LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dorgtsqr()

subroutine dorgtsqr ( integer  m,
integer  n,
integer  mb,
integer  nb,
double precision, dimension( lda, * )  a,
integer  lda,
double precision, dimension( ldt, * )  t,
integer  ldt,
double precision, dimension( * )  work,
integer  lwork,
integer  info 
)

DORGTSQR

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

Purpose:
 DORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,
 which are the first N columns of a product of real orthogonal
 matrices of order M which are returned by DLATSQR

      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

 See the documentation for DLATSQR.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A. M >= N >= 0.
[in]MB
          MB is INTEGER
          The row block size used by DLATSQR to return
          arrays A and T. MB > N.
          (Note that if MB > M, then M is used instead of MB
          as the row block size).
[in]NB
          NB is INTEGER
          The column block size used by DLATSQR to return
          arrays A and T. NB >= 1.
          (Note that if NB > N, then N is used instead of NB
          as the column block size).
[in,out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)

          On entry:

             The elements on and above the diagonal are not accessed.
             The elements below the diagonal represent the unit
             lower-trapezoidal blocked matrix V computed by DLATSQR
             that defines the input matrices Q_in(k) (ones on the
             diagonal are not stored) (same format as the output A
             below the diagonal in DLATSQR).

          On exit:

             The array A contains an M-by-N orthonormal matrix Q_out,
             i.e the columns of A are orthogonal unit vectors.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[in]T
          T is DOUBLE PRECISION array,
          dimension (LDT, N * NIRB)
          where NIRB = Number_of_input_row_blocks
                     = MAX( 1, CEIL((M-N)/(MB-N)) )
          Let NICB = Number_of_input_col_blocks
                   = CEIL(N/NB)

          The upper-triangular block reflectors used to define the
          input matrices Q_in(k), k=(1:NIRB*NICB). The block
          reflectors are stored in compact form in NIRB block
          reflector sequences. Each of NIRB block reflector sequences
          is stored in a larger NB-by-N column block of T and consists
          of NICB smaller NB-by-NB upper-triangular column blocks.
          (same format as the output T in DLATSQR).
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.
          LDT >= max(1,min(NB1,N)).
[out]WORK
          (workspace) DOUBLE PRECISION array, dimension (MAX(2,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK.  LWORK >= (M+NB)*N.
          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 had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
 November 2019, Igor Kozachenko,
                Computer Science Division,
                University of California, Berkeley

Definition at line 174 of file dorgtsqr.f.

176 IMPLICIT NONE
177*
178* -- LAPACK computational routine --
179* -- LAPACK is a software package provided by Univ. of Tennessee, --
180* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181*
182* .. Scalar Arguments ..
183 INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
184* ..
185* .. Array Arguments ..
186 DOUBLE PRECISION A( LDA, * ), T( LDT, * ), WORK( * )
187* ..
188*
189* =====================================================================
190*
191* .. Parameters ..
192 DOUBLE PRECISION ONE, ZERO
193 parameter( one = 1.0d+0, zero = 0.0d+0 )
194* ..
195* .. Local Scalars ..
196 LOGICAL LQUERY
197 INTEGER IINFO, LDC, LWORKOPT, LC, LW, NBLOCAL, J
198* ..
199* .. External Subroutines ..
200 EXTERNAL dcopy, dlamtsqr, dlaset, xerbla
201* ..
202* .. Intrinsic Functions ..
203 INTRINSIC dble, max, min
204* ..
205* .. Executable Statements ..
206*
207* Test the input parameters
208*
209 lquery = lwork.EQ.-1
210 info = 0
211 IF( m.LT.0 ) THEN
212 info = -1
213 ELSE IF( n.LT.0 .OR. m.LT.n ) THEN
214 info = -2
215 ELSE IF( mb.LE.n ) THEN
216 info = -3
217 ELSE IF( nb.LT.1 ) THEN
218 info = -4
219 ELSE IF( lda.LT.max( 1, m ) ) THEN
220 info = -6
221 ELSE IF( ldt.LT.max( 1, min( nb, n ) ) ) THEN
222 info = -8
223 ELSE
224*
225* Test the input LWORK for the dimension of the array WORK.
226* This workspace is used to store array C(LDC, N) and WORK(LWORK)
227* in the call to DLAMTSQR. See the documentation for DLAMTSQR.
228*
229 IF( lwork.LT.2 .AND. (.NOT.lquery) ) THEN
230 info = -10
231 ELSE
232*
233* Set block size for column blocks
234*
235 nblocal = min( nb, n )
236*
237* LWORK = -1, then set the size for the array C(LDC,N)
238* in DLAMTSQR call and set the optimal size of the work array
239* WORK(LWORK) in DLAMTSQR call.
240*
241 ldc = m
242 lc = ldc*n
243 lw = n * nblocal
244*
245 lworkopt = lc+lw
246*
247 IF( ( lwork.LT.max( 1, lworkopt ) ).AND.(.NOT.lquery) ) THEN
248 info = -10
249 END IF
250 END IF
251*
252 END IF
253*
254* Handle error in the input parameters and return workspace query.
255*
256 IF( info.NE.0 ) THEN
257 CALL xerbla( 'DORGTSQR', -info )
258 RETURN
259 ELSE IF ( lquery ) THEN
260 work( 1 ) = dble( lworkopt )
261 RETURN
262 END IF
263*
264* Quick return if possible
265*
266 IF( min( m, n ).EQ.0 ) THEN
267 work( 1 ) = dble( lworkopt )
268 RETURN
269 END IF
270*
271* (1) Form explicitly the tall-skinny M-by-N left submatrix Q1_in
272* of M-by-M orthogonal matrix Q_in, which is implicitly stored in
273* the subdiagonal part of input array A and in the input array T.
274* Perform by the following operation using the routine DLAMTSQR.
275*
276* Q1_in = Q_in * ( I ), where I is a N-by-N identity matrix,
277* ( 0 ) 0 is a (M-N)-by-N zero matrix.
278*
279* (1a) Form M-by-N matrix in the array WORK(1:LDC*N) with ones
280* on the diagonal and zeros elsewhere.
281*
282 CALL dlaset( 'F', m, n, zero, one, work, ldc )
283*
284* (1b) On input, WORK(1:LDC*N) stores ( I );
285* ( 0 )
286*
287* On output, WORK(1:LDC*N) stores Q1_in.
288*
289 CALL dlamtsqr( 'L', 'N', m, n, n, mb, nblocal, a, lda, t, ldt,
290 $ work, ldc, work( lc+1 ), lw, iinfo )
291*
292* (2) Copy the result from the part of the work array (1:M,1:N)
293* with the leading dimension LDC that starts at WORK(1) into
294* the output array A(1:M,1:N) column-by-column.
295*
296 DO j = 1, n
297 CALL dcopy( m, work( (j-1)*ldc + 1 ), 1, a( 1, j ), 1 )
298 END DO
299*
300 work( 1 ) = dble( lworkopt )
301 RETURN
302*
303* End of DORGTSQR
304*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dcopy
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
dlamtsqr
subroutine dlamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
DLAMTSQR
Definition dlamtsqr.f:199
dlaset
subroutine dlaset(uplo, m, n, alpha, beta, a, lda)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition dlaset.f:110
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