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# Copyright (c) 2008-2015 MetPy Developers. |
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# Distributed under the terms of the BSD 3-Clause License. |
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# SPDX-License-Identifier: BSD-3-Clause |
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"""Contains a collection of generally useful calculation tools.""" |
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import numpy as np |
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import numpy.ma as ma |
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from ..package_tools import Exporter |
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exporter = Exporter(globals()) |
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@exporter.export |
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def resample_nn_1d(a, centers): |
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"""Return one-dimensional nearest-neighbor indexes based on user-specified centers. |
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Parameters |
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---------- |
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a : array-like |
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1-dimensional array of numeric values from which to |
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extract indexes of nearest-neighbors |
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centers : array-like |
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1-dimensional array of numeric values representing a subset of values to approximate |
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Returns |
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------- |
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An array of indexes representing values closest to given array values |
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""" |
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ix = [] |
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for center in centers: |
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index = (np.abs(a - center)).argmin() |
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if index not in ix: |
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ix.append(index) |
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return ix |
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@exporter.export |
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def nearest_intersection_idx(a, b): |
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"""Determine the index of the point just before two lines with common x values. |
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Parameters |
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---------- |
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a : array-like |
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1-dimensional array of y-values for line 1 |
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b : array-like |
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1-dimensional array of y-values for line 2 |
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Returns |
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------- |
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An array of indexes representing the index of the values |
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just before the intersection(s) of the two lines. |
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""" |
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# Difference in the two y-value sets |
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difference = a - b |
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# Determine the point just before the intersection of the lines |
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# Will return multiple points for multiple intersections |
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sign_change_idx, = np.nonzero(np.diff(np.sign(difference))) |
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return sign_change_idx |
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@exporter.export |
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def find_intersections(x, a, b, direction='all'): |
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"""Calculate the best estimate of intersection. |
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Calculates the best estimates of the intersection of two y-value |
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data sets that share a common x-value set. |
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Parameters |
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---------- |
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x : array-like |
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1-dimensional array of numeric x-values |
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a : array-like |
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1-dimensional array of y-values for line 1 |
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b : array-like |
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1-dimensional array of y-values for line 2 |
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direction : string |
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specifies direction of crossing. 'all', 'increasing' (a becoming greater than b), |
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or 'decreasing' (b becoming greater than a). |
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Returns |
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------- |
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A tuple (x, y) of array-like with the x and y coordinates of the |
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intersections of the lines. |
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""" |
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# Find the index of the points just before the intersection(s) |
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nearest_idx = nearest_intersection_idx(a, b) |
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next_idx = nearest_idx + 1 |
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# Determine the sign of the change |
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sign_change = np.sign(a[next_idx] - b[next_idx]) |
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# x-values around each intersection |
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_, x0 = _next_non_masked_element(x, nearest_idx) |
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_, x1 = _next_non_masked_element(x, next_idx) |
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# y-values around each intersection for the first line |
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_, a0 = _next_non_masked_element(a, nearest_idx) |
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_, a1 = _next_non_masked_element(a, next_idx) |
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# y-values around each intersection for the second line |
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_, b0 = _next_non_masked_element(b, nearest_idx) |
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_, b1 = _next_non_masked_element(b, next_idx) |
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# Calculate the x-intersection. This comes from finding the equations of the two lines, |
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# one through (x0, a0) and (x1, a1) and the other through (x0, b0) and (x1, b1), |
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# finding their intersection, and reducing with a bunch of algebra. |
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delta_y0 = a0 - b0 |
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delta_y1 = a1 - b1 |
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intersect_x = (delta_y1 * x0 - delta_y0 * x1) / (delta_y1 - delta_y0) |
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# Calculate the y-intersection of the lines. Just plug the x above into the equation |
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# for the line through the a points. One could solve for y like x above, but this |
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# causes weirder unit behavior and seems a little less good numerically. |
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intersect_y = ((intersect_x - x0) / (x1 - x0)) * (a1 - a0) + a0 |
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# Make a mask based on the direction of sign change desired |
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if direction == 'increasing': |
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mask = sign_change > 0 |
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elif direction == 'decreasing': |
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mask = sign_change < 0 |
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elif direction == 'all': |
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return intersect_x, intersect_y |
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else: |
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raise ValueError('Unknown option for direction: {0}'.format(str(direction))) |
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return intersect_x[mask], intersect_y[mask] |
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@exporter.export |
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def interpolate_nans(x, y, kind='linear'): |
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"""Interpolate NaN values in y. |
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Interpolate NaN values in the y dimension. Works with unsorted x values. |
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Parameters |
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---------- |
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x : array-like |
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1-dimensional array of numeric x-values |
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y : array-like |
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1-dimensional array of numeric y-values |
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kind : string |
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specifies the kind of interpolation x coordinate - 'linear' or 'log' |
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Returns |
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------- |
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An array of the y coordinate data with NaN values interpolated. |
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""" |
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x_sort_args = np.argsort(x) |
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x = x[x_sort_args] |
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y = y[x_sort_args] |
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nans = np.isnan(y) |
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if kind is 'linear': |
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y[nans] = np.interp(x[nans], x[~nans], y[~nans]) |
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elif kind is 'log': |
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y[nans] = np.interp(np.log(x[nans]), np.log(x[~nans]), y[~nans]) |
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else: |
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raise ValueError('Unknown option for kind: {0}'.format(str(kind))) |
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return y[x_sort_args] |
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def _next_non_masked_element(a, idx): |
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"""Return the next non masked element of a masked array. |
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If an array is masked, return the next non-masked element (if the given index is masked). |
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If no other unmasked points are after the given masked point, returns none. |
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Parameters |
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---------- |
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a : array-like |
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1-dimensional array of numeric values |
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idx : integer |
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index of requested element |
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Returns |
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------- |
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Index of next non-masked element and next non-masked element |
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""" |
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try: |
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next_idx = idx + a[idx:].mask.argmin() |
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if ma.is_masked(a[next_idx]): |
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return None, None |
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else: |
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return next_idx, a[next_idx] |
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except (AttributeError, TypeError, IndexError): |
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return idx, a[idx] |
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Unidata /
MetPy
