SORBDB5 orthogonalizes the column vector


      X = [ X1 ]


          [ X2 ]


 with respect to the columns of


      Q = [ Q1 ] .


          [ Q2 ]


 The columns of Q must be orthonormal.


 If the projection is zero according to Kahan's "twice is enough"


 criterion, then some other vector from the orthogonal complement


 is returned. This vector is chosen in an arbitrary but deterministic


 way.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

July 2012