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- *DECK SGBDI
- SUBROUTINE SGBDI (ABD, LDA, N, ML, MU, IPVT, DET)
- C***BEGIN PROLOGUE SGBDI
- C***PURPOSE Compute the determinant of a band matrix using the factors
- C computed by SGBCO or SGBFA.
- C***LIBRARY SLATEC (LINPACK)
- C***CATEGORY D3A2
- C***TYPE SINGLE PRECISION (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 SGBDI computes the determinant of a band matrix
- C using the factors computed by SBGCO or SGBFA.
- C If the inverse is needed, use SGBSL N times.
- C
- C On Entry
- C
- C ABD REAL(LDA, N)
- C the output from SBGCO or SGBFA.
- 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 SBGCO or SGBFA.
- C
- C On Return
- C
- C DET REAL(2)
- C determinant of original matrix.
- C Determinant = DET(1) * 10.0**DET(2)
- C with 1.0 .LE. ABS(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 SGBDI
- INTEGER LDA,N,ML,MU,IPVT(*)
- REAL ABD(LDA,*),DET(2)
- C
- REAL TEN
- INTEGER I,M
- C***FIRST EXECUTABLE STATEMENT SGBDI
- M = ML + MU + 1
- DET(1) = 1.0E0
- DET(2) = 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 (DET(1) .EQ. 0.0E0) GO TO 60
- 10 IF (ABS(DET(1)) .GE. 1.0E0) GO TO 20
- DET(1) = TEN*DET(1)
- DET(2) = DET(2) - 1.0E0
- GO TO 10
- 20 CONTINUE
- 30 IF (ABS(DET(1)) .LT. TEN) GO TO 40
- DET(1) = DET(1)/TEN
- DET(2) = DET(2) + 1.0E0
- GO TO 30
- 40 CONTINUE
- 50 CONTINUE
- 60 CONTINUE
- RETURN
- END
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