sorbdb6.f3

!>
!> SORBDB6 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
!>
!>

M1

!>          M1 is INTEGER
!>           The dimension of X1 and the number of rows in Q1. 0 <= M1.
!> 

M2

!>          M2 is INTEGER
!>           The dimension of X2 and the number of rows in Q2. 0 <= M2.
!> 

N

!>          N is INTEGER
!>           The number of columns in Q1 and Q2. 0 <= N.
!> 

X1

!>          X1 is REAL array, dimension (M1)
!>           On entry, the top part of the vector to be orthogonalized.
!>           On exit, the top part of the projected vector.
!> 

INCX1

!>          INCX1 is INTEGER
!>           Increment for entries of X1.
!> 

X2

!>          X2 is REAL array, dimension (M2)
!>           On entry, the bottom part of the vector to be
!>           orthogonalized. On exit, the bottom part of the projected
!>           vector.
!> 

INCX2

!>          INCX2 is INTEGER
!>           Increment for entries of X2.
!> 

Q1

!>          Q1 is REAL array, dimension (LDQ1, N)
!>           The top part of the orthonormal basis matrix.
!> 

LDQ1

!>          LDQ1 is INTEGER
!>           The leading dimension of Q1. LDQ1 >= M1.
!> 

Q2

!>          Q2 is REAL array, dimension (LDQ2, N)
!>           The bottom part of the orthonormal basis matrix.
!> 

LDQ2

!>          LDQ2 is INTEGER
!>           The leading dimension of Q2. LDQ2 >= M2.
!> 

WORK

!>          WORK is REAL array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>           The dimension of the array WORK. LWORK >= N.
!> 

INFO

!>          INFO is INTEGER
!>           = 0:  successful exit.
!>           < 0:  if INFO = -i, the i-th argument had an illegal value.
!> 

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