Current File : //lib/python3/dist-packages/scipy/interpolate/tests/test_fitpack.py
import itertools
import os
import numpy as np
from numpy.testing import (assert_equal, assert_allclose, assert_,
assert_almost_equal, assert_array_almost_equal)
from pytest import raises as assert_raises
import pytest
from scipy._lib._testutils import check_free_memory
from numpy import array, asarray, pi, sin, cos, arange, dot, ravel, sqrt, round
from scipy import interpolate
from scipy.interpolate._fitpack_py import (splrep, splev, bisplrep, bisplev,
sproot, splprep, splint, spalde, splder, splantider, insert, dblint)
from scipy.interpolate.dfitpack import regrid_smth
from scipy.interpolate._fitpack2 import dfitpack_int
def data_file(basename):
return os.path.join(os.path.abspath(os.path.dirname(__file__)),
'data', basename)
def norm2(x):
return sqrt(dot(x.T,x))
def f1(x,d=0):
if d is None:
return "sin"
if x is None:
return "sin(x)"
if d % 4 == 0:
return sin(x)
if d % 4 == 1:
return cos(x)
if d % 4 == 2:
return -sin(x)
if d % 4 == 3:
return -cos(x)
def f2(x,y=0,dx=0,dy=0):
if x is None:
return "sin(x+y)"
d = dx+dy
if d % 4 == 0:
return sin(x+y)
if d % 4 == 1:
return cos(x+y)
if d % 4 == 2:
return -sin(x+y)
if d % 4 == 3:
return -cos(x+y)
def makepairs(x, y):
"""Helper function to create an array of pairs of x and y."""
xy = array(list(itertools.product(asarray(x), asarray(y))))
return xy.T
def put(*a):
"""Produce some output if file run directly"""
import sys
if hasattr(sys.modules['__main__'], '__put_prints'):
sys.stderr.write("".join(map(str, a)) + "\n")
class TestSmokeTests:
"""
Smoke tests (with a few asserts) for fitpack routines -- mostly
check that they are runnable
"""
def check_1(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,at=0,xb=None,xe=None):
if xb is None:
xb = a
if xe is None:
xe = b
x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
x1 = a+(b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
v = f(x)
nk = []
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0/float(N)
tol = 5 * h**(.75*(k-d))
if s > 0:
tol += 1e5*s
return tol
for k in range(1,6):
tck = splrep(x,v,s=s,per=per,k=k,xe=xe)
if at:
t = tck[0][k:-k]
else:
t = x1
nd = []
for d in range(k+1):
tol = err_est(k, d)
err = norm2(f(t,d)-splev(t,tck,d)) / norm2(f(t,d))
assert_(err < tol, (k, d, err, tol))
nd.append((err, tol))
nk.append(nd)
put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" % (f(None),
repr(round(xb,3)),repr(round(xe,3)),
repr(round(a,3)),repr(round(b,3))))
if at:
str = "at knots"
else:
str = "at the middle of nodes"
put(" per=%d s=%s Evaluation %s" % (per,repr(s),str))
put(" k : |f-s|^2 |f'-s'| |f''-.. |f'''-. |f''''- |f'''''")
k = 1
for l in nk:
put(' %d : ' % k)
for r in l:
put(' %.1e %.1e' % r)
put('\n')
k = k+1
def check_2(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
v = f(x)
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0/float(N)
tol = 5 * h**(.75*(k-d))
if s > 0:
tol += 1e5*s
return tol
nk = []
for k in range(1,6):
tck = splrep(x,v,s=s,per=per,k=k,xe=xe)
nk.append([splint(ia,ib,tck),spalde(dx,tck)])
put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" % (f(None),
repr(round(xb,3)),repr(round(xe,3)),
repr(round(a,3)),repr(round(b,3))))
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))))
put(" k : int(s,[a,b]) Int.Error Rel. error of s^(d)(dx) d = 0, .., k")
k = 1
for r in nk:
if r[0] < 0:
sr = '-'
else:
sr = ' '
put(" %d %s%.8f %.1e " % (k,sr,abs(r[0]),
abs(r[0]-(f(ib,-1)-f(ia,-1)))))
d = 0
for dr in r[1]:
err = abs(1-dr/f(dx,d))
tol = err_est(k, d)
assert_(err < tol, (k, d))
put(" %.1e %.1e" % (err, tol))
d = d+1
put("\n")
k = k+1
def check_3(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
v = f(x)
put(" k : Roots of s(x) approx %s x in [%s,%s]:" %
(f(None),repr(round(a,3)),repr(round(b,3))))
for k in range(1,6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
if k == 3:
roots = sproot(tck)
assert_allclose(splev(roots, tck), 0, atol=1e-10, rtol=1e-10)
assert_allclose(roots, pi*array([1, 2, 3, 4]), rtol=1e-3)
put(' %d : %s' % (k, repr(roots.tolist())))
else:
assert_raises(ValueError, sproot, tck)
def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
x1 = a + (b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
v, _ = f(x),f(x1)
put(" u = %s N = %d" % (repr(round(dx,3)),N))
put(" k : [x(u), %s(x(u))] Error of splprep Error of splrep " % (f(0,None)))
for k in range(1,6):
tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
tck = splrep(x,v,s=s,per=per,k=k)
uv = splev(dx,tckp)
err1 = abs(uv[1]-f(uv[0]))
err2 = abs(splev(uv[0],tck)-f(uv[0]))
assert_(err1 < 1e-2)
assert_(err2 < 1e-2)
put(" %d : %s %.1e %.1e" %
(k,repr([round(z,3) for z in uv]),
err1,
err2))
put("Derivatives of parametric cubic spline at u (first function):")
k = 3
tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
for d in range(1,k+1):
uv = splev(dx,tckp,d)
put(" %s " % (repr(uv[0])))
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):
x = xb+(xe-xb)*arange(Nx+1,dtype=float)/float(Nx)
y = yb+(ye-yb)*arange(Ny+1,dtype=float)/float(Ny)
xy = makepairs(x,y)
tck = bisplrep(xy[0],xy[1],f(xy[0],xy[1]),s=s,kx=kx,ky=ky)
tt = [tck[0][kx:-kx],tck[1][ky:-ky]]
t2 = makepairs(tt[0],tt[1])
v1 = bisplev(tt[0],tt[1],tck)
v2 = f2(t2[0],t2[1])
v2.shape = len(tt[0]),len(tt[1])
err = norm2(ravel(v1-v2))
assert_(err < 1e-2, err)
put(err)
def test_smoke_splrep_splev(self):
put("***************** splrep/splev")
self.check_1(s=1e-6)
self.check_1()
self.check_1(at=1)
self.check_1(per=1)
self.check_1(per=1,at=1)
self.check_1(b=1.5*pi)
self.check_1(b=1.5*pi,xe=2*pi,per=1,s=1e-1)
def test_smoke_splint_spalde(self):
put("***************** splint/spalde")
self.check_2()
self.check_2(per=1)
self.check_2(ia=0.2*pi,ib=pi)
self.check_2(ia=0.2*pi,ib=pi,N=50)
def test_smoke_sproot(self):
put("***************** sproot")
self.check_3(a=0.1,b=15)
def test_smoke_splprep_splrep_splev(self):
put("***************** splprep/splrep/splev")
self.check_4()
self.check_4(N=50)
def test_smoke_bisplrep_bisplev(self):
put("***************** bisplev")
self.check_5()
class TestSplev:
def test_1d_shape(self):
x = [1,2,3,4,5]
y = [4,5,6,7,8]
tck = splrep(x, y)
z = splev([1], tck)
assert_equal(z.shape, (1,))
z = splev(1, tck)
assert_equal(z.shape, ())
def test_2d_shape(self):
x = [1, 2, 3, 4, 5]
y = [4, 5, 6, 7, 8]
tck = splrep(x, y)
t = np.array([[1.0, 1.5, 2.0, 2.5],
[3.0, 3.5, 4.0, 4.5]])
z = splev(t, tck)
z0 = splev(t[0], tck)
z1 = splev(t[1], tck)
assert_equal(z, np.row_stack((z0, z1)))
def test_extrapolation_modes(self):
# test extrapolation modes
# * if ext=0, return the extrapolated value.
# * if ext=1, return 0
# * if ext=2, raise a ValueError
# * if ext=3, return the boundary value.
x = [1,2,3]
y = [0,2,4]
tck = splrep(x, y, k=1)
rstl = [[-2, 6], [0, 0], None, [0, 4]]
for ext in (0, 1, 3):
assert_array_almost_equal(splev([0, 4], tck, ext=ext), rstl[ext])
assert_raises(ValueError, splev, [0, 4], tck, ext=2)
class TestSplder:
def setup_method(self):
# non-uniform grid, just to make it sure
x = np.linspace(0, 1, 100)**3
y = np.sin(20 * x)
self.spl = splrep(x, y)
# double check that knots are non-uniform
assert_(np.diff(self.spl[0]).ptp() > 0)
def test_inverse(self):
# Check that antiderivative + derivative is identity.
for n in range(5):
spl2 = splantider(self.spl, n)
spl3 = splder(spl2, n)
assert_allclose(self.spl[0], spl3[0])
assert_allclose(self.spl[1], spl3[1])
assert_equal(self.spl[2], spl3[2])
def test_splder_vs_splev(self):
# Check derivative vs. FITPACK
for n in range(3+1):
# Also extrapolation!
xx = np.linspace(-1, 2, 2000)
if n == 3:
# ... except that FITPACK extrapolates strangely for
# order 0, so let's not check that.
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:
def test_overflow(self):
from numpy.lib.stride_tricks import as_strided
if dfitpack_int.itemsize == 8:
size = 1500000**2
else:
size = 400**2
# Don't allocate a real array, as it's very big, but rely
# on that it's not referenced
x = as_strided(np.zeros(()), shape=(size,))
assert_raises(OverflowError, bisplrep, x, x, x, w=x,
xb=0, xe=1, yb=0, ye=1, 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)
@pytest.mark.skipif(dfitpack_int != np.int64, reason="needs ilp64 fitpack")
def test_ilp64_bisplrep(self):
check_free_memory(28000) # VM size, doesn't actually use the pages
x = np.linspace(0, 1, 400)
y = np.linspace(0, 1, 400)
x, y = np.meshgrid(x, y)
z = np.zeros_like(x)
tck = bisplrep(x, y, z, kx=3, ky=3, s=0)
assert_allclose(bisplev(0.5, 0.5, tck), 0.0)
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_splprep_segfault():
# regression test for gh-3847: splprep segfaults if knots are specified
# for task=-1
t = np.arange(0, 1.1, 0.1)
x = np.sin(2*np.pi*t)
y = np.cos(2*np.pi*t)
tck, u = interpolate.splprep([x, y], s=0)
unew = np.arange(0, 1.01, 0.01)
uknots = tck[0] # using the knots from the previous fitting
tck, u = interpolate.splprep([x, y], task=-1, t=uknots) # here is the crash
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)
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