[n,x,y,nelt,ia,ja,a,isym]=ssmtv(n,x,y,nelt,ia,ja,a,isym);

function [n,x,y,nelt,ia,ja,a,isym]=ssmtv(n,x,y,nelt,ia,ja,a,isym);
%***BEGIN PROLOGUE  SSMTV
%***PURPOSE  SLAP Column Format Sparse Matrix Transpose Vector Product.
%            Routine to calculate the sparse matrix vector product:
%            Y = A'*X, where ' denotes transpose.
%***LIBRARY   SLATEC (SLAP)
%***CATEGORY  D1B4
%***TYPE      SINGLE PRECISION (SSMTV-S, DSMTV-D)
%***KEYWORDS  MATRIX TRANSPOSE VECTOR MULTIPLY, SLAP, SPARSE
%***AUTHOR  Greenbaum, Anne, (Courant Institute)
%           Seager, Mark K., (LLNL)
%             Lawrence Livermore National Laboratory
%             PO BOX 808, L-60
%             Livermore, CA 94550 [phone]
%             [e-mail]
%***DESCRIPTION
%
% *Usage:
%     INTEGER  N, NELT, IA(NELT), JA(NELT), ISYM
%     REAL     X(N), Y(N), A(NELT)
%
%     CALL SSMTV(N, X, Y, NELT, IA, JA, A, ISYM )
%
% *Arguments:
% N      :IN       Integer.
%         Order of the Matrix.
% X      :IN       Real X(N).
%         The vector that should be multiplied by the transpose of
%         the matrix.
% Y      :OUT      Real Y(N).
%         The product of the transpose of the matrix and the vector.
% NELT   :IN       Integer.
%         Number of Non-Zeros stored in A.
% IA     :IN       Integer IA(NELT).
% JA     :IN       Integer JA(NELT).
% A      :IN       Real A(NELT).
%         These arrays should hold the matrix A in the SLAP Column
%         format.  See 'Description', below.
% ISYM   :IN       Integer.
%         Flag to indicate symmetric storage format.
%         If ISYM=0, all non-zero entries of the matrix are stored.
%         If ISYM=1, the matrix is symmetric, and only the upper
%         or lower triangle of the matrix is stored.
%
% *Description
%       =================== S L A P Column format ==================
%       This routine  requires that  the matrix A  be stored in  the
%       SLAP Column format.  In this format the non-zeros are stored
%       counting down columns (except for  the diagonal entry, which
%       must appear first in each  'column')  and are stored  in the
%       real array A.  In other words, for each column in the matrix
%       put the diagonal entry in A.  Then put in the other non-zero
%       elements going down   the  column (except  the diagonal)  in
%       order.  The IA array holds the row  index for each non-zero.
%       The JA array holds the offsets into the IA, A arrays for the
%       beginning of   each    column.    That  is,    IA(JA(ICOL)),
%       A(JA(ICOL)) points to the beginning of the ICOL-th column in
%       IA and  A.  IA(JA(ICOL+1)-1),  A(JA(ICOL+1)-1) points to the
%       end  of   the ICOL-th  column.  Note   that  we  always have
%       JA(N+1) = NELT+1, where  N  is the number of columns in  the
%       matrix and  NELT   is the number of non-zeros in the matrix.
%
%       Here is an example of the  SLAP Column  storage format for a
%       5x5 Matrix (in the A and IA arrays '|'  denotes the end of a
%       column):
%
%           5x5 Matrix      SLAP Column format for 5x5 matrix on left.
%                              1  2  3    4  5    6  7    8    9 10 11
%       |11 12  0  0 15|   A: 11 21 51 | 22 12 | 33 53 | 44 | 55 15 35
%       |21 22  0  0  0|  IA:  1  2  5 |  2  1 |  3  5 |  4 |  5  1  3
%       | 0  0 33  0 35|  JA:  1  4  6    8  9   12
%       | 0  0  0 44  0|
%       |51  0 53  0 55|
%
%       With  the SLAP  format  the 'inner  loops' of  this  routine
%       should vectorize   on machines with   hardware  support  for
%       vector gather/scatter operations.  Your compiler may require
%       a  compiler directive  to  convince   it that there  are  no
%       implicit vector  dependencies.  Compiler directives  for the
%       Alliant FX/Fortran and CRI CFT/CFT77 compilers  are supplied
%       with the standard SLAP distribution.
%
% *Cautions:
%     This   routine   assumes  that  the matrix A is stored in SLAP
%     Column format.  It does not check  for  this (for  speed)  and
%     evil, ugly, ornery and nasty things  will happen if the matrix
%     data  structure  is,  in fact, not SLAP Column.  Beware of the
%     wrong data structure!!!
%
%***SEE ALSO  SSMV
%***REFERENCES  (NONE)
%***ROUTINES CALLED  (NONE)
%***REVISION HISTORY  (YYMMDD)
%   871119  DATE WRITTEN
%   881213  Previous REVISION DATE
%   890915  Made changes requested at July 1989 CML Meeting.  (MKS)
%   890922  Numerous changes to prologue to make closer to SLATEC
%           standard.  (FNF)
%   890929  Numerous changes to reduce SP/DP differences.  (FNF)
%   910411  Prologue converted to Version 4.0 format.  (BAB)
%   920511  Added complete declaration section.  (WRB)
%   930701  Updated CATEGORY section.  (FNF, WRB)
%***end PROLOGUE  SSMTV
%     .. Scalar Arguments ..
%     .. Array Arguments ..
%     .. Local Scalars ..
persistent i ibgn icol iend irow j jbgn jend ; 

if isempty(i), i=0; end;
if isempty(ibgn), ibgn=0; end;
if isempty(icol), icol=0; end;
if isempty(iend), iend=0; end;
if isempty(irow), irow=0; end;
if isempty(j), j=0; end;
if isempty(jbgn), jbgn=0; end;
if isempty(jend), jend=0; end;
%***FIRST EXECUTABLE STATEMENT  SSMTV
%
%         Zero out the result vector.
%
for i = 1 : n;
y(i) = 0;
end; i = fix(n+1);
%
%         Multiply by A-Transpose.
%         A-Transpose is stored by rows...
%VD$R NOCONCUR
for irow = 1 : n;
ibgn = fix(ja(irow));
iend = fix(ja(irow+1) - 1);
%VD$ ASSOC
for i = ibgn : iend;
y(irow) = y(irow) + a(i).*x(ia(i));
end; i = fix(iend+1);
end; irow = fix(n+1);
%
if( isym==1 )
%
%         The matrix is non-symmetric.  Need to get the other half in...
%         This loops assumes that the diagonal is the first entry in
%         each column.
%
for icol = 1 : n;
jbgn = fix(ja(icol) + 1);
jend = fix(ja(icol+1) - 1);
if( jbgn<=jend )
%LLL. OPTION ASSERT (NOHAZARD)
%DIR$ IVDEP
%VD$ NODEPCHK
for j = jbgn : jend;
y(ia(j)) = y(ia(j)) + a(j).*x(icol);
end; j = fix(jend+1);
end;
end; icol = fix(n+1);
end;
%------------- LAST LINE OF SSMTV FOLLOWS ----------------------------
end
%DECK SSMV