ctrco.f
SUBROUTINE CTRCO (T, LDT, N, RCOND, Z, JOB)
C***BEGIN PROLOGUE CTRCO
C***PURPOSE Estimate the condition number of a triangular matrix.
C***LIBRARY SLATEC (LINPACK)
C***CATEGORY D2C3
C***TYPE COMPLEX (STRCO-S, DTRCO-D, CTRCO-C)
C***KEYWORDS CONDITION NUMBER, LINEAR ALGEBRA, LINPACK,
C TRIANGULAR MATRIX
C***AUTHOR Moler, C. B., (U. of New Mexico)
C***DESCRIPTION
C
C CTRCO estimates the condition of a complex triangular matrix.
C
C On Entry
C
C T COMPLEX(LDT,N)
C T contains the triangular matrix. The zero
C elements of the matrix are not referenced, and
C the corresponding elements of the array can be
C used to store other information.
C
C LDT INTEGER
C LDT is the leading dimension of the array T.
C
C N INTEGER
C N is the order of the system.
C
C JOB INTEGER
C = 0 T is lower triangular.
C = nonzero T is upper triangular.
C
C On Return
C
C RCOND REAL
C an estimate of the reciprocal condition of T .
C For the system T*X = B , relative perturbations
C in T and B of size EPSILON may cause
C relative perturbations in X of size EPSILON/RCOND .
C If RCOND is so small that the logical expression
C 1.0 + RCOND .EQ. 1.0
C is true, then T may be singular to working
C precision. In particular, RCOND is zero if
C exact singularity is detected or the estimate
C underflows.
C
C Z COMPLEX(N)
C a work vector whose contents are usually unimportant.
C If T is close to a singular matrix, then Z is
C an approximate null vector in the sense that
C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
C
C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W.
C Stewart, LINPACK Users' Guide, SIAM, 1979.
C***ROUTINES CALLED CAXPY, CSSCAL, SCASUM
C***REVISION HISTORY (YYMMDD)
C 780814 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 900326 Removed duplicate information from DESCRIPTION section.
C (WRB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE CTRCO