*DECK ELTRAN SUBROUTINE ELTRAN (NM, N, LOW, IGH, A, INT, Z) C***BEGIN PROLOGUE ELTRAN C***PURPOSE Accumulates the stabilized elementary similarity C transformations used in the reduction of a real general C matrix to upper Hessenberg form by ELMHES. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4C4 C***TYPE SINGLE PRECISION (ELTRAN-S) C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK C***AUTHOR Smith, B. T., et al. C***DESCRIPTION C C This subroutine is a translation of the ALGOL procedure ELMTRANS, C NUM. MATH. 16, 181-204(1970) by Peters and Wilkinson. C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971). C C This subroutine accumulates the stabilized elementary C similarity transformations used in the reduction of a C REAL GENERAL matrix to upper Hessenberg form by ELMHES. C C On INPUT C C NM must be set to the row dimension of the two-dimensional C array parameters, A and Z, as declared in the calling C program dimension statement. NM is an INTEGER variable. C C N is the order of the matrix A. N is an INTEGER variable. C N must be less than or equal to NM. C C LOW and IGH are two INTEGER variables determined by the C balancing subroutine BALANC. If BALANC has not been C used, set LOW=1 and IGH equal to the order of the matrix, N. C C A contains the multipliers which were used in the reduction C by ELMHES in its lower triangle below the subdiagonal. C A is a two-dimensional REAL array, dimensioned A(NM,IGH). C C INT contains information on the rows and columns interchanged C in the reduction by ELMHES. Only elements LOW through IGH C are used. INT is a one-dimensional INTEGER array, C dimensioned INT(IGH). C C On OUTPUT C C Z contains the transformation matrix produced in the reduction C by ELMHES. Z is a two-dimensional REAL array, dimensioned C Z(NM,N). 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 ELTRAN C INTEGER I,J,N,KL,MM,MP,NM,IGH,LOW,MP1 REAL A(NM,*),Z(NM,*) INTEGER INT(*) C C***FIRST EXECUTABLE STATEMENT ELTRAN DO 80 I = 1, N C DO 60 J = 1, N 60 Z(I,J) = 0.0E0 C Z(I,I) = 1.0E0 80 CONTINUE C KL = IGH - LOW - 1 IF (KL .LT. 1) GO TO 200 C .......... FOR MP=IGH-1 STEP -1 UNTIL LOW+1 DO -- .......... DO 140 MM = 1, KL MP = IGH - MM MP1 = MP + 1 C DO 100 I = MP1, IGH 100 Z(I,MP) = A(I,MP-1) C I = INT(MP) IF (I .EQ. MP) GO TO 140 C DO 130 J = MP, IGH Z(MP,J) = Z(I,J) Z(I,J) = 0.0E0 130 CONTINUE C Z(I,MP) = 1.0E0 140 CONTINUE C 200 RETURN END