ztplqt2()

subroutine ztplqt2	(	integer	m,
		integer	n,
		integer	l,
		complex*16, dimension( lda, * )	a,
		integer	lda,
		complex*16, dimension( ldb, * )	b,
		integer	ldb,
		complex*16, dimension( ldt, * )	t,
		integer	ldt,
		integer	info )

ZTPLQT2 computes a LQ factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Download ZTPLQT2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> ZTPLQT2 computes a LQ a 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 total 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 lower trapezoidal part of B. !> MIN(M,N) >= L >= 0. See Further Details. !>
[in,out]	A	!> A is COMPLEX*16 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*16 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*16 array, dimension (LDT,M) !> The N-by-N upper triangular factor T of the block reflector. !> See Further Details. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. LDT >= max(1,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.

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 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
!>  N-by-N 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,
!>
!>               W = [ 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 (M+N)-by-(M+N) block reflector H is then given by
!>
!>               H = I - W**T * T * W
!>
!>  where W^H is the conjugate transpose of W and T is the upper triangular
!>  factor of the block reflector.
!>