jax.numpy.polyfit#

jax.numpy.polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False)[source]#

Least squares polynomial fit.

LAX-backend implementation of numpy.polyfit().

Unlike NumPy’s implementation of polyfit, jax.numpy.polyfit() will not warn on rank reduction, which indicates an ill conditioned matrix Also, it works best on rcond <= 10e-3 values.

Original docstring below.

Note

This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in numpy.polynomial is preferred. A summary of the differences can be found in the transition guide.

Fit a polynomial p(x) = p[0] * x**deg + ... + p[deg] of degree deg to points (x, y). Returns a vector of coefficients p that minimises the squared error in the order deg, deg-1, … 0.

The Polynomial.fit <numpy.polynomial.polynomial.Polynomial.fit> class method is recommended for new code as it is more stable numerically. See the documentation of the method for more information.

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) – Degree of the fitting polynomial

  • 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.

  • cov (bool or str, optional) – If given and not False, return not just the estimate but also its covariance matrix. By default, the covariance are scaled by chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed to be unreliable except in a relative sense and everything is scaled such that the reduced chi2 is unity. This scaling is omitted if cov='unscaled', as is relevant for the case that the weights are w = 1/sigma, with sigma known to be a reliable estimate of the uncertainty.

Returns

  • p (ndarray, shape (deg + 1,) or (deg + 1, K)) – Polynomial coefficients, highest power first. If y was 2-D, the coefficients for k-th data set are in p[:,k].

  • residuals, rank, singular_values, rcond – These values are only returned if full == True

    • residuals – sum of squared residuals of the least squares fit

    • rank – the effective rank of the scaled Vandermonde

      coefficient matrix

    • singular_values – singular values of the scaled Vandermonde

      coefficient matrix

    • rcond – value of rcond.

    For more details, see numpy.linalg.lstsq.

  • V (ndarray, shape (M,M) or (M,M,K)) – Present only if full == False and cov == True. The covariance matrix of the polynomial coefficient estimates. The diagonal of this matrix are the variance estimates for each coefficient. If y is a 2-D array, then the covariance matrix for the k-th data set are in V[:,:,k]

References

1

Wikipedia, “Curve fitting”, https://en.wikipedia.org/wiki/Curve_fitting

2

Wikipedia, “Polynomial interpolation”, https://en.wikipedia.org/wiki/Polynomial_interpolation