Function fit_spectrum

pyxrf/core/fitting.py:80–234

r""" Perform fitting of a single or or multiple spectra. A single spectra is represented as a 1D ndarray. Multiple spectra collected from scan of a line, 2D or 3D image may be represented as multidimensional array containing spectral information along axis ``axis``. The returned fitt

(data, ref_spectra, *, method="nnls", axis=0, maxiter=100, rate=0.2, epsilon=1e-30)

def fit_spectrum(data, ref_spectra, *, method="nnls", axis=0, maxiter=100, rate=0.2, epsilon=1e-30):
    r"""
    Perform fitting of a single or or multiple spectra. A single spectra is represented as
    a 1D ndarray. Multiple spectra collected from scan of a line, 2D or 3D image may be represented
    as multidimensional array containing spectral information along axis ``axis``. The returned
    fitting result have the same dimensionality as the input data with fitted coefficients
    located along the same axis as the spectrum data.

    Parameters
    ----------
    data : ndarray
        single or multidimensional spectral data. If fitting done for a single spectrum with K energy points,
        ``data`` is a 1D ndarray with K points. If 'data' contains spectra obtained by scanning NxM map,
        ``data`` is 3D ndarray with dimensions (K,N,M), (N,K,M) or (N,M,K). The axis containing spectra
        is specified by the parameter ``axis``, which should be set to 0 (default), 1 or 2 for the for the
        3D example above. Dimensionality of ``data`` array is not restricted and the function will perform
        properly if ``axis`` points to the correct dimension.

    ref_spectra : ndarray (2D)
        array with columns representing the reference spectra. If fitting is performed for Q reference
        spectra, then ``ref_spectra`` has dimensions (K,Q), where K is the number of energy points.

    method : str
        optimization method used for fitting. Currently supported methods are "nnls" and "admm".

    axis : int
        the number of the axis in the ``data`` array that hold the spectral information. If ``data``
        array has ``n`` dimensions, then ``axis`` may take values in the range ``-n .. n-1``. The
        fitting results will be placed in the output data array along the same axis.

    maxiter : int
        maximum number of iterations. Optimization may stop prematurely if convergence criteria are met.

    rate : float
        descent rate for optimization algorithm. Currently is used only for ADMM fitting (1/lambda).

    epsilon : float
        small value used in stopping criterion of ADMM optimization algorithm.

    Returns
    -------
    weights : ndarray
        array with the same number of dimensions as ``data``. Weights are placed along the axis ``axis``.
        For example, if ``data`` has the shape (N,K,M) and ``axis=1``, then ``weights`` has
        the shape (N,Q,M), where Q is the number of spectrum references.

    rfactor : ndarray
        array that contains R-factor value for each fitted spectrum. For example, if ``data`` has shape
        (N,K,M) and ``axis=1``, then ``rfactor`` has shape (N,M)

    results_dict : dict
        dictionary that contains additional information returned by a fitting routine. The contents of
        the dictionary depends on the optimization routine. Common information: ``method`` - string
        that contains the name of the optimization method (``nnls`` or ``admm``).

        NNLS optimization:

            - ``residual`` - an array that contains values of least-squares difference between the observed