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NAME
     dtrdi - compute the determinant and inverse of a  triangular
     matrix A.

SYNOPSIS
     SUBROUTINE DTRDI (DA, LDA, N, DDET, JOB, INFO)

     SUBROUTINE STRDI (SA, LDA, N, SDET, JOB, INFO)

     SUBROUTINE ZTRDI (ZA, LDA, N, ZDET, JOB, INFO)

     SUBROUTINE CTRDI (CA, LDA, N, CDET, JOB, INFO)



     #include <sunperf.h>

     void dtrdi(double *t, int ldt, int n, double *det, int  job,
               int *info) ;

     void strdi(float *t, int ldt, int n, float  *det,  int  job,
               int *info) ;

     void ztrdi(doublecomplex *t, int ldt, int  n,  doublecomplex
               *det, int job, int *info) ;

     void ctrdi(complex *t, int ldt, int  n,  complex  *det,  int
               job, int *info) ;

ARGUMENTS
     xA        On entry, the matrix A.  On exit, the  inverse  of
               the   original   matrix   A  if  the  inverse  was
               requested, otherwise unchanged.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= max(1,N).

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

     JOB       Determines which  operation  the  subroutine  will
               perform:
                    010  no determinant, inverse  of  lower  tri-
               angular A
                    011  no determinant, inverse  of  upper  tri-
               angular A
                    100  determinant, no inverse
                    110  determinant, inverse of lower triangular

               A
                    111  determinant, inverse of upper triangular
               A

     INFO      On exit:
               INFO = 0  Subroutine completed normally.
               INFO * 0  Contains the index of a zero element  of
               A if the inverse is requested and A is singular.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           INDTLO, LDA, N
           PARAMETER        (INDTLO = 110)
           PARAMETER        (N = 5)
           PARAMETER        (LDA = N)
     C
           DOUBLE PRECISION  A(LDA,N), DET(2)
           INTEGER           ICOL, INFO, IROW, JOB
     C
           EXTERNAL          DTRDI
     C
     C     Initialize the array A to store the 5x5 triangular matrix A
     C     shown below.
     C
     C         1
     C         1  -1
     C     A = 1  -2  1
     C         1  -3  3  -1
     C         1  -4  6  -4  1
     C
           DATA A / 5*1.0D0, 8D8, -1.0D0, -2.0D0, -3.0D0, -4.0D0,
          $         2*8D8, 1.0D0, 3.0D0, 6.0D0, 3*8D8, -1.0D0,
          $         -4.0D0, 4*8D8, 1.0D0 /
     C
     C     Print the initial values of the arrays.
     C
           PRINT 1000
           DO 100, IROW = 1, N
             PRINT 1010, (A(IROW,ICOL), ICOL = 1, IROW)
       100 CONTINUE
           PRINT 1020
           PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)
     C
     C     Factor the matrix in banded form.
     C
           JOB = INDTLO
           CALL DTRDI (A, LDA, N, DET, JOB, INFO)
           IF (INFO .EQ. 0) THEN
             PRINT 1030, DET(1) * (10.0 ** DET(2))
             PRINT 1040
             DO 110, IROW = 1, N
               PRINT 1010, (A(IROW,ICOL), ICOL = 1, IROW)
       110   CONTINUE
           ELSE
             PRINT 1050, INFO
           END IF
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (5(3X, F4.1))
      1020 FORMAT (/1X, 'A in triangular form:  (* in unused elements)')
      1030 FORMAT (/1X, 'det(A) = ', F4.1)
      1040 FORMAT (/1X, 'A**(-1):')
      1050 FORMAT (1X, 'A appears singular at ', I2)
     C
           END

SAMPLE OUTPUT
      A in full form:
         1.0
         1.0   -1.0
         1.0   -2.0    1.0
         1.0   -3.0    3.0   -1.0
         1.0   -4.0    6.0   -4.0    1.0

      A in triangular form:  (* in unused elements)
         1.0   ****   ****   ****   ****
         1.0   -1.0   ****   ****   ****
         1.0   -2.0    1.0   ****   ****
         1.0   -3.0    3.0   -1.0   ****
         1.0   -4.0    6.0   -4.0    1.0

      det(A) =  1.0

      A**(-1):
         1.0
         1.0   -1.0
         1.0   -2.0    1.0
         1.0   -3.0    3.0   -1.0
         1.0   -4.0    6.0   -4.0    1.0

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