*DECK BALBAK SUBROUTINE BALBAK (NM, N, LOW, IGH, SCALE, M, Z) C***BEGIN PROLOGUE BALBAK C***PURPOSE Form the eigenvectors of a real general matrix from the C eigenvectors of matrix output from BALANC. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4C4 C***TYPE SINGLE PRECISION (BALBAK-S, CBABK2-C) C***KEYWORDS EIGENVECTORS, EISPACK C***AUTHOR Smith, B. T., et al. C***DESCRIPTION C C This subroutine is a translation of the ALGOL procedure BALBAK, C NUM. MATH. 13, 293-304(1969) by Parlett and Reinsch. C HANDBOOK FOR AUTO. COMP., Vol.II-LINEAR ALGEBRA, 315-326(1971). C C This subroutine forms the eigenvectors of a REAL GENERAL C matrix by back transforming those of the corresponding C balanced matrix determined by BALANC. C C On INPUT C C NM must be set to the row dimension of the two-dimensional C array parameter, Z, as declared in the calling program C dimension statement. NM is an INTEGER variable. C C N is the number of components of the vectors in matrix Z. C N is an INTEGER variable. N must be less than or equal C to NM. C C LOW and IGH are INTEGER variables determined by BALANC. C C SCALE contains information determining the permutations and C scaling factors used by BALANC. SCALE is a one-dimensional C REAL array, dimensioned SCALE(N). C C M is the number of columns of Z to be back transformed. C M is an INTEGER variable. C C Z contains the real and imaginary parts of the eigen- C vectors to be back transformed in its first M columns. C Z is a two-dimensional REAL array, dimensioned Z(NM,M). C C On OUTPUT C C Z contains the real and imaginary parts of the C transformed eigenvectors in its first M columns. C C Questions and comments should be directed to B. S. Garbow, C Applied Mathematics Division, ARGONNE NATIONAL LABORATORY C ------------------------------------------------------------------ C C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- C system Routines - EISPACK Guide, Springer-Verlag, C 1976. C***ROUTINES CALLED (NONE) C***REVISION HISTORY (YYMMDD) C 760101 DATE WRITTEN 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 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE BALBAK C INTEGER I,J,K,M,N,II,NM,IGH,LOW REAL SCALE(*),Z(NM,*) REAL S C C***FIRST EXECUTABLE STATEMENT BALBAK IF (M .EQ. 0) GO TO 200 IF (IGH .EQ. LOW) GO TO 120 C DO 110 I = LOW, IGH S = SCALE(I) C .......... LEFT HAND EIGENVECTORS ARE BACK TRANSFORMED C IF THE FOREGOING STATEMENT IS REPLACED BY C S=1.0E0/SCALE(I). .......... DO 100 J = 1, M 100 Z(I,J) = Z(I,J) * S C 110 CONTINUE C ......... FOR I=LOW-1 STEP -1 UNTIL 1, C IGH+1 STEP 1 UNTIL N DO -- .......... 120 DO 140 II = 1, N I = II IF (I .GE. LOW .AND. I .LE. IGH) GO TO 140 IF (I .LT. LOW) I = LOW - II K = SCALE(I) IF (K .EQ. I) GO TO 140 C DO 130 J = 1, M S = Z(I,J) Z(I,J) = Z(K,J) Z(K,J) = S 130 CONTINUE C 140 CONTINUE C 200 RETURN END