Grad-Schmidt orthonormalization

Grad-Schmidt orthonormalization#

For Gram-Schmidt orthonormalization.

gram_schmidt(vec, n_max=None)[source]#

Gram-Schmidt orthogonalization (sympy).

Parameters:

  • vec (array-like) – list of vectors to be orthogonalized, [[sympy]].

  • n_max (int, optional) – max. of nonzero basis.

Returns:

  • (ndarray) – list of nonzero orthogonalized vectors, [[sympy]].

  • (ndarray) – indices of nonzero vectors, [int].

gram_schmidt_complex(vec, n_max=None, TOL=1e-08)[source]#

Gram-Schmidt orthogonalization for complex vectors by converting to complex.

Parameters:

  • vec (array-like) – list of vectors to be orthogonalized, [[sympy]].

  • n_max (int, optional) – max. of nonzero basis.

  • TOL (float, optional) – absolute tolerance.

Returns:

  • (ndarray) – list of nonzero orthogonalized vectors, [[complex]].

  • (ndarray) – indices of nonzero vectors, [int].

gram_schmidt_float(vec, n_max=None, TOL=1e-08)[source]#

Gram-Schmidt orthogonalization for real vectors by converting to float.

Parameters:

  • vec (array-like) – list of vectors to be orthogonalized, [[sympy]].

  • n_max (int, optional) – max. of nonzero basis.

  • TOL (float, optional) – absolute tolerance.

Returns:

  • (ndarray) – list of nonzero orthogonalized vectors, [[float]].

  • (ndarray) – indices of nonzero vectors, [int].

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