#!/usr/bin/env python
# -*- coding: UTF-8 -*-
# Copyright (c) 2011-2023, wradlib developers.
# Distributed under the MIT License. See LICENSE.txt for more info.
"""
Utility functions
^^^^^^^^^^^^^^^^^
Module util provides a set of useful helpers which are currently not
attributable to the other modules
.. autosummary::
:nosignatures:
:toctree: generated/
{}
"""
__all__ = [
"from_to",
"filter_window_polar",
"filter_window_cartesian",
"find_bbox_indices",
"get_raster_origin",
"calculate_polynomial",
"derivate",
"despeckle",
"import_optional",
"cross_section_ppi",
"UtilMethods",
]
__doc__ = __doc__.format("\n ".join(__all__))
import contextlib
import datetime as dt
import importlib
import inspect
import os
import warnings
from functools import singledispatch
import numpy as np
import xarray as xr
from scipy import ndimage, signal
from scipy.spatial import KDTree
from wradlib import georef, version
class OptionalModuleStub:
"""Stub class for optional imports.
Objects of this class are instantiated when optional modules are not
present on the user's machine.
This allows global imports of optional modules with the code only breaking
when actual attributes from this module are called.
"""
def __init__(self, name):
self.name = name
def __getattr__(self, name):
link = (
"https://docs.wradlib.org/en/stable/"
"installation.html#optional-dependencies"
)
raise AttributeError(
f"Module '{self.name}' is not installed.\n\n"
"You tried to access function/module/attribute "
f"'{name}'\nfrom module '{self.name}'.\nThis module is "
"optional right now in wradlib.\nYou need to "
"separately install this dependency.\n"
f"Please refer to {link}\nfor further instructions."
)
[docs]def import_optional(module):
"""Allowing for lazy loading of optional wradlib modules or dependencies.
This function removes the need to satisfy all dependencies of wradlib
before being able to work with it.
Parameters
----------
module : str
name of the module
Returns
-------
mod : object
if module is present, returns the module object, on ImportError
returns an instance of `OptionalModuleStub` which will raise an
AttributeError as soon as any attribute is accessed.
Examples
--------
Trying to import a module that exists makes the module available as normal.
You can even use an alias. You cannot use the '*' notation, or import only
select functions, but you can simulate most of the standard import syntax
behavior.
>>> m = import_optional('math')
>>> m.log10(100)
2.0
Trying to import a module that does not exist, does not produce
any errors. Only when some function is used, the code triggers an error
>>> m = import_optional('nonexistentmodule') # noqa
>>> m.log10(100) #doctest: +ELLIPSIS
Traceback (most recent call last):
...
AttributeError: Module 'nonexistentmodule' is not installed.
<BLANKLINE>
You tried to access function/module/attribute 'log10'
from module 'nonexistentmodule'.
This module is optional right now in wradlib.
You need to separately install this dependency.
Please refer to https://docs.wradlib.org/en/stable/installation.html#optional-dependencies
for further instructions.
"""
try:
mod = importlib.import_module(module)
except ImportError:
mod = OptionalModuleStub(module)
return mod
def warn(message, category=None, stacklevel=3):
"""Emit user level warning"""
warnings.warn(message, category, stacklevel=stacklevel)
def _shape_to_size(shape):
"""
Compute the size which corresponds to a shape
"""
out = 1
for item in shape:
out *= item
return out
[docs]def from_to(tstart, tend, tdelta):
"""Return a list of timesteps from <tstart> to <tend> of length <tdelta>
Parameters
----------
tstart : str or :py:class:`datetime.datetime`
datetime isostring (%Y%m%d %H:%M:%S), e.g. 2000-01-01 15:34:12 or datetime object
tend : str or :py:class:`datetime.datetime`
datetime isostring (%Y%m%d %H:%M:%S), e.g. 2000-01-01 15:34:12 or datetime object
tdelta : int
representing time interval in SECONDS
Returns
-------
output : list
list of datetime.datetime objects
"""
if not type(tstart) == dt.datetime:
tstart = dt.datetime.strptime(tstart, "%Y-%m-%d %H:%M:%S")
if not type(tend) == dt.datetime:
tend = dt.datetime.strptime(tend, "%Y-%m-%d %H:%M:%S")
tdelta = dt.timedelta(seconds=tdelta)
tsteps = [
tstart,
]
tmptime = tstart
while True:
tmptime = tmptime + tdelta
if tmptime > tend:
break
else:
tsteps.append(tmptime)
return tsteps
def _idvalid(data, *, isinvalid=None, minval=None, maxval=None):
"""Identifies valid entries in an array and returns the corresponding
indices
Invalid values are NaN and Inf. Other invalid values can be passed using
the isinvalid keyword argument.
Parameters
----------
data : :class:`numpy:numpy.ndarray`
isinvalid : list
list of what is considered an invalid value
"""
if isinvalid is None:
isinvalid = [-99.0, 99, -9999.0, -9999]
ix = np.ma.masked_invalid(data).mask
for el in isinvalid:
ix = np.logical_or(ix, np.ma.masked_where(data == el, data).mask)
if minval is not None:
ix = np.logical_or(ix, np.ma.masked_less(data, minval).mask)
if maxval is not None:
ix = np.logical_or(ix, np.ma.masked_greater(data, maxval).mask)
return np.where(np.logical_not(ix))[0]
def meshgrid_n(*arrs):
"""N-dimensional meshgrid
Just pass sequences of coordinates arrays
"""
arrs = tuple(arrs)
lens = list(map(len, arrs))
dim = len(arrs)
sz = 1
for s in lens:
sz *= s
ans = []
for i, arr in enumerate(arrs):
slc = [1] * dim
slc[i] = lens[i]
arr2 = np.asarray(arr).reshape(slc)
for j, sz in enumerate(lens):
if j != i:
arr2 = arr2.repeat(sz, axis=j)
ans.append(arr2)
return tuple(ans)
def gridaspoints(*arrs):
"""Creates an N-dimensional grid form arrs and returns grid points sequence
of point coordinate pairs
"""
# there is a small gotcha here.
# with the convention following the 2013-08-30 sprint in Potsdam it was
# agreed upon that arrays should have shapes (...,z,y,x) similar to the
# convention that polar data should be (...,time,scan,azimuth,range)
#
# Still coordinate tuples are given in the order (x,y,z) [and hopefully not
# more dimensions]. Therefore, np.meshgrid must be fed the axis coordinates
# in shape order (z,y,x) and the result needs to be reversed in order
# for everything to work out.
grid = tuple([dim.ravel() for dim in reversed(np.meshgrid(*arrs, indexing="ij"))])
return np.vstack(grid).transpose()
def issequence(x):
"""Test whether x is a sequence of numbers
Parameters
----------
x : sequence
sequence to test
"""
out = True
try:
# can we get a length on the object
len(x)
except TypeError:
return False
# is the object not a string?
out = np.all(np.isreal(x))
return out
def trapezoid(data, x1, x2, x3, x4):
"""
Applied the trapezoidal function described in :cite:`Vulpiani`
to determine the degree of membership in the non-meteorological
target class.
Parameters
----------
data : :class:`numpy:numpy.ndarray`
Array containing the data
x1 : float
x-value of the first vertex of the trapezoid
x2 : float
x-value of the second vertex of the trapezoid
x3 : float
x-value of the third vertex of the trapezoid
x4 : float
x-value of the fourth vertex of the trapezoid
Returns
-------
d : :class:`numpy:numpy.ndarray`
Array of values describing degree of membership in
nonmeteorological target class.
"""
d = np.ones(np.shape(data))
d[np.logical_or(data <= x1, data >= x4)] = 0
d[np.logical_and(data >= x2, data <= x3)] = 1
d[np.logical_and(data > x1, data < x2)] = (
data[np.logical_and(data > x1, data < x2)] - x1
) / float(x2 - x1)
d[np.logical_and(data > x3, data < x4)] = (
x4 - data[np.logical_and(data > x3, data < x4)]
) / float(x4 - x3)
d[np.isnan(data)] = np.nan
return d
[docs]def filter_window_polar(img, wsize, fun, rscale, *, random=False):
"""Apply a filter of an approximated square window of half size `fsize` \
on a given polar image `img`.
Parameters
----------
img : :class:`numpy:numpy.ndarray`
2d array of values to which the filter is to be applied
wsize : float
Half size of the window centred on the pixel [m]
fun : str
name of the 1d filter from :mod:`scipy:scipy.ndimage`
rscale : float
range [m] scale of the polar grid
random: bool
True to use random azimuthal size to avoid long-term biases.
Returns
-------
output : :class:`numpy:numpy.ndarray`
Array with the same shape as `img`, containing the filter's results.
"""
ascale = 2 * np.pi / img.shape[0]
data_filtered = np.empty(img.shape, dtype=img.dtype)
fun = getattr(ndimage, f"{fun}_filter1d")
nbins = img.shape[-1]
ranges = np.arange(nbins) * rscale + rscale / 2
asize = ranges * ascale
if random:
na = prob_round(wsize / asize).astype(int)
else:
na = np.fix(wsize / asize + 0.5).astype(int)
# Maximum of adjacent azimuths (higher close to the origin) to
# increase performance
na[na > 20] = 20
sr = np.fix(wsize / rscale + 0.5).astype(int)
for sa in np.unique(na):
imax = np.where(na >= sa)[0][-1] + 1
imin = np.where(na <= sa)[0][0]
if sa == 0:
data_filtered[:, imin:imax] = img[:, imin:imax]
imin2 = max(imin - sr, 0)
imax2 = min(imax + sr, nbins)
temp = img[:, imin2:imax2]
temp = fun(temp, size=2 * sa + 1, mode="wrap", axis=0)
temp = fun(temp, size=2 * sr + 1, axis=1)
imin3 = imin - imin2
imax3 = imin3 + imax - imin
data_filtered[:, imin:imax] = temp[:, imin3:imax3]
return data_filtered
def prob_round(x, *, prec=0):
"""Round the float number `x` to the lower or higher integer randomly
following a binomial distribution
Parameters
----------
x : float
prec : int
precision
"""
fixup = np.sign(x) * 10**prec
x *= fixup
intx = x.astype(int)
round_func = intx + np.random.binomial(1, x - intx)
return round_func / fixup
[docs]def filter_window_cartesian(img, wsize, fun, scale, **kwargs):
"""Apply a filter of square window size `fsize` on a given \
cartesian image `img`.
Parameters
----------
img : :class:`numpy:numpy.ndarray`
2d array of values to which the filter is to be applied
wsize : float
Half size of the window centred on the pixel [m]
fun : str
name of the 2d filter from :mod:`scipy:scipy.ndimage`
scale : tuple
tuple of 2 floats
x and y scale of the cartesian grid [m]
Returns
-------
output : :class:`numpy:numpy.ndarray`
Array with the same shape as `img`, containing the filter's results.
"""
fun = getattr(ndimage, f"{fun}_filter")
size = np.fix(wsize / scale + 0.5).astype(int)
data_filtered = fun(img, size, **kwargs)
return data_filtered
def roll2d_polar(img, shift=1, axis=0):
"""Roll a 2D polar array [azimuth,range] by a given `shift` for \
the given `axis`
Parameters
----------
img : :class:`numpy:numpy.ndarray`
2d data array
shift : int
shift to apply to the array
axis : int
axis which will be shifted
Returns
-------
out: :class:`numpy:numpy.ndarray`
new array with shifted values
"""
if shift == 0:
return img
else:
out = np.empty(img.shape)
n = img.shape[axis]
if axis == 0:
if shift > 0:
out[shift:, :] = img[:-shift, :]
out[:shift, :] = img[n - shift :, :]
else:
out[:shift, :] = img[-shift:, :]
out[n + shift :, :] = img[:-shift:, :]
else:
if shift > 0:
out[:, shift:] = img[:, :-shift]
out[:, :shift] = np.nan
else:
out[:, :shift] = img[:, -shift:]
out[:, n + shift :] = np.nan
return out
class UTC(dt.tzinfo):
"""UTC implementation for tzinfo.
Replaces pytz.utc
"""
def __repr__(self):
return "<UTC>"
def utcoffset(self, dtime):
return dt.timedelta(0)
def tzname(self, dtime):
return "UTC"
def dst(self, dtime):
return dt.timedelta(0)
def half_power_radius(r, bwhalf):
"""
Half-power radius.
ported from PyRadarMet
Battan (1973),
Parameters
----------
r : float | :class:`numpy:numpy.ndarray`
Range from radar [m]
bwhalf : float
Half-power beam width [degrees]
Returns
-------
Rhalf : float | :class:`numpy:numpy.ndarray`
Half-power radius [m]
Examples
--------
rhalf = half_power_radius(r,bwhalf)
"""
rhalf = (r * np.deg2rad(bwhalf)) / 2.0
return rhalf
[docs]def get_raster_origin(coords):
"""Return raster origin
Parameters
----------
coords : :class:`numpy:numpy.ndarray`
3-dimensional array (rows, cols, 2) of xy-coordinates
Returns
-------
out : str
'lower' or 'upper'
"""
return "lower" if (coords[1, 1] - coords[0, 0])[1] > 0 else "upper"
[docs]def find_bbox_indices(coords, bbox):
"""Find min/max-indices for NxMx2 array coords using bbox-values.
The bounding box is defined by two points (llx,lly and urx,ury)
It finds the first indices before llx,lly and the first indices
after urx,ury. If no index is found 0 and N/M is returned.
Parameters
----------
coords : :class:`numpy:numpy.ndarray`
3-dimensional array (ny, nx, lon/lat) of floats
bbox : :class:`numpy:numpy.ndarray` | list | tuple
4-element (llx,lly,urx,ury)
Returns
-------
bbind : tuple
4-element tuple of int (llx,lly,urx,ury)
"""
# sort arrays
x_sort = np.argsort(coords[0, :, 0])
y_sort = np.argsort(coords[:, 0, 1])
# find indices in sorted arrays
llx = np.searchsorted(coords[0, :, 0], bbox[0], side="left", sorter=x_sort)
urx = np.searchsorted(coords[0, :, 0], bbox[2], side="right", sorter=x_sort)
lly = np.searchsorted(coords[:, 0, 1], bbox[1], side="left", sorter=y_sort)
ury = np.searchsorted(coords[:, 0, 1], bbox[3], side="right", sorter=y_sort)
# get indices in original array
if llx < len(x_sort):
llx = x_sort[llx]
if urx < len(x_sort):
urx = x_sort[urx]
if lly < len(y_sort):
lly = y_sort[lly]
if ury < len(y_sort):
ury = y_sort[ury]
# check at boundaries
if llx:
llx -= 1
if get_raster_origin(coords) == "lower":
if lly:
lly -= 1
else:
if lly < coords.shape[0]:
lly += 1
bbind = (llx, min(lly, ury), urx, max(lly, ury))
return bbind
def has_geos():
gdal = import_optional("osgeo.gdal")
ogr = import_optional("osgeo.ogr")
pnt1 = ogr.CreateGeometryFromWkt("POINT(10 20)")
pnt2 = ogr.CreateGeometryFromWkt("POINT(30 20)")
ogrex = ogr.GetUseExceptions()
gdalex = gdal.GetUseExceptions()
gdal.DontUseExceptions()
ogr.DontUseExceptions()
hasgeos = pnt1.Union(pnt2) is not None
if ogrex:
ogr.UseExceptions()
if gdalex:
gdal.UseExceptions()
return hasgeos
def get_wradlib_data_path():
wrl_data_path = os.environ.get("WRADLIB_DATA", None)
if wrl_data_path is None:
raise OSError(
"`WRADLIB_DATA` environment variable not set. Please set `WRADLIB_DATA` "
"pointing to the location of `wradlib_data` repository on the filesystem."
)
if not os.path.isdir(wrl_data_path):
raise OSError(f"`WRADLIB_DATA` path {wrl_data_path!r} does not exist.")
return wrl_data_path
def get_wradlib_data_file(relfile):
data_file = os.path.abspath(os.path.join(get_wradlib_data_path(), relfile))
if not os.path.exists(data_file):
try:
from wradlib_data import DATASETS
data_file = DATASETS.fetch(relfile)
except ImportError as err:
raise OSError(f"WRADLIB_DATA file {data_file!r} does not exist.") from err
return data_file
[docs]def calculate_polynomial(data, w):
"""Calculate Polynomial
The function calculate the following polynomial:
.. math::
P = \\sum_{n=0}^{N} w(n) \\cdot data^{n}
Parameters
----------
data : :class:`numpy:numpy.ndarray`
Flat array of data values.
w : :class:`numpy:numpy.ndarray`
Array of shape (N) containing weights.
Returns
-------
poly : :class:`numpy:numpy.ndarray`
Flat array of processed data.
"""
poly = np.zeros_like(data)
for i, c in enumerate(w):
poly += c * data**i
return poly
def medfilt_along_axis(x, n, *, axis=-1):
"""Applies median filter smoothing on one axis of an N-dimensional array."""
kernel_size = np.array(x.shape)
kernel_size[:] = 1
kernel_size[axis] = n
return signal.medfilt(x, kernel_size)
def gradient_along_axis(x, *, axis=-1):
"""Computes gradient along last axis of an N-dimensional array"""
newshape = np.array(x.shape)
newshape[axis] = 1
diff_begin = (x[..., 1] - x[..., 0]).reshape(newshape)
diff_end = (x[..., -1] - x[..., -2]).reshape(newshape)
diffs = (x - np.roll(x, 2, axis)) / 2.0
diffs = np.append(diffs[..., 2:], diff_end, axis=axis)
return np.insert(diffs, [0], diff_begin, axis=axis)
def gradient_from_smoothed(x, *, n=5, axis=-1):
"""Computes gradient of smoothed data along final axis of an array"""
return gradient_along_axis(medfilt_along_axis(x, n=5, axis=axis)).astype("f4")
def center_to_edge(centers):
delta = centers[1] - centers[0]
edges = np.insert(centers + delta / 2, 0, centers[0] - delta / 2)
return edges
def _pad_array(data, pad, *, mode="reflect", **kwargs):
"""Returns array with padding added along last dimension."""
pad_width = [(0,)] * (data.ndim - 1) + [(pad,)]
if mode in ["maximum", "mean", "median", "minimum"]:
kwargs["stat_length"] = kwargs.pop("stat_length", pad)
data = np.pad(data, pad_width, mode=mode, **kwargs)
return data
def _rolling_dim(data, window):
"""Return array with rolling dimension of window-length added at the end."""
shape = data.shape[:-1] + (data.shape[-1] - window + 1, window)
strides = data.strides + (data.strides[-1],)
return np.lib.stride_tricks.as_strided(data, shape=shape, strides=strides)
def _linregress_1d(rhs, *, method="lstsq"):
"""Calculates slope by means of linear regression on last dimension of rhs.
Calculates lhs from size of last dimension of rhs.
Methods 'lstsq', 'cov', 'matrix_inv' and 'cov_nan' are multidimensional.
The other two nan-methods only work on a single system. Hence, the
apply_along_axis.
"""
shape = rhs.shape
rhs = rhs.reshape((-1, rhs.shape[-1]))
if "cov" in method:
lhs = np.arange(rhs.shape[-1])
if "nan" in method:
idx = np.argsort(rhs, axis=-1)
rhs = np.sort(rhs, axis=-1)
lhs = lhs[idx]
# special treatment for wradlib, use fast method by slicing NaN's
if "iter" in method:
nan = np.argmax(np.isnan(rhs), axis=-1)
unique = np.unique(nan)
if len(unique) == 1:
rhs = rhs[..., : unique[0]]
lhs = lhs[..., : unique[0]]
method = "cov"
else:
lhs = np.broadcast_to(lhs, (rhs.shape))
lhs = lhs.T
else:
lhs = np.vander(np.arange(shape[-1], dtype=rhs.dtype), 2)
rhs = rhs.T
if method == "lstsq":
out = np.linalg.lstsq(lhs, rhs, rcond=None)[0][0]
elif method == "lstsq_nan":
out = np.apply_along_axis(_nan_lstsq, 0, rhs, lhs)
elif method == "cov":
out = _cov(lhs, rhs)
elif "cov_nan" in method:
out = _nan_cov(lhs, rhs)
elif method == "matrix_inv":
out = _matrix_inv(lhs, rhs)
elif method == "matrix_inv_nan":
out = np.apply_along_axis(_nan_matrix_inv, 0, rhs, lhs)
else:
raise ValueError(f"Unknown method {method!r}.")
return out.reshape(shape[:-1])
def _nan_lstsq(y, x):
"""Calculate slope by lstsq considering NaN."""
mask = np.isnan(y)
out, _, _, _ = np.linalg.lstsq(x[~mask, :], y[~mask], rcond=None)
return out[0]
def _nan_matrix_inv(y, x):
"""Calculate slope by matrix inversion considering NaN."""
mask = np.isnan(y)
x = x[~mask]
out = np.dot(np.linalg.inv(np.dot(x.T, x)), np.dot(x.T, y[~mask]))
return out[0]
def _matrix_inv(x, y):
"""Calculate slope by matrix inversion considering NaN."""
out = np.dot(np.linalg.inv(np.dot(x.T, x)), np.dot(x.T, y))
return out[0]
def _nan_cov(x, y):
"""Calculate slope using covariances considering NaN."""
y = np.ma.masked_invalid(y)
x = np.ma.masked_array(x, mask=np.ma.getmask(y))
# calculate covariances
cov = np.ma.sum((x - x.mean(axis=0)) * (y - y.mean(axis=0)), axis=0) / y.count(
axis=0
)
# calculate slope
out = cov / (x.std(axis=0) ** 2)
return out
def _cov(x, y):
"""Calculate slope using covariances."""
# calculate covariances
cov = np.sum((x - x.mean(axis=0)) * (y - y.mean(axis=0)), axis=0) / y.shape[0]
# calculate slope
out = cov / (x.std(axis=0) ** 2)
return out
def _lanczos_differentiator(winlen):
"""Returns Lanczos Differentiator."""
m = (winlen - 1) / 2
denom = m * (m + 1.0) * (2 * m + 1.0)
k = np.arange(1, m + 1)
f = 3 * k / denom
return np.r_[f[::-1], [0], -f]
[docs]@singledispatch
def derivate(data, *, winlen=7, method="lanczos_conv", skipna=False, **kwargs):
"""Calculates derivative of data using window of length winlen.
In normal operation the method ('lanczos_conv') uses convolution
to estimate the derivative using Low-noise Lanczos differentiators.
The equivalent method ('lanczos_dot') uses dot-vector sum product.
For further reading please see `Differentiation by integration using \
orthogonal polynomials, a survey <https://arxiv.org/pdf/1102.5219>`_ \
and `Low-noise Lanczos differentiators \
<http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/\
lanczos-low-noise-differentiators/>`_.
The results are very similar to the moving window linear
regression methods (`cov`, `matrix_inv` and `lstsq`), which are slower than
the former (in order of appearance).
All methods will return NaNs in case at least one value in the moving
window is NaN.
If `skipna=True` the locations of NaN results are treated by using local
linear regression by method2 (default to `cov_nan`) where enough valid
neighbouring data is available.
Before applying the actual derivation calculation the data is padded with
`mode='reflect'` by default along the derivation dimension. Padding can be
parametrized using kwargs.
Parameters
----------
data : :class:`numpy:numpy.ndarray`
multidimensional array, note that the derivation dimension must be the
last dimension of the input array.
winlen : int
Width of the derivation window .
method : str
Defaults to 'lanczos_conv'. Can take one of 'lanczos_dot', 'lstsq',
'cov', 'cov_nan', 'matrix_inv'.
skipna : bool
Defaults to False. If True, treat NaN results by applying method2.
Keyword Arguments
-----------------
method2 : str
Defaults to '_nan' methods.
min_periods : int
Minimum number of valid values in moving window for linear regression.
Defaults to winlen // 2 + 1.
pad_mode : str
Defaults to `reflect`. See :func:`numpy:numpy.pad`.
pad_kwargs : dict
Keyword arguments for padding, see :func:`numpy:numpy.pad`
Returns
-------
out : :class:`numpy:numpy.ndarray`
array of derivates with the same shape as data
"""
if (winlen % 2) != 1:
raise ValueError(f"`winlen` must be an odd number, but {winlen} given.")
# Make really sure winlen is an integer
winlen = int(winlen)
shape = data.shape
data = data.reshape((-1, shape[-1]))
# pad data using pad_mode on derivation dimension
pad = winlen // 2
pad_kwargs = kwargs.pop("pad_kwargs", {})
pad_kwargs["mode"] = kwargs.pop("pad_mode", "reflect")
data_pad = _pad_array(data, pad, **pad_kwargs)
data_roll = None
# calculate derivative
if method == "lanczos_conv":
# we use constant nan padding here,
# more sophisticated padding was already done
out = ndimage.convolve1d(
data_pad, _lanczos_differentiator(winlen), axis=-1, mode="constant"
)
# strip padding for convolution method
out = out[..., pad:-pad]
elif method == "finite_difference_vulpiani":
out = (data_pad[..., winlen - 1 :] - data_pad[..., : shape[-1]]) / winlen
else:
data_roll = _rolling_dim(data_pad, winlen)
if method == "lanczos_dot":
out = np.dot(data_roll, _lanczos_differentiator(winlen) * -1)
elif method in ["lstsq", "cov", "cov_nan", "matrix_inv"]:
out = _linregress_1d(data_roll, method=method)
else:
raise ValueError(f"Unknown method {method!r}")
# NaN treatment
if skipna:
# find remaining NaN values with valid neighbours
invalid = np.isnan(out)
if np.any(invalid):
min_periods = kwargs.pop("min_periods", winlen // 2 + 1)
if min_periods < 2:
raise ValueError("`min_periods` need to be >= 2.")
# automatically select method2 if not given
if method in ["lstsq", "matrix_inv"]:
m2 = method + "_nan"
else:
m2 = "cov_nan"
method2 = kwargs.pop("method2", m2)
# bring data into needed shape
data_roll = (
_rolling_dim(data_pad, winlen) if data_roll is None else data_roll
)
data_roll = data_roll.reshape((-1, data_roll.shape[-1]))
# internal speed up by iterating over same NaN counts and using
# faster calculation method
# ToDo: this doesn't seem to speed up anything, rechecking needed
if method2 == "cov_nan_iter":
for n in range(min_periods, winlen):
valid = np.count_nonzero(~np.isnan(data_roll), axis=-1) == n
recalc = valid & invalid.reshape(-1)
if np.any(recalc):
out.flat[recalc] = _linregress_1d(
data_roll[recalc], method=method2
)
else:
valid = np.count_nonzero(~np.isnan(data_roll), axis=-1) >= min_periods
recalc = valid & invalid.reshape(-1)
# and interpolate using _linregress_1d -> method2
if np.any(recalc):
out.flat[recalc] = _linregress_1d(data_roll[recalc], method=method2)
return out.reshape(shape)
@derivate.register(xr.DataArray)
def _derivate_xarray(obj, **kwargs):
"""Calculates derivative of data using window of length winlen.
In normal operation the method ('lanczos_conv') uses convolution
to estimate the derivative using Low-noise Lanczos differentiators.
The equivalent method ('lanczos_dot') uses dot-vector sum product.
For further reading please see `Differentiation by integration using \
orthogonal polynomials, a survey <https://arxiv.org/pdf/1102.5219>`_ \
and `Low-noise Lanczos differentiators \
<http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/\
lanczos-low-noise-differentiators/>`_.
The results are very similar to the moving window linear
regression methods (`cov`, `matrix_inv` and `lstsq`), which are slower than
the former (in order of appearance).
All methods will return NaNs in case at least one value in the moving
window is NaN.
If `skipna=True` the locations of NaN results are treated by using local
linear regression by method2 (default to `cov_nan`) where enough valid
neighbouring data is available.
Before applying the actual derivation calculation the data is padded with
`mode='reflect'` by default along the derivation dimension. Padding can be
parametrized using kwargs.
Parameters
----------
obj : :py:class:`xarray:xarray.DataArray`
input array
Keyword Arguments
-----------------
winlen : int
Width of the derivation window .
method : str
Defaults to 'lanczos_conv'. Can take one of 'lanczos_dot', 'lstsq',
'cov', 'cov_nan', 'matrix_inv'.
skipna : bool
Defaults to False. If True, treat NaN results by applying method2.
method2 : str
Defaults to '_nan' methods.
min_periods : int
Minimum number of valid values in moving window for linear regression.
Defaults to winlen // 2 + 1.
pad_mode : str
Defaults to `reflect`. See :func:`numpy:numpy.pad`.
pad_kwargs : dict
Keyword arguments for padding, see :func:`numpy:numpy.pad`
Returns
-------
out : :py:class:`xarray:xarray.DataArray`
array of derivates
"""
dim0 = obj.wrl.util.dim0()
out = xr.apply_ufunc(
derivate,
obj,
input_core_dims=[[dim0, "range"]],
output_core_dims=[[dim0, "range"]],
dask="parallelized",
dask_gufunc_kwargs=dict(allow_rechunk=True),
)
out.attrs = obj.attrs
return out
[docs]@singledispatch
def despeckle(data, *, n=3, copy=False):
"""Remove floating pixels in between NaNs in a multidimensional array.
Warning
-------
This function changes the original input array if argument copy is set to
False (default).
Parameters
----------
data : :class:`numpy:numpy.ndarray`
Note that the range dimension must be the last dimension of the
input array.
n : int
(must be either 3 or 5, 3 by default),
Width of the window in which we check for speckle
copy : bool
If True, the input array will remain unchanged.
"""
if n not in (3, 5):
raise ValueError("Window size n for function despeckle must be 3 or 5.")
if copy:
data = data.copy()
pad = n // 2
# pad with NaN
data0 = _pad_array(data, pad, mode="constant")
# append n count last dimension
data0 = _rolling_dim(data0, data.shape[-1])
# count NaN's and find speckle
nans = np.count_nonzero(np.isnan(data0), axis=-2) == (n - 1)
# set speckle to NaN
data[nans] = np.nan
return data
@despeckle.register(xr.DataArray)
def _despeckle_xarray(obj, **kwargs):
"""Remove floating pixels in between NaNs in a multidimensional array.
Parameters
----------
obj : :py:class:`xarray:xarray.DataArray`
input array
Keyword Arguments
-----------------
n : int
(must be either 3 or 5, 3 by default),
Width of the window in which we check for speckle
Returns
-------
out : :py:class:`xarray:xarray.DataArray`
output array
"""
dim0 = obj.wrl.util.dim0()
out = xr.apply_ufunc(
despeckle,
obj,
input_core_dims=[[dim0, "range"]],
output_core_dims=[[dim0, "range"]],
kwargs=kwargs,
dask="parallelized",
dask_gufunc_kwargs=dict(allow_rechunk=True),
)
out.attrs = obj.attrs
return out
def show_versions(file=None):
import sys
import xarray as xr
if file is None:
file = sys.stdout
xr.show_versions(file)
print("", file=file)
print(f"wradlib: {version.version}")
@contextlib.contextmanager
def _open_file(name):
# Check if string has been passed
if isinstance(name, str):
with open(name, "rb") as fid:
yield fid
else:
# otherwise assume file-like object and pass
yield name
def has_import(module):
return not isinstance(module, OptionalModuleStub)
[docs]def cross_section_ppi(
obj,
azimuth,
**kwargs,
):
"""Cut a cross-section from PPI volume scans
.. versionadded:: 1.18
This function extracts cross-sections from a PPI volume scan along one or more azimuth angles,
or along a line connecting two given points.
Similar to PyArt's cross_section_ppi function.
Parameters
----------
obj : :py:class:`xarray:xarray.Dataset` - Dataset containing PPI sweeps
from which azimuthal cross-sections will be extracted.
azimuth : int, float, slice, tuple or list
Value of azimuth to extract the cross-section. It can be multiple values
in the form of a slice, or a tuple or list of values.
Alternatively, it can be given a tuple or list containing coordinates of two
arbitrary points in the x,y space of the georeferenced object: [ (x1, y1), (x2,y2) ].
In case two points are given, a cross-section along the line connecting
the points will be generated by selecting the nearest-neighbor values of data.
No interpolation of data is performed. If more than two points are given, only
the first two are used. The resulting dataset has dimensions xyi (which is just
an index along the line connecting the points) and elevation, and
coordinates xy (distance along the line from p1) and z. The xy and z coordinates
should be used for plotting.
Keyword Arguments
-----------------
method : {None, "nearest", "pad", "ffill", "backfill", "bfill"}, optional
Method for inexact matches for selecting azimuth values, from :py:class:`xarray:xarray.Dataset.sel`.
Defaults to None (only exact matches).
tolerance : float, optional
Maximum distance between original and new labels for inexact matches
from :py:class:`xarray:xarray.Dataset.sel`.
bw : float, optional
Beam width in degrees (defaults to None).
Option meant for plotting beams with their true beamwidth instead of filling the
empty space by stretching the beams (because of how matplotlib pcolormesh works).
Defaults to None, which returns a Dataset of cross-sections in the specified azimuth(s).
If set to a certain beamwidth, it will return the same Dataset with additional
"fake" empty beams (extra elevations) so that when plotting with matplotlib pcolormesh
the beamwidths are correctly represented according to their width.
crs : :py:class:`gdal:osgeo.osr.SpatialReference`, :py:class:`cartopy.crs.CRS`, optional
Projection to use with :py:class:`wradlib.georef.xarray.georeference`.
If GDAL OSR SRS, output is in this projection, defaults to AEQD.
npl : int, optional
Number of points to make up the line between p1 and p2, in case the user gives two arbitrary points
instead of an azimuth value. npl should be high enough to accomodate more points along the line that
points of data available (i.e., higher that the resolution of the data). The default value 1000
should be enough for most cases, but in case the result looks low resolution try increasing npl.
Returns
----------
obj : :py:class:`xarray:xarray.Dataset` or :py:class:`xarray:xarray.DataArray`
Dataset of cross-section(s) in the specified azimuth(s) or along the line
connecting the given points.
"""
bw = kwargs.get("bw", None)
npl = kwargs.get("npl", 1000)
crs = kwargs.get("crs")
method = kwargs.get("method", None)
tolerance = kwargs.get("tolerance", None)
if bw is not None:
# Matplotlib's pcolormesh fills the grid by coloring around each of the gridpoints
# up until halfway to the nearest gridpoints.
# Then, we need to create fake rays of nan and/or duplicated data so the filling
# only extends the shading to cover the beamwidth and no more.
# Sort array of elevation angles
sorted_elevs = np.sort(obj.sweep_fixed_angle.data)
# Calculate midpoints between elevation angles
sorted_elevs_midpoints = (sorted_elevs[1:] + sorted_elevs[:-1]) / 2
# Identify spaces in between beams > bw
spaces = sorted_elevs[1:] - sorted_elevs[:-1]
separation_needed = spaces > bw
# Beams separated by exactly 2*bw need only a nan ray at the midpoint
two_bw = np.delete(
sorted_elevs_midpoints, ~(separation_needed * spaces == (2 * bw))
)
# Beams separated by more than 2*bw need two fake nan rays in between
over_two_bw = np.concatenate(
(
np.delete(
sorted_elevs[:-1] + bw, ~(separation_needed * spaces > (2 * bw))
),
np.delete(
sorted_elevs[1:] - bw, ~(separation_needed * spaces > (2 * bw))
),
)
)
# Beams separated between bw and 2*bw need a fake nan ray at midpoint and two duplicated data rays over and below
condition = separation_needed * (spaces < (2 * bw))
under_two_bw_nan = np.delete(sorted_elevs_midpoints, ~condition)
nan_space = np.delete(spaces - bw, ~condition)
under_two_bw_dup_data = np.concatenate(
(
under_two_bw_nan - nan_space,
under_two_bw_nan + nan_space,
)
)
# If the first (lowest) real ray falls in this last case
# we also need to add a nan ray below
if condition[0]:
under_two_bw_nan = np.concatenate(
(np.array(sorted_elevs[0] - bw, ndmin=1), under_two_bw_nan)
)
# Join all fake ray elevations for nan or duplicated data
nan_fake_elevs = np.sort(
np.concatenate((two_bw, over_two_bw, under_two_bw_nan))
)
data_fake_elevs = np.sort(under_two_bw_dup_data)
# Sort volume in ascending order of elevation
obj = obj.sortby("sweep_fixed_angle")
# Generate fake rays array
all_fake_elevs = np.sort(np.concatenate((nan_fake_elevs, data_fake_elevs)))
obj_fake = obj.interp(sweep_fixed_angle=all_fake_elevs, method="nearest")
obj_fake = obj_fake.where(
~obj_fake.sweep_fixed_angle.isin(nan_fake_elevs)
) # fill with nan on corresponding elevations
# set elevation coord correctly because georeferencing is based on this coord
obj_fake.coords["elevation"] = obj_fake["sweep_fixed_angle"]
ds = obj.copy()
if bw is not None:
ds = xr.concat([ds, obj_fake], dim="sweep_fixed_angle")
ds = ds.sortby("sweep_fixed_angle")
# Reduce "sweep_mode" to 1D to be able to georeference
ds["sweep_mode"] = ds["sweep_mode"].min()
# Georeference the data
ds = ds.pipe(georef.georeference, crs=crs)
try:
return ds.sel(azimuth=azimuth, method=method, tolerance=tolerance)
except (TypeError, ValueError, KeyError):
# Is the user providing two points for arbitrary cut?
try:
p1 = azimuth[0]
p2 = azimuth[1]
# this is just for checking that the points are valid:
x1 = p1[0]
y1 = p1[1]
x2 = p2[0]
y2 = p2[1]
# if some of the points is outside the radar volume area raise an exception
test = np.array(
[
~(ds.x.min() < x1 < ds.x.max()),
~(ds.x.min() < x2 < ds.x.max()),
~(ds.y.min() < y1 < ds.y.max()),
~(ds.y.min() < y2 < ds.y.max()),
]
)
if test.any():
raise ValueError(
"At least one of the points given is outside of the radar volume area"
)
except TypeError as err:
# `azimuth` is not a list of azimuths nor a couple of points
raise TypeError(
"Not azimuth values nor points was provided to `azimuth`"
) from err
# Check that the two points given are not the same
try:
if (p1 == p2).all():
raise ValueError(
"p1=p2. The two points given are the same. Please give different points."
)
except AttributeError as err:
if p1 == p2:
raise ValueError(
"p1=p2. The two points given are the same. Please give different points."
) from err
# number of points to make the line between p1 and p2 (should be greater
# than the resolution of the volume)
nn = npl
# List to collect dataset for every elevation
selection = list()
for el in ds.sweep_fixed_angle:
# For every elevation, select the array of x and y coordinates
x = ds.sel(sweep_fixed_angle=el.data.tolist()).x.to_numpy()
y = ds.sel(sweep_fixed_angle=el.data.tolist()).y.to_numpy()
# Create a KDTree class to look for the nearest neighbors
tree = KDTree(np.c_[x.ravel(), y.ravel()])
# Create a line of nn points between the selected p1 and p2
pline = np.linspace(p1, p2, nn)
# Search for the nearest neighbors of pline in the x-y array
dd, ii = tree.query(pline)
# Eliminate repeated selections and unravel into original dimensions
ii = np.unique(ii)
# Stack the azimuth and range coordinates and select the points
sel = (
ds.sel(sweep_fixed_angle=(el.data.tolist()))
.stack(xyi=("azimuth", "range"))
.isel({"xyi": ii})
)
# create values for a new coordinate xy that is the distance to p1 along the line
xy = np.sqrt((sel.x - p1[0]) ** 2 + (sel.y - p1[1]) ** 2)
# Add new coordinates
z_coord = sel.z.to_numpy()
sel2 = sel.drop_vars({"xyi", "range", "azimuth"}).assign_coords(
{"xyi": np.arange(len(xy))}
)
sel2.coords["xy"] = ("xyi", xy.data)
sel2.coords["z"] = ("xyi", z_coord)
selection.append(sel2.expand_dims("sweep_fixed_angle"))
# Reindex the datasets along the "xyi" dimension
selection_reindexed = list()
for ll in range(len(selection)):
# Since the selection of data for each elevation does not necessarily have the
# same amount of xyi points, we reindex the xyi dimension expanding to its
# max length to accomodate all data
xyi_maxlen = np.array([len(ss.xyi) for ss in selection]).max()
selection_reindexed.append(
selection[ll].reindex({"xyi": np.arange(xyi_maxlen)})
)
# Combine into a single dataset
merged = xr.concat(selection_reindexed, dim="sweep_fixed_angle").transpose(
"sweep_fixed_angle", ...
)
# We cannot have coordinates with NaN for plotting, so we fill any NaN by propagating values
merged["xy"] = merged["xy"].ffill("xyi")
merged["z"] = merged["z"].ffill("xyi")
return merged
def docstring(func):
"""Apply docstring and signature to decorated function"""
def wrapper(decorated):
decorated.__doc__ = func.__doc__
decorated.__signature__ = inspect.signature(func)
return decorated
return wrapper
def dim0(obj):
"""Return major dimension (azimuth/elevation) of xarray object."""
return list(set(obj.dims) & {"azimuth", "elevation"})[-1]
def get_apply_ufunc_variables(obj, dim):
dims = {dim, "range"}
keep = xr.Dataset(
{k: v for k, v in obj.data_vars.items() if set(v.dims) & dims != dims}
)
obj = xr.Dataset(
{k: v for k, v in obj.data_vars.items() if set(v.dims) & dims == dims}
)
return obj, keep
def get_dataarray(obj, arr):
if isinstance(arr, str):
arr = obj[arr]
assert isinstance(arr, xr.DataArray)
return arr
class XarrayMethods:
"""BaseClass to bind xarray methods to wradlib SubAccessor
This wraps xarray.DataArray or xarray.Dataset objects and overrides
`__repr__`, `_repr_html_`, `__getitem__` and `__getattr__` of those.
Parameter
---------
obj : xarray.Dataset | xarray.DataArray
"""
def __init__(self, obj):
self._obj = obj
def __repr__(self):
name = self._obj.__class__.__name__
cname = self.__class__.__module__
search = f"xarray.{name}"
replace = f"{cname}(xarray.{name})"
out = self._obj.__repr__()
out = out.replace(search, replace)
return out
def _repr_html_(self):
name = self._obj.__class__.__name__
cname = self.__class__.__module__
search = f"xarray.{name}"
replace = f"{cname}(xarray.{name})"
out = self._obj._repr_html_()
out = out.replace(search, replace)
return out
def __getitem__(self, item):
if (
isinstance(self._obj, xr.DataArray)
or item not in self._obj.data_vars
or not self._obj[item].dims
):
return self._obj[item]
return self.__class__(self._obj[item])
def __getattr__(self, item):
if (
isinstance(self._obj, xr.DataArray)
or item not in self._obj.data_vars
or not self._obj[item].dims
):
return getattr(self._obj, item)
return self.__class__(getattr(self._obj, item))
[docs]class UtilMethods(XarrayMethods):
"""wradlib xarray SubAccessor methods for Util."""
[docs] @docstring(_despeckle_xarray)
def despeckle(self, *args, **kwargs):
if not isinstance(self, UtilMethods):
return despeckle(self, *args, **kwargs)
else:
return despeckle(self._obj, *args, **kwargs)
[docs] @docstring(_derivate_xarray)
def derivate(self, *args, **kwargs):
if not isinstance(self, UtilMethods):
return derivate(self, *args, **kwargs)
else:
return derivate(self._obj, *args, **kwargs)
[docs] @docstring(dim0)
def dim0(self, *args, **kwargs):
if not isinstance(self, UtilMethods):
return dim0(self, *args, **kwargs)
else:
return dim0(self._obj, *args, **kwargs)
if __name__ == "__main__":
print("wradlib: Calling module <util> as main...")
