 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ctplqt()

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

CTPLQT

Purpose:
``` CTPLQT computes a blocked LQ 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, and the order of the triangular matrix A. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix B. N >= 0.``` [in] L ``` L is INTEGER The number of rows of the lower trapezoidal part of B. MIN(M,N) >= L >= 0. See Further Details.``` [in] MB ``` MB is INTEGER The block size to be used in the blocked QR. M >= MB >= 1.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,M) On entry, the lower triangular M-by-M matrix A. On exit, the elements on and below the diagonal of the array contain the lower triangular matrix L.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [in,out] B ``` B is COMPLEX array, dimension (LDB,N) On entry, the pentagonal M-by-N matrix B. The first N-L columns are rectangular, and the last L columns are lower 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 array, dimension (LDT,N) The lower 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 >= MB.``` [out] WORK ` WORK is COMPLEX array, dimension (MB*M)` [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 M-by-(M+N) matrix

C = [ A ] [ B ]

where A is an lower triangular M-by-M matrix, and B is M-by-N pentagonal
matrix consisting of a M-by-(N-L) rectangular matrix B1 on left of a M-by-L
upper trapezoidal matrix B2:
[ B ] = [ B1 ] [ B2 ]
[ B1 ]  <- M-by-(N-L) rectangular
[ B2 ]  <-     M-by-L lower trapezoidal.

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

The matrix W stores the elementary reflectors H(i) in the i-th row
above the diagonal (of A) in the M-by-(M+N) input matrix C
[ C ] = [ A ] [ B ]
[ A ]  <- lower triangular M-by-M
[ B ]  <- M-by-N pentagonal

so that W can be represented as
[ W ] = [ I ] [ V ]
[ I ]  <- identity, M-by-M
[ 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 ] [ V2 ]
[ V1 ] <- M-by-(N-L) rectangular
[ V2 ] <-     M-by-L lower trapezoidal.

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

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

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

Definition at line 172 of file ctplqt.f.

174*
175* -- LAPACK computational routine --
176* -- LAPACK is a software package provided by Univ. of Tennessee, --
177* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178*
179* .. Scalar Arguments ..
180 INTEGER INFO, LDA, LDB, LDT, N, M, L, MB
181* ..
182* .. Array Arguments ..
183 COMPLEX A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
184* ..
185*
186* =====================================================================
187*
188* ..
189* .. Local Scalars ..
190 INTEGER I, IB, LB, NB, IINFO
191* ..
192* .. External Subroutines ..
193 EXTERNAL ctplqt2, ctprfb, xerbla
194* ..
195* .. Executable Statements ..
196*
197* Test the input arguments
198*
199 info = 0
200 IF( m.LT.0 ) THEN
201 info = -1
202 ELSE IF( n.LT.0 ) THEN
203 info = -2
204 ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
205 info = -3
206 ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
207 info = -4
208 ELSE IF( lda.LT.max( 1, m ) ) THEN
209 info = -6
210 ELSE IF( ldb.LT.max( 1, m ) ) THEN
211 info = -8
212 ELSE IF( ldt.LT.mb ) THEN
213 info = -10
214 END IF
215 IF( info.NE.0 ) THEN
216 CALL xerbla( 'CTPLQT', -info )
217 RETURN
218 END IF
219*
220* Quick return if possible
221*
222 IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
223*
224 DO i = 1, m, mb
225*
226* Compute the QR factorization of the current block
227*
228 ib = min( m-i+1, mb )
229 nb = min( n-l+i+ib-1, n )
230 IF( i.GE.l ) THEN
231 lb = 0
232 ELSE
233 lb = nb-n+l-i+1
234 END IF
235*
236 CALL ctplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
237 \$ t(1, i ), ldt, iinfo )
238*
239* Update by applying H**T to B(I+IB:M,:) from the right
240*
241 IF( i+ib.LE.m ) THEN
242 CALL ctprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
243 \$ b( i, 1 ), ldb, t( 1, i ), ldt,
244 \$ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
245 \$ work, m-i-ib+1)
246 END IF
247 END DO
248 RETURN
249*
250* End of CTPLQT
251*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB applies a complex "triangular-pentagonal" block reflector to a complex matrix,...
Definition: ctprfb.f:251
subroutine ctplqt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
CTPLQT2
Definition: ctplqt2.f:162
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