ctrco(3P)

NAME

ctrco - 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

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

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

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

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

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

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

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

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

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

ARGUMENTS

xAMatrix A.

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

NOrder of the matrix A. N >= 0.

xRCONDOn 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.

xWORKScratch array with a dimension of N.

JOBIf 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