*DECK CHIDI SUBROUTINE CHIDI (A, LDA, N, KPVT, DET, INERT, WORK, JOB) C***BEGIN PROLOGUE CHIDI C***PURPOSE Compute the determinant, inertia and inverse of a complex C Hermitian matrix using the factors obtained from CHIFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2D1A, D3D1A C***TYPE COMPLEX (SSIDI-S, DSISI-D, CHIDI-C, CSIDI-C) C***KEYWORDS DETERMINANT, HERMITIAN, INVERSE, LINEAR ALGEBRA, LINPACK, C MATRIX C***AUTHOR Bunch, J., (UCSD) C***DESCRIPTION C C CHIDI computes the determinant, inertia and inverse C of a complex Hermitian matrix using the factors from CHIFA. C C On Entry C C A COMPLEX(LDA,N) C the output from CHIFA. 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 CHIFA. C C WORK COMPLEX(N) C work vector. Contents destroyed. C C JOB INTEGER C JOB has the decimal expansion ABC where C if C .NE. 0, the inverse is computed, C if B .NE. 0, the determinant is computed, C if A .NE. 0, the inertia is computed. C C For example, JOB = 111 gives all three. 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 REAL(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 INERT INTEGER(3) C the inertia of the original matrix. C INERT(1) = number of positive eigenvalues. C INERT(2) = number of negative eigenvalues. C INERT(3) = number of zero eigenvalues. C C Error Condition C C A division by zero may occur if the inverse is requested C and CHICO has set RCOND .EQ. 0.0 C or CHIFA 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, CDOTC, 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 Modified routine equivalence 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 CHIDI INTEGER LDA,N,JOB COMPLEX A(LDA,*),WORK(*) REAL DET(2) INTEGER KPVT(*),INERT(3) C COMPLEX AKKP1,CDOTC,TEMP REAL TEN,D,T,AK,AKP1 INTEGER J,JB,K,KM1,KS,KSTEP LOGICAL NOINV,NODET,NOERT C***FIRST EXECUTABLE STATEMENT CHIDI NOINV = MOD(JOB,10) .EQ. 0 NODET = MOD(JOB,100)/10 .EQ. 0 NOERT = MOD(JOB,1000)/100 .EQ. 0 C IF (NODET .AND. NOERT) GO TO 140 IF (NOERT) GO TO 10 INERT(1) = 0 INERT(2) = 0 INERT(3) = 0 10 CONTINUE IF (NODET) GO TO 20 DET(1) = 1.0E0 DET(2) = 0.0E0 TEN = 10.0E0 20 CONTINUE T = 0.0E0 DO 130 K = 1, N D = REAL(A(K,K)) C C CHECK IF 1 BY 1 C IF (KPVT(K) .GT. 0) GO TO 50 C C 2 BY 2 BLOCK C USE DET (D S) = (D/T * C - T) * T , T = ABS(S) C (S C) C TO AVOID UNDERFLOW/OVERFLOW TROUBLES. C TAKE TWO PASSES THROUGH SCALING. USE T FOR FLAG. C IF (T .NE. 0.0E0) GO TO 30 T = ABS(A(K,K+1)) D = (D/T)*REAL(A(K+1,K+1)) - T GO TO 40 30 CONTINUE D = T T = 0.0E0 40 CONTINUE 50 CONTINUE C IF (NOERT) GO TO 60 IF (D .GT. 0.0E0) INERT(1) = INERT(1) + 1 IF (D .LT. 0.0E0) INERT(2) = INERT(2) + 1 IF (D .EQ. 0.0E0) INERT(3) = INERT(3) + 1 60 CONTINUE C IF (NODET) GO TO 120 DET(1) = D*DET(1) IF (DET(1) .EQ. 0.0E0) GO TO 110 70 IF (ABS(DET(1)) .GE. 1.0E0) GO TO 80 DET(1) = TEN*DET(1) DET(2) = DET(2) - 1.0E0 GO TO 70 80 CONTINUE 90 IF (ABS(DET(1)) .LT. TEN) GO TO 100 DET(1) = DET(1)/TEN DET(2) = DET(2) + 1.0E0 GO TO 90 100 CONTINUE 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE C C COMPUTE INVERSE(A) C IF (NOINV) GO TO 270 K = 1 150 IF (K .GT. N) GO TO 260 KM1 = K - 1 IF (KPVT(K) .LT. 0) GO TO 180 C C 1 BY 1 C A(K,K) = CMPLX(1.0E0/REAL(A(K,K)),0.0E0) IF (KM1 .LT. 1) GO TO 170 CALL CCOPY(KM1,A(1,K),1,WORK,1) DO 160 J = 1, KM1 A(J,K) = CDOTC(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) 1 + CMPLX(REAL(CDOTC(KM1,WORK,1,A(1,K),1)), 2 0.0E0) 170 CONTINUE KSTEP = 1 GO TO 220 180 CONTINUE C C 2 BY 2 C T = ABS(A(K,K+1)) AK = REAL(A(K,K))/T AKP1 = REAL(A(K+1,K+1))/T AKKP1 = A(K,K+1)/T D = T*(AK*AKP1 - 1.0E0) A(K,K) = CMPLX(AKP1/D,0.0E0) A(K+1,K+1) = CMPLX(AK/D,0.0E0) A(K,K+1) = -AKKP1/D IF (KM1 .LT. 1) GO TO 210 CALL CCOPY(KM1,A(1,K+1),1,WORK,1) DO 190 J = 1, KM1 A(J,K+1) = CDOTC(J,A(1,J),1,WORK,1) CALL CAXPY(J-1,WORK(J),A(1,J),1,A(1,K+1),1) 190 CONTINUE A(K+1,K+1) = A(K+1,K+1) 1 + CMPLX(REAL(CDOTC(KM1,WORK,1,A(1,K+1), 2 1)),0.0E0) A(K,K+1) = A(K,K+1) + CDOTC(KM1,A(1,K),1,A(1,K+1),1) CALL CCOPY(KM1,A(1,K),1,WORK,1) DO 200 J = 1, KM1 A(J,K) = CDOTC(J,A(1,J),1,WORK,1) CALL CAXPY(J-1,WORK(J),A(1,J),1,A(1,K),1) 200 CONTINUE A(K,K) = A(K,K) 1 + CMPLX(REAL(CDOTC(KM1,WORK,1,A(1,K),1)), 2 0.0E0) 210 CONTINUE KSTEP = 2 220 CONTINUE C C SWAP C KS = ABS(KPVT(K)) IF (KS .EQ. K) GO TO 250 CALL CSWAP(KS,A(1,KS),1,A(1,K),1) DO 230 JB = KS, K J = K + KS - JB TEMP = CONJG(A(J,K)) A(J,K) = CONJG(A(KS,J)) A(KS,J) = TEMP 230 CONTINUE IF (KSTEP .EQ. 1) GO TO 240 TEMP = A(KS,K+1) A(KS,K+1) = A(K,K+1) A(K,K+1) = TEMP 240 CONTINUE 250 CONTINUE K = K + KSTEP GO TO 150 260 CONTINUE 270 CONTINUE RETURN END