| [n,nelt,ia,ja,a,isym]=ss2y(n,nelt,ia,ja,a,isym); |
function [n,nelt,ia,ja,a,isym]=ss2y(n,nelt,ia,ja,a,isym);
%***BEGIN PROLOGUE SS2Y
%***PURPOSE SLAP Triad to SLAP Column Format Converter.
% Routine to convert from the SLAP Triad to SLAP Column
% format.
%***LIBRARY SLATEC (SLAP)
%***CATEGORY D1B9
%***TYPE SINGLE PRECISION (SS2Y-S, DS2Y-D)
%***KEYWORDS LINEAR SYSTEM, SLAP SPARSE
%***AUTHOR Seager, Mark K., (LLNL)
% Lawrence Livermore National Laboratory
% PO BOX 808, L-60
% Livermore, CA 94550 (510) 423-3141
% seager@llnl.gov
%***DESCRIPTION
%
% *Usage:
% INTEGER N, NELT, IA(NELT), JA(NELT), ISYM
% REAL A(NELT)
%
% CALL SS2Y( N, NELT, IA, JA, A, ISYM )
%
% *Arguments:
% N :IN Integer
% Order of the Matrix.
% NELT :IN Integer.
% Number of non-zeros stored in A.
% IA :INOUT Integer IA(NELT).
% JA :INOUT Integer JA(NELT).
% A :INOUT Real A(NELT).
% These arrays should hold the matrix A in either the SLAP
% Triad format or the SLAP Column format. See 'Description',
% below. If the SLAP Triad format is used, this format is
% translated to the SLAP Column format by this routine.
% 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 lower
% triangle of the matrix is stored.
%
% *Description:
% The Sparse Linear Algebra Package (SLAP) utilizes two matrix
% data structures: 1) the SLAP Triad format or 2) the SLAP
% Column format. The user can hand this routine either of the
% of these data structures. If the SLAP Triad format is give
% as input then this routine transforms it into SLAP Column
% format. The way this routine tells which format is given as
% input is to look at JA(N+1). If JA(N+1) = NELT+1 then we
% have the SLAP Column format. If that equality does not hold
% then it is assumed that the IA, JA, A arrays contain the
% SLAP Triad format.
%
% =================== S L A P Triad format ===================
% This routine requires that the matrix A be stored in the
% SLAP Triad format. In this format only the non-zeros are
% stored. They may appear in *ANY* order. The user supplies
% three arrays of length NELT, where NELT is the number of
% non-zeros in the matrix: (IA(NELT), JA(NELT), A(NELT)). For
% each non-zero the user puts the row and column index of that
% matrix element in the IA and JA arrays. The value of the
% non-zero matrix element is placed in the corresponding
% location of the A array. This is an extremely easy data
% structure to generate. On the other hand it is not too
% efficient on vector computers for the iterative solution of
% linear systems. Hence, SLAP changes this input data
% structure to the SLAP Column format for the iteration (but
% does not change it back).
%
% Here is an example of the SLAP Triad storage format for a
% 5x5 Matrix. Recall that the entries may appear in any order.
%
% 5x5 Matrix SLAP Triad format for 5x5 matrix on left.
% 1 2 3 4 5 6 7 8 9 10 11
% |11 12 0 0 15| A: 51 12 11 33 15 53 55 22 35 44 21
% |21 22 0 0 0| IA: 5 1 1 3 1 5 5 2 3 4 2
% | 0 0 33 0 35| JA: 1 2 1 3 5 3 5 2 5 4 1
% | 0 0 0 44 0|
% |51 0 53 0 55|
%
% =================== 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|
%
%***REFERENCES (NONE)
%***ROUTINES CALLED QS2I1R
%***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)
% 910502 Corrected C***FIRST EXECUTABLE STATEMENT line. (FNF)
% 920511 Added complete declaration section. (WRB)
% 930701 Updated CATEGORY section. (FNF, WRB)
%***end PROLOGUE SS2Y
% .. Scalar Arguments ..
% .. Array Arguments ..
% .. Local Scalars ..
persistent i ibgn icol iend itemp j temp ;
if isempty(temp), temp=0; end;
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(itemp), itemp=0; end;
if isempty(j), j=0; end;
% .. External Subroutines ..
%***FIRST EXECUTABLE STATEMENT SS2Y
%
% Check to see if the (IA,JA,A) arrays are in SLAP Column
% format. If it's not then transform from SLAP Triad.
%
if( ja(n+1)==nelt+1 )
return;
end;
%
% Sort into ascending order by COLUMN (on the ja array).
% This will line up the columns.
%
[ja,ia,a,nelt]=qs2i1r(ja,ia,a,nelt,1);
%
% Loop over each column to see where the column indices change
% in the column index array ja. This marks the beginning of the
% next column.
%
%VD$R NOVECTOR
ja(1) = 1;
for icol = 1 : n - 1;
for j = ja(icol) + 1 : nelt;
if( ja(j)~=icol )
ja(icol+1) = fix(j);
break;
end;
end;
end;
ja(n+1) = fix(nelt + 1);
%
% Mark the n+2 element so that future calls to a SLAP routine
% utilizing the YSMP-Column storage format will be able to tell.
%
ja(n+2) = 0;
%
% Now loop through the IA array making sure that the diagonal
% matrix element appears first in the column. Then sort the
% rest of the column in ascending order.
%
for icol = 1 : n;
ibgn = fix(ja(icol));
iend = fix(ja(icol+1) - 1);
for i = ibgn : iend;
if( ia(i)==icol )
%
% Swap the diagonal element with the first element in the
% column.
%
itemp = fix(ia(i));
ia(i) = fix(ia(ibgn));
ia(ibgn) = fix(itemp);
temp = a(i);
a(i) = a(ibgn);
a(ibgn) = temp;
break;
end;
end;
ibgn = fix(ibgn + 1);
if( ibgn<iend )
for i = ibgn : iend;
for j = i + 1 : iend;
if( ia(i)>ia(j) )
itemp = fix(ia(i));
ia(i) = fix(ia(j));
ia(j) = fix(itemp);
temp = a(i);
a(i) = a(j);
a(j) = temp;
end;
end; j = fix(iend+1);
end; i = fix(iend+1);
end;
end;
%------------- LAST LINE OF SS2Y FOLLOWS ----------------------------
end
%DECK SSBMV
|
|
