464 lines
15 KiB
Python
464 lines
15 KiB
Python
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from __future__ import division, print_function, absolute_import
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import os
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import numpy as np
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from numpy.testing import (assert_equal, assert_allclose, assert_,
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assert_almost_equal, assert_array_almost_equal)
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from pytest import raises as assert_raises
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from numpy import array, asarray, pi, sin, cos, arange, dot, ravel, sqrt, round
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from scipy import interpolate
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from scipy.interpolate.fitpack import (splrep, splev, bisplrep, bisplev,
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sproot, splprep, splint, spalde, splder, splantider, insert, dblint)
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from scipy.interpolate.dfitpack import regrid_smth
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def data_file(basename):
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return os.path.join(os.path.abspath(os.path.dirname(__file__)),
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'data', basename)
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def norm2(x):
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return sqrt(dot(x.T,x))
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def f1(x,d=0):
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if d is None:
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return "sin"
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if x is None:
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return "sin(x)"
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if d % 4 == 0:
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return sin(x)
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if d % 4 == 1:
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return cos(x)
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if d % 4 == 2:
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return -sin(x)
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if d % 4 == 3:
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return -cos(x)
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def f2(x,y=0,dx=0,dy=0):
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if x is None:
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return "sin(x+y)"
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d = dx+dy
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if d % 4 == 0:
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return sin(x+y)
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if d % 4 == 1:
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return cos(x+y)
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if d % 4 == 2:
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return -sin(x+y)
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if d % 4 == 3:
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return -cos(x+y)
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def makepairs(x, y):
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"""Helper function to create an array of pairs of x and y."""
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# Or itertools.product (>= python 2.6)
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xy = array([[a, b] for a in asarray(x) for b in asarray(y)])
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return xy.T
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def put(*a):
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"""Produce some output if file run directly"""
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import sys
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if hasattr(sys.modules['__main__'], '__put_prints'):
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sys.stderr.write("".join(map(str, a)) + "\n")
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class TestSmokeTests(object):
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"""
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Smoke tests (with a few asserts) for fitpack routines -- mostly
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check that they are runnable
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"""
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def check_1(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,at=0,xb=None,xe=None):
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if xb is None:
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xb = a
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if xe is None:
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xe = b
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x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
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x1 = a+(b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
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v,v1 = f(x),f(x1)
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nk = []
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def err_est(k, d):
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# Assume f has all derivatives < 1
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h = 1.0/float(N)
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tol = 5 * h**(.75*(k-d))
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if s > 0:
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tol += 1e5*s
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return tol
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for k in range(1,6):
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tck = splrep(x,v,s=s,per=per,k=k,xe=xe)
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if at:
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t = tck[0][k:-k]
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else:
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t = x1
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nd = []
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for d in range(k+1):
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tol = err_est(k, d)
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err = norm2(f(t,d)-splev(t,tck,d)) / norm2(f(t,d))
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assert_(err < tol, (k, d, err, tol))
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nd.append((err, tol))
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nk.append(nd)
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put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" % (f(None),
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repr(round(xb,3)),repr(round(xe,3)),
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repr(round(a,3)),repr(round(b,3))))
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if at:
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str = "at knots"
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else:
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str = "at the middle of nodes"
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put(" per=%d s=%s Evaluation %s" % (per,repr(s),str))
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put(" k : |f-s|^2 |f'-s'| |f''-.. |f'''-. |f''''- |f'''''")
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k = 1
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for l in nk:
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put(' %d : ' % k)
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for r in l:
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put(' %.1e %.1e' % r)
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put('\n')
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k = k+1
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def check_2(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
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ia=0,ib=2*pi,dx=0.2*pi):
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if xb is None:
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xb = a
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if xe is None:
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xe = b
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x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
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v = f(x)
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def err_est(k, d):
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# Assume f has all derivatives < 1
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h = 1.0/float(N)
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tol = 5 * h**(.75*(k-d))
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if s > 0:
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tol += 1e5*s
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return tol
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nk = []
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for k in range(1,6):
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tck = splrep(x,v,s=s,per=per,k=k,xe=xe)
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nk.append([splint(ia,ib,tck),spalde(dx,tck)])
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put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" % (f(None),
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repr(round(xb,3)),repr(round(xe,3)),
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repr(round(a,3)),repr(round(b,3))))
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put(" per=%d s=%s N=%d [a, b] = [%s, %s] dx=%s" % (per,repr(s),N,repr(round(ia,3)),repr(round(ib,3)),repr(round(dx,3))))
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put(" k : int(s,[a,b]) Int.Error Rel. error of s^(d)(dx) d = 0, .., k")
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k = 1
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for r in nk:
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if r[0] < 0:
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sr = '-'
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else:
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sr = ' '
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put(" %d %s%.8f %.1e " % (k,sr,abs(r[0]),
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abs(r[0]-(f(ib,-1)-f(ia,-1)))))
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d = 0
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for dr in r[1]:
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err = abs(1-dr/f(dx,d))
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tol = err_est(k, d)
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assert_(err < tol, (k, d))
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put(" %.1e %.1e" % (err, tol))
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d = d+1
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put("\n")
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k = k+1
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def check_3(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
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ia=0,ib=2*pi,dx=0.2*pi):
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if xb is None:
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xb = a
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if xe is None:
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xe = b
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x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
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v = f(x)
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put(" k : Roots of s(x) approx %s x in [%s,%s]:" %
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(f(None),repr(round(a,3)),repr(round(b,3))))
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for k in range(1,6):
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tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
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if k == 3:
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roots = sproot(tck)
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assert_allclose(splev(roots, tck), 0, atol=1e-10, rtol=1e-10)
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assert_allclose(roots, pi*array([1, 2, 3, 4]), rtol=1e-3)
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put(' %d : %s' % (k, repr(roots.tolist())))
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else:
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assert_raises(ValueError, sproot, tck)
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def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
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ia=0,ib=2*pi,dx=0.2*pi):
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if xb is None:
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xb = a
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if xe is None:
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xe = b
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x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
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x1 = a + (b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
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v,v1 = f(x),f(x1)
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put(" u = %s N = %d" % (repr(round(dx,3)),N))
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put(" k : [x(u), %s(x(u))] Error of splprep Error of splrep " % (f(0,None)))
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for k in range(1,6):
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tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
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tck = splrep(x,v,s=s,per=per,k=k)
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uv = splev(dx,tckp)
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err1 = abs(uv[1]-f(uv[0]))
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err2 = abs(splev(uv[0],tck)-f(uv[0]))
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assert_(err1 < 1e-2)
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assert_(err2 < 1e-2)
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put(" %d : %s %.1e %.1e" %
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(k,repr([round(z,3) for z in uv]),
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err1,
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err2))
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put("Derivatives of parametric cubic spline at u (first function):")
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k = 3
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tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
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for d in range(1,k+1):
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uv = splev(dx,tckp,d)
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put(" %s " % (repr(uv[0])))
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def check_5(self,f=f2,kx=3,ky=3,xb=0,xe=2*pi,yb=0,ye=2*pi,Nx=20,Ny=20,s=0):
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x = xb+(xe-xb)*arange(Nx+1,dtype=float)/float(Nx)
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y = yb+(ye-yb)*arange(Ny+1,dtype=float)/float(Ny)
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xy = makepairs(x,y)
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tck = bisplrep(xy[0],xy[1],f(xy[0],xy[1]),s=s,kx=kx,ky=ky)
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tt = [tck[0][kx:-kx],tck[1][ky:-ky]]
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t2 = makepairs(tt[0],tt[1])
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v1 = bisplev(tt[0],tt[1],tck)
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v2 = f2(t2[0],t2[1])
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v2.shape = len(tt[0]),len(tt[1])
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err = norm2(ravel(v1-v2))
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assert_(err < 1e-2, err)
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put(err)
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def test_smoke_splrep_splev(self):
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put("***************** splrep/splev")
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self.check_1(s=1e-6)
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self.check_1()
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self.check_1(at=1)
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self.check_1(per=1)
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self.check_1(per=1,at=1)
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self.check_1(b=1.5*pi)
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self.check_1(b=1.5*pi,xe=2*pi,per=1,s=1e-1)
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def test_smoke_splint_spalde(self):
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put("***************** splint/spalde")
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self.check_2()
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self.check_2(per=1)
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self.check_2(ia=0.2*pi,ib=pi)
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self.check_2(ia=0.2*pi,ib=pi,N=50)
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def test_smoke_sproot(self):
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put("***************** sproot")
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self.check_3(a=0.1,b=15)
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def test_smoke_splprep_splrep_splev(self):
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put("***************** splprep/splrep/splev")
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self.check_4()
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self.check_4(N=50)
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def test_smoke_bisplrep_bisplev(self):
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put("***************** bisplev")
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self.check_5()
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class TestSplev(object):
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def test_1d_shape(self):
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x = [1,2,3,4,5]
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y = [4,5,6,7,8]
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tck = splrep(x, y)
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z = splev([1], tck)
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assert_equal(z.shape, (1,))
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z = splev(1, tck)
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assert_equal(z.shape, ())
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def test_2d_shape(self):
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x = [1, 2, 3, 4, 5]
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y = [4, 5, 6, 7, 8]
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tck = splrep(x, y)
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t = np.array([[1.0, 1.5, 2.0, 2.5],
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[3.0, 3.5, 4.0, 4.5]])
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z = splev(t, tck)
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z0 = splev(t[0], tck)
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z1 = splev(t[1], tck)
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assert_equal(z, np.row_stack((z0, z1)))
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def test_extrapolation_modes(self):
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# test extrapolation modes
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# * if ext=0, return the extrapolated value.
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# * if ext=1, return 0
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# * if ext=2, raise a ValueError
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# * if ext=3, return the boundary value.
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x = [1,2,3]
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y = [0,2,4]
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tck = splrep(x, y, k=1)
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rstl = [[-2, 6], [0, 0], None, [0, 4]]
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for ext in (0, 1, 3):
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assert_array_almost_equal(splev([0, 4], tck, ext=ext), rstl[ext])
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assert_raises(ValueError, splev, [0, 4], tck, ext=2)
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class TestSplder(object):
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def setup_method(self):
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# non-uniform grid, just to make it sure
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x = np.linspace(0, 1, 100)**3
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y = np.sin(20 * x)
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self.spl = splrep(x, y)
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# double check that knots are non-uniform
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assert_(np.diff(self.spl[0]).ptp() > 0)
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def test_inverse(self):
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# Check that antiderivative + derivative is identity.
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for n in range(5):
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spl2 = splantider(self.spl, n)
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spl3 = splder(spl2, n)
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assert_allclose(self.spl[0], spl3[0])
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assert_allclose(self.spl[1], spl3[1])
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assert_equal(self.spl[2], spl3[2])
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def test_splder_vs_splev(self):
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# Check derivative vs. FITPACK
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for n in range(3+1):
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# Also extrapolation!
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xx = np.linspace(-1, 2, 2000)
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if n == 3:
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# ... except that FITPACK extrapolates strangely for
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# order 0, so let's not check that.
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xx = xx[(xx >= 0) & (xx <= 1)]
|
||
|
|
|
||
|
|
dy = splev(xx, self.spl, n)
|
||
|
|
spl2 = splder(self.spl, n)
|
||
|
|
dy2 = splev(xx, spl2)
|
||
|
|
if n == 1:
|
||
|
|
assert_allclose(dy, dy2, rtol=2e-6)
|
||
|
|
else:
|
||
|
|
assert_allclose(dy, dy2)
|
||
|
|
|
||
|
|
def test_splantider_vs_splint(self):
|
||
|
|
# Check antiderivative vs. FITPACK
|
||
|
|
spl2 = splantider(self.spl)
|
||
|
|
|
||
|
|
# no extrapolation, splint assumes function is zero outside
|
||
|
|
# range
|
||
|
|
xx = np.linspace(0, 1, 20)
|
||
|
|
|
||
|
|
for x1 in xx:
|
||
|
|
for x2 in xx:
|
||
|
|
y1 = splint(x1, x2, self.spl)
|
||
|
|
y2 = splev(x2, spl2) - splev(x1, spl2)
|
||
|
|
assert_allclose(y1, y2)
|
||
|
|
|
||
|
|
def test_order0_diff(self):
|
||
|
|
assert_raises(ValueError, splder, self.spl, 4)
|
||
|
|
|
||
|
|
def test_kink(self):
|
||
|
|
# Should refuse to differentiate splines with kinks
|
||
|
|
|
||
|
|
spl2 = insert(0.5, self.spl, m=2)
|
||
|
|
splder(spl2, 2) # Should work
|
||
|
|
assert_raises(ValueError, splder, spl2, 3)
|
||
|
|
|
||
|
|
spl2 = insert(0.5, self.spl, m=3)
|
||
|
|
splder(spl2, 1) # Should work
|
||
|
|
assert_raises(ValueError, splder, spl2, 2)
|
||
|
|
|
||
|
|
spl2 = insert(0.5, self.spl, m=4)
|
||
|
|
assert_raises(ValueError, splder, spl2, 1)
|
||
|
|
|
||
|
|
def test_multidim(self):
|
||
|
|
# c can have trailing dims
|
||
|
|
for n in range(3):
|
||
|
|
t, c, k = self.spl
|
||
|
|
c2 = np.c_[c, c, c]
|
||
|
|
c2 = np.dstack((c2, c2))
|
||
|
|
|
||
|
|
spl2 = splantider((t, c2, k), n)
|
||
|
|
spl3 = splder(spl2, n)
|
||
|
|
|
||
|
|
assert_allclose(t, spl3[0])
|
||
|
|
assert_allclose(c2, spl3[1])
|
||
|
|
assert_equal(k, spl3[2])
|
||
|
|
|
||
|
|
|
||
|
|
class TestBisplrep(object):
|
||
|
|
def test_overflow(self):
|
||
|
|
a = np.linspace(0, 1, 620)
|
||
|
|
b = np.linspace(0, 1, 620)
|
||
|
|
x, y = np.meshgrid(a, b)
|
||
|
|
z = np.random.rand(*x.shape)
|
||
|
|
assert_raises(OverflowError, bisplrep, x.ravel(), y.ravel(), z.ravel(), s=0)
|
||
|
|
|
||
|
|
def test_regression_1310(self):
|
||
|
|
# Regression test for gh-1310
|
||
|
|
data = np.load(data_file('bug-1310.npz'))['data']
|
||
|
|
|
||
|
|
# Shouldn't crash -- the input data triggers work array sizes
|
||
|
|
# that caused previously some data to not be aligned on
|
||
|
|
# sizeof(double) boundaries in memory, which made the Fortran
|
||
|
|
# code to crash when compiled with -O3
|
||
|
|
bisplrep(data[:,0], data[:,1], data[:,2], kx=3, ky=3, s=0,
|
||
|
|
full_output=True)
|
||
|
|
|
||
|
|
|
||
|
|
def test_dblint():
|
||
|
|
# Basic test to see it runs and gives the correct result on a trivial
|
||
|
|
# problem. Note that `dblint` is not exposed in the interpolate namespace.
|
||
|
|
x = np.linspace(0, 1)
|
||
|
|
y = np.linspace(0, 1)
|
||
|
|
xx, yy = np.meshgrid(x, y)
|
||
|
|
rect = interpolate.RectBivariateSpline(x, y, 4 * xx * yy)
|
||
|
|
tck = list(rect.tck)
|
||
|
|
tck.extend(rect.degrees)
|
||
|
|
|
||
|
|
assert_almost_equal(dblint(0, 1, 0, 1, tck), 1)
|
||
|
|
assert_almost_equal(dblint(0, 0.5, 0, 1, tck), 0.25)
|
||
|
|
assert_almost_equal(dblint(0.5, 1, 0, 1, tck), 0.75)
|
||
|
|
assert_almost_equal(dblint(-100, 100, -100, 100, tck), 1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_splev_der_k():
|
||
|
|
# regression test for gh-2188: splev(x, tck, der=k) gives garbage or crashes
|
||
|
|
# for x outside of knot range
|
||
|
|
|
||
|
|
# test case from gh-2188
|
||
|
|
tck = (np.array([0., 0., 2.5, 2.5]),
|
||
|
|
np.array([-1.56679978, 2.43995873, 0., 0.]),
|
||
|
|
1)
|
||
|
|
t, c, k = tck
|
||
|
|
x = np.array([-3, 0, 2.5, 3])
|
||
|
|
|
||
|
|
# an explicit form of the linear spline
|
||
|
|
assert_allclose(splev(x, tck), c[0] + (c[1] - c[0]) * x/t[2])
|
||
|
|
assert_allclose(splev(x, tck, 1), (c[1]-c[0]) / t[2])
|
||
|
|
|
||
|
|
# now check a random spline vs splder
|
||
|
|
np.random.seed(1234)
|
||
|
|
x = np.sort(np.random.random(30))
|
||
|
|
y = np.random.random(30)
|
||
|
|
t, c, k = splrep(x, y)
|
||
|
|
|
||
|
|
x = [t[0] - 1., t[-1] + 1.]
|
||
|
|
tck2 = splder((t, c, k), k)
|
||
|
|
assert_allclose(splev(x, (t, c, k), k), splev(x, tck2))
|
||
|
|
|
||
|
|
|
||
|
|
def test_bisplev_integer_overflow():
|
||
|
|
np.random.seed(1)
|
||
|
|
|
||
|
|
x = np.linspace(0, 1, 11)
|
||
|
|
y = x
|
||
|
|
z = np.random.randn(11, 11).ravel()
|
||
|
|
kx = 1
|
||
|
|
ky = 1
|
||
|
|
|
||
|
|
nx, tx, ny, ty, c, fp, ier = regrid_smth(
|
||
|
|
x, y, z, None, None, None, None, kx=kx, ky=ky, s=0.0)
|
||
|
|
tck = (tx[:nx], ty[:ny], c[:(nx - kx - 1) * (ny - ky - 1)], kx, ky)
|
||
|
|
|
||
|
|
xp = np.zeros([2621440])
|
||
|
|
yp = np.zeros([2621440])
|
||
|
|
|
||
|
|
assert_raises((RuntimeError, MemoryError), bisplev, xp, yp, tck)
|
||
|
|
|