LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sormtr()

 subroutine sormtr ( character SIDE, character UPLO, character TRANS, integer M, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer LWORK, integer INFO )

SORMTR

Purpose:
``` SORMTR 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 SSYTRD:

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 SSYTRD; = 'L': Lower triangle of A contains elementary reflectors from SSYTRD.``` [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 REAL array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SSYTRD.``` [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 REAL 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 SSYTRD.``` [in,out] C ``` C is REAL 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 REAL 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 170 of file sormtr.f.

172 *
173 * -- LAPACK computational routine --
174 * -- LAPACK is a software package provided by Univ. of Tennessee, --
175 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
176 *
177 * .. Scalar Arguments ..
178  CHARACTER SIDE, TRANS, UPLO
179  INTEGER INFO, LDA, LDC, LWORK, M, N
180 * ..
181 * .. Array Arguments ..
182  REAL A( LDA, * ), C( LDC, * ), TAU( * ),
183  \$ WORK( * )
184 * ..
185 *
186 * =====================================================================
187 *
188 * .. Local Scalars ..
189  LOGICAL LEFT, LQUERY, UPPER
190  INTEGER I1, I2, IINFO, LWKOPT, MI, NI, NB, NQ, NW
191 * ..
192 * .. External Functions ..
193  LOGICAL LSAME
194  INTEGER ILAENV
195  EXTERNAL ilaenv, lsame
196 * ..
197 * .. External Subroutines ..
198  EXTERNAL sormql, sormqr, xerbla
199 * ..
200 * .. Intrinsic Functions ..
201  INTRINSIC max
202 * ..
203 * .. Executable Statements ..
204 *
205 * Test the input arguments
206 *
207  info = 0
208  left = lsame( side, 'L' )
209  upper = lsame( uplo, 'U' )
210  lquery = ( lwork.EQ.-1 )
211 *
212 * NQ is the order of Q and NW is the minimum dimension of WORK
213 *
214  IF( left ) THEN
215  nq = m
216  nw = max( 1, n )
217  ELSE
218  nq = n
219  nw = max( 1, m )
220  END IF
221  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
222  info = -1
223  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
224  info = -2
225  ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'T' ) )
226  \$ THEN
227  info = -3
228  ELSE IF( m.LT.0 ) THEN
229  info = -4
230  ELSE IF( n.LT.0 ) THEN
231  info = -5
232  ELSE IF( lda.LT.max( 1, nq ) ) THEN
233  info = -7
234  ELSE IF( ldc.LT.max( 1, m ) ) THEN
235  info = -10
236  ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
237  info = -12
238  END IF
239 *
240  IF( info.EQ.0 ) THEN
241  IF( upper ) THEN
242  IF( left ) THEN
243  nb = ilaenv( 1, 'SORMQL', side // trans, m-1, n, m-1,
244  \$ -1 )
245  ELSE
246  nb = ilaenv( 1, 'SORMQL', side // trans, m, n-1, n-1,
247  \$ -1 )
248  END IF
249  ELSE
250  IF( left ) THEN
251  nb = ilaenv( 1, 'SORMQR', side // trans, m-1, n, m-1,
252  \$ -1 )
253  ELSE
254  nb = ilaenv( 1, 'SORMQR', side // trans, m, n-1, n-1,
255  \$ -1 )
256  END IF
257  END IF
258  lwkopt = nw*nb
259  work( 1 ) = lwkopt
260  END IF
261 *
262  IF( info.NE.0 ) THEN
263  CALL xerbla( 'SORMTR', -info )
264  RETURN
265  ELSE IF( lquery ) THEN
266  RETURN
267  END IF
268 *
269 * Quick return if possible
270 *
271  IF( m.EQ.0 .OR. n.EQ.0 .OR. nq.EQ.1 ) THEN
272  work( 1 ) = 1
273  RETURN
274  END IF
275 *
276  IF( left ) THEN
277  mi = m - 1
278  ni = n
279  ELSE
280  mi = m
281  ni = n - 1
282  END IF
283 *
284  IF( upper ) THEN
285 *
286 * Q was determined by a call to SSYTRD with UPLO = 'U'
287 *
288  CALL sormql( side, trans, mi, ni, nq-1, a( 1, 2 ), lda, tau, c,
289  \$ ldc, work, lwork, iinfo )
290  ELSE
291 *
292 * Q was determined by a call to SSYTRD with UPLO = 'L'
293 *
294  IF( left ) THEN
295  i1 = 2
296  i2 = 1
297  ELSE
298  i1 = 1
299  i2 = 2
300  END IF
301  CALL sormqr( side, trans, mi, ni, nq-1, a( 2, 1 ), lda, tau,
302  \$ c( i1, i2 ), ldc, work, lwork, iinfo )
303  END IF
304  work( 1 ) = lwkopt
305  RETURN
306 *
307 * End of SORMTR
308 *
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 sormql(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQL
Definition: sormql.f:168
subroutine sormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQR
Definition: sormqr.f:168
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