 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dopmtr()

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

DOPMTR

Purpose:
``` DOPMTR 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 DSPTRD 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 DSPTRD; = 'L': Lower triangular packed storage used in previous call to DSPTRD.``` [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 DOUBLE PRECISION 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 DSPTRD. AP is modified by the routine but restored on exit.``` [in] TAU ``` TAU is DOUBLE PRECISION 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 DSPTRD.``` [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 (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 dopmtr.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 DOUBLE PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
161* ..
162*
163* =====================================================================
164*
165* .. Parameters ..
166 DOUBLE PRECISION ONE
167 parameter( one = 1.0d+0 )
168* ..
169* .. Local Scalars ..
170 LOGICAL FORWRD, LEFT, NOTRAN, UPPER
171 INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
172 DOUBLE PRECISION AII
173* ..
174* .. External Functions ..
175 LOGICAL LSAME
176 EXTERNAL lsame
177* ..
178* .. External Subroutines ..
179 EXTERNAL dlarf, 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( 'DOPMTR', -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 DSPTRD 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 dlarf( 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 DSPTRD 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 dlarf( 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 DOPMTR
335*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:124
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