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

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

Purpose:

!>
!> ZTPQRT computes a blocked QR factorization of a complex
!>  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 !>

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 185 of file ztpqrt.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER INFO, LDA, LDB, LDT, N, M, L, NB
*     ..
*     .. Array Arguments ..
      COMPLEX*16 A( LDA, * ), B( LDB, * ), T( LDT, * ), WORK( * )
*     ..
*
* =====================================================================
*
*     ..
*     .. Local Scalars ..
      INTEGER    I, IB, LB, MB, IINFO
*     ..
*     .. External Subroutines ..
      EXTERNAL   ztpqrt2, ztprfb, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( l.LT.0 .OR. (l.GT.min(m,n) .AND. min(m,n).GE.0)) THEN
         info = -3
      ELSE IF( nb.LT.1 .OR. (nb.GT.n .AND. n.GT.0)) THEN
         info = -4
      ELSE IF( lda.LT.max( 1, n ) ) THEN
         info = -6
      ELSE IF( ldb.LT.max( 1, m ) ) THEN
         info = -8
      ELSE IF( ldt.LT.nb ) THEN
         info = -10
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZTPQRT', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 ) RETURN
*
      DO i = 1, n, nb
*
*     Compute the QR factorization of the current block
*
         ib = min( n-i+1, nb )
         mb = min( m-l+i+ib-1, m )
         IF( i.GE.l ) THEN
            lb = 0
         ELSE
            lb = mb-m+l-i+1
         END IF
*
         CALL ztpqrt2( mb, ib, lb, a(i,i), lda, b( 1, i ), ldb,
     $                 t(1, i ), ldt, iinfo )
*
*     Update by applying H**H to B(:,I+IB:N) from the left
*
         IF( i+ib.LE.n ) THEN
            CALL ztprfb( 'L', 'C', 'F', 'C', mb, n-i-ib+1, ib, lb,
     $                    b( 1, i ), ldb, t( 1, i ), ldt,
     $                    a( i, i+ib ), lda, b( 1, i+ib ), ldb,
     $                    work, ib )
         END IF
      END DO
      RETURN
*
*     End of ZTPQRT
*

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