orthax.orthfit

orthax.orthfit(x, y, deg, rec, rcond=None, full=False, w=None)Source 

Least squares fit of orthogonal series to data.

Return the coefficients of an orthogonal series of degree deg that is the least squares fit to the data values y given at points x. If y is 1-D the returned coefficients will also be 1-D. If y is 2-D multiple fits are done, one for each column of y, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form

\[p(x) = c_0 + c_1 * P_1(x) + ... + c_n * P_n(x),\]

where n is deg.

Parameters:

x (array_like, shape (M,)) – x-coordinates of the M sample points (x[i], y[i]).
y (array_like, shape (M,) or (M, K)) – y-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.
deg (int or 1-D array_like) – Degree(s) of the fitting polynomials. If deg is a single integer all terms up to and including the deg’th term are included in the fit. A tuple of integers specifying the degrees of the terms to include may be used instead.
rec (AbstractRecurrenceRelation) – Recurrence relation for the family of orthogonal polynomials.
rcond (float, optional) – Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.
full (bool, optional) – Switch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.
w (array_like, shape (M,), optional) – Weights. If not None, the weight w[i] applies to the unsquared residual y[i] - y_hat[i] at x[i]. Ideally the weights are chosen so that the errors of the products w[i]*y[i] all have the same variance. When using inverse-variance weighting, use w[i] = 1/sigma(y[i]). The default value is None.

Returns:

coef (ndarray, shape (M,) or (M, K)) – Orthogonal coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.
[residuals, rank, singular_values, rcond] (list) – These values are only returned if full == True
- residuals – sum of squared residuals of the least squares fit
- rank – the numerical rank of the scaled Vandermonde matrix
- singular_values – singular values of the scaled Vandermonde matrix
- rcond – value of rcond.
For more details, see jax.numpy.linalg.lstsq.