:mod:`ocelot.common.math_op`
============================

.. py:module:: ocelot.common.math_op

.. autoapi-nested-parse::

   statistical analysis functions, fitting, optimization and the like



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   ocelot.common.math_op.complete_gamma
   ocelot.common.math_op.conj_sym
   ocelot.common.math_op.invert_cdf
   ocelot.common.math_op.rolling_mean
   ocelot.common.math_op.rolling_window
   ocelot.common.math_op.convolve
   ocelot.common.math_op.deconvolve
   ocelot.common.math_op.peaks
   ocelot.common.math_op.gs_search
   ocelot.common.math_op.fit_gauss_2d
   ocelot.common.math_op.fit_gauss_1d
   ocelot.common.math_op.fwhm
   ocelot.common.math_op.fwhm3
   ocelot.common.math_op.stats
   ocelot.common.math_op.find_saturation
   ocelot.common.math_op.find_nearest_idx
   ocelot.common.math_op.find_nearest
   ocelot.common.math_op.n_moment
   ocelot.common.math_op.std_moment
   ocelot.common.math_op.bin_array
   ocelot.common.math_op.bin_scale
   ocelot.common.math_op.index_of
   ocelot.common.math_op.corr_f_py
   ocelot.common.math_op.corr_f_np
   ocelot.common.math_op.correlation2d
   ocelot.common.math_op.corr_c_py
   ocelot.common.math_op.corr_c_np
   ocelot.common.math_op.correlation2d_center
   ocelot.common.math_op.mut_coh_func_py
   ocelot.common.math_op.gauss_fit


.. data:: numba_avail
   :annotation: = True

   

.. function:: complete_gamma(a, z)

   return 'complete' gamma function


.. function:: conj_sym(x)

   function to make "nearly conjugate symmetric" vector in order to
   compute matplab IFFT function with 'symmetric' option:
   MATLAB
   >> ifft(x, 'symmetric')
   PYTHON
   >> numpy.fft.ifft(conj_sym(x))


.. function:: invert_cdf(y, x)

   Invert cumulative distribution function of the probability distribution

   Example:
   --------
   # analytical formula for the beam distribution
   f = lambda x: A * np.exp(-(x - mu) ** 2 / (2. * sigma ** 2))

   # we are interesting in range from -30 to 30 e.g. [um]
   x = np.linspace(-30, 30, num=100)

   # Inverted cumulative distribution function
   i_cdf = invert_cdf(y=f(x), x=x)

   # get beam distribution (200 000 coordinates)
   tau = i_cdf(np.random.rand(200000))


   :param y: array, [y0, y1, y2, ... yn] yi = y(xi)
   :param x: array, [x0, x1, x2, ... xn] xi
   :return: function


.. function:: rolling_mean(x, window)

   Fat method for rolling mean

   Example:
   --------
   X = np.random.rand(10000)

   X_mean = rolling_mean(X, 500)

   :param x: np.array, len(a) must be larger than window
   :param window: int, length of the window
   :return: np.array, len = len(x) + 1 - window


.. function:: rolling_window(x, window)

   Function return x-array slices with length of the window, which can be used for rolling analysis.

   Example:
   --------
   X = np.random.rand(10000)

   X_std = np.std(rolling_window(X, 500), 1)
   X_mean = np.mean(rolling_window(X, 500), 1)


   :param x: np.array, len(a) must be larger than window
   :param window: int, length of the window
   :return: np.array, shape: (len(a) + 1 - window, window)


.. function:: convolve(f, g)

   FFT based convolution

   :param f: array
   :param g: array
   :return: array, (f * g)[n]


.. function:: deconvolve(f, g)

   FFT based deconvolution

   :param f: array
   :param g: array
   :return: array,


.. function:: peaks(x, y, n=0)

   

.. function:: gs_search(f, bracket, tol=1e-06, nmax=50)

   golden section search


.. function:: fit_gauss_2d(x, y, F)


.. function:: fit_gauss_1d(x, F)


.. function:: fwhm(x, F)


.. function:: fwhm3(valuelist, height=0.5, peakpos=-1, total=1)

   calculates the full width at half maximum (fwhm) of the array.
   the function will return the fwhm with sub-pixel interpolation. 
   It will start at the maximum position and 'walk' left and right until it approaches the half values.
   if total==1, it will start at the edges and 'walk' towards peak until it approaches the half values.
   INPUT:
   - valuelist: e.g. the list containing the temporal shape of a pulse
   OPTIONAL INPUT:
   -peakpos: position of the peak to examine (list index)
   the global maximum will be used if omitted.
   if total = 1 - 
   OUTPUT:
   - peakpos(index), interpolated_width(npoints), [index_l, index_r]


.. function:: stats(outputs)

   return mean, std, median and extreme (farthest from mean) of a time series 


.. function:: find_saturation(power, z, n_smooth=5)


.. function:: find_nearest_idx(array, value)


.. function:: find_nearest(array, value)


.. function:: n_moment(x, counts, c, n)


.. function:: std_moment(x, counts)


.. function:: bin_array(array, bin_size)


.. function:: bin_scale(scale, bin_size)


.. function:: index_of(array, value)


.. function:: corr_f_py(corr, val, n_skip=1, norm=1)


.. function:: corr_f_np(corr, val, n_skip=1, norm=1, count=0)


.. data:: corr_f_nb
   

   

.. function:: correlation2d(val, norm=0, n_skip=1, use_numba=numba_avail)


.. function:: corr_c_py(corr, n_corr, val, norm)


.. function:: corr_c_np(corr, n_corr, val, norm)


.. data:: corr_c_nb
   

   

.. function:: correlation2d_center(n_corr, val, norm=0, use_numba=1)


.. function:: mut_coh_func_py(J, fld, norm=1)

   Mutual Coherence function


.. data:: mut_coh_func
   

   

.. function:: gauss_fit(X, Y)