*DECK CGBDI SUBROUTINE CGBDI (ABD, LDA, N, ML, MU, IPVT, DET) C***BEGIN PROLOGUE CGBDI C***PURPOSE Compute the determinant of a complex band matrix using the C factors from CGBCO or CGBFA. C***LIBRARY SLATEC (LINPACK) C***CATEGORY D3C2 C***TYPE COMPLEX (SGBDI-S, DGBDI-D, CGBDI-C) C***KEYWORDS BANDED, DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK, C MATRIX C***AUTHOR Moler, C. B., (U. of New Mexico) C***DESCRIPTION C C CGBDI computes the determinant of a band matrix C using the factors computed by CGBCO or CGBFA. C If the inverse is needed, use CGBSL N times. C C On Entry C C ABD COMPLEX(LDA, N) C the output from CGBCO or CGBFA. C C LDA INTEGER C the leading dimension of the array ABD . C C N INTEGER C the order of the original matrix. C C ML INTEGER C number of diagonals below the main diagonal. C C MU INTEGER C number of diagonals above the main diagonal. C C IPVT INTEGER(N) C the pivot vector from CGBCO or CGBFA. C C On Return C C DET COMPLEX(2) C determinant of original matrix. C Determinant = DET(1) * 10.0**DET(2) C with 1.0 .LE. CABS1(DET(1)) .LT. 10.0 C or DET(1) = 0.0 . 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 (NONE) 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 CGBDI INTEGER LDA,N,ML,MU,IPVT(*) COMPLEX ABD(LDA,*),DET(2) C REAL TEN INTEGER I,M COMPLEX ZDUM REAL CABS1 C CABS1(ZDUM) = ABS(REAL(ZDUM)) + ABS(AIMAG(ZDUM)) C***FIRST EXECUTABLE STATEMENT CGBDI M = ML + MU + 1 DET(1) = (1.0E0,0.0E0) DET(2) = (0.0E0,0.0E0) TEN = 10.0E0 DO 50 I = 1, N IF (IPVT(I) .NE. I) DET(1) = -DET(1) DET(1) = ABD(M,I)*DET(1) IF (CABS1(DET(1)) .EQ. 0.0E0) GO TO 60 10 IF (CABS1(DET(1)) .GE. 1.0E0) GO TO 20 DET(1) = CMPLX(TEN,0.0E0)*DET(1) DET(2) = DET(2) - (1.0E0,0.0E0) GO TO 10 20 CONTINUE 30 IF (CABS1(DET(1)) .LT. TEN) GO TO 40 DET(1) = DET(1)/CMPLX(TEN,0.0E0) DET(2) = DET(2) + (1.0E0,0.0E0) GO TO 30 40 CONTINUE 50 CONTINUE 60 CONTINUE RETURN END