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NAME
     zpbdi - compute the  determinant  of  a  symmetric  positive
     definite   matrix  A  in  banded  storage,  which  has  been
     Cholesky-factored by xPBCO or xPBFA.

SYNOPSIS
     SUBROUTINE DPBDI (DA, LDA, N, NDIAG, DDET)

     SUBROUTINE SPBDI (SA, LDA, N, NDIAG, SDET)

     SUBROUTINE ZPBDI (ZA, LDA, N, NDIAG, DDET)

     SUBROUTINE CPBDI (CA, LDA, N, NDIAG, SDET)



     #include <sunperf.h>

     void dpbdi(double *abd, int lda, int n, int m, double *det);

     void spbdi(float *abd, int lda, int n, int m, float *det);

     void zpbdi(doublecomplex *abd, int lda, int n, int m, double
               *det);

     void cpbdi(complex *abd, int lda, int n, int m, float *det);

ARGUMENTS
     xA        Cholesky factorization of the matrix  A,  as  com-
               puted by xPBCO or xPBFA.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= NDIAG + 1.

     N         Order of the original matrix A.  N >= 0.

     NDIAG     Number of diagonals.  N-1 >= NDIAG >= 0 but if N =
               0 then NDIAG = 0.

     xDET      On exit, the determinant of  the  matrix  A.   The
               determinant is stored as b * (10 ** expon) where b
               is stored  in   DET(1)  and  expon  is  stored  in
               DET(2).   1.0  <=  |DET(1)|  <= 10.0  or  DET(1) =
               0.0.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           LDA, N, NDIAG
           PARAMETER        (N = 4)
           PARAMETER        (NDIAG = 1)
           PARAMETER        (LDA = NDIAG + 1)
     C
           DOUBLE PRECISION  A(LDA,N), DET(2)
           INTEGER           ICOL, INFO, IROW, NDIAG
           EXTERNAL          DPBDI, DPBFA
     C
     C     Initialize the array A to store in banded storage mode
     C     the matrix A shown below.
     C
     C          2  -1   0   0
     C     A = -1   2  -1   0
     C          0  -1   2  -1
     C          0   0  -1   2
     C
           DATA A / 8D8, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0 /
     C
           PRINT 1000
           PRINT 1010, A(2,1), A(1,2)
           PRINT 1010, A(3,1), A(2,2), A(1,3)
           PRINT 1020,         A(3,2), A(2,3), A(1,4)
           PRINT 1030,                 A(3,3), A(2,4)
           PRINT 1040
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)
           CALL DPBFA (A, LDA, N, NDIAG, INFO)
           IF (INFO .EQ. 0) THEN
             CALL DPBDI (A, LDA, N, NDIAG, DET)
             PRINT 1050, DET(1) * (10.0D0 ** DET(2))
           ELSE
             PRINT 1060
           END IF
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(3X, F5.1))
      1020 FORMAT (8X, 3(3X, F5.1))
      1030 FORMAT (16X, 3(3X, F5.1))
      1040 FORMAT (/1X, 'A in banded form:  (* in unused entries)')
      1050 FORMAT (/1X, 'The determinant of A is ', F5.1)
      1060 FORMAT (/1X, 'A is not positive definite.')
     C
           END

SAMPLE OUTPUT
      A in full form:
          2.0    -1.0
         -1.0     2.0    -1.0
                 -1.0     2.0    -1.0
                         -1.0     2.0

      A in banded form:  (* in unused entries)
        *****    -1.0    -1.0    -1.0
          2.0     2.0     2.0     2.0

      The determinant of A is   5.0

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