dorbdb6()

subroutine dorbdb6	(	integer	m1,
		integer	m2,
		integer	n,
		double precision, dimension(*)	x1,
		integer	incx1,
		double precision, dimension(*)	x2,
		integer	incx2,
		double precision, dimension(ldq1,*)	q1,
		integer	ldq1,
		double precision, dimension(ldq2,*)	q2,
		integer	ldq2,
		double precision, dimension(*)	work,
		integer	lwork,
		integer	info )

DORBDB6

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Purpose:

!>
!> DORBDB6 orthogonalizes the column vector
!>      X = [ X1 ]
!>          [ X2 ]
!> with respect to the columns of
!>      Q = [ Q1 ] .
!>          [ Q2 ]
!> The columns of Q must be orthonormal. The orthogonalized vector will
!> be zero if and only if it lies entirely in the range of Q.
!>
!> The projection is computed with at most two iterations of the
!> classical Gram-Schmidt algorithm, see
!> * L. Giraud, J. Langou, M. Rozložník. 
!>   2002. CERFACS Technical Report No. TR/PA/02/33. URL:
!>   https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
!>
!>

Parameters

[in]	M1	!> M1 is INTEGER !> The dimension of X1 and the number of rows in Q1. 0 <= M1. !>
[in]	M2	!> M2 is INTEGER !> The dimension of X2 and the number of rows in Q2. 0 <= M2. !>
[in]	N	!> N is INTEGER !> The number of columns in Q1 and Q2. 0 <= N. !>
[in,out]	X1	!> X1 is DOUBLE PRECISION array, dimension (M1) !> On entry, the top part of the vector to be orthogonalized. !> On exit, the top part of the projected vector. !>
[in]	INCX1	!> INCX1 is INTEGER !> Increment for entries of X1. !>
[in,out]	X2	!> X2 is DOUBLE PRECISION array, dimension (M2) !> On entry, the bottom part of the vector to be !> orthogonalized. On exit, the bottom part of the projected !> vector. !>
[in]	INCX2	!> INCX2 is INTEGER !> Increment for entries of X2. !>
[in]	Q1	!> Q1 is DOUBLE PRECISION array, dimension (LDQ1, N) !> The top part of the orthonormal basis matrix. !>
[in]	LDQ1	!> LDQ1 is INTEGER !> The leading dimension of Q1. LDQ1 >= M1. !>
[in]	Q2	!> Q2 is DOUBLE PRECISION array, dimension (LDQ2, N) !> The bottom part of the orthonormal basis matrix. !>
[in]	LDQ2	!> LDQ2 is INTEGER !> The leading dimension of Q2. LDQ2 >= M2. !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (LWORK) !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= 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.