# ocelot.common.math_op¶

statistical analysis functions, fitting, optimization and the like

## Module Contents¶

### Functions¶

 complete_gamma(a, z) return ‘complete’ gamma function function to make “nearly conjugate symmetric” vector in order to invert_cdf(y, x) Invert cumulative distribution function of the probability distribution rolling_mean(x, window) Fat method for rolling mean rolling_window(x, window) Function return x-array slices with length of the window, which can be used for rolling analysis. convolve(f, g) FFT based convolution deconvolve(f, g) FFT based deconvolution peaks(x, y, n=0) gs_search(f, bracket, tol=1e-06, nmax=50) golden section search fit_gauss_2d(x, y, F) fit_gauss_1d(x, F) fwhm(x, F) fwhm3(valuelist, height=0.5, peakpos=-1, total=1) calculates the full width at half maximum (fwhm) of the array. stats(outputs) return mean, std, median and extreme (farthest from mean) of a time series find_saturation(power, z, n_smooth=5) find_nearest_idx(array, value) find_nearest(array, value) n_moment(x, counts, c, n) std_moment(x, counts) bin_array(array, bin_size) bin_scale(scale, bin_size) index_of(array, value) corr_f_py(corr, val, n_skip=1, norm=1) corr_f_np(corr, val, n_skip=1, norm=1, count=0) correlation2d(val, norm=0, n_skip=1, use_numba=numba_avail) corr_c_py(corr, n_corr, val, norm) corr_c_np(corr, n_corr, val, norm) correlation2d_center(n_corr, val, norm=0, use_numba=1) mut_coh_func_py(J, fld, norm=1) Mutual Coherence function gauss_fit(X, Y)
ocelot.common.math_op.numba_avail = True
ocelot.common.math_op.complete_gamma(a, z)

return ‘complete’ gamma function

ocelot.common.math_op.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))

ocelot.common.math_op.invert_cdf(y, x)

Invert cumulative distribution function of the probability distribution

# 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))

Parameters
• y – array, [y0, y1, y2, … yn] yi = y(xi)

• x – array, [x0, x1, x2, … xn] xi

Returns

function

ocelot.common.math_op.rolling_mean(x, window)

Fat method for rolling mean

X = np.random.rand(10000)

X_mean = rolling_mean(X, 500)

Parameters
• x – np.array, len(a) must be larger than window

• window – int, length of the window

Returns

np.array, len = len(x) + 1 - window

ocelot.common.math_op.rolling_window(x, window)

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

X = np.random.rand(10000)

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

Parameters
• x – np.array, len(a) must be larger than window

• window – int, length of the window

Returns

np.array, shape: (len(a) + 1 - window, window)

ocelot.common.math_op.convolve(f, g)

FFT based convolution

Parameters
• f – array

• g – array

Returns

array, (f * g)[n]

ocelot.common.math_op.deconvolve(f, g)

FFT based deconvolution

Parameters
• f – array

• g – array

Returns

array,

ocelot.common.math_op.peaks(x, y, n=0)

golden section search

ocelot.common.math_op.fit_gauss_2d(x, y, F)
ocelot.common.math_op.fit_gauss_1d(x, F)
ocelot.common.math_op.fwhm(x, F)
ocelot.common.math_op.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]

ocelot.common.math_op.stats(outputs)

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

ocelot.common.math_op.find_saturation(power, z, n_smooth=5)
ocelot.common.math_op.find_nearest_idx(array, value)
ocelot.common.math_op.find_nearest(array, value)
ocelot.common.math_op.n_moment(x, counts, c, n)
ocelot.common.math_op.std_moment(x, counts)
ocelot.common.math_op.bin_array(array, bin_size)
ocelot.common.math_op.bin_scale(scale, bin_size)
ocelot.common.math_op.index_of(array, value)
ocelot.common.math_op.corr_f_py(corr, val, n_skip=1, norm=1)
ocelot.common.math_op.corr_f_np(corr, val, n_skip=1, norm=1, count=0)
ocelot.common.math_op.corr_f_nb
ocelot.common.math_op.correlation2d(val, norm=0, n_skip=1, use_numba=numba_avail)
ocelot.common.math_op.corr_c_py(corr, n_corr, val, norm)
ocelot.common.math_op.corr_c_np(corr, n_corr, val, norm)
ocelot.common.math_op.corr_c_nb
ocelot.common.math_op.correlation2d_center(n_corr, val, norm=0, use_numba=1)
ocelot.common.math_op.mut_coh_func_py(J, fld, norm=1)

Mutual Coherence function

ocelot.common.math_op.mut_coh_func
ocelot.common.math_op.gauss_fit(X, Y)