# Copyright (c) 2016,2017,2018 MetPy Developers.
# Distributed under the terms of the BSD 3-Clause License.
# SPDX-License-Identifier: BSD-3-Clause
"""Contains a collection of generally useful calculation tools."""
from __future__ import division
import functools
from operator import itemgetter
import warnings
import numpy as np
try:
from numpy.core.numeric import normalize_axis_index
except ImportError: # Only available in numpy >=1.13.0
def normalize_axis_index(a, n):
"""No op version of :func:`numpy.core.numeric.normalize_axis_index`."""
return a
import numpy.ma as ma
from scipy.spatial import cKDTree
import xarray as xr
from . import height_to_pressure_std, pressure_to_height_std
from ..cbook import broadcast_indices
from ..deprecation import deprecated, metpyDeprecation
from ..interpolate.one_dimension import interpolate_1d, interpolate_nans_1d, log_interpolate_1d
from ..package_tools import Exporter
from ..units import atleast_1d, check_units, concatenate, diff, units
from ..xarray import CFConventionHandler, preprocess_xarray
exporter = Exporter(globals())
DIR_STRS = [
'N', 'NNE', 'NE', 'ENE',
'E', 'ESE', 'SE', 'SSE',
'S', 'SSW', 'SW', 'WSW',
'W', 'WNW', 'NW', 'NNW'
]
BASE_DEGREE_MULTIPLIER = 22.5 * units.degree
DIR_DICT = {dir_str: i * BASE_DEGREE_MULTIPLIER for i, dir_str in enumerate(DIR_STRS)}
[docs]@exporter.export
@preprocess_xarray
def resample_nn_1d(a, centers):
"""Return one-dimensional nearest-neighbor indexes based on user-specified centers.
Parameters
----------
a : array-like
1-dimensional array of numeric values from which to
extract indexes of nearest-neighbors
centers : array-like
1-dimensional array of numeric values representing a subset of values to approximate
Returns
-------
An array of indexes representing values closest to given array values
"""
ix = []
for center in centers:
index = (np.abs(a - center)).argmin()
if index not in ix:
ix.append(index)
return ix
[docs]@exporter.export
@preprocess_xarray
def nearest_intersection_idx(a, b):
"""Determine the index of the point just before two lines with common x values.
Parameters
----------
a : array-like
1-dimensional array of y-values for line 1
b : array-like
1-dimensional array of y-values for line 2
Returns
-------
An array of indexes representing the index of the values
just before the intersection(s) of the two lines.
"""
# Difference in the two y-value sets
difference = a - b
# Determine the point just before the intersection of the lines
# Will return multiple points for multiple intersections
sign_change_idx, = np.nonzero(np.diff(np.sign(difference)))
return sign_change_idx
[docs]@exporter.export
@preprocess_xarray
@units.wraps(('=A', '=B'), ('=A', '=B', '=B'))
def find_intersections(x, a, b, direction='all'):
"""Calculate the best estimate of intersection.
Calculates the best estimates of the intersection of two y-value
data sets that share a common x-value set.
Parameters
----------
x : array-like
1-dimensional array of numeric x-values
a : array-like
1-dimensional array of y-values for line 1
b : array-like
1-dimensional array of y-values for line 2
direction : string, optional
specifies direction of crossing. 'all', 'increasing' (a becoming greater than b),
or 'decreasing' (b becoming greater than a). Defaults to 'all'.
Returns
-------
A tuple (x, y) of array-like with the x and y coordinates of the
intersections of the lines.
"""
# Find the index of the points just before the intersection(s)
nearest_idx = nearest_intersection_idx(a, b)
next_idx = nearest_idx + 1
# Determine the sign of the change
sign_change = np.sign(a[next_idx] - b[next_idx])
# x-values around each intersection
_, x0 = _next_non_masked_element(x, nearest_idx)
_, x1 = _next_non_masked_element(x, next_idx)
# y-values around each intersection for the first line
_, a0 = _next_non_masked_element(a, nearest_idx)
_, a1 = _next_non_masked_element(a, next_idx)
# y-values around each intersection for the second line
_, b0 = _next_non_masked_element(b, nearest_idx)
_, b1 = _next_non_masked_element(b, next_idx)
# Calculate the x-intersection. This comes from finding the equations of the two lines,
# one through (x0, a0) and (x1, a1) and the other through (x0, b0) and (x1, b1),
# finding their intersection, and reducing with a bunch of algebra.
delta_y0 = a0 - b0
delta_y1 = a1 - b1
intersect_x = (delta_y1 * x0 - delta_y0 * x1) / (delta_y1 - delta_y0)
# Calculate the y-intersection of the lines. Just plug the x above into the equation
# for the line through the a points. One could solve for y like x above, but this
# causes weirder unit behavior and seems a little less good numerically.
intersect_y = ((intersect_x - x0) / (x1 - x0)) * (a1 - a0) + a0
# If there's no intersections, return
if len(intersect_x) == 0:
return intersect_x, intersect_y
# Check for duplicates
duplicate_mask = (np.ediff1d(intersect_x, to_end=1) != 0)
# Make a mask based on the direction of sign change desired
if direction == 'increasing':
mask = sign_change > 0
elif direction == 'decreasing':
mask = sign_change < 0
elif direction == 'all':
return intersect_x[duplicate_mask], intersect_y[duplicate_mask]
else:
raise ValueError('Unknown option for direction: {0}'.format(str(direction)))
return intersect_x[mask & duplicate_mask], intersect_y[mask & duplicate_mask]
[docs]@exporter.export
@preprocess_xarray
@deprecated('0.9', addendum=(' This function has been moved to metpy.interpolate and renamed '
'interpolate_nans_1d.'), pending=False)
def interpolate_nans(x, y, kind='linear'):
"""Wrap interpolate_nans_1d for deprecated interpolate_nans."""
return interpolate_nans_1d(x, y, kind=kind)
interpolate_nans.__doc__ = (interpolate_nans_1d.__doc__
+ '\n .. deprecated:: 0.9.0\n Function has been renamed '
'`interpolate_nans_1d` and moved to `metpy.interpolate`, and '
'will be removed from MetPy in 0.12.0.')
def _next_non_masked_element(a, idx):
"""Return the next non masked element of a masked array.
If an array is masked, return the next non-masked element (if the given index is masked).
If no other unmasked points are after the given masked point, returns none.
Parameters
----------
a : array-like
1-dimensional array of numeric values
idx : integer
index of requested element
Returns
-------
Index of next non-masked element and next non-masked element
"""
try:
next_idx = idx + a[idx:].mask.argmin()
if ma.is_masked(a[next_idx]):
return None, None
else:
return next_idx, a[next_idx]
except (AttributeError, TypeError, IndexError):
return idx, a[idx]
def _delete_masked_points(*arrs):
"""Delete masked points from arrays.
Takes arrays and removes masked points to help with calculations and plotting.
Parameters
----------
arrs : one or more array-like
source arrays
Returns
-------
arrs : one or more array-like
arrays with masked elements removed
"""
if any(hasattr(a, 'mask') for a in arrs):
keep = ~functools.reduce(np.logical_or, (np.ma.getmaskarray(a) for a in arrs))
return tuple(ma.asarray(a[keep]) for a in arrs)
else:
return arrs
[docs]@exporter.export
@preprocess_xarray
def reduce_point_density(points, radius, priority=None):
r"""Return a mask to reduce the density of points in irregularly-spaced data.
This function is used to down-sample a collection of scattered points (e.g. surface
data), returning a mask that can be used to select the points from one or more arrays
(e.g. arrays of temperature and dew point). The points selected can be controlled by
providing an array of ``priority`` values (e.g. rainfall totals to ensure that
stations with higher precipitation remain in the mask).
Parameters
----------
points : (N, K) array-like
N locations of the points in K dimensional space
radius : float
minimum radius allowed between points
priority : (N, K) array-like, optional
If given, this should have the same shape as ``points``; these values will
be used to control selection priority for points.
Returns
-------
(N,) array-like of boolean values indicating whether points should be kept. This
can be used directly to index numpy arrays to return only the desired points.
Examples
--------
>>> metpy.calc.reduce_point_density(np.array([1, 2, 3]), 1.)
array([ True, False, True])
>>> metpy.calc.reduce_point_density(np.array([1, 2, 3]), 1.,
... priority=np.array([0.1, 0.9, 0.3]))
array([False, True, False])
"""
# Handle 1D input
if points.ndim < 2:
points = points.reshape(-1, 1)
# Make a kd-tree to speed searching of data.
tree = cKDTree(points)
# Need to use sorted indices rather than sorting the position
# so that the keep mask matches *original* order.
if priority is not None:
# Need to sort the locations in decreasing priority.
sorted_indices = np.argsort(priority)[::-1]
else:
# Take advantage of iterator nature of range here to avoid making big lists
sorted_indices = range(len(points))
# Keep all points initially
keep = np.ones(len(points), dtype=np.bool)
# Loop over all the potential points
for ind in sorted_indices:
# Only proceed if we haven't already excluded this point
if keep[ind]:
# Find the neighbors and eliminate them
neighbors = tree.query_ball_point(points[ind], radius)
keep[neighbors] = False
# We just removed ourselves, so undo that
keep[ind] = True
return keep
def _get_bound_pressure_height(pressure, bound, heights=None, interpolate=True):
"""Calculate the bounding pressure and height in a layer.
Given pressure, optional heights, and a bound, return either the closest pressure/height
or interpolated pressure/height. If no heights are provided, a standard atmosphere is
assumed.
Parameters
----------
pressure : `pint.Quantity`
Atmospheric pressures
bound : `pint.Quantity`
Bound to retrieve (in pressure or height)
heights : `pint.Quantity`, optional
Atmospheric heights associated with the pressure levels. Defaults to using
heights calculated from ``pressure`` assuming a standard atmosphere.
interpolate : boolean, optional
Interpolate the bound or return the nearest. Defaults to True.
Returns
-------
`pint.Quantity`
The bound pressure and height.
"""
# Make sure pressure is monotonically decreasing
sort_inds = np.argsort(pressure)[::-1]
pressure = pressure[sort_inds]
if heights is not None:
heights = heights[sort_inds]
# Bound is given in pressure
if bound.dimensionality == {'[length]': -1.0, '[mass]': 1.0, '[time]': -2.0}:
# If the bound is in the pressure data, we know the pressure bound exactly
if bound in pressure:
bound_pressure = bound
# If we have heights, we know the exact height value, otherwise return standard
# atmosphere height for the pressure
if heights is not None:
bound_height = heights[pressure == bound_pressure]
else:
bound_height = pressure_to_height_std(bound_pressure)
# If bound is not in the data, return the nearest or interpolated values
else:
if interpolate:
bound_pressure = bound # Use the user specified bound
if heights is not None: # Interpolate heights from the height data
bound_height = log_interpolate_1d(bound_pressure, pressure, heights)
else: # If not heights given, use the standard atmosphere
bound_height = pressure_to_height_std(bound_pressure)
else: # No interpolation, find the closest values
idx = (np.abs(pressure - bound)).argmin()
bound_pressure = pressure[idx]
if heights is not None:
bound_height = heights[idx]
else:
bound_height = pressure_to_height_std(bound_pressure)
# Bound is given in height
elif bound.dimensionality == {'[length]': 1.0}:
# If there is height data, see if we have the bound or need to interpolate/find nearest
if heights is not None:
if bound in heights: # Bound is in the height data
bound_height = bound
bound_pressure = pressure[heights == bound]
else: # Bound is not in the data
if interpolate:
bound_height = bound
# Need to cast back to the input type since interp (up to at least numpy
# 1.13 always returns float64. This can cause upstream users problems,
# resulting in something like np.append() to upcast.
bound_pressure = np.interp(np.atleast_1d(bound), heights,
pressure).astype(bound.dtype) * pressure.units
else:
idx = (np.abs(heights - bound)).argmin()
bound_pressure = pressure[idx]
bound_height = heights[idx]
else: # Don't have heights, so assume a standard atmosphere
bound_height = bound
bound_pressure = height_to_pressure_std(bound)
# If interpolation is on, this is all we need, if not, we need to go back and
# find the pressure closest to this and refigure the bounds
if not interpolate:
idx = (np.abs(pressure - bound_pressure)).argmin()
bound_pressure = pressure[idx]
bound_height = pressure_to_height_std(bound_pressure)
# Bound has invalid units
else:
raise ValueError('Bound must be specified in units of length or pressure.')
# If the bound is out of the range of the data, we shouldn't extrapolate
if not (_greater_or_close(bound_pressure, np.nanmin(pressure) * pressure.units)
and _less_or_close(bound_pressure, np.nanmax(pressure) * pressure.units)):
raise ValueError('Specified bound is outside pressure range.')
if heights is not None:
if not (_less_or_close(bound_height, np.nanmax(heights) * heights.units)
and _greater_or_close(bound_height, np.nanmin(heights) * heights.units)):
raise ValueError('Specified bound is outside height range.')
return bound_pressure, bound_height
[docs]@exporter.export
@preprocess_xarray
@check_units('[length]')
def get_layer_heights(heights, depth, *args, **kwargs):
"""Return an atmospheric layer from upper air data with the requested bottom and depth.
This function will subset an upper air dataset to contain only the specified layer using
the heights only.
Parameters
----------
heights : array-like
Atmospheric heights
depth : `pint.Quantity`
The thickness of the layer
*args : array-like
Atmospheric variable(s) measured at the given pressures
bottom : `pint.Quantity`, optional
The bottom of the layer
interpolate : bool, optional
Interpolate the top and bottom points if they are not in the given data. Defaults
to True.
with_agl : bool, optional
Returns the heights as above ground level by subtracting the minimum height in the
provided heights. Defaults to False.
Returns
-------
`pint.Quantity, pint.Quantity`
The height and data variables of the layer
"""
bottom = kwargs.pop('bottom', None)
interpolate = kwargs.pop('interpolate', True)
with_agl = kwargs.pop('with_agl', False)
# Make sure pressure and datavars are the same length
for datavar in args:
if len(heights) != len(datavar):
raise ValueError('Height and data variables must have the same length.')
# If we want things in AGL, subtract the minimum height from all height values
if with_agl:
sfc_height = np.min(heights)
heights = heights - sfc_height
# If the bottom is not specified, make it the surface
if bottom is None:
bottom = heights[0]
# Make heights and arguments base units
heights = heights.to_base_units()
bottom = bottom.to_base_units()
# Calculate the top of the layer
top = bottom + depth
ret = [] # returned data variables in layer
# Ensure heights are sorted in ascending order
sort_inds = np.argsort(heights)
heights = heights[sort_inds]
# Mask based on top and bottom
inds = _greater_or_close(heights, bottom) & _less_or_close(heights, top)
heights_interp = heights[inds]
# Interpolate heights at bounds if necessary and sort
if interpolate:
# If we don't have the bottom or top requested, append them
if top not in heights_interp:
heights_interp = np.sort(np.append(heights_interp, top)) * heights.units
if bottom not in heights_interp:
heights_interp = np.sort(np.append(heights_interp, bottom)) * heights.units
ret.append(heights_interp)
for datavar in args:
# Ensure that things are sorted in ascending order
datavar = datavar[sort_inds]
if interpolate:
# Interpolate for the possibly missing bottom/top values
datavar_interp = interpolate_1d(heights_interp, heights, datavar)
datavar = datavar_interp
else:
datavar = datavar[inds]
ret.append(datavar)
return ret
[docs]@exporter.export
@preprocess_xarray
@check_units('[pressure]')
def get_layer(pressure, *args, **kwargs):
r"""Return an atmospheric layer from upper air data with the requested bottom and depth.
This function will subset an upper air dataset to contain only the specified layer. The
bottom of the layer can be specified with a pressure or height above the surface
pressure. The bottom defaults to the surface pressure. The depth of the layer can be
specified in terms of pressure or height above the bottom of the layer. If the top and
bottom of the layer are not in the data, they are interpolated by default.
Parameters
----------
pressure : array-like
Atmospheric pressure profile
*args : array-like
Atmospheric variable(s) measured at the given pressures
heights: array-like, optional
Atmospheric heights corresponding to the given pressures. Defaults to using
heights calculated from ``p`` assuming a standard atmosphere.
bottom : `pint.Quantity`, optional
The bottom of the layer as a pressure or height above the surface pressure. Defaults
to the highest pressure or lowest height given.
depth : `pint.Quantity`, optional
The thickness of the layer as a pressure or height above the bottom of the layer.
Defaults to 100 hPa.
interpolate : bool, optional
Interpolate the top and bottom points if they are not in the given data. Defaults
to True.
Returns
-------
`pint.Quantity, pint.Quantity`
The pressure and data variables of the layer
"""
# Pop off keyword arguments
heights = kwargs.pop('heights', None)
bottom = kwargs.pop('bottom', None)
depth = kwargs.pop('depth', 100 * units.hPa)
interpolate = kwargs.pop('interpolate', True)
# If we get the depth kwarg, but it's None, set it to the default as well
if depth is None:
depth = 100 * units.hPa
# Make sure pressure and datavars are the same length
for datavar in args:
if len(pressure) != len(datavar):
raise ValueError('Pressure and data variables must have the same length.')
# If the bottom is not specified, make it the surface pressure
if bottom is None:
bottom = np.nanmax(pressure) * pressure.units
bottom_pressure, bottom_height = _get_bound_pressure_height(pressure, bottom,
heights=heights,
interpolate=interpolate)
# Calculate the top if whatever units depth is in
if depth.dimensionality == {'[length]': -1.0, '[mass]': 1.0, '[time]': -2.0}:
top = bottom_pressure - depth
elif depth.dimensionality == {'[length]': 1}:
top = bottom_height + depth
else:
raise ValueError('Depth must be specified in units of length or pressure')
top_pressure, _ = _get_bound_pressure_height(pressure, top, heights=heights,
interpolate=interpolate)
ret = [] # returned data variables in layer
# Ensure pressures are sorted in ascending order
sort_inds = np.argsort(pressure)
pressure = pressure[sort_inds]
# Mask based on top and bottom pressure
inds = (_less_or_close(pressure, bottom_pressure)
& _greater_or_close(pressure, top_pressure))
p_interp = pressure[inds]
# Interpolate pressures at bounds if necessary and sort
if interpolate:
# If we don't have the bottom or top requested, append them
if not np.any(np.isclose(top_pressure, p_interp)):
p_interp = np.sort(np.append(p_interp, top_pressure)) * pressure.units
if not np.any(np.isclose(bottom_pressure, p_interp)):
p_interp = np.sort(np.append(p_interp, bottom_pressure)) * pressure.units
ret.append(p_interp[::-1])
for datavar in args:
# Ensure that things are sorted in ascending order
datavar = datavar[sort_inds]
if interpolate:
# Interpolate for the possibly missing bottom/top values
datavar_interp = log_interpolate_1d(p_interp, pressure, datavar)
datavar = datavar_interp
else:
datavar = datavar[inds]
ret.append(datavar[::-1])
return ret
[docs]@exporter.export
@preprocess_xarray
@deprecated('0.9', addendum=(' This function has been moved to metpy.interpolate and renamed '
'interpolate_1d.'), pending=False)
def interp(x, xp, *args, **kwargs):
"""Wrap interpolate_1d for deprecated interp."""
return interpolate_1d(x, xp, *args, **kwargs)
interp.__doc__ = (interpolate_1d.__doc__
+ '\n .. deprecated:: 0.9.0\n Function has been renamed '
'`interpolate_1d` and moved to `metpy.interpolate`, and '
'will be removed from MetPy in 0.12.0.')
[docs]@exporter.export
@preprocess_xarray
def find_bounding_indices(arr, values, axis, from_below=True):
"""Find the indices surrounding the values within arr along axis.
Returns a set of above, below, good. Above and below are lists of arrays of indices.
These lists are formulated such that they can be used directly to index into a numpy
array and get the expected results (no extra slices or ellipsis necessary). `good` is
a boolean array indicating the "columns" that actually had values to bound the desired
value(s).
Parameters
----------
arr : array-like
Array to search for values
values: array-like
One or more values to search for in `arr`
axis : int
The dimension of `arr` along which to search.
from_below : bool, optional
Whether to search from "below" (i.e. low indices to high indices). If `False`,
the search will instead proceed from high indices to low indices. Defaults to `True`.
Returns
-------
above : list of arrays
List of broadcasted indices to the location above the desired value
below : list of arrays
List of broadcasted indices to the location below the desired value
good : array
Boolean array indicating where the search found proper bounds for the desired value
"""
# The shape of generated indices is the same as the input, but with the axis of interest
# replaced by the number of values to search for.
indices_shape = list(arr.shape)
indices_shape[axis] = len(values)
# Storage for the found indices and the mask for good locations
indices = np.empty(indices_shape, dtype=np.int)
good = np.empty(indices_shape, dtype=np.bool)
# Used to put the output in the proper location
store_slice = [slice(None)] * arr.ndim
# Loop over all of the values and for each, see where the value would be found from a
# linear search
for level_index, value in enumerate(values):
# Look for changes in the value of the test for <= value in consecutive points
# Taking abs() because we only care if there is a flip, not which direction.
switches = np.abs(np.diff((arr <= value).astype(np.int), axis=axis))
# Good points are those where it's not just 0's along the whole axis
good_search = np.any(switches, axis=axis)
if from_below:
# Look for the first switch; need to add 1 to the index since argmax is giving the
# index within the difference array, which is one smaller.
index = switches.argmax(axis=axis) + 1
else:
# Generate a list of slices to reverse the axis of interest so that searching from
# 0 to N is starting at the "top" of the axis.
arr_slice = [slice(None)] * arr.ndim
arr_slice[axis] = slice(None, None, -1)
# Same as above, but we use the slice to come from the end; then adjust those
# indices to measure from the front.
index = arr.shape[axis] - 1 - switches[tuple(arr_slice)].argmax(axis=axis)
# Set all indices where the results are not good to 0
index[~good_search] = 0
# Put the results in the proper slice
store_slice[axis] = level_index
indices[tuple(store_slice)] = index
good[tuple(store_slice)] = good_search
# Create index values for broadcasting arrays
above = broadcast_indices(arr, indices, arr.ndim, axis)
below = broadcast_indices(arr, indices - 1, arr.ndim, axis)
return above, below, good
[docs]@exporter.export
@preprocess_xarray
@deprecated('0.9', addendum=(' This function has been moved to metpy.interpolate and renamed '
'log_interpolate_1d.'), pending=False)
def log_interp(x, xp, *args, **kwargs):
"""Wrap log_interpolate_1d for deprecated log_interp."""
return log_interpolate_1d(x, xp, *args, **kwargs)
log_interp.__doc__ = (log_interpolate_1d.__doc__
+ '\n .. deprecated:: 0.9.0\n Function has been renamed '
'`log_interpolate_1d` and moved to `metpy.interpolate`, and '
'will be removed from MetPy in 0.12.0.')
def _greater_or_close(a, value, **kwargs):
r"""Compare values for greater or close to boolean masks.
Returns a boolean mask for values greater than or equal to a target within a specified
absolute or relative tolerance (as in :func:`numpy.isclose`).
Parameters
----------
a : array-like
Array of values to be compared
value : float
Comparison value
Returns
-------
array-like
Boolean array where values are greater than or nearly equal to value.
"""
return (a > value) | np.isclose(a, value, **kwargs)
def _less_or_close(a, value, **kwargs):
r"""Compare values for less or close to boolean masks.
Returns a boolean mask for values less than or equal to a target within a specified
absolute or relative tolerance (as in :func:`numpy.isclose`).
Parameters
----------
a : array-like
Array of values to be compared
value : float
Comparison value
Returns
-------
array-like
Boolean array where values are less than or nearly equal to value.
"""
return (a < value) | np.isclose(a, value, **kwargs)
[docs]@deprecated('0.8', addendum=' This function has been replaced by the signed delta distance'
'calculation lat_lon_grid_deltas and will be removed in MetPy'
' 0.11.',
pending=False)
@exporter.export
@preprocess_xarray
def lat_lon_grid_spacing(longitude, latitude, **kwargs):
r"""Calculate the distance between grid points that are in a latitude/longitude format.
Calculate the distance between grid points when the grid spacing is defined by
delta lat/lon rather than delta x/y
Parameters
----------
longitude : array_like
array of longitudes defining the grid
latitude : array_like
array of latitudes defining the grid
kwargs
Other keyword arguments to pass to :class:`~pyproj.Geod`
Returns
-------
dx, dy: 2D arrays of distances between grid points in the x and y direction
Notes
-----
Accepts, 1D or 2D arrays for latitude and longitude
Assumes [Y, X] for 2D arrays
.. deprecated:: 0.8.0
Function has been replaced with the signed delta distance calculation
`lat_lon_grid_deltas` and will be removed from MetPy in 0.11.0.
"""
# Use the absolute value of the signed function replacing this
dx, dy = lat_lon_grid_deltas(longitude, latitude, **kwargs)
return np.abs(dx), np.abs(dy)
[docs]@exporter.export
@preprocess_xarray
def lat_lon_grid_deltas(longitude, latitude, **kwargs):
r"""Calculate the delta between grid points that are in a latitude/longitude format.
Calculate the signed delta distance between grid points when the grid spacing is defined by
delta lat/lon rather than delta x/y
Parameters
----------
longitude : array_like
array of longitudes defining the grid
latitude : array_like
array of latitudes defining the grid
kwargs
Other keyword arguments to pass to :class:`~pyproj.Geod`
Returns
-------
dx, dy:
at least two dimensional arrays of signed deltas between grid points in the x and y
direction
Notes
-----
Accepts 1D, 2D, or higher arrays for latitude and longitude
Assumes [..., Y, X] for >=2 dimensional arrays
"""
from pyproj import Geod
# Inputs must be the same number of dimensions
if latitude.ndim != longitude.ndim:
raise ValueError('Latitude and longitude must have the same number of dimensions.')
# If we were given 1D arrays, make a mesh grid
if latitude.ndim < 2:
longitude, latitude = np.meshgrid(longitude, latitude)
geod_args = {'ellps': 'sphere'}
if kwargs:
geod_args = kwargs
g = Geod(**geod_args)
forward_az, _, dy = g.inv(longitude[..., :-1, :], latitude[..., :-1, :],
longitude[..., 1:, :], latitude[..., 1:, :])
dy[(forward_az < -90.) | (forward_az > 90.)] *= -1
forward_az, _, dx = g.inv(longitude[..., :, :-1], latitude[..., :, :-1],
longitude[..., :, 1:], latitude[..., :, 1:])
dx[(forward_az < 0.) | (forward_az > 180.)] *= -1
return dx * units.meter, dy * units.meter
[docs]@exporter.export
def grid_deltas_from_dataarray(f):
"""Calculate the horizontal deltas between grid points of a DataArray.
Calculate the signed delta distance between grid points of a DataArray in the horizontal
directions, whether the grid is lat/lon or x/y.
Parameters
----------
f : `xarray.DataArray`
Parsed DataArray on a latitude/longitude grid, in (..., lat, lon) or (..., y, x)
dimension order
Returns
-------
dx, dy:
arrays of signed deltas between grid points in the x and y directions with dimensions
matching those of `f`.
See Also
--------
lat_lon_grid_deltas
"""
if f.metpy.crs['grid_mapping_name'] == 'latitude_longitude':
dx, dy = lat_lon_grid_deltas(f.metpy.x, f.metpy.y,
initstring=f.metpy.cartopy_crs.proj4_init)
slc_x = slc_y = tuple([np.newaxis] * (f.ndim - 2) + [slice(None)] * 2)
else:
dx = np.diff(f.metpy.x.metpy.unit_array.to('m').magnitude) * units('m')
dy = np.diff(f.metpy.y.metpy.unit_array.to('m').magnitude) * units('m')
slc = [np.newaxis] * (f.ndim - 2)
slc_x = tuple(slc + [np.newaxis, slice(None)])
slc_y = tuple(slc + [slice(None), np.newaxis])
return dx[slc_x], dy[slc_y]
def xarray_derivative_wrap(func):
"""Decorate the derivative functions to make them work nicely with DataArrays.
This will automatically determine if the coordinates can be pulled directly from the
DataArray, or if a call to lat_lon_grid_deltas is needed.
"""
@functools.wraps(func)
def wrapper(f, **kwargs):
if 'x' in kwargs or 'delta' in kwargs:
# Use the usual DataArray to pint.Quantity preprocessing wrapper
return preprocess_xarray(func)(f, **kwargs)
elif isinstance(f, xr.DataArray):
# Get axis argument, defaulting to first dimension
axis = f.metpy.find_axis_name(kwargs.get('axis', 0))
# Initialize new kwargs with the axis number
new_kwargs = {'axis': f.get_axis_num(axis)}
if f[axis].attrs.get('_metpy_axis') == 'T':
# Time coordinate, need to convert to seconds from datetimes
new_kwargs['x'] = f[axis].metpy.as_timestamp().metpy.unit_array
elif CFConventionHandler.check_axis(f[axis], 'lon'):
# Longitude coordinate, need to get grid deltas
new_kwargs['delta'], _ = grid_deltas_from_dataarray(f)
elif CFConventionHandler.check_axis(f[axis], 'lat'):
# Latitude coordinate, need to get grid deltas
_, new_kwargs['delta'] = grid_deltas_from_dataarray(f)
else:
# General coordinate, use as is
new_kwargs['x'] = f[axis].metpy.unit_array
# Calculate and return result as a DataArray
result = func(f.metpy.unit_array, **new_kwargs)
return xr.DataArray(result.magnitude,
coords=f.coords,
dims=f.dims,
attrs={'units': str(result.units)})
else:
# Error
raise ValueError('Must specify either "x" or "delta" for value positions when "f" '
'is not a DataArray.')
return wrapper
[docs]@exporter.export
@xarray_derivative_wrap
def first_derivative(f, **kwargs):
"""Calculate the first derivative of a grid of values.
Works for both regularly-spaced data and grids with varying spacing.
Either `x` or `delta` must be specified, or `f` must be given as an `xarray.DataArray` with
attached coordinate and projection information. If `f` is an `xarray.DataArray`, and `x` or
`delta` are given, `f` will be converted to a `pint.Quantity` and the derivative returned
as a `pint.Quantity`, otherwise, if neither `x` nor `delta` are given, the attached
coordinate information belonging to `axis` will be used and the derivative will be returned
as an `xarray.DataArray`.
This uses 3 points to calculate the derivative, using forward or backward at the edges of
the grid as appropriate, and centered elsewhere. The irregular spacing is handled
explicitly, using the formulation as specified by [Bowen2005]_.
Parameters
----------
f : array-like
Array of values of which to calculate the derivative
axis : int or str, optional
The array axis along which to take the derivative. If `f` is ndarray-like, must be an
integer. If `f` is a `DataArray`, can be a string (referring to either the coordinate
dimension name or the axis type) or integer (referring to axis number), unless using
implicit conversion to `pint.Quantity`, in which case it must be an integer. Defaults
to 0.
x : array-like, optional
The coordinate values corresponding to the grid points in `f`.
delta : array-like, optional
Spacing between the grid points in `f`. Should be one item less than the size
of `f` along `axis`.
Returns
-------
array-like
The first derivative calculated along the selected axis.
See Also
--------
second_derivative
"""
n, axis, delta = _process_deriv_args(f, kwargs)
# create slice objects --- initially all are [:, :, ..., :]
slice0 = [slice(None)] * n
slice1 = [slice(None)] * n
slice2 = [slice(None)] * n
delta_slice0 = [slice(None)] * n
delta_slice1 = [slice(None)] * n
# First handle centered case
slice0[axis] = slice(None, -2)
slice1[axis] = slice(1, -1)
slice2[axis] = slice(2, None)
delta_slice0[axis] = slice(None, -1)
delta_slice1[axis] = slice(1, None)
combined_delta = delta[tuple(delta_slice0)] + delta[tuple(delta_slice1)]
delta_diff = delta[tuple(delta_slice1)] - delta[tuple(delta_slice0)]
center = (- delta[tuple(delta_slice1)] / (combined_delta * delta[tuple(delta_slice0)])
* f[tuple(slice0)]
+ delta_diff / (delta[tuple(delta_slice0)] * delta[tuple(delta_slice1)])
* f[tuple(slice1)]
+ delta[tuple(delta_slice0)] / (combined_delta * delta[tuple(delta_slice1)])
* f[tuple(slice2)])
# Fill in "left" edge with forward difference
slice0[axis] = slice(None, 1)
slice1[axis] = slice(1, 2)
slice2[axis] = slice(2, 3)
delta_slice0[axis] = slice(None, 1)
delta_slice1[axis] = slice(1, 2)
combined_delta = delta[tuple(delta_slice0)] + delta[tuple(delta_slice1)]
big_delta = combined_delta + delta[tuple(delta_slice0)]
left = (- big_delta / (combined_delta * delta[tuple(delta_slice0)])
* f[tuple(slice0)]
+ combined_delta / (delta[tuple(delta_slice0)] * delta[tuple(delta_slice1)])
* f[tuple(slice1)]
- delta[tuple(delta_slice0)] / (combined_delta * delta[tuple(delta_slice1)])
* f[tuple(slice2)])
# Now the "right" edge with backward difference
slice0[axis] = slice(-3, -2)
slice1[axis] = slice(-2, -1)
slice2[axis] = slice(-1, None)
delta_slice0[axis] = slice(-2, -1)
delta_slice1[axis] = slice(-1, None)
combined_delta = delta[tuple(delta_slice0)] + delta[tuple(delta_slice1)]
big_delta = combined_delta + delta[tuple(delta_slice1)]
right = (delta[tuple(delta_slice1)] / (combined_delta * delta[tuple(delta_slice0)])
* f[tuple(slice0)]
- combined_delta / (delta[tuple(delta_slice0)] * delta[tuple(delta_slice1)])
* f[tuple(slice1)]
+ big_delta / (combined_delta * delta[tuple(delta_slice1)])
* f[tuple(slice2)])
return concatenate((left, center, right), axis=axis)
[docs]@exporter.export
@xarray_derivative_wrap
def second_derivative(f, **kwargs):
"""Calculate the second derivative of a grid of values.
Works for both regularly-spaced data and grids with varying spacing.
Either `x` or `delta` must be specified, or `f` must be given as an `xarray.DataArray` with
attached coordinate and projection information. If `f` is an `xarray.DataArray`, and `x` or
`delta` are given, `f` will be converted to a `pint.Quantity` and the derivative returned
as a `pint.Quantity`, otherwise, if neither `x` nor `delta` are given, the attached
coordinate information belonging to `axis` will be used and the derivative will be returned
as an `xarray.DataArray`.
This uses 3 points to calculate the derivative, using forward or backward at the edges of
the grid as appropriate, and centered elsewhere. The irregular spacing is handled
explicitly, using the formulation as specified by [Bowen2005]_.
Parameters
----------
f : array-like
Array of values of which to calculate the derivative
axis : int or str, optional
The array axis along which to take the derivative. If `f` is ndarray-like, must be an
integer. If `f` is a `DataArray`, can be a string (referring to either the coordinate
dimension name or the axis type) or integer (referring to axis number), unless using
implicit conversion to `pint.Quantity`, in which case it must be an integer. Defaults
to 0.
x : array-like, optional
The coordinate values corresponding to the grid points in `f`.
delta : array-like, optional
Spacing between the grid points in `f`. There should be one item less than the size
of `f` along `axis`.
Returns
-------
array-like
The second derivative calculated along the selected axis.
See Also
--------
first_derivative
"""
n, axis, delta = _process_deriv_args(f, kwargs)
# create slice objects --- initially all are [:, :, ..., :]
slice0 = [slice(None)] * n
slice1 = [slice(None)] * n
slice2 = [slice(None)] * n
delta_slice0 = [slice(None)] * n
delta_slice1 = [slice(None)] * n
# First handle centered case
slice0[axis] = slice(None, -2)
slice1[axis] = slice(1, -1)
slice2[axis] = slice(2, None)
delta_slice0[axis] = slice(None, -1)
delta_slice1[axis] = slice(1, None)
combined_delta = delta[tuple(delta_slice0)] + delta[tuple(delta_slice1)]
center = 2 * (f[tuple(slice0)] / (combined_delta * delta[tuple(delta_slice0)])
- f[tuple(slice1)] / (delta[tuple(delta_slice0)]
* delta[tuple(delta_slice1)])
+ f[tuple(slice2)] / (combined_delta * delta[tuple(delta_slice1)]))
# Fill in "left" edge
slice0[axis] = slice(None, 1)
slice1[axis] = slice(1, 2)
slice2[axis] = slice(2, 3)
delta_slice0[axis] = slice(None, 1)
delta_slice1[axis] = slice(1, 2)
combined_delta = delta[tuple(delta_slice0)] + delta[tuple(delta_slice1)]
left = 2 * (f[tuple(slice0)] / (combined_delta * delta[tuple(delta_slice0)])
- f[tuple(slice1)] / (delta[tuple(delta_slice0)] * delta[tuple(delta_slice1)])
+ f[tuple(slice2)] / (combined_delta * delta[tuple(delta_slice1)]))
# Now the "right" edge
slice0[axis] = slice(-3, -2)
slice1[axis] = slice(-2, -1)
slice2[axis] = slice(-1, None)
delta_slice0[axis] = slice(-2, -1)
delta_slice1[axis] = slice(-1, None)
combined_delta = delta[tuple(delta_slice0)] + delta[tuple(delta_slice1)]
right = 2 * (f[tuple(slice0)] / (combined_delta * delta[tuple(delta_slice0)])
- f[tuple(slice1)] / (delta[tuple(delta_slice0)] * delta[tuple(delta_slice1)])
+ f[tuple(slice2)] / (combined_delta * delta[tuple(delta_slice1)]))
return concatenate((left, center, right), axis=axis)
[docs]@exporter.export
def gradient(f, **kwargs):
"""Calculate the gradient of a grid of values.
Works for both regularly-spaced data, and grids with varying spacing.
Either `coordinates` or `deltas` must be specified, or `f` must be given as an
`xarray.DataArray` with attached coordinate and projection information. If `f` is an
`xarray.DataArray`, and `coordinates` or `deltas` are given, `f` will be converted to a
`pint.Quantity` and the gradient returned as a tuple of `pint.Quantity`, otherwise, if
neither `coordinates` nor `deltas` are given, the attached coordinate information belonging
to `axis` will be used and the gradient will be returned as a tuple of `xarray.DataArray`.
Parameters
----------
f : array-like
Array of values of which to calculate the derivative
coordinates : array-like, optional
Sequence of arrays containing the coordinate values corresponding to the
grid points in `f` in axis order.
deltas : array-like, optional
Sequence of arrays or scalars that specify the spacing between the grid points in `f`
in axis order. There should be one item less than the size of `f` along the applicable
axis.
axes : sequence, optional
Sequence of strings (if `f` is a `xarray.DataArray` and implicit conversion to
`pint.Quantity` is not used) or integers that specify the array axes along which to
take the derivatives. Defaults to all axes of `f`. If given, and used with
`coordinates` or `deltas`, its length must be less than or equal to that of the
`coordinates` or `deltas` given.
Returns
-------
tuple of array-like
The first derivative calculated along each specified axis of the original array
See Also
--------
laplacian, first_derivative
Notes
-----
`gradient` previously accepted `x` as a parameter for coordinate values. This has been
deprecated in 0.9 in favor of `coordinates`.
If this function is used without the `axes` parameter, the length of `coordinates` or
`deltas` (as applicable) should match the number of dimensions of `f`.
"""
pos_kwarg, positions, axes = _process_gradient_args(f, kwargs)
return tuple(first_derivative(f, axis=axis, **{pos_kwarg: positions[ind]})
for ind, axis in enumerate(axes))
[docs]@exporter.export
def laplacian(f, **kwargs):
"""Calculate the laplacian of a grid of values.
Works for both regularly-spaced data, and grids with varying spacing.
Either `coordinates` or `deltas` must be specified, or `f` must be given as an
`xarray.DataArray` with attached coordinate and projection information. If `f` is an
`xarray.DataArray`, and `coordinates` or `deltas` are given, `f` will be converted to a
`pint.Quantity` and the gradient returned as a tuple of `pint.Quantity`, otherwise, if
neither `coordinates` nor `deltas` are given, the attached coordinate information belonging
to `axis` will be used and the gradient will be returned as a tuple of `xarray.DataArray`.
Parameters
----------
f : array-like
Array of values of which to calculate the derivative
coordinates : array-like, optional
The coordinate values corresponding to the grid points in `f`
deltas : array-like, optional
Spacing between the grid points in `f`. There should be one item less than the size
of `f` along the applicable axis.
axes : sequence, optional
Sequence of strings (if `f` is a `xarray.DataArray` and implicit conversion to
`pint.Quantity` is not used) or integers that specify the array axes along which to
take the derivatives. Defaults to all axes of `f`. If given, and used with
`coordinates` or `deltas`, its length must be less than or equal to that of the
`coordinates` or `deltas` given.
Returns
-------
array-like
The laplacian
See Also
--------
gradient, second_derivative
Notes
-----
`laplacian` previously accepted `x` as a parameter for coordinate values. This has been
deprecated in 0.9 in favor of `coordinates`.
If this function is used without the `axes` parameter, the length of `coordinates` or
`deltas` (as applicable) should match the number of dimensions of `f`.
"""
pos_kwarg, positions, axes = _process_gradient_args(f, kwargs)
derivs = [second_derivative(f, axis=axis, **{pos_kwarg: positions[ind]})
for ind, axis in enumerate(axes)]
laplac = sum(derivs)
if isinstance(derivs[0], xr.DataArray):
# Patch in the units that are dropped
laplac.attrs['units'] = derivs[0].attrs['units']
return laplac
def _broadcast_to_axis(arr, axis, ndim):
"""Handle reshaping coordinate array to have proper dimensionality.
This puts the values along the specified axis.
"""
if arr.ndim == 1 and arr.ndim < ndim:
new_shape = [1] * ndim
new_shape[axis] = arr.size
arr = arr.reshape(*new_shape)
return arr
def _process_gradient_args(f, kwargs):
"""Handle common processing of arguments for gradient and gradient-like functions."""
axes = kwargs.get('axes', range(f.ndim))
def _check_length(positions):
if 'axes' in kwargs and len(positions) < len(axes):
raise ValueError('Length of "coordinates" or "deltas" cannot be less than that '
'of "axes".')
elif 'axes' not in kwargs and len(positions) != len(axes):
raise ValueError('Length of "coordinates" or "deltas" must match the number of '
'dimensions of "f" when "axes" is not given.')
if 'deltas' in kwargs:
if 'coordinates' in kwargs or 'x' in kwargs:
raise ValueError('Cannot specify both "coordinates" and "deltas".')
_check_length(kwargs['deltas'])
return 'delta', kwargs['deltas'], axes
elif 'coordinates' in kwargs:
_check_length(kwargs['coordinates'])
return 'x', kwargs['coordinates'], axes
elif 'x' in kwargs:
warnings.warn('The use of "x" as a parameter for coordinate values has been '
'deprecated. Use "coordinates" instead.', metpyDeprecation)
_check_length(kwargs['x'])
return 'x', kwargs['x'], axes
elif isinstance(f, xr.DataArray):
return 'pass', axes, axes # only the axis argument matters
else:
raise ValueError('Must specify either "coordinates" or "deltas" for value positions '
'when "f" is not a DataArray.')
def _process_deriv_args(f, kwargs):
"""Handle common processing of arguments for derivative functions."""
n = f.ndim
axis = normalize_axis_index(kwargs.get('axis', 0), n)
if f.shape[axis] < 3:
raise ValueError('f must have at least 3 point along the desired axis.')
if 'delta' in kwargs:
if 'x' in kwargs:
raise ValueError('Cannot specify both "x" and "delta".')
delta = atleast_1d(kwargs['delta'])
if delta.size == 1:
diff_size = list(f.shape)
diff_size[axis] -= 1
delta_units = getattr(delta, 'units', None)
delta = np.broadcast_to(delta, diff_size, subok=True)
if delta_units is not None:
delta = delta * delta_units
else:
delta = _broadcast_to_axis(delta, axis, n)
elif 'x' in kwargs:
x = _broadcast_to_axis(kwargs['x'], axis, n)
delta = diff(x, axis=axis)
else:
raise ValueError('Must specify either "x" or "delta" for value positions.')
return n, axis, delta
[docs]@exporter.export
@preprocess_xarray
def parse_angle(input_dir):
"""Calculate the meteorological angle from directional text.
Works for abbrieviations or whole words (E -> 90 | South -> 180)
and also is able to parse 22.5 degreee angles such as ESE/East South East
Parameters
----------
input_dir : string or array-like strings
Directional text such as west, [south-west, ne], etc
Returns
-------
angle
The angle in degrees
"""
if isinstance(input_dir, str):
# abb_dirs = abbrieviated directions
abb_dirs = [_abbrieviate_direction(input_dir)]
elif isinstance(input_dir, list):
input_dir_str = ','.join(input_dir)
abb_dir_str = _abbrieviate_direction(input_dir_str)
abb_dirs = abb_dir_str.split(',')
return itemgetter(*abb_dirs)(DIR_DICT)
def _abbrieviate_direction(ext_dir_str):
"""Convert extended (non-abbrievated) directions to abbrieviation."""
return (ext_dir_str
.upper()
.replace('_', '')
.replace('-', '')
.replace(' ', '')
.replace('NORTH', 'N')
.replace('EAST', 'E')
.replace('SOUTH', 'S')
.replace('WEST', 'W')
)