TESTING/MATGEN/slarot.f(3)

NAME
TESTING/MATGEN/slarot.f

SYNOPSIS

  Functions/Subroutines
subroutine slarot (lrows, lleft, lright, nl, c, s, a, lda, xleft, xright)
SLAROT

Function/Subroutine Documentation

  subroutine slarot (logical lrows, logical lleft, logical lright, integer nl, real c, real s, real, dimension( * ) a, integer lda, real xleft, real xright)

SLAROT

Purpose:

        SLAROT applies a (Givens) rotation to two adjacent rows or
        columns, where one element of the first and/or last column/row
        for use on matrices stored in some format other than GE, so
        that elements of the matrix may be used or modified for which
        no array element is provided.
        One example is a symmetric matrix in SB format (bandwidth=4), for
        which UPLO='L':  Two adjacent rows will have the format:
        row j:     C> C> C> C> C> .  .  .  .
        row j+1:      C> C> C> C> C> .  .  .  .
        '*' indicates elements for which storage is provided,
        '.' indicates elements for which no storage is provided, but
        are not necessarily zero; their values are determined by
        symmetry.  ' ' indicates elements which are necessarily zero,
         and have no storage provided.
        Those columns which have two '*'s can be handled by SROT.
        Those columns which have no '*'s can be ignored, since as long
        as the Givens rotations are carefully applied to preserve
        symmetry, their values are determined.
        Those columns which have one '*' have to be handled separately,
        by using separate variables 'p' and 'q':
        row j:     C> C> C> C> C> p  .  .  .
        row j+1:   q  C> C> C> C> C> .  .  .  .
        The element p would have to be set correctly, then that column
        is rotated, setting p to its new value.  The next call to
        SLAROT would rotate columns j and j+1, using p, and restore
        symmetry.  The element q would start out being zero, and be
        made non-zero by the rotation.  Later, rotations would presumably
        be chosen to zero q out.
        Typical Calling Sequences: rotating the i-th and (i+1)-st rows.
        ------- ------- ---------
          General dense matrix:
                  CALL SLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S,
                          A(i,1),LDA, DUMMY, DUMMY)
          General banded matrix in GB format:
                  j = MAX(1, i-KL )
                  NL = MIN( N, i+KU+1 ) + 1-j
                  CALL SLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S,
                          A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT )
                  [ note that i+1-j is just MIN(i,KL+1) ]
          Symmetric banded matrix in SY format, bandwidth K,
          lower triangle only:
                  j = MAX(1, i-K )
                  NL = MIN( K+1, i ) + 1
                  CALL SLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S,
                          A(i,j), LDA, XLEFT, XRIGHT )
          Same, but upper triangle only:
                  NL = MIN( K+1, N-i ) + 1
                  CALL SLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S,
                          A(i,i), LDA, XLEFT, XRIGHT )
          Symmetric banded matrix in SB format, bandwidth K,
          lower triangle only:
                  [ same as for SY, except:]
                      . . . .
                          A(i+1-j,j), LDA-1, XLEFT, XRIGHT )
                  [ note that i+1-j is just MIN(i,K+1) ]
          Same, but upper triangle only:
                       . . .
                          A(K+1,i), LDA-1, XLEFT, XRIGHT )
          Rotating columns is just the transpose of rotating rows, except
          for GB and SB: (rotating columns i and i+1)
          GB:
                  j = MAX(1, i-KU )
                  NL = MIN( N, i+KL+1 ) + 1-j
                  CALL SLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S,
                          A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM )
                  [note that KU+j+1-i is just MAX(1,KU+2-i)]
          SB: (upper triangle)
                       . . . . . .
                          A(K+j+1-i,i),LDA-1, XTOP, XBOTTM )
          SB: (lower triangle)
                       . . . . . .
                          A(1,i),LDA-1, XTOP, XBOTTM )

      LROWS  - LOGICAL
               If .TRUE., then SLAROT will rotate two rows.  If .FALSE.,
               then it will rotate two columns.
               Not modified.
      LLEFT  - LOGICAL
               If .TRUE., then XLEFT will be used instead of the
               corresponding element of A for the first element in the
               second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.)
               If .FALSE., then the corresponding element of A will be
               used.
               Not modified.
      LRIGHT - LOGICAL
               If .TRUE., then XRIGHT will be used instead of the
               corresponding element of A for the last element in the
               first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If
               .FALSE., then the corresponding element of A will be used.
               Not modified.
      NL     - INTEGER
               The length of the rows (if LROWS=.TRUE.) or columns (if
               LROWS=.FALSE.) to be rotated.  If XLEFT and/or XRIGHT are
               used, the columns/rows they are in should be included in
               NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at
               least 2.  The number of rows/columns to be rotated
               exclusive of those involving XLEFT and/or XRIGHT may
               not be negative, i.e., NL minus how many of LLEFT and
               LRIGHT are .TRUE. must be at least zero; if not, XERBLA
               will be called.
               Not modified.
      C, S   - REAL
               Specify the Givens rotation to be applied.  If LROWS is
               true, then the matrix ( c  s )
                                     (-s  c )  is applied from the left;
               if false, then the transpose thereof is applied from the
               right.  For a Givens rotation, C**2 + S**2 should be 1,
               but this is not checked.
               Not modified.
      A      - REAL array.
               The array containing the rows/columns to be rotated.  The
               first element of A should be the upper left element to
               be rotated.
               Read and modified.
      LDA    - INTEGER
               The 'effective' leading dimension of A.  If A contains
               a matrix stored in GE or SY format, then this is just
               the leading dimension of A as dimensioned in the calling
               routine.  If A contains a matrix stored in band (GB or SB)
               format, then this should be *one less* than the leading
               dimension used in the calling routine.  Thus, if
               A were dimensioned A(LDA,*) in SLAROT, then A(1,j) would
               be the j-th element in the first of the two rows
               to be rotated, and A(2,j) would be the j-th in the second,
               regardless of how the array may be stored in the calling
               routine.  [A cannot, however, actually be dimensioned thus,
               since for band format, the row number may exceed LDA, which
               is not legal FORTRAN.]
               If LROWS=.TRUE., then LDA must be at least 1, otherwise
               it must be at least NL minus the number of .TRUE. values
               in XLEFT and XRIGHT.
               Not modified.
      XLEFT  - REAL
               If LLEFT is .TRUE., then XLEFT will be used and modified
               instead of A(2,1) (if LROWS=.TRUE.) or A(1,2)
               (if LROWS=.FALSE.).
               Read and modified.
      XRIGHT - REAL
               If LRIGHT is .TRUE., then XRIGHT will be used and modified
               instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1)
               (if LROWS=.FALSE.).
               Read and modified.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 224 of file slarot.f.

Author

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