LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ cungqr()

 subroutine cungqr ( integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info )

CUNGQR

Purpose:
``` CUNGQR generates an M-by-N complex matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M

Q  =  H(1) H(2) . . . H(k)

as returned by CGEQRF.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix Q. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q. M >= N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF in the first k columns of its array argument A. On exit, the M-by-N matrix Q.``` [in] LDA ``` LDA is INTEGER The first dimension of the array A. LDA >= max(1,M).``` [in] TAU ``` TAU is COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF.``` [out] WORK ``` WORK is COMPLEX 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. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, 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 has an illegal value```

Definition at line 127 of file cungqr.f.

128*
129* -- LAPACK computational routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 INTEGER INFO, K, LDA, LWORK, M, N
135* ..
136* .. Array Arguments ..
137 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 COMPLEX ZERO
144 parameter( zero = ( 0.0e+0, 0.0e+0 ) )
145* ..
146* .. Local Scalars ..
147 LOGICAL LQUERY
148 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
149 \$ LWKOPT, NB, NBMIN, NX
150* ..
151* .. External Subroutines ..
152 EXTERNAL clarfb, clarft, cung2r, xerbla
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max, min
156* ..
157* .. External Functions ..
158 INTEGER ILAENV
159 REAL SROUNDUP_LWORK
160 EXTERNAL ilaenv, sroundup_lwork
161* ..
162* .. Executable Statements ..
163*
164* Test the input arguments
165*
166 info = 0
167 nb = ilaenv( 1, 'CUNGQR', ' ', m, n, k, -1 )
168 lwkopt = max( 1, n )*nb
169 work( 1 ) = sroundup_lwork(lwkopt)
170 lquery = ( lwork.EQ.-1 )
171 IF( m.LT.0 ) THEN
172 info = -1
173 ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
174 info = -2
175 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
176 info = -3
177 ELSE IF( lda.LT.max( 1, m ) ) THEN
178 info = -5
179 ELSE IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
180 info = -8
181 END IF
182 IF( info.NE.0 ) THEN
183 CALL xerbla( 'CUNGQR', -info )
184 RETURN
185 ELSE IF( lquery ) THEN
186 RETURN
187 END IF
188*
189* Quick return if possible
190*
191 IF( n.LE.0 ) THEN
192 work( 1 ) = 1
193 RETURN
194 END IF
195*
196 nbmin = 2
197 nx = 0
198 iws = n
199 IF( nb.GT.1 .AND. nb.LT.k ) THEN
200*
201* Determine when to cross over from blocked to unblocked code.
202*
203 nx = max( 0, ilaenv( 3, 'CUNGQR', ' ', m, n, k, -1 ) )
204 IF( nx.LT.k ) THEN
205*
206* Determine if workspace is large enough for blocked code.
207*
208 ldwork = n
209 iws = ldwork*nb
210 IF( lwork.LT.iws ) THEN
211*
212* Not enough workspace to use optimal NB: reduce NB and
213* determine the minimum value of NB.
214*
215 nb = lwork / ldwork
216 nbmin = max( 2, ilaenv( 2, 'CUNGQR', ' ', m, n, k, -1 ) )
217 END IF
218 END IF
219 END IF
220*
221 IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
222*
223* Use blocked code after the last block.
224* The first kk columns are handled by the block method.
225*
226 ki = ( ( k-nx-1 ) / nb )*nb
227 kk = min( k, ki+nb )
228*
229* Set A(1:kk,kk+1:n) to zero.
230*
231 DO 20 j = kk + 1, n
232 DO 10 i = 1, kk
233 a( i, j ) = zero
234 10 CONTINUE
235 20 CONTINUE
236 ELSE
237 kk = 0
238 END IF
239*
240* Use unblocked code for the last or only block.
241*
242 IF( kk.LT.n )
243 \$ CALL cung2r( m-kk, n-kk, k-kk, a( kk+1, kk+1 ), lda,
244 \$ tau( kk+1 ), work, iinfo )
245*
246 IF( kk.GT.0 ) THEN
247*
248* Use blocked code
249*
250 DO 50 i = ki + 1, 1, -nb
251 ib = min( nb, k-i+1 )
252 IF( i+ib.LE.n ) THEN
253*
254* Form the triangular factor of the block reflector
255* H = H(i) H(i+1) . . . H(i+ib-1)
256*
257 CALL clarft( 'Forward', 'Columnwise', m-i+1, ib,
258 \$ a( i, i ), lda, tau( i ), work, ldwork )
259*
260* Apply H to A(i:m,i+ib:n) from the left
261*
262 CALL clarfb( 'Left', 'No transpose', 'Forward',
263 \$ 'Columnwise', m-i+1, n-i-ib+1, ib,
264 \$ a( i, i ), lda, work, ldwork, a( i, i+ib ),
265 \$ lda, work( ib+1 ), ldwork )
266 END IF
267*
268* Apply H to rows i:m of current block
269*
270 CALL cung2r( m-i+1, ib, ib, a( i, i ), lda, tau( i ), work,
271 \$ iinfo )
272*
273* Set rows 1:i-1 of current block to zero
274*
275 DO 40 j = i, i + ib - 1
276 DO 30 l = 1, i - 1
277 a( l, j ) = zero
278 30 CONTINUE
279 40 CONTINUE
280 50 CONTINUE
281 END IF
282*
283 work( 1 ) = sroundup_lwork(iws)
284 RETURN
285*
286* End of CUNGQR
287*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
subroutine clarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition clarfb.f:197
subroutine clarft(direct, storev, n, k, v, ldv, tau, t, ldt)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition clarft.f:163
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
subroutine cung2r(m, n, k, a, lda, tau, work, info)
CUNG2R
Definition cung2r.f:114
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