SUBROUTINE CTRCO(T,LDT,N,RCOND,Z,JOB) C***BEGIN PROLOGUE CTRCO C***DATE WRITTEN 780814 (YYMMDD) C***REVISION DATE 820801 (YYMMDD) C***CATEGORY NO. D2C3 C***KEYWORDS COMPLEX,CONDITION,FACTOR,LINEAR ALGEBRA,LINPACK,MATRIX, C TRIANGULAR C***AUTHOR MOLER, C. B., (U. OF NEW MEXICO) C***PURPOSE Estimates the condition of a COMPLEX TRIANGULAR matrix. 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 LINPACK. This version dated 08/14/78 . C Cleve Moler, University of New Mexico, Argonne National Lab. C C Subroutines and Functions C C BLAS CAXPY,CSSCAL,SCASUM C Fortran ABS,AIMAG,AMAX1,CMPLX,CONJG,REAL C***REFERENCES DONGARRA J.J., BUNCH J.R., MOLER C.B., STEWART G.W., C *LINPACK USERS GUIDE*, SIAM, 1979. C***ROUTINES CALLED CAXPY,CSSCAL,SCASUM C***END PROLOGUE CTRCO