# Source code for pyart.util.sigmath

```"""
Function for mathematical, signal processing and numerical routines.

"""

import numpy as np
from scipy import signal

[docs]def angular_texture_2d(image, N, interval):
"""
Compute the angular texture of an image. Uses convolutions
in order to speed up texture calculation by a factor of ~50
compared to using ndimage.generic_filter.

Parameters
----------
image : 2D array of floats
The array containing the velocities in which to calculate
texture from.
N : int
This is the window size for calculating texture. The texture will be
calculated from an N by N window centered around the gate.
interval : float
The absolute value of the maximum velocity. In conversion to
radial coordinates, pi will be defined to be interval
and -pi will be -interval. It is recommended that interval be
set to the Nyquist velocity.

Returns
-------
std_dev : float array
Texture of the radial velocity field.

"""
# transform distribution from original interval to [-pi, pi]
interval_max = interval
interval_min = -interval
half_width = (interval_max - interval_min) / 2.
center = interval_min + half_width

# Calculate parameters needed for angular std. dev
im = (np.asarray(image) - center) / (half_width) * np.pi
x = np.cos(im)
y = np.sin(im)

# Calculate convolution
kernel = np.ones((N, N))
xs = signal.convolve2d(x, kernel, mode="same", boundary="symm")
ys = signal.convolve2d(y, kernel, mode="same", boundary="symm")
ns = N**2

# Calculate norm over specified window
xmean = xs/ns
ymean = ys/ns
norm = np.sqrt(xmean**2 + ymean**2)
std_dev = np.sqrt(-2 * np.log(norm)) * (half_width) / np.pi
return std_dev

[docs]def rolling_window(a, window):
""" Create a rolling window object for application of functions
eg: result=np.ma.std(array, 11), 1). """
shape = a.shape[:-1] + (a.shape[-1] - window + 1, window)
strides = a.strides + (a.strides[-1], )
return np.lib.stride_tricks.as_strided(a, shape=shape, strides=strides)

""" Determine a texture field using an 11pt stdev
print(fld.shape)
tex = np.ma.zeros(fld.shape)
for timestep in range(tex.shape[0]):
ray = np.ma.std(rolling_window(fld[timestep, :], 11), 1)
tex[timestep, 5:-5] = ray
tex[timestep, 0:4] = np.ones(4) * ray[0]
tex[timestep, -5:] = np.ones(5) * ray[-1]
return tex

"""
Compute field texture along ray using a user specified
window size.

Parameters
----------
The radar object where the field is.
var : str
Name of the field which texture has to be computed.
wind_size : int, optional
Optional. Size of the rolling window used.

Returns
-------