naginterfaces.library.orthog.real_​gram_​schmidt¶

naginterfaces.library.orthog.real_gram_schmidt(a, n1)[source]

real_gram_schmidt applies the Schmidt orthogonalization process to vectors in -dimensional space, .

For full information please refer to the NAG Library document for f05aa

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f05/f05aaf.html

Parameters
afloat, array-like, shape

Columns to contain the vectors to be orthogonalized. The vectors are stored by columns in elements to .

n1int

The indices of the first and last columns of to be orthogonalized.

Returns
afloat, ndarray, shape

These vectors are overwritten by the orthonormal vectors.

ccfloat

Is used to indicate linear dependence of the original vectors. The nearer is to , the more likely vector is dependent on vectors to . See Further Comments.

icolint

The column number corresponding to . See Further Comments.

Raises
NagValueError
(errno )

On entry, and .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

real_gram_schmidt applies the Schmidt orthogonalization process to linearly independent vectors in -dimensional space, . The effect of this process is to replace the original vectors by orthonormal vectors which have the property that the th vector is linearly dependent on the first of the original vectors, and that the sum of squares of the elements of the th vector is equal to , for . Inner-products are accumulated using additional precision.