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82 lines
2.4 KiB
Fortran
82 lines
2.4 KiB
Fortran
*DECK SPBDI
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SUBROUTINE SPBDI (ABD, LDA, N, M, DET)
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C***BEGIN PROLOGUE SPBDI
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C***PURPOSE Compute the determinant of a symmetric positive definite
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C band matrix using the factors computed by SPBCO or SPBFA.
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C***LIBRARY SLATEC (LINPACK)
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C***CATEGORY D3B2
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C***TYPE SINGLE PRECISION (SPBDI-S, DPBDI-D, CPBDI-C)
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C***KEYWORDS BANDED, DETERMINANT, INVERSE, LINEAR ALGEBRA, LINPACK,
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C MATRIX, POSITIVE DEFINITE
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C***AUTHOR Moler, C. B., (U. of New Mexico)
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C***DESCRIPTION
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C
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C SPBDI computes the determinant
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C of a real symmetric positive definite band matrix
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C using the factors computed by SPBCO or SPBFA.
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C If the inverse is needed, use SPBSL N times.
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C
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C On Entry
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C
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C ABD REAL(LDA, N)
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C the output from SPBCO or SPBFA.
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C
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C LDA INTEGER
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C the leading dimension of the array ABD .
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C
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C N INTEGER
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C the order of the matrix A .
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C
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C M INTEGER
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C the number of diagonals above the main diagonal.
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C
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C On Return
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C
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C DET REAL(2)
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C determinant of original matrix in the form
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C Determinant = DET(1) * 10.0**DET(2)
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C with 1.0 .LE. DET(1) .LT. 10.0
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C or DET(1) .EQ. 0.0 .
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C
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C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
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C Stewart, LINPACK Users' Guide, SIAM, 1979.
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C***ROUTINES CALLED (NONE)
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C***REVISION HISTORY (YYMMDD)
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C 780814 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900326 Removed duplicate information from DESCRIPTION section.
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C (WRB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE SPBDI
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INTEGER LDA,N,M
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REAL ABD(LDA,*)
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REAL DET(2)
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C
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REAL S
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INTEGER I
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C***FIRST EXECUTABLE STATEMENT SPBDI
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C
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C COMPUTE DETERMINANT
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C
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DET(1) = 1.0E0
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DET(2) = 0.0E0
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S = 10.0E0
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DO 50 I = 1, N
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DET(1) = ABD(M+1,I)**2*DET(1)
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IF (DET(1) .EQ. 0.0E0) GO TO 60
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10 IF (DET(1) .GE. 1.0E0) GO TO 20
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DET(1) = S*DET(1)
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DET(2) = DET(2) - 1.0E0
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GO TO 10
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20 CONTINUE
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30 IF (DET(1) .LT. S) GO TO 40
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DET(1) = DET(1)/S
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DET(2) = DET(2) + 1.0E0
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GO TO 30
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40 CONTINUE
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50 CONTINUE
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60 CONTINUE
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RETURN
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END
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