Code covered by the BSD License

Highlights fromslatec

from slatec by Ben Barrowes
The slatec library converted into matlab functions.

[n,b,x,il,jl,l,dinv,iu,ju,u]=dslui4(n,b,x,il,jl,l,dinv,iu,ju,u);
```function [n,b,x,il,jl,l,dinv,iu,ju,u]=dslui4(n,b,x,il,jl,l,dinv,iu,ju,u);
%***BEGIN PROLOGUE  DSLUI4
%***PURPOSE  SLAP Backsolve for LDU Factorization.
%            Routine to solve a system of the form  (L*D*U)' X = B,
%            where L is a unit lower triangular matrix, D is a diagonal
%            matrix, and U is a unit upper triangular matrix and '
%            denotes transpose.
%***LIBRARY   SLATEC (SLAP)
%***CATEGORY  D2E
%***TYPE      doubleprecision (SSLUI4-S, DSLUI4-D)
%***KEYWORDS  ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM SOLVE,
%             SLAP, SPARSE
%***AUTHOR  Greenbaum, Anne, (Courant Institute)
%           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, IL(NL), JL(NL), IU(NU), JU(NU)
%     doubleprecision B(N), X(N), L(NL), DINV(N), U(NU)
%
%     CALL DSLUI4( N, B, X, IL, JL, L, DINV, IU, JU, U )
%
% *Arguments:
% N      :IN       Integer
%         Order of the Matrix.
% B      :IN       doubleprecision B(N).
%         Right hand side.
% X      :OUT      doubleprecision X(N).
%         Solution of (L*D*U)trans x = b.
% IL     :IN       Integer IL(NL).
% JL     :IN       Integer JL(NL).
% L      :IN       doubleprecision L(NL).
%         IL, JL, L contain the unit lower triangular  factor of the
%         incomplete decomposition of some matrix stored in SLAP Row
%         format.  The diagonal of ones *IS* stored.  This structure
%         can    be  set  up  by   the  DSILUS  routine.   See   the
%         'Description',  below for  more  details about  the   SLAP
%         format.  (NL is the number of non-zeros in the L array.)
% DINV   :IN       doubleprecision DINV(N).
%         Inverse of the diagonal matrix D.
% IU     :IN       Integer IU(NU).
% JU     :IN       Integer JU(NU).
% U      :IN       doubleprecision U(NU).
%         IU, JU, U contain the  unit upper triangular factor of the
%         incomplete  decomposition of some  matrix stored  in  SLAP
%         Column  format.   The diagonal of  ones *IS* stored.  This
%         structure can be set up by the  DSILUS routine.  See   the
%         'Description',  below for  more  details  about  the  SLAP
%         format.  (NU is the number of non-zeros in the U array.)
%
% *Description:
%       This routine is supplied with the SLAP package as  a routine
%       to  perform  the  MTSOLV  operation  in  the SBCG  iteration
%       routine for the  driver DSLUBC.   It must  be called via the
%       SLAP  MTSOLV calling  sequence convention interface  routine
%       DSLUTI.
%         **** THIS ROUTINE ITSELF DOES NOT CONFORM TO THE ****
%               **** SLAP MSOLVE CALLING CONVENTION ****
%
%       IL, JL, L should contain the unit lower triangular factor of
%       the incomplete decomposition of the A matrix  stored in SLAP
%       Row format.  IU, JU, U should contain  the unit upper factor
%       of the  incomplete decomposition of  the A matrix  stored in
%       SLAP Column format This ILU factorization can be computed by
%       the DSILUS routine. The diagonals (which are all one's) are
%       stored.
%
%       =================== 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
%       doubleprecision 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|
%
%       ==================== S L A P Row format ====================
%
%       This routine requires  that the matrix A  be  stored  in the
%       SLAP  Row format.   In this format  the non-zeros are stored
%       counting across  rows (except for the diagonal  entry, which
%       must  appear first  in each  'row')  and  are stored  in the
%       doubleprecision  array A.  In other words, for each row  in
%       the matrix  put the diagonal  entry in A.   Then put in  the
%       other  non-zero elements  going across  the row  (except the
%       diagonal) in order.  The JA array holds the column index for
%       each non-zero.  The IA array holds the offsets  into the JA,
%       A  arrays  for  the   beginning  of  each  row.    That  is,
%       JA(IA(IROW)),A(IA(IROW)) are the first elements of the IROW-
%       th row in  JA and A,  and  JA(IA(IROW+1)-1), A(IA(IROW+1)-1)
%       are  the last elements  of the  IROW-th row.   Note  that we
%       always have  IA(N+1) = NELT+1, where N is the number of rows
%       in the matrix  and  NELT is the  number of non-zeros  in the
%       matrix.
%
%       Here is an example of the SLAP Row storage format for a  5x5
%       Matrix (in the A and JA arrays '|' denotes the end of a row):
%
%           5x5 Matrix         SLAP Row format for 5x5 matrix on left.
%                              1  2  3    4  5    6  7    8    9 10 11
%       |11 12  0  0 15|   A: 11 12 15 | 22 21 | 33 35 | 44 | 55 51 53
%       |21 22  0  0  0|  JA:  1  2  5 |  2  1 |  3  5 |  4 |  5  1  3
%       | 0  0 33  0 35|  IA:  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.
%
%***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)
%   921113  Corrected C***CATEGORY line.  (FNF)
%   930701  Updated CATEGORY section.  (FNF, WRB)
%***end PROLOGUE  DSLUI4
%     .. Scalar Arguments ..
%     .. Array Arguments ..
persistent i icol irow j jbgn jend ;

l_shape=size(l);l=reshape(l,1,[]);
u_shape=size(u);u=reshape(u,1,[]);
il_shape=size(il);il=reshape(il,1,[]);
iu_shape=size(iu);iu=reshape(iu,1,[]);
jl_shape=size(jl);jl=reshape(jl,1,[]);
ju_shape=size(ju);ju=reshape(ju,1,[]);
%     .. Local Scalars ..
if isempty(i), i=0; end;
if isempty(icol), icol=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  DSLUI4
for i = 1 : n;
x(i) = b(i);
end; i = fix(n+1);
%
%         Solve  U'*Y = X,  storing result in X, U stored by columns.
for irow = 2 : n;
jbgn = fix(ju(irow));
jend = fix(ju(irow+1) - 1);
if( jbgn<=jend )
%LLL. OPTION ASSERT (NOHAZARD)
%DIR\$ IVDEP
%VD\$ ASSOC
%VD\$ NODEPCHK
for j = jbgn : jend;
x(irow) = x(irow) - u(j).*x(iu(j));
end; j = fix(jend+1);
end;
end; irow = fix(n+1);
%
%         Solve  D*Z = Y,  storing result in X.
for i = 1 : n;
x(i) = x(i).*dinv(i);
end; i = fix(n+1);
%
%         Solve  L'*X = Z, L stored by rows.
for icol = n : -1: 2 ;
jbgn = fix(il(icol));
jend = fix(il(icol+1) - 1);
if( jbgn<=jend )
%LLL. OPTION ASSERT (NOHAZARD)
%DIR\$ IVDEP
%VD\$ NODEPCHK
for j = jbgn : jend;
x(jl(j)) = x(jl(j)) - l(j).*x(icol);
end; j = fix(jend+1);
end;
end; icol = fix(2 -1);
%------------- LAST LINE OF DSLUI4 FOLLOWS ----------------------------
l_shape=zeros(l_shape);l_shape(:)=l(1:numel(l_shape));l=l_shape;
u_shape=zeros(u_shape);u_shape(:)=u(1:numel(u_shape));u=u_shape;
il_shape=zeros(il_shape);il_shape(:)=il(1:numel(il_shape));il=il_shape;
iu_shape=zeros(iu_shape);iu_shape(:)=iu(1:numel(iu_shape));iu=iu_shape;
jl_shape=zeros(jl_shape);jl_shape(:)=jl(1:numel(jl_shape));jl=jl_shape;
ju_shape=zeros(ju_shape);ju_shape(:)=ju(1:numel(ju_shape));ju=ju_shape;
end
%DECK DSLUI
```