*DECK DPPDI SUBROUTINE DPPDI (AP, N, DET, JOB) C***BEGIN PROLOGUE DPPDI C***PURPOSE Compute the determinant and inverse of a real symmetric C positive definite matrix using factors from DPPCO or DPPFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D2B1B, D3B1B C***TYPE DOUBLE PRECISION (SPPDI-S, DPPDI-D, CPPDI-C) C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX, C PACKED, POSITIVE DEFINITE C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C DPPDI computes the determinant and inverse C of a double precision symmetric positive definite matrix C using the factors computed by DPPCO or DPPFA . C C On Entry C C AP DOUBLE PRECISION (N*(N+1)/2) C the output from DPPCO or DPPFA. 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 AP the upper triangular half of the inverse . C The strict lower triangle is unaltered. C C DET DOUBLE PRECISION(2) C determinant of original matrix 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 DPPDI INTEGER N,JOB DOUBLE PRECISION AP(*) DOUBLE PRECISION DET(2) C DOUBLE PRECISION T DOUBLE PRECISION S INTEGER I,II,J,JJ,JM1,J1,K,KJ,KK,KP1,K1 C***FIRST EXECUTABLE STATEMENT DPPDI C C COMPUTE DETERMINANT C IF (JOB/10 .EQ. 0) GO TO 70 DET(1) = 1.0D0 DET(2) = 0.0D0 S = 10.0D0 II = 0 DO 50 I = 1, N II = II + I DET(1) = AP(II)**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 KK = 0 DO 100 K = 1, N K1 = KK + 1 KK = KK + K AP(KK) = 1.0D0/AP(KK) T = -AP(KK) CALL DSCAL(K-1,T,AP(K1),1) KP1 = K + 1 J1 = KK + 1 KJ = KK + K IF (N .LT. KP1) GO TO 90 DO 80 J = KP1, N T = AP(KJ) AP(KJ) = 0.0D0 CALL DAXPY(K,T,AP(K1),1,AP(J1),1) J1 = J1 + J KJ = KJ + J 80 CONTINUE 90 CONTINUE 100 CONTINUE C C FORM INVERSE(R) * TRANS(INVERSE(R)) C JJ = 0 DO 130 J = 1, N J1 = JJ + 1 JJ = JJ + J JM1 = J - 1 K1 = 1 KJ = J1 IF (JM1 .LT. 1) GO TO 120 DO 110 K = 1, JM1 T = AP(KJ) CALL DAXPY(K,T,AP(J1),1,AP(K1),1) K1 = K1 + K KJ = KJ + 1 110 CONTINUE 120 CONTINUE T = AP(JJ) CALL DSCAL(J,T,AP(J1),1) 130 CONTINUE 140 CONTINUE RETURN END