chaospy.fit_regression

chaospy.fit_regression(polynomials, abscissas, evals, model=None, retall=0)

Fit a polynomial chaos expansion using linear regression.

Args:

polynomials (numpoly.ndpoly):

Polynomial expansion with polynomials.shape == (M,) and polynomials.dim=D.

abscissas (numpy.ndarray):

Collocation nodes with abscissas.shape == (D, K).

evals (numpy.ndarray):

Model evaluations with len(evals) == K.

model (Optional[sklearn.base.BaseEstimator]):

By default regression is done using the classical least-square method. However, if provided, and sklearn regression model can be used instead.

retall (int):

What the function should return. 0: only return fitted polynomials, with shape evals.shape[1:]. 1: polynomials, and Fourier coefficients, 2: polynomials, coefficients and polynomial evaluations.

Returns:

(chaospy.ndpoly, numpy.ndarray, numpy.ndarray):

Returned value as determined by retval.

Examples:

>>> x, y = chaospy.variable(2)
>>> polynomials = chaospy.polynomial([1, x, y])
>>> abscissas = [[-1, -1, 1, 1],  [-1, 1, -1, 1]]
>>> evals = [0, 1, 1, 2]
>>> chaospy.fit_regression(polynomials, abscissas, evals).round(14)
polynomial(0.5*q1+0.5*q0+1.0)
>>> model = sklearn.linear_model.LinearRegression(fit_intercept=False)
>>> chaospy.fit_regression(
...     polynomials, abscissas, evals, model=model).round(14)
polynomial(0.5*q1+0.5*q0+1.0)