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/* ========================================================================== */
/* === UMF_transpose ======================================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Version 4.1 (Apr. 30, 2003), Copyright (c) 2003 by Timothy A. */
/* Davis. All Rights Reserved. See ../README for License. */
/* email: davis@cise.ufl.edu CISE Department, Univ. of Florida. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* -------------------------------------------------------------------------- */
/* Not user-callable. Computes a permuted transpose, R = (A (P,Q(1:nq)))' in
MATLAB notation, where R is in column-form. A is n_row-by-n_col, the
row-form matrix R is n_row-by-nq, where nq <= n_col. A may be singular.
The complex version can do transpose (') or array transpose (.').
Uses Gustavson's method (Two Fast Algorithms for Sparse Matrices:
Multiplication and Permuted Transposition, ACM Trans. on Math. Softw.,
vol 4, no 3, pp. 250-269).
*/
#include "umf_internal.h"
#include "umf_is_permutation.h"
GLOBAL Int UMF_transpose
(
Int n_row, /* A is n_row-by-n_col */
Int n_col,
const Int Ap [ ], /* size n_col+1 */
const Int Ai [ ], /* size nz = Ap [n_col] */
const double Ax [ ], /* size nz if present */
const Int P [ ], /* P [k] = i means original row i is kth row in A(P,Q)*/
/* P is identity if not present */
/* size n_row, if present */
const Int Q [ ], /* Q [k] = j means original col j is kth col in A(P,Q)*/
/* Q is identity if not present */
/* size nq, if present */
Int nq, /* size of Q, ignored if Q is (Int *) NULL */
/* output matrix: Rp, Ri, Rx, and Rz: */
Int Rp [ ], /* size n_row+1 */
Int Ri [ ], /* size nz */
double Rx [ ], /* size nz, if present */
Int W [ ], /* size max (n_row,n_col) workspace */
Int check /* if true, then check inputs */
#ifdef COMPLEX
, const double Az [ ] /* size nz */
, double Rz [ ] /* size nz */
, Int do_conjugate /* if true, then do conjugate transpose */
/* otherwise, do array transpose */
#endif
)
{
/* ---------------------------------------------------------------------- */
/* local variables */
/* ---------------------------------------------------------------------- */
Int i, j, k, p, bp, newj, do_values ;
/* ---------------------------------------------------------------------- */
/* check inputs */
/* ---------------------------------------------------------------------- */
#ifndef NDEBUG
Int nz ;
ASSERT (n_col >= 0) ;
nz = (Ap != (Int *) NULL) ? Ap [n_col] : 0 ;
DEBUG2 (("UMF_transpose: "ID"-by-"ID" nz "ID"\n", n_row, n_col, nz)) ;
#endif
if (check)
{
/* UMFPACK_symbolic skips this check */
/* UMFPACK_transpose always does this check */
if (!Ai || !Ap || !Ri || !Rp || !W)
{
return (UMFPACK_ERROR_argument_missing) ;
}
if (n_row <= 0 || n_col <= 0) /* n_row,n_col must be > 0 */
{
return (UMFPACK_ERROR_n_nonpositive) ;
}
if (!UMF_is_permutation (P, W, n_row, n_row) ||
!UMF_is_permutation (Q, W, nq, nq))
{
return (UMFPACK_ERROR_invalid_permutation) ;
}
if (!AMD_valid (n_row, n_col, Ap, Ai))
{
return (UMFPACK_ERROR_invalid_matrix) ;
}
}
#ifndef NDEBUG
DEBUG2 (("UMF_transpose, input matrix:\n")) ;
UMF_dump_col_matrix (Ax,
#ifdef COMPLEX
Az,
#endif
Ai, Ap, n_row, n_col, nz) ;
#endif
/* ---------------------------------------------------------------------- */
/* count the entries in each row of A */
/* ---------------------------------------------------------------------- */
/* use W as workspace for RowCount */
for (i = 0 ; i < n_row ; i++)
{
W [i] = 0 ;
Rp [i] = 0 ;
}
if (Q != (Int *) NULL)
{
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
i = Ai [p] ;
ASSERT (i >= 0 && i < n_row) ;
W [i]++ ;
}
}
}
else
{
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
i = Ai [p] ;
ASSERT (i >= 0 && i < n_row) ;
W [i]++ ;
}
}
}
/* ---------------------------------------------------------------------- */
/* compute the row pointers for R = A (P,Q) */
/* ---------------------------------------------------------------------- */
if (P != (Int *) NULL)
{
Rp [0] = 0 ;
for (k = 0 ; k < n_row ; k++)
{
i = P [k] ;
ASSERT (i >= 0 && i < n_row) ;
Rp [k+1] = Rp [k] + W [i] ;
}
for (k = 0 ; k < n_row ; k++)
{
i = P [k] ;
ASSERT (i >= 0 && i < n_row) ;
W [i] = Rp [k] ;
}
}
else
{
Rp [0] = 0 ;
for (i = 0 ; i < n_row ; i++)
{
Rp [i+1] = Rp [i] + W [i] ;
}
for (i = 0 ; i < n_row ; i++)
{
W [i] = Rp [i] ;
}
}
ASSERT (Rp [n_row] <= Ap [n_col]) ;
/* at this point, W holds the permuted row pointers */
/* ---------------------------------------------------------------------- */
/* construct the row form of B */
/* ---------------------------------------------------------------------- */
do_values = Ax && Rx ;
#ifdef COMPLEX
do_values = do_values && Az && Rz ;
#endif
#ifdef COMPLEX
if (do_conjugate && do_values)
{
if (Q != (Int *) NULL)
{
/* R = A (P,Q)' */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = newj ;
Rx [bp] = Ax [p] ;
Rz [bp] = -Az [p] ;
}
}
}
else
{
/* R = A (P,:)' */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = j ;
Rx [bp] = Ax [p] ;
Rz [bp] = -Az [p] ;
}
}
}
}
else
#endif
{
if (Q != (Int *) NULL)
{
if (do_values)
{
/* R = A (P,Q).' */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = newj ;
Rx [bp] = Ax [p] ;
#ifdef COMPLEX
Rz [bp] = Az [p] ;
#endif
}
}
}
else
{
/* R = pattern of A (P,Q).' */
for (newj = 0 ; newj < nq ; newj++)
{
j = Q [newj] ;
ASSERT (j >= 0 && j < n_col) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
Ri [W [Ai [p]]++] = newj ;
}
}
}
}
else
{
if (do_values)
{
/* R = A (P,:).' */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
bp = W [Ai [p]]++ ;
Ri [bp] = j ;
Rx [bp] = Ax [p] ;
#ifdef COMPLEX
Rz [bp] = Az [p] ;
#endif
}
}
}
else
{
/* R = pattern of A (P,:).' */
for (j = 0 ; j < n_col ; j++)
{
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
Ri [W [Ai [p]]++] = j ;
}
}
}
}
}
#ifndef NDEBUG
for (k = 0 ; k < n_row ; k++)
{
if (P != (Int *) NULL)
{
i = P [k] ;
}
else
{
i = k ;
}
DEBUG3 ((ID": W[i] "ID" Rp[k+1] "ID"\n", i, W [i], Rp [k+1])) ;
ASSERT (W [i] == Rp [k+1]) ;
}
DEBUG2 (("UMF_transpose, output matrix:\n")) ;
UMF_dump_col_matrix (Rx,
#ifdef COMPLEX
Rz,
#endif
Ri, Rp, n_col, n_row, Rp [n_row]) ;
ASSERT (AMD_valid (n_col, n_row, Rp, Ri)) ;
#endif
return (UMFPACK_OK) ;
}
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