*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