*DECK DPODI SUBROUTINE DPODI (A, LDA, N, DET, JOB) C***BEGIN PROLOGUE DPODI C***PURPOSE Compute the determinant and inverse of a certain real C symmetric positive definite matrix using the factors C computed by DPOCO, DPOFA or DQRDC. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B1B, D3B1B C***TYPE DOUBLE PRECISION (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 DPODI computes the determinant and inverse of a certain C double precision symmetric positive definite matrix (see below) C using the factors computed by DPOCO, DPOFA or DQRDC. C C On Entry C C A DOUBLE PRECISION(LDA, N) C the output A from DPOCO or DPOFA C or the output X from DQRDC. 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 DPOCO or DPOFA was used to factor A , then C DPODI produces the upper half of INVERSE(A) . C If DQRDC was used to decompose X , then C DPODI produces the upper half of inverse(TRANS(X)*X) C where TRANS(X) is the 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 DOUBLE PRECISION(2) C determinant of A or of TRANS(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 DPOCO or DPOFA 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 DAXPY, DSCAL 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 DPODI INTEGER LDA,N,JOB DOUBLE PRECISION A(LDA,*) DOUBLE PRECISION DET(2) C DOUBLE PRECISION T DOUBLE PRECISION S INTEGER I,J,JM1,K,KP1 C***FIRST EXECUTABLE STATEMENT DPODI C C COMPUTE DETERMINANT C IF (JOB/10 .EQ. 0) GO TO 70 DET(1) = 1.0D0 DET(2) = 0.0D0 S = 10.0D0 DO 50 I = 1, N DET(1) = A(I,I)**2*DET(1) IF (DET(1) .EQ. 0.0D0) GO TO 60 10 IF (DET(1) .GE. 1.0D0) GO TO 20 DET(1) = S*DET(1) DET(2) = DET(2) - 1.0D0 GO TO 10 20 CONTINUE 30 IF (DET(1) .LT. S) GO TO 40 DET(1) = DET(1)/S DET(2) = DET(2) + 1.0D0 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) = 1.0D0/A(K,K) T = -A(K,K) CALL DSCAL(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) = 0.0D0 CALL DAXPY(K,T,A(1,K),1,A(1,J),1) 80 CONTINUE 90 CONTINUE 100 CONTINUE C C FORM INVERSE(R) * TRANS(INVERSE(R)) C DO 130 J = 1, N JM1 = J - 1 IF (JM1 .LT. 1) GO TO 120 DO 110 K = 1, JM1 T = A(K,J) CALL DAXPY(K,T,A(1,J),1,A(1,K),1) 110 CONTINUE 120 CONTINUE T = A(J,J) CALL DSCAL(J,T,A(1,J),1) 130 CONTINUE 140 CONTINUE RETURN END