Function polyfit

numpy/polynomial/polynomial.py:1348–1499

Least-squares fit of a polynomial to data. Return the coefficients of a polynomial 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 e

(x, y, deg, rcond=None, full=False, w=None)

def polyfit(x, y, deg, rcond=None, full=False, w=None):
    """
    Least-squares fit of a polynomial to data.

    Return the coefficients of a polynomial 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

    .. math::  p(x) = c_0 + c_1 * x + ... + c_n * x^n,

    where `n` is `deg`.

    Parameters
    ----------
    x : array_like, shape (`M`,)
        x-coordinates of the `M` sample (data) points ``(x[i], y[i])``.
    y : array_like, shape (`M`,) or (`M`, `K`)
        y-coordinates of the sample points.  Several sets of sample points
        sharing the same x-coordinates can be (independently) fit with one
        call to `polyfit` by passing in for `y` a 2-D array that contains
        one data set 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. For NumPy versions >= 1.11.0 a list of integers specifying the
        degrees of the terms to include may be used instead.
    rcond : float, optional
        Relative condition number of the fit.  Singular values smaller
        than `rcond`, relative to the largest singular value, will be
        ignored.  The default value is ``len(x)*eps``, where `eps` is the
        relative precision of the platform's float type, about 2e-16 in
        most cases.
    full : bool, optional
        Switch determining the nature of the return value.  When ``False``
        (the default) just the coefficients are returned; when ``True``,
        diagnostic information from the singular value decomposition (used
        to solve the fit's matrix equation) 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 (`deg` + 1,) or (`deg` + 1, `K`)
        Polynomial coefficients ordered from low to high.  If `y` was 2-D,
        the coefficients in column `k` of `coef` represent the polynomial
        fit to the data in `y`'s `k`-th column.

    [residuals, rank, singular_values, rcond] : list
        These values are only returned if ``full == True``

        - residuals -- sum of squared residuals of the least squares fit