LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ dormhr()

subroutine dormhr ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  ILO,
integer  IHI,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DORMHR

Download DORMHR + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DORMHR overwrites the general real M-by-N matrix C with

                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      Q * C          C * Q
 TRANS = 'T':      Q**T * C       C * Q**T

 where Q is a real orthogonal matrix of order nq, with nq = m if
 SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
 IHI-ILO elementary reflectors, as returned by DGEHRD:

 Q = H(ilo) H(ilo+1) . . . H(ihi-1).
Parameters
[in]SIDE
          SIDE is CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.
[in]M
          M is INTEGER
          The number of rows of the matrix C. M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix C. N >= 0.
[in]ILO
          ILO is INTEGER
[in]IHI
          IHI is INTEGER

          ILO and IHI must have the same values as in the previous call
          of DGEHRD. Q is equal to the unit matrix except in the
          submatrix Q(ilo+1:ihi,ilo+1:ihi).
          If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
          ILO = 1 and IHI = 0, if M = 0;
          if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
          ILO = 1 and IHI = 0, if N = 0.
[in]A
          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L'
                               (LDA,N) if SIDE = 'R'
          The vectors which define the elementary reflectors, as
          returned by DGEHRD.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension
                               (M-1) if SIDE = 'L'
                               (N-1) if SIDE = 'R'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DGEHRD.
[in,out]C
          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N matrix C.
          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M).
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
          blocksize.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 180 of file dormhr.f.

180 *
181 * -- LAPACK computational routine (version 3.7.0) --
182 * -- LAPACK is a software package provided by Univ. of Tennessee, --
183 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
184 * December 2016
185 *
186 * .. Scalar Arguments ..
187  CHARACTER side, trans
188  INTEGER ihi, ilo, info, lda, ldc, lwork, m, n
189 * ..
190 * .. Array Arguments ..
191  DOUBLE PRECISION a( lda, * ), c( ldc, * ), tau( * ), work( * )
192 * ..
193 *
194 * =====================================================================
195 *
196 * .. Local Scalars ..
197  LOGICAL left, lquery
198  INTEGER i1, i2, iinfo, lwkopt, mi, nb, nh, ni, nq, nw
199 * ..
200 * .. External Functions ..
201  LOGICAL lsame
202  INTEGER ilaenv
203  EXTERNAL lsame, ilaenv
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL dormqr, xerbla
207 * ..
208 * .. Intrinsic Functions ..
209  INTRINSIC max, min
210 * ..
211 * .. Executable Statements ..
212 *
213 * Test the input arguments
214 *
215  info = 0
216  nh = ihi - ilo
217  left = lsame( side, 'L' )
218  lquery = ( lwork.EQ.-1 )
219 *
220 * NQ is the order of Q and NW is the minimum dimension of WORK
221 *
222  IF( left ) THEN
223  nq = m
224  nw = n
225  ELSE
226  nq = n
227  nw = m
228  END IF
229  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
230  info = -1
231  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'T' ) )
232  $ THEN
233  info = -2
234  ELSE IF( m.LT.0 ) THEN
235  info = -3
236  ELSE IF( n.LT.0 ) THEN
237  info = -4
238  ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, nq ) ) THEN
239  info = -5
240  ELSE IF( ihi.LT.min( ilo, nq ) .OR. ihi.GT.nq ) THEN
241  info = -6
242  ELSE IF( lda.LT.max( 1, nq ) ) THEN
243  info = -8
244  ELSE IF( ldc.LT.max( 1, m ) ) THEN
245  info = -11
246  ELSE IF( lwork.LT.max( 1, nw ) .AND. .NOT.lquery ) THEN
247  info = -13
248  END IF
249 *
250  IF( info.EQ.0 ) THEN
251  IF( left ) THEN
252  nb = ilaenv( 1, 'DORMQR', side // trans, nh, n, nh, -1 )
253  ELSE
254  nb = ilaenv( 1, 'DORMQR', side // trans, m, nh, nh, -1 )
255  END IF
256  lwkopt = max( 1, nw )*nb
257  work( 1 ) = lwkopt
258  END IF
259 *
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'DORMHR', -info )
262  RETURN
263  ELSE IF( lquery ) THEN
264  RETURN
265  END IF
266 *
267 * Quick return if possible
268 *
269  IF( m.EQ.0 .OR. n.EQ.0 .OR. nh.EQ.0 ) THEN
270  work( 1 ) = 1
271  RETURN
272  END IF
273 *
274  IF( left ) THEN
275  mi = nh
276  ni = n
277  i1 = ilo + 1
278  i2 = 1
279  ELSE
280  mi = m
281  ni = nh
282  i1 = 1
283  i2 = ilo + 1
284  END IF
285 *
286  CALL dormqr( side, trans, mi, ni, nh, a( ilo+1, ilo ), lda,
287  $ tau( ilo ), c( i1, i2 ), ldc, work, lwork, iinfo )
288 *
289  work( 1 ) = lwkopt
290  RETURN
291 *
292 * End of DORMHR
293 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:169
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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