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* ======================================================================
* NIST Guide to Available Math Software.
* Source for module DGESL from package SLATEC.
* Retrieved from CAMSUN on Sat Sep 25 04:27:36 1999.
* ======================================================================
*DECK DGESL
SUBROUTINE DGESL (A, LDA, N, IPVT, B, JOB)
C***BEGIN PROLOGUE DGESL
C***PURPOSE Solve the real system A*X=B or TRANS(A)*X=B using the
C factors computed by DGECO or DGEFA.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2A1
C***TYPE DOUBLE PRECISION (SGESL-S, DGESL-D, CGESL-C)
C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C DGESL solves the double precision system
C A * X = B or TRANS(A) * X = B
C using the factors computed by DGECO or DGEFA.
C
C On Entry
C
C A DOUBLE PRECISION(LDA, N)
C the output from DGECO or DGEFA.
C
C LDA INTEGER
C the leading dimension of the array A .
C
C N INTEGER
C the order of the matrix A .
C
C IPVT INTEGER(N)
C the pivot vector from DGECO or DGEFA.
C
C B DOUBLE PRECISION(N)
C the right hand side vector.
C
C JOB INTEGER
C = 0 to solve A*X = B ,
C = nonzero to solve TRANS(A)*X = B where
C TRANS(A) is the transpose.
C
C On Return
C
C B the solution vector X .
C
C Error Condition
C
C A division by zero will occur if the input factor contains a
C zero on the diagonal. Technically this indicates singularity
C but it is often caused by improper arguments or improper
C setting of LDA . It will not occur if the subroutines are
C called correctly and if DGECO has set RCOND .GT. 0.0
C or DGEFA has set INFO .EQ. 0 .
C
C To compute INVERSE(A) * C where C is a matrix
C with P columns
C CALL DGECO(A,LDA,N,IPVT,RCOND,Z)
C IF (RCOND is too small) GO TO ...
C DO 10 J = 1, P
C CALL DGESL(A,LDA,N,IPVT,C(1,J),0)
C 10 CONTINUE
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED DAXPY, DDOT
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE DGESL
INTEGER LDA,N,IPVT(*),JOB
DOUBLE PRECISION A(LDA,*),B(*)
C
DOUBLE PRECISION DDOT,T
INTEGER K,KB,L,NM1
C***FIRST EXECUTABLE STATEMENT DGESL
NM1 = N - 1
IF (JOB .NE. 0) GO TO 50
C
C JOB = 0 , SOLVE A * X = B
C FIRST SOLVE L*Y = B
C
IF (NM1 .LT. 1) GO TO 30
DO 20 K = 1, NM1
L = IPVT(K)
T = B(L)
IF (L .EQ. K) GO TO 10
B(L) = B(K)
B(K) = T
10 CONTINUE
CALL DAXPY(N-K,T,A(K+1,K),1,B(K+1),1)
20 CONTINUE
30 CONTINUE
C
C NOW SOLVE U*X = Y
C
DO 40 KB = 1, N
K = N + 1 - KB
B(K) = B(K)/A(K,K)
T = -B(K)
CALL DAXPY(K-1,T,A(1,K),1,B(1),1)
40 CONTINUE
GO TO 100
50 CONTINUE
C
C JOB = NONZERO, SOLVE TRANS(A) * X = B
C FIRST SOLVE TRANS(U)*Y = B
C
DO 60 K = 1, N
T = DDOT(K-1,A(1,K),1,B(1),1)
B(K) = (B(K) - T)/A(K,K)
60 CONTINUE
C
C NOW SOLVE TRANS(L)*X = Y
C
IF (NM1 .LT. 1) GO TO 90
DO 80 KB = 1, NM1
K = N - KB
B(K) = B(K) + DDOT(N-K,A(K+1,K),1,B(K+1),1)
L = IPVT(K)
IF (L .EQ. K) GO TO 70
T = B(L)
B(L) = B(K)
B(K) = T
70 CONTINUE
80 CONTINUE
90 CONTINUE
100 CONTINUE
RETURN
END
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