bodies of the template
// functions defined in the SPARSE_SSM_BOOL_OP and SPARSE_SMS_BOOL_OP
// macros.

#define SPARSE_SMSM_BOOL_OP(F, OP, M1, M2, LHS_ZERO, RHS_ZERO) \
  SparseBoolMatrix \
  F (const M1& m1, const M2& m2) \
  { \
    SparseBoolMatrix r; \
    \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
    \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
    \
    if (m1_nr == 1 && m1_nc == 1) \
      { \
      if (m2_nr > 0 && m2_nc > 0) \
        { \
          if ((m1.elem(0,0) != LHS_ZERO) OP RHS_ZERO) \
            { \
            r = SparseBoolMatrix (m2_nr, m2_nc, true); \
            for (octave_idx_type j = 0; j < m2_nc; j++) \
              for (octave_idx_type i = m2.cidx(j); i < m2.cidx(j+1); i++) \
                if (! ((m1.elem(0,0) != LHS_ZERO) OP (m2.data(i) != RHS_ZERO))) \
                  r.data (m2.ridx (i) + j * m2_nr) = false; \
            r.maybe_compress (true); \
            } \
          else \
            { \
            r = SparseBoolMatrix (m2_nr, m2_nc, m2.nnz ()); \
            r.cidx (0) = static_cast<octave_idx_type> (0); \
            octave_idx_type nel = 0; \
            for (octave_idx_type j = 0; j < m2_nc; j++) \
              { \
                for (octave_idx_type i = m2.cidx(j); i < m2.cidx(j+1); i++) \
                  if ((m1.elem(0,0) != LHS_ZERO) OP (m2.data(i) != RHS_ZERO)) \
                  { \
                    r.ridx (nel) = m2.ridx (i); \
                    r.data (nel++) = true; \
                  } \
                r.cidx (j + 1) = nel; \
              } \
            r.maybe_compress (false); \
            } \
        } \
      } \
    else if (m2_nr == 1 && m2_nc == 1) \
      { \
      if (m1_nr > 0 && m1_nc > 0) \
        { \
          if (LHS_ZERO OP (m2.elem(0,0) != RHS_ZERO)) \
            { \
            r = SparseBoolMatrix (m1_nr, m1_nc, true); \
            for (octave_idx_type j = 0; j < m1_nc; j++) \
              for (octave_idx_type i = m1.cidx(j); i < m1.cidx(j+1); i++) \
                if (! ((m1.data(i) != LHS_ZERO) OP (m2.elem(0,0) != RHS_ZERO))) \
                  r.data (m1.ridx (i) + j * m1_nr) = false; \
            r.maybe_compress (true); \
            } \
          else \
            { \
            r = SparseBoolMatrix (m1_nr, m1_nc, m1.nnz ()); \
            r.cidx (0) = static_cast<octave_idx_type> (0); \
            octave_idx_type nel = 0; \
            for (octave_idx_type j = 0; j < m1_nc; j++) \
              { \
                for (octave_idx_type i = m1.cidx(j); i < m1.cidx(j+1); i++) \
                  if ((m1.data(i) != LHS_ZERO) OP (m2.elem(0,0) != RHS_ZERO)) \
                  { \
                    r.ridx (nel) = m1.ridx (i); \
                    r.data (nel++) = true; \
                  } \
                r.cidx (j + 1) = nel; \
              } \
            r.maybe_compress (false); \
            } \
        } \
      } \
    else if (m1_nr == m2_nr && m1_nc == m2_nc) \
      { \
      if (m1_nr != 0 || m1_nc != 0) \
        { \
            r = SparseBoolMatrix (m1_nr, m1_nc, m1.nnz () + m2.nnz ()); \
            r.cidx (0) = static_cast<octave_idx_type> (0); \
            octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
              { \
                octave_idx_type i1 = m1.cidx (j); \
                octave_idx_type e1 = m1.cidx (j+1); \
                octave_idx_type i2 = m2.cidx (j); \
                octave_idx_type e2 = m2.cidx (j+1); \
                while (i1 < e1 || i2 < e2) \
                  { \
                    if (i1 == e1 || (i2 < e2 && m1.ridx(i1) > m2.ridx(i2))) \
                      { \
                        if (LHS_ZERO OP m2.data (i2) != RHS_ZERO) \
                          { \
                            r.ridx (nel) = m2.ridx (i2); \
                            r.data (nel++) = true; \
                          } \
                        i2++; \
                      } \
                    else if (i2 == e2 || m1.ridx(i1) < m2.ridx(i2)) \
                      { \
                        if (m1.data (i1) != LHS_ZERO OP RHS_ZERO) \
                          { \
                            r.ridx (nel) = m1.ridx (i1); \
                            r.data (nel++) = true; \
                          } \
                        i1++; \
                      } \
                    else \
                      { \
                        if (m1.data (i1) != LHS_ZERO OP m2.data(i2) != RHS_ZERO) \
                          { \
                            r.ridx (nel) = m1.ridx (i1); \
                            r.data (nel++) = true; \
                          } \
                        i1++; \
                        i2++; \
                      } \
                  } \
                r.cidx (j + 1) = nel; \
              } \
            r.maybe_compress (false); \
        } \
      }           \
    else \
      { \
      if ((m1_nr != 0 || m1_nc != 0) && (m2_nr != 0 || m2_nc != 0)) \
        gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
      } \
    return r; \
  }

#define SPARSE_SMSM_BOOL_OPS2(M1, M2, LHS_ZERO, RHS_ZERO) \
  SPARSE_SMSM_BOOL_OP (mx_el_and, &&, M1, M2, LHS_ZERO, RHS_ZERO) \
  SPARSE_SMSM_BOOL_OP (mx_el_or,  ||, M1, M2, LHS_ZERO, RHS_ZERO) \

#define SPARSE_SMSM_BOOL_OPS(M1, M2, ZERO) \
  SPARSE_SMSM_BOOL_OPS2(M1, M2, ZERO, ZERO)

#define SPARSE_SMSM_OP_DECLS(R1, R2, M1, M2, API) \
  SPARSE_SMSM_BIN_OP_DECLS (R1, R2, M1, M2, API) \
  SPARSE_SMSM_CMP_OP_DECLS (M1, M2, API) \
  SPARSE_SMSM_BOOL_OP_DECLS (M1, M2, API)

// matrix by matrix operations.

#define SPARSE_MSM_BIN_OP_DECLS(R1, R2, M1, M2, API)  \
  SPARSE_BIN_OP_DECL (R1, operator +, M1, M2, API); \
  SPARSE_BIN_OP_DECL (R1, operator -, M1, M2, API); \
  SPARSE_BIN_OP_DECL (R2, product,    M1, M2, API); \
  SPARSE_BIN_OP_DECL (R2, quotient,   M1, M2, API);

#define SPARSE_MSM_BIN_OP_1(R, F, OP, M1, M2)   \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m2_nr == 1 && m2_nc == 1) \
      r = R (m1 OP m2.elem(0,0)); \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
        r = R (m1_nr, m1_nc); \
        \
        for (octave_idx_type j = 0; j < m1_nc; j++) \
        for (octave_idx_type i = 0; i < m1_nr; i++) \
          r.elem (i, j) = m1.elem (i, j) OP m2.elem (i, j); \
      } \
    return r; \
  }

#define SPARSE_MSM_BIN_OP_2(R, F, OP, M1, M2, ZERO) \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m2_nr == 1 && m2_nc == 1) \
      r = R (m1 OP m2.elem(0,0)); \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
      /* Count num of non-zero elements */ \
      octave_idx_type nel = 0; \
      for (octave_idx_type j = 0; j < m1_nc; j++) \
        for (octave_idx_type i = 0; i < m1_nr; i++) \
          if ((m1.elem(i, j) OP m2.elem(i, j)) != ZERO) \
            nel++; \
      \
        r = R (m1_nr, m1_nc, nel); \
        \
      octave_idx_type ii = 0; \
      r.cidx (0) = 0; \
        for (octave_idx_type j = 0 ; j < m1_nc ; j++) \
          { \
          for (octave_idx_type i = 0 ; i < m1_nr ; i++)     \
            {     \
              if ((m1.elem(i, j) OP m2.elem(i, j)) != ZERO) \
              { \
                r.data (ii) = m1.elem(i, j) OP m2.elem(i,j); \
                r.ridx (ii++) = i; \
              } \
            } \
          r.cidx(j+1) = ii; \
        } \
      } \
 \
    return r; \
  }

// FIXME Pass a specific ZERO value
#define SPARSE_MSM_BIN_OPS(R1, R2, M1, M2) \
  SPARSE_MSM_BIN_OP_1 (R1, operator +,  +, M1, M2) \
  SPARSE_MSM_BIN_OP_1 (R1, operator -,  -, M1, M2) \
  SPARSE_MSM_BIN_OP_2 (R2, product,     *, M1, M2, 0.0) \
  SPARSE_MSM_BIN_OP_2 (R2, quotient,    /, M1, M2, 0.0)

#define SPARSE_MSM_CMP_OP_DECLS(M1, M2, API) \
  SPARSE_CMP_OP_DECL (mx_el_lt, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_le, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ge, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_gt, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_eq, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M1, M2, API);

#define SPARSE_MSM_EQNE_OP_DECLS(M1, M2, API) \
  SPARSE_CMP_OP_DECL (mx_el_eq, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M1, M2, API);

#define SPARSE_MSM_CMP_OP(F, OP, M1, C1, M2, C2)      \
  SparseBoolMatrix \
  F (const M1& m1, const M2& m2) \
  { \
    SparseBoolMatrix r; \
    \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
    \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
    \
    if (m2_nr == 1 && m2_nc == 1) \
      r = SparseBoolMatrix (F (m1, m2.elem(0,0))); \
    else if (m1_nr == m2_nr && m1_nc == m2_nc) \
      { \
      if (m1_nr != 0 || m1_nc != 0) \
        { \
          /* Count num of non-zero elements */ \
          octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            for (octave_idx_type i = 0; i < m1_nr; i++) \
            if (C1 (m1.elem(i, j)) OP C2 (m2.elem(i, j))) \
              nel++; \
            \
            r = SparseBoolMatrix (m1_nr, m1_nc, nel); \
            \
          octave_idx_type ii = 0; \
          r.cidx (0) = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            { \
              for (octave_idx_type i = 0; i < m1_nr; i++) \
              { \
                bool el = C1 (m1.elem(i, j)) OP C2 (m2.elem(i, j)); \
                if (el) \
                  { \
                  r.data(ii) = el; \
                  r.ridx(ii++) = i; \
                  } \
              } \
            r.cidx(j+1) = ii; \
            } \
        } \
      }           \
    else \
      { \
      if ((m1_nr != 0 || m1_nc != 0) && (m2_nr != 0 || m2_nc != 0)) \
        gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
      } \
    return r; \
  }

#define SPARSE_MSM_CMP_OPS(M1, Z1, C1, M2, Z2, C2)  \
  SPARSE_MSM_CMP_OP (mx_el_lt, <,  M1, C1, M2, C2) \
  SPARSE_MSM_CMP_OP (mx_el_le, <=, M1, C1, M2, C2) \
  SPARSE_MSM_CMP_OP (mx_el_ge, >=, M1, C1, M2, C2) \
  SPARSE_MSM_CMP_OP (mx_el_gt, >,  M1, C1, M2, C2) \
  SPARSE_MSM_CMP_OP (mx_el_eq, ==, M1,   , M2,   ) \
  SPARSE_MSM_CMP_OP (mx_el_ne, !=, M1,   , M2,   )

#define SPARSE_MSM_EQNE_OPS(M1, Z1, C1, M2, Z2, C2)  \
  SPARSE_MSM_CMP_OP (mx_el_eq, ==, M1,   , M2,   ) \
  SPARSE_MSM_CMP_OP (mx_el_ne, !=, M1,   , M2,   )

#define SPARSE_MSM_BOOL_OP_DECLS(M1, M2, API) \
  SPARSE_BOOL_OP_DECL (mx_el_and, M1, M2, API); \
  SPARSE_BOOL_OP_DECL (mx_el_or,  M1, M2, API);

#define SPARSE_MSM_BOOL_OP(F, OP, M1, M2, LHS_ZERO, RHS_ZERO) \
  SparseBoolMatrix \
  F (const M1& m1, const M2& m2) \
  { \
    SparseBoolMatrix r; \
    \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
    \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
    \
    if (m2_nr == 1 && m2_nc == 1) \
      r = SparseBoolMatrix  (F (m1, m2.elem(0,0))); \
    else if (m1_nr == m2_nr && m1_nc == m2_nc) \
      { \
      if (m1_nr != 0 || m1_nc != 0) \
        { \
          /* Count num of non-zero elements */ \
          octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            for (octave_idx_type i = 0; i < m1_nr; i++) \
            if ((m1.elem(i, j) != LHS_ZERO) \
                OP (m2.elem(i, j) != RHS_ZERO)) \
              nel++; \
            \
            r = SparseBoolMatrix (m1_nr, m1_nc, nel); \
            \
          octave_idx_type ii = 0; \
          r.cidx (0) = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            { \
              for (octave_idx_type i = 0; i < m1_nr; i++) \
              { \
                bool el = (m1.elem(i, j) != LHS_ZERO) \
                  OP (m2.elem(i, j) != RHS_ZERO);       \
                if (el) \
                  { \
                  r.data(ii) = el; \
                  r.ridx(ii++) = i; \
                  } \
              } \
            r.cidx(j+1) = ii; \
            } \
        } \
      }           \
    else \
      { \
      if ((m1_nr != 0 || m1_nc != 0) && (m2_nr != 0 || m2_nc != 0)) \
        gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
      } \
    return r; \
  }

#define SPARSE_MSM_BOOL_OPS2(M1, M2, LHS_ZERO, RHS_ZERO) \
  SPARSE_MSM_BOOL_OP (mx_el_and, &&, M1, M2, LHS_ZERO, RHS_ZERO) \
  SPARSE_MSM_BOOL_OP (mx_el_or,  ||, M1, M2, LHS_ZERO, RHS_ZERO) \

#define SPARSE_MSM_BOOL_OPS(M1, M2, ZERO) \
  SPARSE_MSM_BOOL_OPS2(M1, M2, ZERO, ZERO)

#define SPARSE_MSM_OP_DECLS(R1, R2, M1, M2, API) \
  SPARSE_MSM_BIN_OP_DECLS (R1, R2, M1, M2, API) \
  SPARSE_MSM_CMP_OP_DECLS (M1, M2, API) \
  SPARSE_MSM_BOOL_OP_DECLS (M1, M2, API)

// matrix by matrix operations.

#define SPARSE_SMM_BIN_OP_DECLS(R1, R2, M1, M2, API)  \
  SPARSE_BIN_OP_DECL (R1, operator +, M1, M2, API); \
  SPARSE_BIN_OP_DECL (R1, operator -, M1, M2, API); \
  SPARSE_BIN_OP_DECL (R2, product,    M1, M2, API); \
  SPARSE_BIN_OP_DECL (R2, quotient,   M1, M2, API);

#define SPARSE_SMM_BIN_OP_1(R, F, OP, M1, M2)   \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m1_nr == 1 && m1_nc == 1) \
      r = R (m1.elem(0,0) OP m2); \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
        r = R (m1_nr, m1_nc); \
        \
        for (octave_idx_type j = 0; j < m1_nc; j++) \
        for (octave_idx_type i = 0; i < m1_nr; i++) \
          r.elem (i, j) = m1.elem (i, j) OP m2.elem (i, j); \
      } \
    return r; \
  }

#define SPARSE_SMM_BIN_OP_2(R, F, OP, M1, M2, ZERO) \
  R \
  F (const M1& m1, const M2& m2) \
  { \
    R r; \
 \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
 \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
 \
    if (m1_nr == 1 && m1_nc == 1) \
      r = R (m1.elem(0,0) OP m2); \
    else if (m1_nr != m2_nr || m1_nc != m2_nc) \
      gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
    else \
      { \
      /* Count num of non-zero elements */ \
      octave_idx_type nel = 0; \
      for (octave_idx_type j = 0; j < m1_nc; j++) \
        for (octave_idx_type i = 0; i < m1_nr; i++) \
          if ((m1.elem(i, j) OP m2.elem(i, j)) != ZERO) \
            nel++; \
      \
        r = R (m1_nr, m1_nc, nel); \
        \
      octave_idx_type ii = 0; \
      r.cidx (0) = 0; \
        for (octave_idx_type j = 0 ; j < m1_nc ; j++) \
          { \
          for (octave_idx_type i = 0 ; i < m1_nr ; i++)     \
            {     \
              if ((m1.elem(i, j) OP m2.elem(i, j)) != ZERO) \
              { \
                r.data (ii) = m1.elem(i, j) OP m2.elem(i,j); \
                r.ridx (ii++) = i; \
              } \
            } \
          r.cidx(j+1) = ii; \
        } \
      } \
 \
    return r; \
  }

// FIXME Pass a specific ZERO value
#define SPARSE_SMM_BIN_OPS(R1, R2, M1, M2) \
  SPARSE_SMM_BIN_OP_1 (R1, operator +,  +, M1, M2) \
  SPARSE_SMM_BIN_OP_1 (R1, operator -,  -, M1, M2) \
  SPARSE_SMM_BIN_OP_2 (R2, product,     *, M1, M2, 0.0) \
  SPARSE_SMM_BIN_OP_2 (R2, quotient,    /, M1, M2, 0.0)

#define SPARSE_SMM_CMP_OP_DECLS(M1, M2, API) \
  SPARSE_CMP_OP_DECL (mx_el_lt, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_le, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ge, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_gt, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_eq, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M1, M2, API);

#define SPARSE_SMM_EQNE_OP_DECLS(M1, M2, API) \
  SPARSE_CMP_OP_DECL (mx_el_eq, M1, M2, API); \
  SPARSE_CMP_OP_DECL (mx_el_ne, M1, M2, API);

#define SPARSE_SMM_CMP_OP(F, OP, M1, C1, M2, C2)      \
  SparseBoolMatrix \
  F (const M1& m1, const M2& m2) \
  { \
    SparseBoolMatrix r; \
    \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
    \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
    \
    if (m1_nr == 1 && m1_nc == 1) \
      r = SparseBoolMatrix (F (m1.elem(0,0), m2)); \
    else if (m1_nr == m2_nr && m1_nc == m2_nc) \
      { \
      if (m1_nr != 0 || m1_nc != 0) \
        { \
          /* Count num of non-zero elements */ \
          octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            for (octave_idx_type i = 0; i < m1_nr; i++) \
            if (C1 (m1.elem(i, j)) OP C2 (m2.elem(i, j))) \
              nel++; \
            \
            r = SparseBoolMatrix (m1_nr, m1_nc, nel); \
            \
          octave_idx_type ii = 0; \
          r.cidx (0) = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            { \
              for (octave_idx_type i = 0; i < m1_nr; i++) \
              { \
                bool el = C1 (m1.elem(i, j)) OP C2 (m2.elem(i, j)); \
                if (el) \
                  { \
                  r.data(ii) = el; \
                  r.ridx(ii++) = i; \
                  } \
              } \
            r.cidx(j+1) = ii; \
            } \
        } \
      }           \
    else \
      { \
      if ((m1_nr != 0 || m1_nc != 0) && (m2_nr != 0 || m2_nc != 0)) \
        gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
      } \
    return r; \
  }

#define SPARSE_SMM_CMP_OPS(M1, Z1, C1, M2, Z2, C2)  \
  SPARSE_SMM_CMP_OP (mx_el_lt, <,  M1, C1, M2, C2) \
  SPARSE_SMM_CMP_OP (mx_el_le, <=, M1, C1, M2, C2) \
  SPARSE_SMM_CMP_OP (mx_el_ge, >=, M1, C1, M2, C2) \
  SPARSE_SMM_CMP_OP (mx_el_gt, >,  M1, C1, M2, C2) \
  SPARSE_SMM_CMP_OP (mx_el_eq, ==, M1,   , M2,   ) \
  SPARSE_SMM_CMP_OP (mx_el_ne, !=, M1,   , M2,   )

#define SPARSE_SMM_EQNE_OPS(M1, Z1, C1, M2, Z2, C2)  \
  SPARSE_SMM_CMP_OP (mx_el_eq, ==, M1,   , M2,   ) \
  SPARSE_SMM_CMP_OP (mx_el_ne, !=, M1,   , M2,   )

#define SPARSE_SMM_BOOL_OP_DECLS(M1, M2, API) \
  SPARSE_BOOL_OP_DECL (mx_el_and, M1, M2, API); \
  SPARSE_BOOL_OP_DECL (mx_el_or,  M1, M2, API);

#define SPARSE_SMM_BOOL_OP(F, OP, M1, M2, LHS_ZERO, RHS_ZERO) \
  SparseBoolMatrix \
  F (const M1& m1, const M2& m2) \
  { \
    SparseBoolMatrix r; \
    \
    octave_idx_type m1_nr = m1.rows (); \
    octave_idx_type m1_nc = m1.cols (); \
    \
    octave_idx_type m2_nr = m2.rows (); \
    octave_idx_type m2_nc = m2.cols (); \
    \
    if (m1_nr == 1 && m1_nc == 1) \
      r = SparseBoolMatrix (F (m1.elem(0,0), m2)); \
    else if (m1_nr == m2_nr && m1_nc == m2_nc) \
      { \
      if (m1_nr != 0 || m1_nc != 0) \
        { \
          /* Count num of non-zero elements */ \
          octave_idx_type nel = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            for (octave_idx_type i = 0; i < m1_nr; i++) \
            if ((m1.elem(i, j) != LHS_ZERO) \
                OP (m2.elem(i, j) != RHS_ZERO)) \
              nel++; \
            \
            r = SparseBoolMatrix (m1_nr, m1_nc, nel); \
            \
          octave_idx_type ii = 0; \
          r.cidx (0) = 0; \
          for (octave_idx_type j = 0; j < m1_nc; j++) \
            { \
              for (octave_idx_type i = 0; i < m1_nr; i++) \
              { \
                bool el = (m1.elem(i, j) != LHS_ZERO) \
                  OP (m2.elem(i, j) != RHS_ZERO);       \
                if (el) \
                  { \
                  r.data(ii) = el; \
                  r.ridx(ii++) = i; \
                  } \
              } \
            r.cidx(j+1) = ii; \
            } \
        } \
      }           \
    else \
      { \
      if ((m1_nr != 0 || m1_nc != 0) && (m2_nr != 0 || m2_nc != 0)) \
        gripe_nonconformant (#F, m1_nr, m1_nc, m2_nr, m2_nc); \
      } \
    return r; \
  }

#define SPARSE_SMM_BOOL_OPS2(M1, M2, LHS_ZERO, RHS_ZERO) \
  SPARSE_SMM_BOOL_OP (mx_el_and, &&, M1, M2, LHS_ZERO, RHS_ZERO) \
  SPARSE_SMM_BOOL_OP (mx_el_or,  ||, M1, M2, LHS_ZERO, RHS_ZERO) \

#define SPARSE_SMM_BOOL_OPS(M1, M2, ZERO) \
  SPARSE_SMM_BOOL_OPS2(M1, M2, ZERO, ZERO)

#define SPARSE_SMM_OP_DECLS(R1, R2, M1, M2, API) \
  SPARSE_SMM_BIN_OP_DECLS (R1, R2, M1, M2, API) \
  SPARSE_SMM_CMP_OP_DECLS (M1, M2, API) \
  SPARSE_SMM_BOOL_OP_DECLS (M1, M2, API)

// Avoid some code duplication.  Maybe we should use templates.

#define SPARSE_CUMSUM(RET_TYPE, ELT_TYPE, FCN)  \
 \
  octave_idx_type nr = rows (); \
  octave_idx_type nc = cols (); \
 \
  RET_TYPE retval; \
 \
  if (nr > 0 && nc > 0) \
    { \
      if ((nr == 1 && dim == -1) || dim == 1) \
      /* Ugly!! Is there a better way? */ \
        retval = transpose (). FCN (0) .transpose (); \
      else \
      { \
          octave_idx_type nel = 0; \
        for (octave_idx_type i = 0; i < nc; i++) \
            { \
              ELT_TYPE t = ELT_TYPE (); \
            for (octave_idx_type j = cidx (i); j < cidx (i+1); j++)     \
                { \
                  t += data(j); \
                  if (t != ELT_TYPE ()) \
                { \
                      if (j == cidx(i+1) - 1) \
                  nel += nr - ridx(j);  \
                  else \
                  nel += ridx(j+1) - ridx(j); \
                } \
                } \
          } \
        retval = RET_TYPE (nr, nc, nel); \
          retval.cidx(0) = 0; \
        octave_idx_type ii = 0; \
        for (octave_idx_type i = 0; i < nc; i++) \
            { \
              ELT_TYPE t = ELT_TYPE (); \
            for (octave_idx_type j = cidx (i); j < cidx (i+1); j++)     \
                { \
                  t += data(j); \
                  if (t != ELT_TYPE ()) \
                    { \
                      if (j == cidx(i+1) - 1) \
                        { \
                          for (octave_idx_type k = ridx(j); k < nr; k++) \
                            { \
                               retval.data (ii) = t; \
                               retval.ridx (ii++) = k; \
                            } \
                        } \
                  else \
                  { \
                          for (octave_idx_type k = ridx(j); k < ridx(j+1); k++) \
                            { \
                               retval.data (ii) = t; \
                               retval.ridx (ii++) = k; \
                            } \
                        } \
                    } \
                } \
              retval.cidx(i+1) = ii; \
          } \
      } \
    } \
  else \
    retval = RET_TYPE (nr,nc); \
 \
  return retval


#define SPARSE_CUMPROD(RET_TYPE, ELT_TYPE, FCN) \
 \
  octave_idx_type nr = rows (); \
  octave_idx_type nc = cols (); \
 \
  RET_TYPE retval; \
 \
  if (nr > 0 && nc > 0) \
    { \
      if ((nr == 1 && dim == -1) || dim == 1) \
      /* Ugly!! Is there a better way? */ \
        retval = transpose (). FCN (0) .transpose (); \
      else \
      { \
          octave_idx_type nel = 0; \
        for (octave_idx_type i = 0; i < nc; i++) \
            { \
            octave_idx_type jj = 0; \
            for (octave_idx_type j = cidx (i); j < cidx (i+1); j++) \
                { \
              if (jj == ridx(j)) \
                    { \
                      nel++; \
                      jj++; \
                    } \
                  else \
                    break; \
                } \
          } \
        retval = RET_TYPE (nr, nc, nel); \
          retval.cidx(0) = 0; \
        octave_idx_type ii = 0; \
        for (octave_idx_type i = 0; i < nc; i++) \
            { \
              ELT_TYPE t = ELT_TYPE (1.); \
            octave_idx_type jj = 0; \
            for (octave_idx_type j = cidx (i); j < cidx (i+1); j++) \
                { \
              if (jj == ridx(j)) \
                    { \
                      t *= data(j); \
                      retval.data(ii) = t; \
                      retval.ridx(ii++) = jj++; \
                    } \
                  else \
                    break; \
                } \
              retval.cidx(i+1) = ii; \
          } \
      } \
    } \
  else \
    retval = RET_TYPE (nr,nc); \
 \
  return retval

#define SPARSE_BASE_REDUCTION_OP(RET_TYPE, EL_TYPE, ROW_EXPR, COL_EXPR, \
                           INIT_VAL, MT_RESULT) \
 \
  octave_idx_type nr = rows (); \
  octave_idx_type nc = cols (); \
 \
  RET_TYPE retval; \
 \
  if (nr > 0 && nc > 0) \
    { \
      if ((nr == 1 && dim == -1) || dim == 1) \
      { \
          /* Define j here to allow fancy definition for prod method */ \
          octave_idx_type j = 0; \
        OCTAVE_LOCAL_BUFFER (EL_TYPE, tmp, nr); \
          \
        for (octave_idx_type i = 0; i < nr; i++) \
          tmp[i] = INIT_VAL; \
        for (j = 0; j < nc; j++) \
            { \
            for (octave_idx_type i = cidx(j); i < cidx(j + 1); i++) \
                { \
                ROW_EXPR; \
                } \
          } \
        octave_idx_type nel = 0; \
        for (octave_idx_type i = 0; i < nr; i++) \
          if (tmp[i] != EL_TYPE ())  \
            nel++ ; \
        retval = RET_TYPE (nr, static_cast<octave_idx_type> (1), nel); \
        retval.cidx(0) = 0; \
        retval.cidx(1) = nel; \
        nel = 0; \
        for (octave_idx_type i = 0; i < nr; i++) \
          if (tmp[i] != EL_TYPE ())  \
            { \
            retval.data(nel) = tmp[i]; \
            retval.ridx(nel++) = i; \
            } \
      } \
      else \
      { \
        OCTAVE_LOCAL_BUFFER (EL_TYPE, tmp, nc); \
          \
        for (octave_idx_type j = 0; j < nc; j++) \
          { \
            tmp[j] = INIT_VAL; \
            for (octave_idx_type i = cidx(j); i < cidx(j + 1); i++) \
                { \
              COL_EXPR; \
                } \
          } \
        octave_idx_type nel = 0; \
        for (octave_idx_type i = 0; i < nc; i++) \
          if (tmp[i] != EL_TYPE ())  \
            nel++ ; \
        retval = RET_TYPE (static_cast<octave_idx_type> (1), nc, nel); \
        retval.cidx(0) = 0; \
        nel = 0; \
        for (octave_idx_type i = 0; i < nc; i++) \
          if (tmp[i] != EL_TYPE ())  \
            { \
            retval.data(nel) = tmp[i]; \
            retval.ridx(nel++) = 0; \
            retval.cidx(i+1) = retval.cidx(i) + 1; \
            } \
          else \
            retval.cidx(i+1) = retval.cidx(i); \
      } \
    } \
  else if (nc == 0 && (nr == 0 || (nr == 1 && dim == -1))) \
    { \
      if (MT_RESULT) \
        { \
          retval = RET_TYPE (static_cast<octave_idx_type> (1), \
                             static_cast<octave_idx_type> (1), \
                             static_cast<octave_idx_type> (1)); \
          retval.cidx(0) = 0; \
          retval.cidx(1) = 1; \
          retval.ridx(0) = 0; \
          retval.data(0) = MT_RESULT; \
        } \
      else \
          retval = RET_TYPE (static_cast<octave_idx_type> (1), \
                             static_cast<octave_idx_type> (1), \
                             static_cast<octave_idx_type> (0)); \
    } \
  else if (nr == 0 && (dim == 0 || dim == -1)) \
    { \
      if (MT_RESULT) \
        { \
          retval = RET_TYPE (static_cast<octave_idx_type> (1), nc, nc); \
          retval.cidx (0) = 0; \
          for (octave_idx_type i = 0; i < nc ; i++) \
            { \
              retval.ridx (i) = 0; \
              retval.cidx (i+1) = i; \
            retval.data (i) = MT_RESULT; \
          } \
        } \
      else \
        retval = RET_TYPE (static_cast<octave_idx_type> (1), nc, \
                     static_cast<octave_idx_type> (0)); \
    } \
  else if (nc == 0 && dim == 1) \
    { \
      if (MT_RESULT) \
        { \
          retval = RET_TYPE (nr, static_cast<octave_idx_type> (1), nr); \
          retval.cidx(0) = 0; \
          retval.cidx(1) = nr; \
          for (octave_idx_type i = 0; i < nr; i++) \
          { \
            retval.ridx(i) = i; \
            retval.data(i) = MT_RESULT; \
          } \
        } \
      else \
        retval = RET_TYPE (nr, static_cast<octave_idx_type> (1), \
                     static_cast<octave_idx_type> (0)); \
    } \
  else \
    retval.resize (nr > 0, nc > 0); \
 \
  return retval

#define SPARSE_REDUCTION_OP_ROW_EXPR(OP) \
  tmp[ridx(i)] OP data (i)

#define SPARSE_REDUCTION_OP_COL_EXPR(OP) \
  tmp[j] OP data (i)

#define SPARSE_REDUCTION_OP(RET_TYPE, EL_TYPE, OP, INIT_VAL, MT_RESULT) \
  SPARSE_BASE_REDUCTION_OP (RET_TYPE, EL_TYPE, \
                  SPARSE_REDUCTION_OP_ROW_EXPR (OP), \
                  SPARSE_REDUCTION_OP_COL_EXPR (OP), \
                  INIT_VAL, MT_RESULT)


// Don't break from this loop if the test succeeds because
// we are looping over the rows and not the columns in the inner
// loop.
#define SPARSE_ANY_ALL_OP_ROW_CODE(TEST_OP, TEST_TRUE_VAL) \
  if (data (i) TEST_OP 0.0) \
    tmp[ridx(i)] = TEST_TRUE_VAL; \

#define SPARSE_ANY_ALL_OP_COL_CODE(TEST_OP, TEST_TRUE_VAL) \
  if (data (i) TEST_OP 0.0) \
    { \
      tmp[j] = TEST_TRUE_VAL; \
      break; \
    }

#define SPARSE_ANY_ALL_OP(DIM, INIT_VAL, MT_RESULT, TEST_OP, TEST_TRUE_VAL) \
  SPARSE_BASE_REDUCTION_OP (SparseBoolMatrix, char, \
                  SPARSE_ANY_ALL_OP_ROW_CODE (TEST_OP, TEST_TRUE_VAL), \
                  SPARSE_ANY_ALL_OP_COL_CODE (TEST_OP, TEST_TRUE_VAL), \
                  INIT_VAL, MT_RESULT)

#define SPARSE_ALL_OP(DIM) \
  if ((rows() == 1 && dim == -1) || dim == 1) \
    return transpose (). all (0). transpose(); \
  else \
    { \
      SPARSE_ANY_ALL_OP (DIM, (cidx(j+1) - cidx(j) < nc ? false : true), \
                   true, ==, false); \
    }

#define SPARSE_ANY_OP(DIM) SPARSE_ANY_ALL_OP (DIM, false, false, !=, true)

#define SPARSE_SPARSE_MUL( RET_TYPE, RET_EL_TYPE, EL_TYPE ) \
  octave_idx_type nr = m.rows (); \
  octave_idx_type nc = m.cols (); \
  \
  octave_idx_type a_nr = a.rows (); \
  octave_idx_type a_nc = a.cols (); \
  \
  if (nr == 1 && nc == 1) \
   { \
     RET_EL_TYPE s = m.elem(0,0); \
     octave_idx_type nz = a.nnz(); \
     RET_TYPE r (a_nr, a_nc, nz); \
     \
     for (octave_idx_type i = 0; i < nz; i++) \
       { \
         OCTAVE_QUIT; \
       r.data(i) = s * a.data(i); \
       r.ridx(i) = a.ridx(i); \
       } \
     for (octave_idx_type i = 0; i < a_nc + 1; i++) \
       { \
         OCTAVE_QUIT; \
         r.cidx(i) = a.cidx(i); \
       } \
     \
     r.maybe_compress (true); \
     return r; \
   } \
  else if (a_nr == 1 && a_nc == 1) \
   { \
     RET_EL_TYPE s = a.elem(0,0); \
     octave_idx_type nz = m.nnz(); \
     RET_TYPE r (nr, nc, nz); \
     \
     for (octave_idx_type i = 0; i < nz; i++) \
       { \
         OCTAVE_QUIT; \
       r.data(i) = m.data(i) * s; \
       r.ridx(i) = m.ridx(i); \
       } \
     for (octave_idx_type i = 0; i < nc + 1; i++) \
       { \
         OCTAVE_QUIT; \
         r.cidx(i) = m.cidx(i); \
       } \
     \
     r.maybe_compress (true); \
     return r; \
   } \
  else if (nc != a_nr) \
    { \
      gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); \
      return RET_TYPE (); \
    } \
  else \
    { \
      OCTAVE_LOCAL_BUFFER (octave_idx_type, w, nr); \
      RET_TYPE retval (nr, a_nc, static_cast<octave_idx_type> (0)); \
      for (octave_idx_type i = 0; i < nr; i++) \
      w[i] = 0; \
      retval.xcidx(0) = 0; \
      \
      octave_idx_type nel = 0; \
      \
      for (octave_idx_type i = 0; i < a_nc; i++) \
        { \
          for (octave_idx_type j = a.cidx(i); j < a.cidx(i+1); j++) \
            { \
              octave_idx_type  col = a.ridx(j); \
              for (octave_idx_type k = m.cidx(col) ; k < m.cidx(col+1); k++) \
            { \
              if (w[m.ridx(k)] < i + 1) \
                    { \
                  w[m.ridx(k)] = i + 1; \
                  nel++; \
                } \
                OCTAVE_QUIT; \
            } \
          } \
          retval.xcidx(i+1) = nel; \
      } \
      \
      if (nel == 0) \
      return RET_TYPE (nr, a_nc); \
      else \
      {  \
          for (octave_idx_type i = 0; i < nr; i++) \
          w[i] = 0; \
        \
          OCTAVE_LOCAL_BUFFER (RET_EL_TYPE, Xcol, nr); \
          \
        retval.change_capacity (nel); \
        /* The optimal break-point as estimated from simulations */ \
        /* Note that Mergesort is O(nz log(nz)) while searching all */ \
        /* values is O(nr), where nz here is non-zero per row of */ \
        /* length nr. The test itself was then derived from the */ \
        /* simulation with random square matrices and the observation */ \
        /* of the number of non-zero elements in the output matrix */ \
        /* it was found that the breakpoints were */ \
        /*   nr: 500  1000  2000  5000 10000 */ \
        /*   nz:   6    25    97   585  2202 */ \
        /* The below is a simplication of the 'polyfit'-ed parameters */ \
        /* to these breakpoints */ \
          octave_idx_type n_per_col = (a_nc > 43000 ? 43000 : \
                              (a_nc * a_nc) / 43000); \
        octave_idx_type ii = 0; \
        octave_idx_type *ri = retval.xridx(); \
        octave_sort<octave_idx_type> sort; \
        \
        for (octave_idx_type i = 0; i < a_nc ; i++) \
          { \
            if (retval.xcidx(i+1) - retval.xcidx(i) > n_per_col) \
            { \
              for (octave_idx_type j = a.cidx(i); j < a.cidx(i+1); j++) \
                { \
                  octave_idx_type col = a.ridx(j); \
                  EL_TYPE tmpval = a.data(j); \
                  for (octave_idx_type k = m.cidx(col) ; \
                     k < m.cidx(col+1); k++) \
                  { \
                    OCTAVE_QUIT; \
                    octave_idx_type row = m.ridx(k); \
                    if (w[row] < i + 1) \
                      { \
                        w[row] = i + 1; \
                        Xcol[row] = tmpval * m.data(k); \
                      } \
                    else \
                      Xcol[row] += tmpval * m.data(k); \
                  } \
                } \
              for (octave_idx_type k = 0; k < nr; k++) \
                if (w[k] == i + 1) \
                  { \
                    retval.xdata(ii) = Xcol[k]; \
                    retval.xridx(ii++) = k; \
                  } \
            } \
            else \
            { \
              for (octave_idx_type j = a.cidx(i); j < a.cidx(i+1); j++) \
                { \
                  octave_idx_type col = a.ridx(j); \
                  EL_TYPE tmpval = a.data(j); \
                  for (octave_idx_type k = m.cidx(col) ; \
                    k < m.cidx(col+1); k++) \
                  { \
                    OCTAVE_QUIT; \
                    octave_idx_type row = m.ridx(k); \
                    if (w[row] < i + 1) \
                      { \
                        w[row] = i + 1; \
                        retval.xridx(ii++) = row;\
                        Xcol[row] = tmpval * m.data(k); \
                      } \
                    else \
                      Xcol[row] += tmpval * m.data(k); \
                  } \
                } \
              sort.sort (ri + retval.xcidx(i), ii - retval.xcidx(i)); \
                for (octave_idx_type k = retval.xcidx(i); k < ii; k++) \
                retval.xdata(k) = Xcol[retval.xridx(k)]; \
            }  \
          } \
        retval.maybe_compress (true);\
        return retval; \
      } \
    }

#define SPARSE_FULL_MUL( RET_TYPE, EL_TYPE, ZERO ) \
  octave_idx_type nr = m.rows (); \
  octave_idx_type nc = m.cols (); \
  \
  octave_idx_type a_nr = a.rows (); \
  octave_idx_type a_nc = a.cols (); \
  \
  if (nr == 1 && nc == 1) \
    { \
      RET_TYPE retval = m.elem (0,0) * a; \
      return retval; \
    } \
  else if (nc != a_nr) \
    { \
      gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); \
      return RET_TYPE (); \
    } \
  else \
    { \
      RET_TYPE retval (nr, a_nc, ZERO); \
      \
      for (octave_idx_type i = 0; i < a_nc ; i++) \
        { \
          for (octave_idx_type j = 0; j < a_nr; j++) \
            { \
              OCTAVE_QUIT; \
              \
              EL_TYPE tmpval = a.elem(j,i); \
              for (octave_idx_type k = m.cidx(j) ; k < m.cidx(j+1); k++) \
                retval.elem (m.ridx(k),i) += tmpval * m.data(k); \
            } \
        } \
      return retval; \
    }

#define SPARSE_FULL_TRANS_MUL( RET_TYPE, EL_TYPE, ZERO, CONJ_OP ) \
  octave_idx_type nr = m.rows (); \
  octave_idx_type nc = m.cols (); \
  \
  octave_idx_type a_nr = a.rows (); \
  octave_idx_type a_nc = a.cols (); \
  \
  if (nr == 1 && nc == 1) \
    { \
      RET_TYPE retval = CONJ_OP (m.elem(0,0)) * a; \
      return retval; \
    } \
  else if (nr != a_nr) \
    { \
      gripe_nonconformant ("operator *", nc, nr, a_nr, a_nc); \
      return RET_TYPE (); \
    } \
  else \
    { \
      RET_TYPE retval (nc, a_nc); \
      \
      for (octave_idx_type i = 0; i < a_nc ; i++) \
        { \
          for (octave_idx_type j = 0; j < nc; j++) \
            { \
              OCTAVE_QUIT; \
              \
              EL_TYPE acc = ZERO; \
              for (octave_idx_type k = m.cidx(j) ; k < m.cidx(j+1); k++) \
                acc += a.elem (m.ridx(k),i) * CONJ_OP (m.data(k)); \
              retval.xelem (j,i) = acc; \
            } \
        } \
      return retval; \
    }

#define FULL_SPARSE_MUL( RET_TYPE, EL_TYPE, ZERO ) \
  octave_idx_type nr = m.rows (); \
  octave_idx_type nc = m.cols (); \
  \
  octave_idx_type a_nr = a.rows (); \
  octave_idx_type a_nc = a.cols (); \
  \
  if (a_nr == 1 && a_nc == 1) \
    { \
      RET_TYPE retval = m * a.elem (0,0); \
      return retval; \
    } \
  else if (nc != a_nr) \
    { \
      gripe_nonconformant ("operator *", nr, nc, a_nr, a_nc); \
      return RET_TYPE (); \
    } \
  else \
    { \
      RET_TYPE retval (nr, a_nc, ZERO); \
      \
      for (octave_idx_type i = 0; i < a_nc ; i++) \
        { \
          OCTAVE_QUIT; \
          for (octave_idx_type j = a.cidx(i); j < a.cidx(i+1); j++) \
            { \
              octave_idx_type col = a.ridx(j); \
              EL_TYPE tmpval = a.data(j); \
              \
              for (octave_idx_type k = 0 ; k < nr; k++) \
                retval.xelem (k,i) += tmpval * m.elem(k,col); \
            } \
        } \
      return retval; \
    }

#define FULL_SPARSE_MUL_TRANS( RET_TYPE, EL_TYPE, ZERO, CONJ_OP ) \
  octave_idx_type nr = m.rows (); \
  octave_idx_type nc = m.cols (); \
  \
  octave_idx_type a_nr = a.rows (); \
  octave_idx_type a_nc = a.cols (); \
  \
  if (a_nr == 1 && a_nc == 1) \
    { \
      RET_TYPE retval = m * CONJ_OP (a.elem(0,0)); \
      return retval; \
    } \
  else if (nc != a_nc) \
    { \
      gripe_nonconformant ("operator *", nr, nc, a_nc, a_nr); \
      return RET_TYPE (); \
    } \
  else \
    { \
      RET_TYPE retval (nr, a_nr, ZERO); \
      \
      for (octave_idx_type i = 0; i < a_nc ; i++) \
        { \
          OCTAVE_QUIT; \
          for (octave_idx_type j = a.cidx(i); j < a.cidx(i+1); j++) \
            { \
              octave_idx_type col = a.ridx(j); \
              EL_TYPE tmpval = CONJ_OP (a.data(j)); \
              for (octave_idx_type k = 0 ; k < nr; k++) \
                retval.xelem (k,col) += tmpval * m.elem(k,i); \
            } \
        } \
      return retval; \
    }

#endif

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

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