Orthogonalizes a column vector with respect to the orthonormal basis matrix.
Syntax
call sorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info )
call dorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info )
call cunbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info )
call zunbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info )
Include Files
- mkl.fi, lapack.f90
Description
The ?orbdb6/?unbdb6 routines orthogonalize the column vector
with respect to the columns of
The columns of Q must be orthonormal.
If the projection is zero according to Kahan's "twice is enough" criterion, then the zero vector is returned.
Input Parameters
- m1
INTEGER
The dimension of x1 and the number of rows in q1. 0 ≤m1.
- m2
INTEGER
The dimension of x2 and the number of rows in q2. 0 ≤m2.
- n
INTEGER
The number of columns in q1 and q2. 0 ≤n.
- x1
REAL for sordb5
DOUBLE PRECISION for dordb5
COMPLEX for cundb5
COMPLEX*16 for zundb5
Array of size m1.
The top part of the vector to be orthogonalized.
- incx1
INTEGER
Increment for entries of x1.
- x2
REAL for sordb5
DOUBLE PRECISION for dordb5
COMPLEX for cundb5
COMPLEX*16 for zundb5
Array of size m2.
The bottom part of the vector to be orthogonalized.
- incx2
INTEGER
Increment for entries of x2.
- q1
REAL for sordb5
DOUBLE PRECISION for dordb5
COMPLEX for cundb5
COMPLEX*16 for zundb5
Array of size (ldq1, n).
The top part of the orthonormal basis matrix.
- ldq1
INTEGER
The leading dimension of q1. ldq1≥m1.
- q2
REAL for sordb5
DOUBLE PRECISION for dordb5
COMPLEX for cundb5
COMPLEX*16 for zundb5
Array of size (ldq2, n).
The bottom part of the orthonormal basis matrix.
- ldq2
INTEGER
The leading dimension of q2. ldq2≥m2.
- work
REAL for sordb5
DOUBLE PRECISION for dordb5
COMPLEX for cundb5
COMPLEX*16 for zundb5
Workspace array of size lwork.
- lwork
INTEGER
The size of the array work. lwork≥n.
Output Parameters
- x1
The top part of the projected vector.
- x2
The bottom part of the projected vector.
- info
INTEGER.
= 0: successful exit
< 0: if info = -i, the i-th argument has an illegal value.