LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dorgqr()

subroutine dorgqr ( integer  m,
integer  n,
integer  k,
double precision, dimension( lda, * )  a,
integer  lda,
double precision, dimension( * )  tau,
double precision, dimension( * )  work,
integer  lwork,
integer  info 
)

DORGQR

Download DORGQR + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DORGQR generates an M-by-N real 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 DGEQRF.
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 DOUBLE PRECISION 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 DGEQRF 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 DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DGEQRF.
[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. 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 127 of file dorgqr.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 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO
144 parameter( zero = 0.0d+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 dlarfb, dlarft, dorg2r, xerbla
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC max, min
156* ..
157* .. External Functions ..
158 INTEGER ILAENV
159 EXTERNAL ilaenv
160* ..
161* .. Executable Statements ..
162*
163* Test the input arguments
164*
165 info = 0
166 nb = ilaenv( 1, 'DORGQR', ' ', m, n, k, -1 )
167 lwkopt = max( 1, n )*nb
168 work( 1 ) = lwkopt
169 lquery = ( lwork.EQ.-1 )
170 IF( m.LT.0 ) THEN
171 info = -1
172 ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
173 info = -2
174 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
175 info = -3
176 ELSE IF( lda.LT.max( 1, m ) ) THEN
177 info = -5
178 ELSE IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
179 info = -8
180 END IF
181 IF( info.NE.0 ) THEN
182 CALL xerbla( 'DORGQR', -info )
183 RETURN
184 ELSE IF( lquery ) THEN
185 RETURN
186 END IF
187*
188* Quick return if possible
189*
190 IF( n.LE.0 ) THEN
191 work( 1 ) = 1
192 RETURN
193 END IF
194*
195 nbmin = 2
196 nx = 0
197 iws = n
198 IF( nb.GT.1 .AND. nb.LT.k ) THEN
199*
200* Determine when to cross over from blocked to unblocked code.
201*
202 nx = max( 0, ilaenv( 3, 'DORGQR', ' ', m, n, k, -1 ) )
203 IF( nx.LT.k ) THEN
204*
205* Determine if workspace is large enough for blocked code.
206*
207 ldwork = n
208 iws = ldwork*nb
209 IF( lwork.LT.iws ) THEN
210*
211* Not enough workspace to use optimal NB: reduce NB and
212* determine the minimum value of NB.
213*
214 nb = lwork / ldwork
215 nbmin = max( 2, ilaenv( 2, 'DORGQR', ' ', m, n, k, -1 ) )
216 END IF
217 END IF
218 END IF
219*
220 IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
221*
222* Use blocked code after the last block.
223* The first kk columns are handled by the block method.
224*
225 ki = ( ( k-nx-1 ) / nb )*nb
226 kk = min( k, ki+nb )
227*
228* Set A(1:kk,kk+1:n) to zero.
229*
230 DO 20 j = kk + 1, n
231 DO 10 i = 1, kk
232 a( i, j ) = zero
233 10 CONTINUE
234 20 CONTINUE
235 ELSE
236 kk = 0
237 END IF
238*
239* Use unblocked code for the last or only block.
240*
241 IF( kk.LT.n )
242 $ CALL dorg2r( m-kk, n-kk, k-kk, a( kk+1, kk+1 ), lda,
243 $ tau( kk+1 ), work, iinfo )
244*
245 IF( kk.GT.0 ) THEN
246*
247* Use blocked code
248*
249 DO 50 i = ki + 1, 1, -nb
250 ib = min( nb, k-i+1 )
251 IF( i+ib.LE.n ) THEN
252*
253* Form the triangular factor of the block reflector
254* H = H(i) H(i+1) . . . H(i+ib-1)
255*
256 CALL dlarft( 'Forward', 'Columnwise', m-i+1, ib,
257 $ a( i, i ), lda, tau( i ), work, ldwork )
258*
259* Apply H to A(i:m,i+ib:n) from the left
260*
261 CALL dlarfb( 'Left', 'No transpose', 'Forward',
262 $ 'Columnwise', m-i+1, n-i-ib+1, ib,
263 $ a( i, i ), lda, work, ldwork, a( i, i+ib ),
264 $ lda, work( ib+1 ), ldwork )
265 END IF
266*
267* Apply H to rows i:m of current block
268*
269 CALL dorg2r( m-i+1, ib, ib, a( i, i ), lda, tau( i ), work,
270 $ iinfo )
271*
272* Set rows 1:i-1 of current block to zero
273*
274 DO 40 j = i, i + ib - 1
275 DO 30 l = 1, i - 1
276 a( l, j ) = zero
277 30 CONTINUE
278 40 CONTINUE
279 50 CONTINUE
280 END IF
281*
282 work( 1 ) = iws
283 RETURN
284*
285* End of DORGQR
286*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
ilaenv
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
dlarfb
subroutine dlarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.
Definition dlarfb.f:197
dlarft
subroutine dlarft(direct, storev, n, k, v, ldv, tau, t, ldt)
DLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition dlarft.f:163
dorg2r
subroutine dorg2r(m, n, k, a, lda, tau, work, info)
DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf ...
Definition dorg2r.f:114
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