dtrdi(3P)

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:
010no determinant, inverse of lower triangular A
011no determinant, inverse of upper triangular A
100determinant, no inverse
110determinant, inverse of lower triangular A
111determinant, inverse of upper triangular A

INFO On exit:
INFO = 0Subroutine completed normally.
INFO ∗ 0Contains 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