bandr.f
SUBROUTINE BANDR (NM, N, MB, A, D, E, E2, MATZ, Z)
C***BEGIN PROLOGUE BANDR
C***PURPOSE Reduce a real symmetric band matrix to symmetric
C tridiagonal matrix and, optionally, accumulate
C orthogonal similarity transformations.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C1B1
C***TYPE SINGLE PRECISION (BANDR-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 BANDRD,
C NUM. MATH. 12, 231-241(1968) by Schwarz.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 273-283(1971).
C
C This subroutine reduces a REAL SYMMETRIC BAND matrix
C to a symmetric tridiagonal matrix using and optionally
C accumulating orthogonal similarity transformations.
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 MB is the (half) band width of the matrix, defined as the
C number of adjacent diagonals, including the principal
C diagonal, required to specify the non-zero portion of the
C lower triangle of the matrix. MB is less than or equal
C to N. MB is an INTEGER variable.
C
C A contains the lower triangle of the real symmetric band
C matrix. Its lowest subdiagonal is stored in the last
C N+1-MB positions of the first column, its next subdiagonal
C in the last N+2-MB positions of the second column, further
C subdiagonals similarly, and finally its principal diagonal
C in the N positions of the last column. Contents of storage
C locations not part of the matrix are arbitrary. A is a
C two-dimensional REAL array, dimensioned A(NM,MB).
C
C MATZ should be set to .TRUE. if the transformation matrix is
C to be accumulated, and to .FALSE. otherwise. MATZ is a
C LOGICAL variable.
C
C On OUTPUT
C
C A has been destroyed, except for its last two columns which
C contain a copy of the tridiagonal matrix.
C
C D contains the diagonal elements of the tridiagonal matrix.
C D is a one-dimensional REAL array, dimensioned D(N).
C
C E contains the subdiagonal elements of the tridiagonal
C matrix in its last N-1 positions. E(1) is set to zero.
C E is a one-dimensional REAL array, dimensioned E(N).
C
C E2 contains the squares of the corresponding elements of E.
C E2 may coincide with E if the squares are not needed.
C E2 is a one-dimensional REAL array, dimensioned E2(N).
C
C Z contains the orthogonal transformation matrix produced in
C the reduction if MATZ has been set to .TRUE. Otherwise, Z
C is not referenced. Z is a two-dimensional REAL array,
C dimensioned 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 890531 Changed all specific intrinsics to generic. (WRB)
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 BANDR