dtpmqrt()

subroutine dtpmqrt	(	character	side,
		character	trans,
		integer	m,
		integer	n,
		integer	k,
		integer	l,
		integer	nb,
		double precision, dimension( ldv, * )	v,
		integer	ldv,
		double precision, dimension( ldt, * )	t,
		integer	ldt,
		double precision, dimension( lda, * )	a,
		integer	lda,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		double precision, dimension( * )	work,
		integer	info )

DTPMQRT

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Purpose:

!>
!> DTPMQRT applies a real orthogonal matrix Q obtained from a
!>  real block reflector H to a general
!> real matrix C, which consists of two blocks A and B.
!> 

Parameters

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**T from the Left; !> = 'R': apply Q or Q**T from the Right. !>
[in]	TRANS	!> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'T': Transpose, apply Q**T. !>
[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. N >= 0. !>
[in]	K	!> K is INTEGER !> The number of elementary reflectors whose product defines !> the matrix Q. !>
[in]	L	!> L is INTEGER !> The order of the trapezoidal part of V. !> K >= L >= 0. See Further Details. !>
[in]	NB	!> NB is INTEGER !> The block size used for the storage of T. K >= NB >= 1. !> This must be the same value of NB used to generate T !> in CTPQRT. !>
[in]	V	!> V is DOUBLE PRECISION array, dimension (LDV,K) !> The i-th column must contain the vector which defines the !> elementary reflector H(i), for i = 1,2,...,k, as returned by !> CTPQRT in B. See Further Details. !>
[in]	LDV	!> LDV is INTEGER !> The leading dimension of the array V. !> If SIDE = 'L', LDV >= max(1,M); !> if SIDE = 'R', LDV >= max(1,N). !>
[in]	T	!> T is DOUBLE PRECISION array, dimension (LDT,K) !> The upper triangular factors of the block reflectors !> as returned by CTPQRT, stored as a NB-by-K matrix. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. LDT >= NB. !>
[in,out]	A	!> A is DOUBLE PRECISION array, dimension !> (LDA,N) if SIDE = 'L' or !> (LDA,K) if SIDE = 'R' !> On entry, the K-by-N or M-by-K matrix A. !> On exit, A is overwritten by the corresponding block of !> Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. !> If SIDE = 'L', LDC >= max(1,K); !> If SIDE = 'R', LDC >= max(1,M). !>
[in,out]	B	!> B is DOUBLE PRECISION array, dimension (LDB,N) !> On entry, the M-by-N matrix B. !> On exit, B is overwritten by the corresponding block of !> Q*C or Q**T*C or C*Q or C*Q**T. See Further Details. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. !> LDB >= max(1,M). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array. The dimension of WORK is !> N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. !>
[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 columns of the pentagonal matrix V contain the elementary reflectors
!>  H(1), H(2), ..., H(K); V is composed of a rectangular block V1 and a
!>  trapezoidal block V2:
!>
!>        V = [V1]
!>            [V2].
!>
!>  The size of the trapezoidal block V2 is determined by the parameter L,
!>  where 0 <= L <= K; V2 is upper trapezoidal, consisting of the first L
!>  rows of a K-by-K upper triangular matrix.  If L=K, V2 is upper triangular;
!>  if L=0, there is no trapezoidal block, hence V = V1 is rectangular.
!>
!>  If SIDE = 'L':  C = [A]  where A is K-by-N,  B is M-by-N and V is M-by-K.
!>                      [B]
!>
!>  If SIDE = 'R':  C = [A B]  where A is M-by-K, B is M-by-N and V is N-by-K.
!>
!>  The real orthogonal matrix Q is formed from V and T.
!>
!>  If TRANS='N' and SIDE='L', C is on exit replaced with Q * C.
!>
!>  If TRANS='T' and SIDE='L', C is on exit replaced with Q**T * C.
!>
!>  If TRANS='N' and SIDE='R', C is on exit replaced with C * Q.
!>
!>  If TRANS='T' and SIDE='R', C is on exit replaced with C * Q**T.
!>