TESTING/MATGEN/dlarot.f(3)

NAME
TESTING/MATGEN/dlarot.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine dlarot (logical lrows, logical lleft, logical lright, integer nl, double precision c, double precision s, double precision, dimension( * ) a, integer lda, double precision xleft, double precision xright)

DLAROT

Purpose:

    !>
    !>    DLAROT 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  and :
    !>
    !>    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
    !>    DLAROT 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 DLAROT(.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 DLAROT( .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 DLAROT( .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 DLAROT( .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 DLAROT( .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 DLAROT 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   - DOUBLE PRECISION
    !>           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      - DOUBLE PRECISION 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  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 DLAROT, 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  - DOUBLE PRECISION
    !>           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 - DOUBLE PRECISION
    !>           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 dlarot.f.

Author

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