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The procedure in this paper could replace this code:
modepy/modepy/quadrature/construction.py
Lines 171 to 188 in 8f06f1c
| def orthogonalize_basis( | |
| integrate: Callable[[Integrand], np.inexact], | |
| basis: Sequence[Integrand], | |
| ) -> Sequence[LinearCombinationIntegrand]: | |
| r""" | |
| Let :math:`\Omega\subset\mathbb C^n` be a domain. (Domains | |
| over the reals are allowable as well.) Returns linear combinations | |
| of functions in *basis* that is orthogonal under the (complex-valued) | |
| :math:`L^2` inner product induced by *integrate*. | |
| :arg integrate: Computes an integral of the passed integrand over | |
| :math:`\Omega`. Must use integration nodes compatible with | |
| *basis*. | |
| :arg basis: A sequence of functions that accept an array of nodes | |
| of shape either ``(n, nnodes)`` or ``(nnodes,)`` and return | |
| an array of shape ``(nnodes,)`` with the value of the | |
| basis function at the node. | |
| """ |
(not exactly, since the initial basis is fixed, but morally)
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