*DECK CGESL SUBROUTINE CGESL (A, LDA, N, IPVT, B, JOB) C***BEGIN PROLOGUE CGESL C***PURPOSE Solve the complex system A*X=B or CTRANS(A)*X=B using the C factors computed by CGECO or CGEFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2C1 C***TYPE COMPLEX (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 CGESL solves the complex system C A * X = B or CTRANS(A) * X = B C using the factors computed by CGECO or CGEFA. C C On Entry C C A COMPLEX(LDA, N) C the output from CGECO or CGEFA. 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 CGECO or CGEFA. C C B COMPLEX(N) C the right hand side vector. C C JOB INTEGER C = 0 to solve A*X = B , C = nonzero to solve CTRANS(A)*X = B where C CTRANS(A) is the conjugate 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 CGECO has set RCOND .GT. 0.0 C or CGEFA has set INFO .EQ. 0 . C C To compute INVERSE(A) * C where C is a matrix C with P columns C CALL CGECO(A,LDA,N,IPVT,RCOND,Z) C IF (RCOND is too small) GO TO ... C DO 10 J = 1, P C CALL CGESL(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 CAXPY, CDOTC 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 CGESL INTEGER LDA,N,IPVT(*),JOB COMPLEX A(LDA,*),B(*) C COMPLEX CDOTC,T INTEGER K,KB,L,NM1 C***FIRST EXECUTABLE STATEMENT CGESL 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 CAXPY(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 CAXPY(K-1,T,A(1,K),1,B(1),1) 40 CONTINUE GO TO 100 50 CONTINUE C C JOB = NONZERO, SOLVE CTRANS(A) * X = B C FIRST SOLVE CTRANS(U)*Y = B C DO 60 K = 1, N T = CDOTC(K-1,A(1,K),1,B(1),1) B(K) = (B(K) - T)/CONJG(A(K,K)) 60 CONTINUE C C NOW SOLVE CTRANS(L)*X = Y C IF (NM1 .LT. 1) GO TO 90 DO 80 KB = 1, NM1 K = N - KB B(K) = B(K) + CDOTC(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