Source code for padasip.filters.llncosh

"""
.. versionadded:: 1.2.0

The least lncosh (Llncosh) algorithm (proposed in https://doi.org/10.1016/j.sigpro.2019.107348)
is similar to LMS adaptive filter.

The Llncosh filter can be created as follows

    >>> import padasip as pa
    >>> pa.filters.FilterLlncosh(n)

where :code:`n` is the size (number of taps) of the filter.

Content of this page:

.. contents::
   :local:
   :depth: 1

.. seealso:: :ref:`filters`

Algorithm Explanation
==========================

The lncosh cost function is the natural logarithm of hyperbolic cosine function,
which behaves like a hybrid of the mean square error and mean absolute error
criteria according to its positive parameter `lambd`.

Minimal Working Examples
==============================

If you have measured data you may filter it as follows

.. code-block:: python

    import numpy as np
    import matplotlib.pylab as plt
    import padasip as pa

    # creation of data
    N = 500
    x = np.random.normal(0, 1, (N, 4))  # input matrix
    v = np.random.normal(0, 0.1, N)  # noise
    d = 2 * x[:, 0] + 0.1 * x[:, 1] - 4 * x[:, 2] + 0.5 * x[:, 3] + v  # target

    # identification
    f = pa.filters.FilterLlncosh(n=4, mu=0.1, lambd=0.1, w="random")
    y, e, w = f.run(d, x)

    # show results
    plt.figure(figsize=(15, 9))
    plt.subplot(211);
    plt.title("Adaptation");
    plt.xlabel("samples - k")
    plt.plot(d, "b", label="d - target")
    plt.plot(y, "g", label="y - output");
    plt.legend()
    plt.subplot(212);
    plt.title("Filter error");
    plt.xlabel("samples - k")
    plt.plot(10 * np.log10(e ** 2), "r", label="e - error [dB]");
    plt.legend()
    plt.tight_layout()
    plt.show()

Code Explanation
====================
"""
import numpy as np

from padasip.filters.base_filter import AdaptiveFilter


class FilterLlncosh(AdaptiveFilter):
    """
    This class represents an adaptive Llncosh filter.
    """
    kind = "Llncosh"

    def __init__(self, n, mu=0.01, lambd=3, **kwargs):
        """
        **Kwargs:**

        * `lambd` : lambda (float). Cost function shape parameter.

        """
        super().__init__(n, mu, **kwargs)
        self.lambd = lambd

    def learning_rule(self, e, x):
        """
        Override the parent class.
        """
        return self.mu * np.tanh(self.lambd * e) * x