LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dlarot()

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 "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
    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 "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 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.
Date
December 2016

Definition at line 228 of file dlarot.f.

228 *
229 * -- LAPACK auxiliary routine (version 3.7.0) --
230 * -- LAPACK is a software package provided by Univ. of Tennessee, --
231 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
232 * December 2016
233 *
234 * .. Scalar Arguments ..
235  LOGICAL lleft, lright, lrows
236  INTEGER lda, nl
237  DOUBLE PRECISION c, s, xleft, xright
238 * ..
239 * .. Array Arguments ..
240  DOUBLE PRECISION a( * )
241 * ..
242 *
243 * =====================================================================
244 *
245 * .. Local Scalars ..
246  INTEGER iinc, inext, ix, iy, iyt, nt
247 * ..
248 * .. Local Arrays ..
249  DOUBLE PRECISION xt( 2 ), yt( 2 )
250 * ..
251 * .. External Subroutines ..
252  EXTERNAL drot, xerbla
253 * ..
254 * .. Executable Statements ..
255 *
256 * Set up indices, arrays for ends
257 *
258  IF( lrows ) THEN
259  iinc = lda
260  inext = 1
261  ELSE
262  iinc = 1
263  inext = lda
264  END IF
265 *
266  IF( lleft ) THEN
267  nt = 1
268  ix = 1 + iinc
269  iy = 2 + lda
270  xt( 1 ) = a( 1 )
271  yt( 1 ) = xleft
272  ELSE
273  nt = 0
274  ix = 1
275  iy = 1 + inext
276  END IF
277 *
278  IF( lright ) THEN
279  iyt = 1 + inext + ( nl-1 )*iinc
280  nt = nt + 1
281  xt( nt ) = xright
282  yt( nt ) = a( iyt )
283  END IF
284 *
285 * Check for errors
286 *
287  IF( nl.LT.nt ) THEN
288  CALL xerbla( 'DLAROT', 4 )
289  RETURN
290  END IF
291  IF( lda.LE.0 .OR. ( .NOT.lrows .AND. lda.LT.nl-nt ) ) THEN
292  CALL xerbla( 'DLAROT', 8 )
293  RETURN
294  END IF
295 *
296 * Rotate
297 *
298  CALL drot( nl-nt, a( ix ), iinc, a( iy ), iinc, c, s )
299  CALL drot( nt, xt, 1, yt, 1, c, s )
300 *
301 * Stuff values back into XLEFT, XRIGHT, etc.
302 *
303  IF( lleft ) THEN
304  a( 1 ) = xt( 1 )
305  xleft = yt( 1 )
306  END IF
307 *
308  IF( lright ) THEN
309  xright = xt( nt )
310  a( iyt ) = yt( nt )
311  END IF
312 *
313  RETURN
314 *
315 * End of DLAROT
316 *
subroutine drot(N, DX, INCX, DY, INCY, C, S)
DROT
Definition: drot.f:94
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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