LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ 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 
)
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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2017
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 174 of file ctplqt.f.

174 *
175 * -- LAPACK computational routine (version 3.7.1) --
176 * -- LAPACK is a software package provided by Univ. of Tennessee, --
177 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
178 * June 2017
179 *
180 * .. Scalar Arguments ..
181  INTEGER info, lda, ldb, ldt, n, m, l, mb
182 * ..
183 * .. Array Arguments ..
184  COMPLEX a( lda, * ), b( ldb, * ), t( ldt, * ), work( * )
185 * ..
186 *
187 * =====================================================================
188 *
189 * ..
190 * .. Local Scalars ..
191  INTEGER i, ib, lb, nb, iinfo
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL ctplqt2, ctprfb, xerbla
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input arguments
199 *
200  info = 0
201  IF( m.LT.0 ) THEN
202  info = -1
203  ELSE IF( n.LT.0 ) THEN
204  info = -2
205  ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
206  info = -3
207  ELSE IF( mb.LT.1 .OR. (mb.GT.m .AND. m.GT.0)) THEN
208  info = -4
209  ELSE IF( lda.LT.max( 1, m ) ) THEN
210  info = -6
211  ELSE IF( ldb.LT.max( 1, m ) ) THEN
212  info = -8
213  ELSE IF( ldt.LT.mb ) THEN
214  info = -10
215  END IF
216  IF( info.NE.0 ) THEN
217  CALL xerbla( 'CTPLQT', -info )
218  RETURN
219  END IF
220 *
221 * Quick return if possible
222 *
223  IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
224 *
225  DO i = 1, m, mb
226 *
227 * Compute the QR factorization of the current block
228 *
229  ib = min( m-i+1, mb )
230  nb = min( n-l+i+ib-1, n )
231  IF( i.GE.l ) THEN
232  lb = 0
233  ELSE
234  lb = nb-n+l-i+1
235  END IF
236 *
237  CALL ctplqt2( ib, nb, lb, a(i,i), lda, b( i, 1 ), ldb,
238  $ t(1, i ), ldt, iinfo )
239 *
240 * Update by applying H**T to B(I+IB:M,:) from the right
241 *
242  IF( i+ib.LE.m ) THEN
243  CALL ctprfb( 'R', 'N', 'F', 'R', m-i-ib+1, nb, ib, lb,
244  $ b( i, 1 ), ldb, t( 1, i ), ldt,
245  $ a( i+ib, i ), lda, b( i+ib, 1 ), ldb,
246  $ work, m-i-ib+1)
247  END IF
248  END DO
249  RETURN
250 *
251 * End of CTPLQT
252 *
subroutine ctprfb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
CTPRFB applies a real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ctprfb.f:253
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ctplqt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
Definition: ctplqt2.f:162
Here is the call graph for this function:
Here is the caller graph for this function: