Source code for pygimli.core.math

# -*- coding: utf-8 -*-
"""Collection of mathematical functions."""

import numpy as np
from .core import (angle, besselI0, besselI1, besselK0, besselK1, cos,
                   cot, det, dot, exp, exp10, imag, log, log10, max, median,
                   min, pow, rand, randn, real, rms, round, rrms, sign,
                   sin, sqrt, sum, toComplex, unique)




def symlog(x, tol=1e-12, linearSpread=0):
    """Symmetric bi-logarithmic transformation (as used in matplotlib).

    Transforms a signed values in a logarithmic way preserving the sign.
    All absolute values below a certain threshold are treated zero or linearly
    distributed (if linearSpread>0).

    .. math::

        f(x) = sign(x) * (log10(1 + abs(x)/tol) + s/2)

    Parameters
    ----------
    x : iterable
        array to be transformed
    tol : float [None]
        tolerance for minimum values to be treated zero (or linear)
    linearSpread : float
        define how wide linear transformation is done (0-not, 1-one decade)

    Returns
    -------
    y : np.array
        transformed array of same size

    See Also
    --------
    pygimli.math.symlogInv
    """
    if tol is None:
        tol = np.min(np.abs(x))

    x = np.atleast_1d(x)
    res = np.ones_like(x) * np.nan  # avoid signs of nan
    fi = np.isfinite(x)
    res[fi] = np.sign(x[fi]) * (np.log10(1 + np.abs(x[fi]/tol))+linearSpread/2)

    return res





def symlogInv(y, tol=1e-12, linearSpread=0):
    """Inverse symlog transformation.

    .. math::

        f(y) = sign(y) * (10^(abs(y)-s/2) - 1) * tol

    Parameters
    ----------
    y : iterable
        array to be transformed
    tol : float [None]
        tolerance for minimum values to be treated zero (or linear)
    linearSpread : float
        define how wide linear transformation is done (0-not, 1-one decade)

    Returns
    -------
    x : np.array
        transformed array of same size

    See Also
    --------
    pygimli.math.symlog
    """
    return (10**(np.abs(y)-linearSpread/2) - 1.) * tol * np.sign(y)





def logMean(spec, model, axis=0):
    """Compute log-mean (log-weighted mean) value of distribution.

    spec : array
        abscissa values (spectral axis)
    model : array|array-2d
        matrix of density values
    axis : int [0]
        axis to sum over
    """
    sum_model = np.sum(model, axis=axis)
    sum_spec_model = np.sum(np.log(np.reshape(spec, [-1, 1]))*model, axis=axis)
    return np.exp(sum_spec_model / sum_model)