LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 ``` 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```
Contributors:
``` November 2019, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 173 of file zungtsqr.f.

175  IMPLICIT NONE
176 *
177 * -- LAPACK computational routine --
178 * -- LAPACK is a software package provided by Univ. of Tennessee, --
179 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
180 *
181 * .. Scalar Arguments ..
182  INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
183 * ..
184 * .. Array Arguments ..
185  COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
186 * ..
187 *
188 * =====================================================================
189 *
190 * .. Parameters ..
191  COMPLEX*16 CONE, CZERO
192  parameter( cone = ( 1.0d+0, 0.0d+0 ),
193  \$ czero = ( 0.0d+0, 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 zcopy, zlamtsqr, zlaset, xerbla
201 * ..
202 * .. Intrinsic Functions ..
203  INTRINSIC dcmplx, 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 ZLAMTSQR. See the documentation for ZLAMTSQR.
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 ZLAMTSQR call and set the optimal size of the work array
239 * WORK(LWORK) in ZLAMTSQR 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( 'ZUNGTSQR', -info )
258  RETURN
259  ELSE IF ( lquery ) THEN
260  work( 1 ) = dcmplx( lworkopt )
261  RETURN
262  END IF
263 *
264 * Quick return if possible
265 *
266  IF( min( m, n ).EQ.0 ) THEN
267  work( 1 ) = dcmplx( 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 ZLAMTSQR.
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 zlaset( 'F', m, n, czero, cone, 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 zlamtsqr( '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 zcopy( m, work( (j-1)*ldc + 1 ), 1, a( 1, j ), 1 )
298  END DO
299 *
300  work( 1 ) = dcmplx( lworkopt )
301  RETURN
302 *
303 * End of ZUNGTSQR
304 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
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
subroutine zlamtsqr(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
ZLAMTSQR
Definition: zlamtsqr.f:197
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