1 2 SUBROUTINE CBABK2(NM,N,LOW,IGH,SCALE,M,ZR,ZI) 3C***BEGIN PROLOGUE CBABK2 4C***DATE WRITTEN 760101 (YYMMDD) 5C***REVISION DATE 830518 (YYMMDD) 6C***CATEGORY NO. D4C4 7C***KEYWORDS EIGENVALUES,EIGENVECTORS,EISPACK 8C***AUTHOR SMITH, B. T., ET AL. 9C***PURPOSE Forms eigenvectors of complex general matrix from 10C eigenvectors of matrix output from CBAL. 11C***DESCRIPTION 12C 13C This subroutine is a translation of the ALGOL procedure 14C CBABK2, which is a complex version of BALBAK, 15C NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch. 16C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 315-326(1971). 17C 18C This subroutine forms the eigenvectors of a COMPLEX GENERAL 19C matrix by back transforming those of the corresponding 20C balanced matrix determined by CBAL. 21C 22C On INPUT 23C 24C NM must be set to the row dimension of two-dimensional 25C array parameters as declared in the calling program 26C dimension statement. 27C 28C N is the order of the matrix. 29C 30C LOW and IGH are integers determined by CBAL. 31C 32C SCALE contains information determining the permutations 33C and scaling factors used by CBAL. 34C 35C M is the number of eigenvectors to be back transformed. 36C 37C ZR and ZI contain the real and imaginary parts, 38C respectively, of the eigenvectors to be 39C back transformed in their first M columns. 40C 41C On OUTPUT 42C 43C ZR and ZI contain the real and imaginary parts, 44C respectively, of the transformed eigenvectors 45C in their first M columns. 46C 47C Questions and comments should be directed to B. S. Garbow, 48C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY 49C ------------------------------------------------------------------ 50C***REFERENCES B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW, 51C Y. IKEBE, V. C. KLEMA, C. B. MOLER, *MATRIX EIGEN- 52C SYSTEM ROUTINES - EISPACK GUIDE*, SPRINGER-VERLAG, 53C 1976. 54C***ROUTINES CALLED (NONE) 55C***END PROLOGUE CBABK2 56 57 58