LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ztpqrt()

 subroutine ztpqrt ( integer M, integer N, integer L, integer NB, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldt, * ) T, integer LDT, complex*16, dimension( * ) WORK, integer INFO )

ZTPQRT

Purpose:
``` ZTPQRT computes a blocked QR factorization of a complex
"triangular-pentagonal" matrix C, which is composed of a
triangular block A and pentagonal block B, using the compact
WY representation for Q.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix B. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix B, and the order of the triangular matrix A. N >= 0.``` [in] L ``` L is INTEGER The number of rows of the upper trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.``` [in] NB ``` NB is INTEGER The block size to be used in the blocked QR. N >= NB >= 1.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the upper triangular N-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the upper triangular matrix R.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in,out] B ``` B is COMPLEX*16 array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B. The first M-L rows are rectangular, and the last L rows are upper trapezoidal. On exit, B contains the pentagonal matrix V. See Further Details.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,M).``` [out] T ``` T is COMPLEX*16 array, dimension (LDT,N) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Further Details.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= NB.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (NB*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Further Details:
```  The input matrix C is a (N+M)-by-N matrix

C = [ A ]
[ B ]

where A is an upper triangular N-by-N matrix, and B is M-by-N pentagonal
matrix consisting of a (M-L)-by-N rectangular matrix B1 on top of a L-by-N
upper trapezoidal matrix B2:

B = [ B1 ]  <- (M-L)-by-N rectangular
[ B2 ]  <-     L-by-N upper trapezoidal.

The upper trapezoidal matrix B2 consists of the first L rows of a
N-by-N upper triangular matrix, where 0 <= L <= MIN(M,N).  If L=0,
B is rectangular M-by-N; if M=L=N, B is upper triangular.

The matrix W stores the elementary reflectors H(i) in the i-th column
below the diagonal (of A) in the (N+M)-by-N input matrix C

C = [ A ]  <- upper triangular N-by-N
[ B ]  <- M-by-N pentagonal

so that W can be represented as

W = [ I ]  <- identity, N-by-N
[ V ]  <- M-by-N, same form as B.

Thus, all of information needed for W is contained on exit in B, which
we call V above.  Note that V has the same form as B; that is,

V = [ V1 ] <- (M-L)-by-N rectangular
[ V2 ] <-     L-by-N upper trapezoidal.

The columns of V represent the vectors which define the H(i)'s.

The number of blocks is B = ceiling(N/NB), where each
block is of order NB except for the last block, which is of order
IB = N - (B-1)*NB.  For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB
for the last block) T's are stored in the NB-by-N matrix T as

T = [T1 T2 ... TB].```

Definition at line 187 of file ztpqrt.f.

189 *
190 * -- LAPACK computational routine --
191 * -- LAPACK is a software package provided by Univ. of Tennessee, --
192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193 *
194 * .. Scalar Arguments ..
195  INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
196 * ..
197 * .. Array Arguments ..
198  COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
199 * ..
200 *
201 * =====================================================================
202 *
203 * ..
204 * .. Local Scalars ..
205  INTEGER I, IB, LB, MB, IINFO
206 * ..
207 * .. External Subroutines ..
208  EXTERNAL ztpqrt2, ztprfb, xerbla
209 * ..
210 * .. Executable Statements ..
211 *
212 * Test the input arguments
213 *
214  info = 0
215  IF( m.LT.0 ) THEN
216  info = -1
217  ELSE IF( n.LT.0 ) THEN
218  info = -2
219  ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
220  info = -3
221  ELSE IF( nb.LT.1 .OR. (nb.GT.n .AND. n.GT.0)) THEN
222  info = -4
223  ELSE IF( lda.LT.max( 1, n ) ) THEN
224  info = -6
225  ELSE IF( ldb.LT.max( 1, m ) ) THEN
226  info = -8
227  ELSE IF( ldt.LT.nb ) THEN
228  info = -10
229  END IF
230  IF( info.NE.0 ) THEN
231  CALL xerbla( 'ZTPQRT', -info )
232  RETURN
233  END IF
234 *
235 * Quick return if possible
236 *
237  IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
238 *
239  DO i = 1, n, nb
240 *
241 * Compute the QR factorization of the current block
242 *
243  ib = min( n-i+1, nb )
244  mb = min( m-l+i+ib-1, m )
245  IF( i.GE.l ) THEN
246  lb = 0
247  ELSE
248  lb = mb-m+l-i+1
249  END IF
250 *
251  CALL ztpqrt2( mb, ib, lb, a(i,i), lda, b( 1, i ), ldb,
252  \$ t(1, i ), ldt, iinfo )
253 *
254 * Update by applying H**H to B(:,I+IB:N) from the left
255 *
256  IF( i+ib.LE.n ) THEN
257  CALL ztprfb( 'L', 'C', 'F', 'C', mb, n-i-ib+1, ib, lb,
258  \$ b( 1, i ), ldb, t( 1, i ), ldt,
259  \$ a( i, i+ib ), lda, b( 1, i+ib ), ldb,
260  \$ work, ib )
261  END IF
262  END DO
263  RETURN
264 *
265 * End of ZTPQRT
266 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
ZTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ztprfb.f:251
subroutine ztpqrt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
ZTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix,...
Definition: ztpqrt2.f:173
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