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111 lines
3.8 KiB
Fortran
111 lines
3.8 KiB
Fortran
*DECK ORTRAN
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SUBROUTINE ORTRAN (NM, N, LOW, IGH, A, ORT, Z)
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C***BEGIN PROLOGUE ORTRAN
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C***PURPOSE Accumulate orthogonal similarity transformations in the
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C reduction of real general matrix by ORTHES.
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C***LIBRARY SLATEC (EISPACK)
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C***CATEGORY D4C4
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C***TYPE SINGLE PRECISION (ORTRAN-S)
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C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
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C***AUTHOR Smith, B. T., et al.
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C***DESCRIPTION
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C
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C This subroutine is a translation of the ALGOL procedure ORTRANS,
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C NUM. MATH. 16, 181-204(1970) by Peters and Wilkinson.
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C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 372-395(1971).
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C
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C This subroutine accumulates the orthogonal similarity
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C transformations used in the reduction of a REAL GENERAL
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C matrix to upper Hessenberg form by ORTHES.
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C
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C On INPUT
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C
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C NM must be set to the row dimension of the two-dimensional
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C array parameters, A and Z, as declared in the calling
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C program dimension statement. NM is an INTEGER variable.
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C
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C N is the order of the matrix A. N is an INTEGER variable.
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C N must be less than or equal to NM.
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C
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C LOW and IGH are two INTEGER variables determined by the
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C balancing subroutine BALANC. If BALANC has not been
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C used, set LOW=1 and IGH equal to the order of the matrix, N.
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C
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C A contains some information about the orthogonal trans-
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C formations used in the reduction to Hessenberg form by
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C ORTHES in its strict lower triangle. A is a two-dimensional
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C REAL array, dimensioned A(NM,IGH).
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C
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C ORT contains further information about the orthogonal trans-
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C formations used in the reduction by ORTHES. Only elements
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C LOW through IGH are used. ORT is a one-dimensional REAL
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C array, dimensioned ORT(IGH).
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C
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C On OUTPUT
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C
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C Z contains the transformation matrix produced in the reduction
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C by ORTHES to the upper Hessenberg form. Z is a two-
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C dimensional REAL array, dimensioned Z(NM,N).
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C
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C ORT has been used for temporary storage as is not restored.
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C
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C Questions and comments should be directed to B. S. Garbow,
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C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
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C ------------------------------------------------------------------
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C
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C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
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C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
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C system Routines - EISPACK Guide, Springer-Verlag,
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C 1976.
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C***ROUTINES CALLED (NONE)
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C***REVISION HISTORY (YYMMDD)
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C 760101 DATE WRITTEN
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C 890831 Modified array declarations. (WRB)
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C 890831 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE ORTRAN
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C
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INTEGER I,J,N,KL,MM,MP,NM,IGH,LOW,MP1
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REAL A(NM,*),ORT(*),Z(NM,*)
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REAL G
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C
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C .......... INITIALIZE Z TO IDENTITY MATRIX ..........
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C***FIRST EXECUTABLE STATEMENT ORTRAN
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DO 80 I = 1, N
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C
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DO 60 J = 1, N
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60 Z(I,J) = 0.0E0
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C
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Z(I,I) = 1.0E0
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80 CONTINUE
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C
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KL = IGH - LOW - 1
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IF (KL .LT. 1) GO TO 200
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C .......... FOR MP=IGH-1 STEP -1 UNTIL LOW+1 DO -- ..........
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DO 140 MM = 1, KL
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MP = IGH - MM
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IF (A(MP,MP-1) .EQ. 0.0E0) GO TO 140
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MP1 = MP + 1
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C
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DO 100 I = MP1, IGH
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100 ORT(I) = A(I,MP-1)
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C
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DO 130 J = MP, IGH
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G = 0.0E0
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C
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DO 110 I = MP, IGH
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110 G = G + ORT(I) * Z(I,J)
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C .......... DIVISOR BELOW IS NEGATIVE OF H FORMED IN ORTHES.
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C DOUBLE DIVISION AVOIDS POSSIBLE UNDERFLOW ..........
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G = (G / ORT(MP)) / A(MP,MP-1)
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C
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DO 120 I = MP, IGH
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120 Z(I,J) = Z(I,J) + G * ORT(I)
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C
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130 CONTINUE
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C
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140 CONTINUE
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C
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200 RETURN
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END
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