 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sopmtr()

 subroutine sopmtr ( character SIDE, character UPLO, character TRANS, integer M, integer N, real, dimension( * ) AP, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer INFO )

SOPMTR

Purpose:
``` SOPMTR 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 SSPTRD using packed
storage:

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 triangular packed storage used in previous call to SSPTRD; = 'L': Lower triangular packed storage used in previous call to SSPTRD.``` [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] AP ``` AP is REAL array, dimension (M*(M+1)/2) if SIDE = 'L' (N*(N+1)/2) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SSPTRD. AP is modified by the routine but restored on exit.``` [in] TAU ``` TAU is REAL array, dimension (M-1) if SIDE = 'L' or (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SSPTRD.``` [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 (N) if SIDE = 'L' (M) if SIDE = 'R'``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 148 of file sopmtr.f.

150 *
151 * -- LAPACK computational routine --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 *
155 * .. Scalar Arguments ..
156  CHARACTER SIDE, TRANS, UPLO
157  INTEGER INFO, LDC, M, N
158 * ..
159 * .. Array Arguments ..
160  REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  REAL ONE
167  parameter( one = 1.0e+0 )
168 * ..
169 * .. Local Scalars ..
170  LOGICAL FORWRD, LEFT, NOTRAN, UPPER
171  INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
172  REAL AII
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  EXTERNAL lsame
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL slarf, xerbla
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC max
183 * ..
184 * .. Executable Statements ..
185 *
186 * Test the input arguments
187 *
188  info = 0
189  left = lsame( side, 'L' )
190  notran = lsame( trans, 'N' )
191  upper = lsame( uplo, 'U' )
192 *
193 * NQ is the order of Q
194 *
195  IF( left ) THEN
196  nq = m
197  ELSE
198  nq = n
199  END IF
200  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
201  info = -1
202  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
203  info = -2
204  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
205  info = -3
206  ELSE IF( m.LT.0 ) THEN
207  info = -4
208  ELSE IF( n.LT.0 ) THEN
209  info = -5
210  ELSE IF( ldc.LT.max( 1, m ) ) THEN
211  info = -9
212  END IF
213  IF( info.NE.0 ) THEN
214  CALL xerbla( 'SOPMTR', -info )
215  RETURN
216  END IF
217 *
218 * Quick return if possible
219 *
220  IF( m.EQ.0 .OR. n.EQ.0 )
221  \$ RETURN
222 *
223  IF( upper ) THEN
224 *
225 * Q was determined by a call to SSPTRD with UPLO = 'U'
226 *
227  forwrd = ( left .AND. notran ) .OR.
228  \$ ( .NOT.left .AND. .NOT.notran )
229 *
230  IF( forwrd ) THEN
231  i1 = 1
232  i2 = nq - 1
233  i3 = 1
234  ii = 2
235  ELSE
236  i1 = nq - 1
237  i2 = 1
238  i3 = -1
239  ii = nq*( nq+1 ) / 2 - 1
240  END IF
241 *
242  IF( left ) THEN
243  ni = n
244  ELSE
245  mi = m
246  END IF
247 *
248  DO 10 i = i1, i2, i3
249  IF( left ) THEN
250 *
251 * H(i) is applied to C(1:i,1:n)
252 *
253  mi = i
254  ELSE
255 *
256 * H(i) is applied to C(1:m,1:i)
257 *
258  ni = i
259  END IF
260 *
261 * Apply H(i)
262 *
263  aii = ap( ii )
264  ap( ii ) = one
265  CALL slarf( side, mi, ni, ap( ii-i+1 ), 1, tau( i ), c, ldc,
266  \$ work )
267  ap( ii ) = aii
268 *
269  IF( forwrd ) THEN
270  ii = ii + i + 2
271  ELSE
272  ii = ii - i - 1
273  END IF
274  10 CONTINUE
275  ELSE
276 *
277 * Q was determined by a call to SSPTRD with UPLO = 'L'.
278 *
279  forwrd = ( left .AND. .NOT.notran ) .OR.
280  \$ ( .NOT.left .AND. notran )
281 *
282  IF( forwrd ) THEN
283  i1 = 1
284  i2 = nq - 1
285  i3 = 1
286  ii = 2
287  ELSE
288  i1 = nq - 1
289  i2 = 1
290  i3 = -1
291  ii = nq*( nq+1 ) / 2 - 1
292  END IF
293 *
294  IF( left ) THEN
295  ni = n
296  jc = 1
297  ELSE
298  mi = m
299  ic = 1
300  END IF
301 *
302  DO 20 i = i1, i2, i3
303  aii = ap( ii )
304  ap( ii ) = one
305  IF( left ) THEN
306 *
307 * H(i) is applied to C(i+1:m,1:n)
308 *
309  mi = m - i
310  ic = i + 1
311  ELSE
312 *
313 * H(i) is applied to C(1:m,i+1:n)
314 *
315  ni = n - i
316  jc = i + 1
317  END IF
318 *
319 * Apply H(i)
320 *
321  CALL slarf( side, mi, ni, ap( ii ), 1, tau( i ),
322  \$ c( ic, jc ), ldc, work )
323  ap( ii ) = aii
324 *
325  IF( forwrd ) THEN
326  ii = ii + nq - i + 1
327  ELSE
328  ii = ii - nq + i - 2
329  END IF
330  20 CONTINUE
331  END IF
332  RETURN
333 *
334 * End of SOPMTR
335 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:124
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