*DECK CSIDI SUBROUTINE CSIDI (A, LDA, N, KPVT, DET, WORK, JOB) C***BEGIN PROLOGUE CSIDI C***PURPOSE Compute the determinant and inverse of a complex symmetric C matrix using the factors from CSIFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2C1, D3C1 C***TYPE COMPLEX (SSIDI-S, DSIDI-D, CHIDI-C, CSIDI-C) C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, C SYMMETRIC C***AUTHOR Bunch, J., (UCSD) C***DESCRIPTION C C CSIDI computes the determinant and inverse C of a complex symmetric matrix using the factors from CSIFA. C C On Entry C C A COMPLEX(LDA,N) C the output from CSIFA. 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 KVPT INTEGER(N) C the pivot vector from CSIFA. C C WORK COMPLEX(N) C work vector. Contents destroyed. C C JOB INTEGER C JOB has the decimal expansion AB where C If B .NE. 0, the inverse is computed, C If A .NE. 0, the determinant is computed, C C For example, JOB = 11 gives both. C C On Return C C Variables not requested by JOB are not used. C C A contains the upper triangle of the inverse of C the original matrix. The strict lower triangle C is never referenced. C C DET COMPLEX(2) C determinant of original matrix. C Determinant = DET(1) * 10.0**DET(2) C with 1.0 .LE. ABS(DET(1)) .LT. 10.0 C or DET(1) = 0.0. C C Error Condition C C A division by zero may occur if the inverse is requested C and CSICO has set RCOND .EQ. 0.0 C or CSIFA has set INFO .NE. 0 . 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, CCOPY, CDOTU, CSWAP C***REVISION HISTORY (YYMMDD) C 780814 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 890831 Modified array declarations. (WRB) C 891107 Corrected category and modified routine equivalence C list. (WRB) C 891107 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 CSIDI INTEGER LDA,N,JOB COMPLEX A(LDA,*),DET(2),WORK(*) INTEGER KPVT(*) C COMPLEX AK,AKP1,AKKP1,CDOTU,D,T,TEMP REAL TEN INTEGER J,JB,K,KM1,KS,KSTEP LOGICAL NOINV,NODET COMPLEX ZDUM REAL CABS1 CABS1(ZDUM) = ABS(REAL(ZDUM)) + ABS(AIMAG(ZDUM)) C C***FIRST EXECUTABLE STATEMENT CSIDI NOINV = MOD(JOB,10) .EQ. 0 NODET = MOD(JOB,100)/10 .EQ. 0 C IF (NODET) GO TO 100 DET(1) = (1.0E0,0.0E0) DET(2) = (0.0E0,0.0E0) TEN = 10.0E0 T = (0.0E0,0.0E0) DO 90 K = 1, N D = A(K,K) C C CHECK IF 1 BY 1 C IF (KPVT(K) .GT. 0) GO TO 30 C C 2 BY 2 BLOCK C USE DET (D T) = (D/T * C - T) * T C (T C) C TO AVOID UNDERFLOW/OVERFLOW TROUBLES. C TAKE TWO PASSES THROUGH SCALING. USE T FOR FLAG. C IF (CABS1(T) .NE. 0.0E0) GO TO 10 T = A(K,K+1) D = (D/T)*A(K+1,K+1) - T GO TO 20 10 CONTINUE D = T T = (0.0E0,0.0E0) 20 CONTINUE 30 CONTINUE C DET(1) = D*DET(1) IF (CABS1(DET(1)) .EQ. 0.0E0) GO TO 80 40 IF (CABS1(DET(1)) .GE. 1.0E0) GO TO 50 DET(1) = CMPLX(TEN,0.0E0)*DET(1) DET(2) = DET(2) - (1.0E0,0.0E0) GO TO 40 50 CONTINUE 60 IF (CABS1(DET(1)) .LT. TEN) GO TO 70 DET(1) = DET(1)/CMPLX(TEN,0.0E0) DET(2) = DET(2) + (1.0E0,0.0E0) GO TO 60 70 CONTINUE 80 CONTINUE 90 CONTINUE 100 CONTINUE C C COMPUTE INVERSE(A) C IF (NOINV) GO TO 230 K = 1 110 IF (K .GT. N) GO TO 220 KM1 = K - 1 IF (KPVT(K) .LT. 0) GO TO 140 C C 1 BY 1 C A(K,K) = (1.0E0,0.0E0)/A(K,K) IF (KM1 .LT. 1) GO TO 130 CALL CCOPY(KM1,A(1,K),1,WORK,1) DO 120 J = 1, KM1 A(J,K) = CDOTU(J,A(1,J),1,WORK,1) CALL CAXPY(J-1,WORK(J),A(1,J),1,A(1,K),1) 120 CONTINUE A(K,K) = A(K,K) + CDOTU(KM1,WORK,1,A(1,K),1) 130 CONTINUE KSTEP = 1 GO TO 180 140 CONTINUE C C 2 BY 2 C T = A(K,K+1) AK = A(K,K)/T AKP1 = A(K+1,K+1)/T AKKP1 = A(K,K+1)/T D = T*(AK*AKP1 - (1.0E0,0.0E0)) A(K,K) = AKP1/D A(K+1,K+1) = AK/D A(K,K+1) = -AKKP1/D IF (KM1 .LT. 1) GO TO 170 CALL CCOPY(KM1,A(1,K+1),1,WORK,1) DO 150 J = 1, KM1 A(J,K+1) = CDOTU(J,A(1,J),1,WORK,1) CALL CAXPY(J-1,WORK(J),A(1,J),1,A(1,K+1),1) 150 CONTINUE A(K+1,K+1) = A(K+1,K+1) 1 + CDOTU(KM1,WORK,1,A(1,K+1),1) A(K,K+1) = A(K,K+1) + CDOTU(KM1,A(1,K),1,A(1,K+1),1) CALL CCOPY(KM1,A(1,K),1,WORK,1) DO 160 J = 1, KM1 A(J,K) = CDOTU(J,A(1,J),1,WORK,1) CALL CAXPY(J-1,WORK(J),A(1,J),1,A(1,K),1) 160 CONTINUE A(K,K) = A(K,K) + CDOTU(KM1,WORK,1,A(1,K),1) 170 CONTINUE KSTEP = 2 180 CONTINUE C C SWAP C KS = ABS(KPVT(K)) IF (KS .EQ. K) GO TO 210 CALL CSWAP(KS,A(1,KS),1,A(1,K),1) DO 190 JB = KS, K J = K + KS - JB TEMP = A(J,K) A(J,K) = A(KS,J) A(KS,J) = TEMP 190 CONTINUE IF (KSTEP .EQ. 1) GO TO 200 TEMP = A(KS,K+1) A(KS,K+1) = A(K,K+1) A(K,K+1) = TEMP 200 CONTINUE 210 CONTINUE K = K + KSTEP GO TO 110 220 CONTINUE 230 CONTINUE RETURN END