TESTING/MATGEN/zlarot.f(3)

NAME
TESTING/MATGEN/zlarot.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine zlarot (logical lrows, logical lleft, logical lright, integer nl, complex*16 c, complex*16 s, complex*16, dimension( * ) a, integer lda, complex*16 xleft, complex*16 xright)

ZLAROT

Purpose:

        ZLAROT 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 DROT.
        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
        ZLAROT 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 ZLAROT(.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 ZLAROT( .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 ZLAROT( .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 ZLAROT( .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 ZLAROT( .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 ZLAROT 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   - COMPLEX*16
               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 (not conjugated) thereof is
               applied from the right.  Note that in contrast to the
               output of ZROTG or to most versions of ZROT, both C and S
               are complex.  For a Givens rotation, |C|**2 + |S|**2 should
               be 1, but this is not checked.
               Not modified.
      A      - COMPLEX*16 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, HE, 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, HB, 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 ZLAROT, 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  - COMPLEX*16
               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 - COMPLEX*16
               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 227 of file zlarot.f.

Author

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