*DECK DGEDI SUBROUTINE DGEDI (A, LDA, N, IPVT, DET, WORK, JOB) C***BEGIN PROLOGUE DGEDI C***PURPOSE Compute the determinant and inverse of a matrix using the C factors computed by DGECO or DGEFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D3A1, D2A1 C***TYPE DOUBLE PRECISION (SGEDI-S, DGEDI-D, CGEDI-C) C***KEYWORDS DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, MATRIX C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C DGEDI computes the determinant and inverse of a matrix C using the factors computed by DGECO or DGEFA. C C On Entry C C A DOUBLE PRECISION(LDA, N) C the output from DGECO or DGEFA. 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 IPVT INTEGER(N) C the pivot vector from DGECO or DGEFA. C C WORK DOUBLE PRECISION(N) C work vector. Contents destroyed. 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 inverse of original matrix if requested. C Otherwise unchanged. 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. ABS(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 DGECO has set RCOND .GT. 0.0 or DGEFA has set C 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, DSWAP C***REVISION HISTORY (YYMMDD) C 780814 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) 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 DGEDI INTEGER LDA,N,IPVT(*),JOB DOUBLE PRECISION A(LDA,*),DET(2),WORK(*) C DOUBLE PRECISION T DOUBLE PRECISION TEN INTEGER I,J,K,KB,KP1,L,NM1 C***FIRST EXECUTABLE STATEMENT DGEDI C C COMPUTE DETERMINANT C IF (JOB/10 .EQ. 0) GO TO 70 DET(1) = 1.0D0 DET(2) = 0.0D0 TEN = 10.0D0 DO 50 I = 1, N IF (IPVT(I) .NE. I) DET(1) = -DET(1) DET(1) = A(I,I)*DET(1) IF (DET(1) .EQ. 0.0D0) GO TO 60 10 IF (ABS(DET(1)) .GE. 1.0D0) GO TO 20 DET(1) = TEN*DET(1) DET(2) = DET(2) - 1.0D0 GO TO 10 20 CONTINUE 30 IF (ABS(DET(1)) .LT. TEN) GO TO 40 DET(1) = DET(1)/TEN DET(2) = DET(2) + 1.0D0 GO TO 30 40 CONTINUE 50 CONTINUE 60 CONTINUE 70 CONTINUE C C COMPUTE INVERSE(U) C IF (MOD(JOB,10) .EQ. 0) GO TO 150 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(U)*INVERSE(L) C NM1 = N - 1 IF (NM1 .LT. 1) GO TO 140 DO 130 KB = 1, NM1 K = N - KB KP1 = K + 1 DO 110 I = KP1, N WORK(I) = A(I,K) A(I,K) = 0.0D0 110 CONTINUE DO 120 J = KP1, N T = WORK(J) CALL DAXPY(N,T,A(1,J),1,A(1,K),1) 120 CONTINUE L = IPVT(K) IF (L .NE. K) CALL DSWAP(N,A(1,K),1,A(1,L),1) 130 CONTINUE 140 CONTINUE 150 CONTINUE RETURN END