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@ -1,7 +1,6 @@
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#!/usr/bin/env python
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#!/usr/bin/env python
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from __future__ import absolute_import, division
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from __future__ import absolute_import, division
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import numpy as np
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import numpy as np
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import scipy.signal
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# import scipy.sparse.linalg # @UnusedImport
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# import scipy.sparse.linalg # @UnusedImport
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import scipy.sparse as sparse
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import scipy.sparse as sparse
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from numpy import ones, zeros, prod, sin, diff, pi, inf, vstack, linspace
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from numpy import ones, zeros, prod, sin, diff, pi, inf, vstack, linspace
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@ -106,12 +105,15 @@ def _get_turnpoint(xvals):
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turnpoint = 0
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turnpoint = 0
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last = len(xvals)
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last = len(xvals)
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if xvals[0] < xvals[1]: # x is increasing?
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if xvals[0] < xvals[1]: # x is increasing?
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compare = lambda a, b: a < b
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def compare(a, b):
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return a < b
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else: # no, x is decreasing
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else: # no, x is decreasing
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compare = lambda a, b: a > b
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def compare(a, b):
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return a > b
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for i in range(1, last): # yes
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for i in range(1, last): # yes
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if compare(xvals[i], xvals[i - 1]): # search where x starts to fall or rise
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# search where x starts to fall or rise
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if compare(xvals[i], xvals[i - 1]):
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turnpoint = i
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turnpoint = i
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break
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break
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@ -245,44 +247,52 @@ def sgolay2d(z, window_size, order, derivative=None):
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Z = np.zeros((new_shape))
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Z = np.zeros((new_shape))
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# top band
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# top band
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band = z[0, :]
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band = z[0, :]
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Z[:half_size, half_size:-half_size] = band - np.abs(np.flipud(z[1:half_size + 1, :]) - band)
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Z[:half_size, half_size:-half_size] = band - \
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np.abs(np.flipud(z[1:half_size + 1, :]) - band)
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# bottom band
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# bottom band
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band = z[-1, :]
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band = z[-1, :]
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Z[-half_size:, half_size:-half_size] = band + np.abs(np.flipud(z[-half_size - 1:-1, :]) - band)
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Z[-half_size:, half_size:-half_size] = band + \
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np.abs(np.flipud(z[-half_size - 1:-1, :]) - band)
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# left band
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# left band
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band = np.tile(z[:, 0].reshape(-1, 1), [1, half_size])
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band = np.tile(z[:, 0].reshape(-1, 1), [1, half_size])
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Z[half_size:-half_size, :half_size] = band - np.abs(np.fliplr(z[:, 1:half_size + 1]) - band)
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Z[half_size:-half_size, :half_size] = band - \
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np.abs(np.fliplr(z[:, 1:half_size + 1]) - band)
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# right band
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# right band
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band = np.tile(z[:, -1].reshape(-1, 1), [1, half_size])
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band = np.tile(z[:, -1].reshape(-1, 1), [1, half_size])
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Z[half_size:-half_size, -half_size:] = band + np.abs(np.fliplr(z[:, -half_size - 1:-1]) - band)
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Z[half_size:-half_size, -half_size:] = band + \
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np.abs(np.fliplr(z[:, -half_size - 1:-1]) - band)
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# central band
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# central band
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Z[half_size:-half_size, half_size:-half_size] = z
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Z[half_size:-half_size, half_size:-half_size] = z
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# top left corner
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# top left corner
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band = z[0, 0]
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band = z[0, 0]
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Z[:half_size, :half_size] = band - \
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Z[:half_size, :half_size] = band - \
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np.abs(np.flipud(np.fliplr(z[1:half_size + 1, 1:half_size + 1])) - band)
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np.abs(
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np.flipud(np.fliplr(z[1:half_size + 1, 1:half_size + 1])) - band)
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# bottom right corner
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# bottom right corner
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band = z[-1, -1]
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band = z[-1, -1]
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Z[-half_size:, -half_size:] = band + \
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Z[-half_size:, -half_size:] = band + \
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np.abs(np.flipud(np.fliplr(z[-half_size - 1:-1, -half_size - 1:-1])) - band)
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np.abs(
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np.flipud(np.fliplr(z[-half_size - 1:-1, -half_size - 1:-1])) - band)
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# top right corner
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# top right corner
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band = Z[half_size, -half_size:]
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band = Z[half_size, -half_size:]
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Z[:half_size, -half_size:] = band - \
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Z[:half_size, -half_size:] = band - \
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np.abs(np.flipud(Z[half_size + 1:2 * half_size + 1, -half_size:]) - band)
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np.abs(
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np.flipud(Z[half_size + 1:2 * half_size + 1, -half_size:]) - band)
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# bottom left corner
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# bottom left corner
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band = Z[-half_size:, half_size].reshape(-1, 1)
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band = Z[-half_size:, half_size].reshape(-1, 1)
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Z[-half_size:, :half_size] = band - \
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Z[-half_size:, :half_size] = band - \
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np.abs(np.fliplr(Z[-half_size:, half_size + 1:2 * half_size + 1]) - band)
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np.abs(
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np.fliplr(Z[-half_size:, half_size + 1:2 * half_size + 1]) - band)
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# solve system and convolve
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# solve system and convolve
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sgn = {None:1}.get(derivative , -1)
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sgn = {None: 1}.get(derivative, -1)
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dims = {None: (0,), 'col': (1,), 'row': (2,), 'both':(1, 2)}[derivative]
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dims = {None: (0,), 'col': (1,), 'row': (2,), 'both': (1, 2)}[derivative]
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res = tuple(fftconvolve(Z, sgn * np.linalg.pinv(A)[i].reshape((window_size, -1)), mode='valid')
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res = tuple(fftconvolve(Z, sgn * np.linalg.pinv(A)[i].reshape((window_size, -1)), mode='valid')
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for i in dims)
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for i in dims)
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if len(dims)>1:
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if len(dims) > 1:
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return res
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return res
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return res[0]
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return res[0]
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@ -597,7 +607,8 @@ class SmoothSpline(PPform):
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di = di.T
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di = di.T
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ci = ci.T
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ci = ci.T
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ai = ai.T
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ai = ai.T
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coefs = vstack([val.ravel() for val in [di, ci, bi, ai] if val.size>0])
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coefs = vstack([val.ravel()
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for val in [di, ci, bi, ai] if val.size > 0])
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return coefs
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return coefs
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def _compute_coefs(self, xx, yy, p=None, var=1):
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def _compute_coefs(self, xx, yy, p=None, var=1):
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@ -643,7 +654,7 @@ class SmoothSpline(PPform):
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QQ = (6 * (1 - p)) * (QDQ) + p * R
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QQ = (6 * (1 - p)) * (QDQ) + p * R
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return QQ
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return QQ
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def _compute_u(self,QQ, p, dydx, n):
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def _compute_u(self, QQ, p, dydx, n):
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# Make sure it uses symmetric matrix solver
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# Make sure it uses symmetric matrix solver
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ddydx = diff(dydx, axis=0)
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ddydx = diff(dydx, axis=0)
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# sp.linalg.use_solver(useUmfpack=True)
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# sp.linalg.use_solver(useUmfpack=True)
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@ -715,7 +726,7 @@ def _catmull_rom_slope(x, y, dx, dydx, *args):
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def _cardinal_slope(x, y, dx, dydx, tension):
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def _cardinal_slope(x, y, dx, dydx, tension):
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yp = (1-tension) * _catmull_rom_slope(x, y, dx, dydx)
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yp = (1 - tension) * _catmull_rom_slope(x, y, dx, dydx)
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return yp
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return yp
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@ -978,6 +989,7 @@ class StinemanInterp(object):
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--------
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--------
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slopes, Pchip
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slopes, Pchip
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'''
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'''
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def __init__(self, x, y, yp=None, method='parabola', monotone=False):
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def __init__(self, x, y, yp=None, method='parabola', monotone=False):
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if yp is None:
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if yp is None:
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yp = slopes(x, y, method, monotone=monotone)
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yp = slopes(x, y, method, monotone=monotone)
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@ -1171,7 +1183,7 @@ def interp3(x, y, z, v, xi, yi, zi, method='cubic'):
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def somefunc(x, y, z):
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def somefunc(x, y, z):
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return x**2 + y**2 - z**2 + x*y*z
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return x**2 + y**2 - z**2 + x * y * z
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def test_interp3():
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def test_interp3():
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@ -1214,7 +1226,6 @@ def test_smoothing_spline():
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plt.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
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plt.plot(x, y, x1, y1, '.', x1, dy1, 'ro', x1, y01, 'r-')
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plt.show('hold')
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plt.show('hold')
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pass
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# tck = interpolate.splrep(x, y, s=len(x))
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# tck = interpolate.splrep(x, y, s=len(x))
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