LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ ctpqrt()

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

CTPQRT

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

Purpose:
 CTPQRT 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 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 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 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 array, dimension (NB*N)
[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.
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 ctpqrt.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 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 ctpqrt2, ctprfb, 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( 'CTPQRT', -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 ctpqrt2( 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 ctprfb( '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 CTPQRT
266 *
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 real or complex "triangular-pentagonal" blocked reflector to a real or complex matri...
Definition: ctprfb.f:251
subroutine ctpqrt2(M, N, L, A, LDA, B, LDB, T, LDT, INFO)
CTPQRT2 computes a QR factorization of a real or complex "triangular-pentagonal" matrix,...
Definition: ctpqrt2.f:173
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