LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dorglq()

subroutine dorglq ( 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 
)

DORGLQ

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

Purpose:
 DORGLQ generates an M-by-N real matrix Q with orthonormal rows,
 which is defined as the first M rows of a product of K elementary
 reflectors of order N

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

 as returned by DGELQF.
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. N >= M.
[in]K
          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the i-th row must contain the vector which defines
          the elementary reflector H(i), for i = 1,2,...,k, as returned
          by DGELQF in the first k rows 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 DGELQF.
[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,M).
          For optimum performance LWORK >= M*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 126 of file dorglq.f.

127*
128* -- LAPACK computational routine --
129* -- LAPACK is a software package provided by Univ. of Tennessee, --
130* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*
132* .. Scalar Arguments ..
133 INTEGER INFO, K, LDA, LWORK, M, N
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 DOUBLE PRECISION ZERO
143 parameter( zero = 0.0d+0 )
144* ..
145* .. Local Scalars ..
146 LOGICAL LQUERY
147 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
148 $ LWKOPT, NB, NBMIN, NX
149* ..
150* .. External Subroutines ..
151 EXTERNAL dlarfb, dlarft, dorgl2, xerbla
152* ..
153* .. Intrinsic Functions ..
154 INTRINSIC max, min
155* ..
156* .. External Functions ..
157 INTEGER ILAENV
158 EXTERNAL ilaenv
159* ..
160* .. Executable Statements ..
161*
162* Test the input arguments
163*
164 info = 0
165 nb = ilaenv( 1, 'DORGLQ', ' ', m, n, k, -1 )
166 lwkopt = max( 1, m )*nb
167 work( 1 ) = lwkopt
168 lquery = ( lwork.EQ.-1 )
169 IF( m.LT.0 ) THEN
170 info = -1
171 ELSE IF( n.LT.m ) THEN
172 info = -2
173 ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
174 info = -3
175 ELSE IF( lda.LT.max( 1, m ) ) THEN
176 info = -5
177 ELSE IF( lwork.LT.max( 1, m ) .AND. .NOT.lquery ) THEN
178 info = -8
179 END IF
180 IF( info.NE.0 ) THEN
181 CALL xerbla( 'DORGLQ', -info )
182 RETURN
183 ELSE IF( lquery ) THEN
184 RETURN
185 END IF
186*
187* Quick return if possible
188*
189 IF( m.LE.0 ) THEN
190 work( 1 ) = 1
191 RETURN
192 END IF
193*
194 nbmin = 2
195 nx = 0
196 iws = m
197 IF( nb.GT.1 .AND. nb.LT.k ) THEN
198*
199* Determine when to cross over from blocked to unblocked code.
200*
201 nx = max( 0, ilaenv( 3, 'DORGLQ', ' ', m, n, k, -1 ) )
202 IF( nx.LT.k ) THEN
203*
204* Determine if workspace is large enough for blocked code.
205*
206 ldwork = m
207 iws = ldwork*nb
208 IF( lwork.LT.iws ) THEN
209*
210* Not enough workspace to use optimal NB: reduce NB and
211* determine the minimum value of NB.
212*
213 nb = lwork / ldwork
214 nbmin = max( 2, ilaenv( 2, 'DORGLQ', ' ', m, n, k, -1 ) )
215 END IF
216 END IF
217 END IF
218*
219 IF( nb.GE.nbmin .AND. nb.LT.k .AND. nx.LT.k ) THEN
220*
221* Use blocked code after the last block.
222* The first kk rows are handled by the block method.
223*
224 ki = ( ( k-nx-1 ) / nb )*nb
225 kk = min( k, ki+nb )
226*
227* Set A(kk+1:m,1:kk) to zero.
228*
229 DO 20 j = 1, kk
230 DO 10 i = kk + 1, m
231 a( i, j ) = zero
232 10 CONTINUE
233 20 CONTINUE
234 ELSE
235 kk = 0
236 END IF
237*
238* Use unblocked code for the last or only block.
239*
240 IF( kk.LT.m )
241 $ CALL dorgl2( m-kk, n-kk, k-kk, a( kk+1, kk+1 ), lda,
242 $ tau( kk+1 ), work, iinfo )
243*
244 IF( kk.GT.0 ) THEN
245*
246* Use blocked code
247*
248 DO 50 i = ki + 1, 1, -nb
249 ib = min( nb, k-i+1 )
250 IF( i+ib.LE.m ) THEN
251*
252* Form the triangular factor of the block reflector
253* H = H(i) H(i+1) . . . H(i+ib-1)
254*
255 CALL dlarft( 'Forward', 'Rowwise', n-i+1, ib, a( i, i ),
256 $ lda, tau( i ), work, ldwork )
257*
258* Apply H**T to A(i+ib:m,i:n) from the right
259*
260 CALL dlarfb( 'Right', 'Transpose', 'Forward', 'Rowwise',
261 $ m-i-ib+1, n-i+1, ib, a( i, i ), lda, work,
262 $ ldwork, a( i+ib, i ), lda, work( ib+1 ),
263 $ ldwork )
264 END IF
265*
266* Apply H**T to columns i:n of current block
267*
268 CALL dorgl2( ib, n-i+1, ib, a( i, i ), lda, tau( i ), work,
269 $ iinfo )
270*
271* Set columns 1:i-1 of current block to zero
272*
273 DO 40 j = 1, i - 1
274 DO 30 l = i, i + ib - 1
275 a( l, j ) = zero
276 30 CONTINUE
277 40 CONTINUE
278 50 CONTINUE
279 END IF
280*
281 work( 1 ) = iws
282 RETURN
283*
284* End of DORGLQ
285*
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
dorgl2
subroutine dorgl2(m, n, k, a, lda, tau, work, info)
DORGL2
Definition dorgl2.f:113
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