DTRCO(3)

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

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

LIBRARY
SLATEC (LINPACK)

CATEGORY
D2A3

TYPE
DOUBLE PRECISION (STRCO-S, DTRCO-D, CTRCO-C)

KEYWORDS
CONDITION NUMBER, LINEAR ALGEBRA, LINPACK, TRIANGULAR MATRIX

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

DESCRIPTION
DTRCO estimates the condition of a double precision triangular matrix. On Entry T DOUBLE PRECISION(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 DOUBLE PRECISION 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 DOUBLE PRECISION(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
DASUM, DAXPY, DSCAL

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)