 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dormtr()

 subroutine dormtr ( character SIDE, character UPLO, character TRANS, integer M, integer N, 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 )

DORMTR

Purpose:
``` DORMTR 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
nq-1 elementary reflectors, as returned by DSYTRD:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-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] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A contains elementary reflectors from DSYTRD; = 'L': Lower triangle of A contains elementary reflectors from DSYTRD.``` [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] 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 DSYTRD.``` [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 DSYTRD.``` [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```

Definition at line 169 of file dormtr.f.

171 *
172 * -- LAPACK computational routine --
173 * -- LAPACK is a software package provided by Univ. of Tennessee, --
174 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175 *
176 * .. Scalar Arguments ..
177  CHARACTER SIDE, TRANS, UPLO
178  INTEGER INFO, LDA, LDC, LWORK, M, N
179 * ..
180 * .. Array Arguments ..
181  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
182 * ..
183 *
184 * =====================================================================
185 *
186 * .. Local Scalars ..
187  LOGICAL LEFT, LQUERY, UPPER
188  INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  INTEGER ILAENV
193  EXTERNAL lsame, ilaenv
194 * ..
195 * .. External Subroutines ..
196  EXTERNAL dormql, dormqr, xerbla
197 * ..
198 * .. Intrinsic Functions ..
199  INTRINSIC max
200 * ..
201 * .. Executable Statements ..
202 *
203 * Test the input arguments
204 *
205  info = 0
206  left = lsame( side, 'L' )
207  upper = lsame( uplo, 'U' )
208  lquery = ( lwork.EQ.-1 )
209 *
210 * NQ is the order of Q and NW is the minimum dimension of WORK
211 *
212  IF( left ) THEN
213  nq = m
214  nw = max( 1, n )
215  ELSE
216  nq = n
217  nw = max( 1, m )
218  END IF
219  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
220  info = -1
221  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
222  info = -2
223  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'T' ) )
224  \$ THEN
225  info = -3
226  ELSE IF( m.LT.0 ) THEN
227  info = -4
228  ELSE IF( n.LT.0 ) THEN
229  info = -5
230  ELSE IF( lda.LT.max( 1, nq ) ) THEN
231  info = -7
232  ELSE IF( ldc.LT.max( 1, m ) ) THEN
233  info = -10
234  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
235  info = -12
236  END IF
237 *
238  IF( info.EQ.0 ) THEN
239  IF( upper ) THEN
240  IF( left ) THEN
241  nb = ilaenv( 1, 'DORMQL', side // trans, m-1, n, m-1,
242  \$ -1 )
243  ELSE
244  nb = ilaenv( 1, 'DORMQL', side // trans, m, n-1, n-1,
245  \$ -1 )
246  END IF
247  ELSE
248  IF( left ) THEN
249  nb = ilaenv( 1, 'DORMQR', side // trans, m-1, n, m-1,
250  \$ -1 )
251  ELSE
252  nb = ilaenv( 1, 'DORMQR', side // trans, m, n-1, n-1,
253  \$ -1 )
254  END IF
255  END IF
256  lwkopt = nw*nb
257  work( 1 ) = lwkopt
258  END IF
259 *
260  IF( info.NE.0 ) THEN
261  CALL xerbla( 'DORMTR', -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. nq.EQ.1 ) THEN
270  work( 1 ) = 1
271  RETURN
272  END IF
273 *
274  IF( left ) THEN
275  mi = m - 1
276  ni = n
277  ELSE
278  mi = m
279  ni = n - 1
280  END IF
281 *
282  IF( upper ) THEN
283 *
284 * Q was determined by a call to DSYTRD with UPLO = 'U'
285 *
286  CALL dormql( side, trans, mi, ni, nq-1, a( 1, 2 ), lda, tau, c,
287  \$ ldc, work, lwork, iinfo )
288  ELSE
289 *
290 * Q was determined by a call to DSYTRD with UPLO = 'L'
291 *
292  IF( left ) THEN
293  i1 = 2
294  i2 = 1
295  ELSE
296  i1 = 1
297  i2 = 2
298  END IF
299  CALL dormqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
300  \$ c( i1, i2 ), ldc, work, lwork, iinfo )
301  END IF
302  work( 1 ) = lwkopt
303  RETURN
304 *
305 * End of DORMTR
306 *
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQR
Definition: dormqr.f:167
subroutine dormql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMQL
Definition: dormql.f:167
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