Condition Number of a Triangular Matrix

Calling Sequence

CALL DTRCO	(DA, LDA, N, DRCOND, DWORK, 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 *da, int lda, int n, double *drcond, int job)
void strco	(float *sa, int lda, int n, float *srcond, int job)
void ztrco	(doublecomplex *za, int lda, int n, double *drcond, int job)
void ctrco	(complex *ca, int lda, 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