CTRCO(3)

SYNOPSIS
SUBROUTINE CTRCO (T, LDT, N, RCOND, Z, JOB)

NAME
ctrco - Estimate the condition number of a triangular matrix.

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2C3

TYPE
COMPLEX (STRCO-S, DTRCO-D, CTRCO-C)

KEYWORDS
CONDITION NUMBER, LINEAR ALGEBRA, LINPACK, TRIANGULAR MATRIX

AUTHOR
Moler, C. B., (U. of New Mexico)

DESCRIPTION
CTRCO estimates the condition of a complex triangular matrix. On Entry T COMPLEX(LDT,N) T contains the triangular matrix. The zero elements of the matrix are not referenced, and the corresponding elements of the array can be used to store other information. LDT INTEGER LDT is the leading dimension of the array T. N INTEGER N is the order of the system. JOB INTEGER = 0 T is lower triangular. = nonzero T is upper triangular. On Return RCOND REAL an estimate of the reciprocal condition of T . For the system T*X = B , relative perturbations in T and B of size EPSILON may cause relative perturbations in X of size EPSILON/RCOND . If RCOND is so small that the logical expression 1.0 + RCOND .EQ. 1.0 is true, then T may be singular to working precision. In particular, RCOND is zero if exact singularity is detected or the estimate underflows. Z COMPLEX(N) a work vector whose contents are usually unimportant. If T is close to a singular matrix, then Z is an approximate null vector in the sense that NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .

REFERENCES
J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide, SIAM, 1979.

ROUTINES CALLED
CAXPY, CSSCAL, SCASUM

REVISION HISTORY (YYMMDD)
780814 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)