dtrco(3P)

NAME

dtrco - estimate the condition number of a triangular matrix A. It is typical to follow a call to xTRCO with a call to xTRSL to solve Ax = b or to xTRDI to compute the determinant and inverse of A.

SYNOPSIS

SUBROUTINE DTRCO (DA, LDA, N, DRCOND, DWORK, JOB)

SUBROUTINE STRCO (SA, LDA, N, SRCOND, SWORK, JOB)

SUBROUTINE ZTRCO (ZA, LDA, N, DRCOND, ZWORK, JOB)

SUBROUTINE CTRCO (CA, LDA, N, SRCOND, CWORK, JOB)

#include <sunperf.h>

void dtrco(double ∗t, int ldt, int n, double ∗drcond, int job);

void strco(float ∗t, int ldt, int n, float ∗srcond, int job);

void ztrco(doublecomplex ∗t, int ldt, int n, double ∗drcond, int job);

void ctrco(complex ∗t, int ldt, int n, float ∗srcond, int job);

ARGUMENTS

xA Matrix A.

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

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

xRCOND On exit, an estimate of the reciprocal condition number of A. 0.0 <= RCOND <= 1.0. As the value of RCOND gets smaller, operations with A such as solving Ax = b may become less stable. If RCOND satisfies RCOND + 1.0 = 1.0 then A may be singular to working precision.

xWORK Scratch array with a dimension of N.

JOB If JOB = 0, then A is lower triangular; otherwise A is upper triangular.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           ILOWER, LDA, N
      PARAMETER        (ILOWER = 0)
      PARAMETER        (N = 5)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), RCOND, WORK(N)
      INTEGER           ICOL, IROW, JOB
C
      EXTERNAL          DTRCO
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 1 1
C         1 1 1 1
C         1 1 1 1 1
C
      DATA A / 5∗1.0D0, 8D8, 4∗1.0D0, 2∗8D8, 3∗1.0D0, 3∗8D8,
     $         2∗1.0D0, 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     Estimate the condition number of the matrix.
C
      JOB = ILOWER
      CALL DTRCO (A, LDA, N, RCOND, WORK, JOB)
      PRINT 1030, RCOND
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, ’Reciprocal of the condition number:’, F4.1)
C
      END

SAMPLE OUTPUT

A in full form:
    1.0
    1.0    1.0
    1.0    1.0    1.0
    1.0    1.0    1.0    1.0
    1.0    1.0    1.0    1.0    1.0

A in triangular form: (∗ in unused elements)
    1.0   ∗∗∗∗   ∗∗∗∗   ∗∗∗∗   ∗∗∗∗
    1.0    1.0   ∗∗∗∗   ∗∗∗∗   ∗∗∗∗
    1.0    1.0    1.0   ∗∗∗∗   ∗∗∗∗
    1.0    1.0    1.0    1.0   ∗∗∗∗
    1.0    1.0    1.0    1.0    1.0

Reciprocal of the condition number: 0.1