LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zungtsqr()

subroutine zungtsqr ( integer  m,
integer  n,
integer  mb,
integer  nb,
complex*16, dimension( lda, * )  a,
integer  lda,
complex*16, dimension( ldt, * )  t,
integer  ldt,
complex*16, dimension( * )  work,
integer  lwork,
integer  info 
)

ZUNGTSQR

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

Purpose:
 ZUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal
 columns, which are the first N columns of a product of comlpex unitary
 matrices of order M which are returned by ZLATSQR

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

 See the documentation for ZLATSQR.
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 ZLATSQR 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 ZLATSQR 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 COMPLEX*16 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 ZLATSQR
             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 ZLATSQR).

          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 COMPLEX*16 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 ZLATSQR).
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T.
          LDT >= max(1,min(NB1,N)).
[out]WORK
          (workspace) COMPLEX*16 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 zungtsqr.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 COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
187* ..
188*
189* =====================================================================
190*
191* .. Parameters ..
192 COMPLEX*16 CONE, CZERO
193 parameter( cone = ( 1.0d+0, 0.0d+0 ),
194 $ czero = ( 0.0d+0, 0.0d+0 ) )
195* ..
196* .. Local Scalars ..
197 LOGICAL LQUERY
198 INTEGER IINFO, LDC, LWORKOPT, LC, LW, NBLOCAL, J
199* ..
200* .. External Subroutines ..
201 EXTERNAL zcopy, zlamtsqr, zlaset, xerbla
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC dcmplx, max, min
205* ..
206* .. Executable Statements ..
207*
208* Test the input parameters
209*
210 lquery = lwork.EQ.-1
211 info = 0
212 IF( m.LT.0 ) THEN
213 info = -1
214 ELSE IF( n.LT.0 .OR. m.LT.n ) THEN
215 info = -2
216 ELSE IF( mb.LE.n ) THEN
217 info = -3
218 ELSE IF( nb.LT.1 ) THEN
219 info = -4
220 ELSE IF( lda.LT.max( 1, m ) ) THEN
221 info = -6
222 ELSE IF( ldt.LT.max( 1, min( nb, n ) ) ) THEN
223 info = -8
224 ELSE
225*
226* Test the input LWORK for the dimension of the array WORK.
227* This workspace is used to store array C(LDC, N) and WORK(LWORK)
228* in the call to ZLAMTSQR. See the documentation for ZLAMTSQR.
229*
230 IF( lwork.LT.2 .AND. (.NOT.lquery) ) THEN
231 info = -10
232 ELSE
233*
234* Set block size for column blocks
235*
236 nblocal = min( nb, n )
237*
238* LWORK = -1, then set the size for the array C(LDC,N)
239* in ZLAMTSQR call and set the optimal size of the work array
240* WORK(LWORK) in ZLAMTSQR call.
241*
242 ldc = m
243 lc = ldc*n
244 lw = n * nblocal
245*
246 lworkopt = lc+lw
247*
248 IF( ( lwork.LT.max( 1, lworkopt ) ).AND.(.NOT.lquery) ) THEN
249 info = -10
250 END IF
251 END IF
252*
253 END IF
254*
255* Handle error in the input parameters and return workspace query.
256*
257 IF( info.NE.0 ) THEN
258 CALL xerbla( 'ZUNGTSQR', -info )
259 RETURN
260 ELSE IF ( lquery ) THEN
261 work( 1 ) = dcmplx( lworkopt )
262 RETURN
263 END IF
264*
265* Quick return if possible
266*
267 IF( min( m, n ).EQ.0 ) THEN
268 work( 1 ) = dcmplx( lworkopt )
269 RETURN
270 END IF
271*
272* (1) Form explicitly the tall-skinny M-by-N left submatrix Q1_in
273* of M-by-M orthogonal matrix Q_in, which is implicitly stored in
274* the subdiagonal part of input array A and in the input array T.
275* Perform by the following operation using the routine ZLAMTSQR.
276*
277* Q1_in = Q_in * ( I ), where I is a N-by-N identity matrix,
278* ( 0 ) 0 is a (M-N)-by-N zero matrix.
279*
280* (1a) Form M-by-N matrix in the array WORK(1:LDC*N) with ones
281* on the diagonal and zeros elsewhere.
282*
283 CALL zlaset( 'F', m, n, czero, cone, work, ldc )
284*
285* (1b) On input, WORK(1:LDC*N) stores ( I );
286* ( 0 )
287*
288* On output, WORK(1:LDC*N) stores Q1_in.
289*
290 CALL zlamtsqr( 'L', 'N', m, n, n, mb, nblocal, a, lda, t, ldt,
291 $ work, ldc, work( lc+1 ), lw, iinfo )
292*
293* (2) Copy the result from the part of the work array (1:M,1:N)
294* with the leading dimension LDC that starts at WORK(1) into
295* the output array A(1:M,1:N) column-by-column.
296*
297 DO j = 1, n
298 CALL zcopy( m, work( (j-1)*ldc + 1 ), 1, a( 1, j ), 1 )
299 END DO
300*
301 work( 1 ) = dcmplx( lworkopt )
302 RETURN
303*
304* End of ZUNGTSQR
305*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zcopy
subroutine zcopy(n, zx, incx, zy, incy)
ZCOPY
Definition zcopy.f:81
zlamtsqr
subroutine zlamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
ZLAMTSQR
Definition zlamtsqr.f:199
zlaset
subroutine zlaset(uplo, m, n, alpha, beta, a, lda)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition zlaset.f:106
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