*DECK CGBSL SUBROUTINE CGBSL (ABD, LDA, N, ML, MU, IPVT, B, JOB) C***BEGIN PROLOGUE CGBSL C***PURPOSE Solve the complex band system A*X=B or CTRANS(A)*X=B using C the factors computed by CGBCO or CGBFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2C2 C***TYPE COMPLEX (SGBSL-S, DGBSL-D, CGBSL-C) C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C CGBSL solves the complex band system C A * X = B or CTRANS(A) * X = B C using the factors computed by CGBCO or CGBFA. C C On Entry C C ABD COMPLEX(LDA, N) C the output from CGBCO or CGBFA. C C LDA INTEGER C the leading dimension of the array ABD . C C N INTEGER C the order of the original matrix. C C ML INTEGER C number of diagonals below the main diagonal. C C MU INTEGER C number of diagonals above the main diagonal. C C IPVT INTEGER(N) C the pivot vector from CGBCO or CGBFA. 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 CGBCO has set RCOND .GT. 0.0 C or CGBFA has set INFO .EQ. 0 . C C To compute INVERSE(A) * C where C is a matrix C with P columns C CALL CGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z) C IF (RCOND is too small) GO TO ... C DO 10 J = 1, P C CALL CGBSL(ABD,LDA,N,ML,MU,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 890531 Changed all specific intrinsics to generic. (WRB) 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 CGBSL INTEGER LDA,N,ML,MU,IPVT(*),JOB COMPLEX ABD(LDA,*),B(*) C COMPLEX CDOTC,T INTEGER K,KB,L,LA,LB,LM,M,NM1 C***FIRST EXECUTABLE STATEMENT CGBSL M = MU + ML + 1 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 (ML .EQ. 0) GO TO 30 IF (NM1 .LT. 1) GO TO 30 DO 20 K = 1, NM1 LM = MIN(ML,N-K) L = IPVT(K) T = B(L) IF (L .EQ. K) GO TO 10 B(L) = B(K) B(K) = T 10 CONTINUE CALL CAXPY(LM,T,ABD(M+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)/ABD(M,K) LM = MIN(K,M) - 1 LA = M - LM LB = K - LM T = -B(K) CALL CAXPY(LM,T,ABD(LA,K),1,B(LB),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 LM = MIN(K,M) - 1 LA = M - LM LB = K - LM T = CDOTC(LM,ABD(LA,K),1,B(LB),1) B(K) = (B(K) - T)/CONJG(ABD(M,K)) 60 CONTINUE C C NOW SOLVE CTRANS(L)*X = Y C IF (ML .EQ. 0) GO TO 90 IF (NM1 .LT. 1) GO TO 90 DO 80 KB = 1, NM1 K = N - KB LM = MIN(ML,N-K) B(K) = B(K) + CDOTC(LM,ABD(M+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