*DECK CPODI SUBROUTINE CPODI (A, LDA, N, DET, JOB) C***BEGIN PROLOGUE CPODI C***PURPOSE Compute the determinant and inverse of a certain complex C Hermitian positive definite matrix using the factors C computed by CPOCO, CPOFA, or CQRDC. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2D1B, D3D1B C***TYPE COMPLEX (SPODI-S, DPODI-D, CPODI-C) C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, C POSITIVE DEFINITE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C CPODI computes the determinant and inverse of a certain C complex Hermitian positive definite matrix (see below) C using the factors computed by CPOCO, CPOFA or CQRDC. C C On Entry C C A COMPLEX(LDA, N) C the output A from CPOCO or CPOFA C or the output X from CQRDC. 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 JOB INTEGER C = 11 both determinant and inverse. C = 01 inverse only. C = 10 determinant only. C C On Return C C A If CPOCO or CPOFA was used to factor A then C CPODI produces the upper half of INVERSE(A) . C If CQRDC was used to decompose X then C CPODI produces the upper half of INVERSE(CTRANS(X)*X) C where CTRANS(X) is the conjugate transpose. C Elements of A below the diagonal are unchanged. C If the units digit of JOB is zero, A is unchanged. C C DET REAL(2) C determinant of A or of CTRANS(X)*X if requested. C Otherwise not referenced. C Determinant = DET(1) * 10.0**DET(2) C with 1.0 .LE. DET(1) .LT. 10.0 C or DET(1) .EQ. 0.0 . C C Error Condition C C a division by zero will occur if the input factor contains C a zero on the diagonal and the inverse is requested. C It will not occur if the subroutines are called correctly C and if CPOCO or CPOFA has set INFO .EQ. 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, CSCAL 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 CPODI INTEGER LDA,N,JOB COMPLEX A(LDA,*) REAL DET(2) C COMPLEX T REAL S INTEGER I,J,JM1,K,KP1 C***FIRST EXECUTABLE STATEMENT CPODI C C COMPUTE DETERMINANT C IF (JOB/10 .EQ. 0) GO TO 70 DET(1) = 1.0E0 DET(2) = 0.0E0 S = 10.0E0 DO 50 I = 1, N DET(1) = REAL(A(I,I))**2*DET(1) IF (DET(1) .EQ. 0.0E0) GO TO 60 10 IF (DET(1) .GE. 1.0E0) GO TO 20 DET(1) = S*DET(1) DET(2) = DET(2) - 1.0E0 GO TO 10 20 CONTINUE 30 IF (DET(1) .LT. S) GO TO 40 DET(1) = DET(1)/S DET(2) = DET(2) + 1.0E0 GO TO 30 40 CONTINUE 50 CONTINUE 60 CONTINUE 70 CONTINUE C C COMPUTE INVERSE(R) C IF (MOD(JOB,10) .EQ. 0) GO TO 140 DO 100 K = 1, N A(K,K) = (1.0E0,0.0E0)/A(K,K) T = -A(K,K) CALL CSCAL(K-1,T,A(1,K),1) KP1 = K + 1 IF (N .LT. KP1) GO TO 90 DO 80 J = KP1, N T = A(K,J) A(K,J) = (0.0E0,0.0E0) CALL CAXPY(K,T,A(1,K),1,A(1,J),1) 80 CONTINUE 90 CONTINUE 100 CONTINUE C C FORM INVERSE(R) * CTRANS(INVERSE(R)) C DO 130 J = 1, N JM1 = J - 1 IF (JM1 .LT. 1) GO TO 120 DO 110 K = 1, JM1 T = CONJG(A(K,J)) CALL CAXPY(K,T,A(1,J),1,A(1,K),1) 110 CONTINUE 120 CONTINUE T = CONJG(A(J,J)) CALL CSCAL(J,T,A(1,J),1) 130 CONTINUE 140 CONTINUE RETURN END