Static code analysis and corrections

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_fitpack.py

@@ -0,0 +1,463 @@
+from __future__ import division, print_function, absolute_import
+
+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
+
+from numpy import array, asarray, pi, sin, cos, arange, dot, ravel, sqrt, round
+from scipy import interpolate
+from scipy.interpolate.fitpack import (splrep, splev, bisplrep, bisplev,
+     sproot, splprep, splint, spalde, splder, splantider, insert, dblint)
+from scipy.interpolate.dfitpack import regrid_smth
+
+
+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."""
+    # Or itertools.product (>= python 2.6)
+    xy = array([[a, b] for a in asarray(x) for b in 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(object):
+    """
+    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,v1 = f(x),f(x1)
+        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,v1 = 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(object):
+    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(object):
+    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(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)
+

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_fitpack2.py

@@ -0,0 +1,511 @@
+# Created by Pearu Peterson, June 2003
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import (assert_equal, assert_almost_equal, assert_array_equal,
+        assert_array_almost_equal, assert_allclose)
+from scipy._lib._numpy_compat import suppress_warnings
+from pytest import raises as assert_raises
+
+from numpy import array, diff, linspace, meshgrid, ones, pi, shape
+from scipy.interpolate.fitpack import bisplrep, bisplev
+from scipy.interpolate.fitpack2 import (UnivariateSpline,
+        LSQUnivariateSpline, InterpolatedUnivariateSpline,
+        LSQBivariateSpline, SmoothBivariateSpline, RectBivariateSpline,
+        LSQSphereBivariateSpline, SmoothSphereBivariateSpline,
+        RectSphereBivariateSpline)
+
+
+class TestUnivariateSpline(object):
+    def test_linear_constant(self):
+        x = [1,2,3]
+        y = [3,3,3]
+        lut = UnivariateSpline(x,y,k=1)
+        assert_array_almost_equal(lut.get_knots(),[1,3])
+        assert_array_almost_equal(lut.get_coeffs(),[3,3])
+        assert_almost_equal(lut.get_residual(),0.0)
+        assert_array_almost_equal(lut([1,1.5,2]),[3,3,3])
+
+    def test_preserve_shape(self):
+        x = [1, 2, 3]
+        y = [0, 2, 4]
+        lut = UnivariateSpline(x, y, k=1)
+        arg = 2
+        assert_equal(shape(arg), shape(lut(arg)))
+        assert_equal(shape(arg), shape(lut(arg, nu=1)))
+        arg = [1.5, 2, 2.5]
+        assert_equal(shape(arg), shape(lut(arg)))
+        assert_equal(shape(arg), shape(lut(arg, nu=1)))
+
+    def test_linear_1d(self):
+        x = [1,2,3]
+        y = [0,2,4]
+        lut = UnivariateSpline(x,y,k=1)
+        assert_array_almost_equal(lut.get_knots(),[1,3])
+        assert_array_almost_equal(lut.get_coeffs(),[0,4])
+        assert_almost_equal(lut.get_residual(),0.0)
+        assert_array_almost_equal(lut([1,1.5,2]),[0,1,2])
+
+    def test_subclassing(self):
+        # See #731
+
+        class ZeroSpline(UnivariateSpline):
+            def __call__(self, x):
+                return 0*array(x)
+
+        sp = ZeroSpline([1,2,3,4,5], [3,2,3,2,3], k=2)
+        assert_array_equal(sp([1.5, 2.5]), [0., 0.])
+
+    def test_empty_input(self):
+        # Test whether empty input returns an empty output. Ticket 1014
+        x = [1,3,5,7,9]
+        y = [0,4,9,12,21]
+        spl = UnivariateSpline(x, y, k=3)
+        assert_array_equal(spl([]), array([]))
+
+    def test_resize_regression(self):
+        """Regression test for #1375."""
+        x = [-1., -0.65016502, -0.58856235, -0.26903553, -0.17370892,
+             -0.10011001, 0., 0.10011001, 0.17370892, 0.26903553, 0.58856235,
+             0.65016502, 1.]
+        y = [1.,0.62928599, 0.5797223, 0.39965815, 0.36322694, 0.3508061,
+             0.35214793, 0.3508061, 0.36322694, 0.39965815, 0.5797223,
+             0.62928599, 1.]
+        w = [1.00000000e+12, 6.88875973e+02, 4.89314737e+02, 4.26864807e+02,
+             6.07746770e+02, 4.51341444e+02, 3.17480210e+02, 4.51341444e+02,
+             6.07746770e+02, 4.26864807e+02, 4.89314737e+02, 6.88875973e+02,
+             1.00000000e+12]
+        spl = UnivariateSpline(x=x, y=y, w=w, s=None)
+        desired = array([0.35100374, 0.51715855, 0.87789547, 0.98719344])
+        assert_allclose(spl([0.1, 0.5, 0.9, 0.99]), desired, atol=5e-4)
+
+    def test_out_of_range_regression(self):
+        # Test different extrapolation modes. See ticket 3557
+        x = np.arange(5, dtype=float)
+        y = x**3
+
+        xp = linspace(-8, 13, 100)
+        xp_zeros = xp.copy()
+        xp_zeros[np.logical_or(xp_zeros < 0., xp_zeros > 4.)] = 0
+        xp_clip = xp.copy()
+        xp_clip[xp_clip < x[0]] = x[0]
+        xp_clip[xp_clip > x[-1]] = x[-1]
+
+        for cls in [UnivariateSpline, InterpolatedUnivariateSpline]:
+            spl = cls(x=x, y=y)
+            for ext in [0, 'extrapolate']:
+                assert_allclose(spl(xp, ext=ext), xp**3, atol=1e-16)
+                assert_allclose(cls(x, y, ext=ext)(xp), xp**3, atol=1e-16)
+            for ext in [1, 'zeros']:
+                assert_allclose(spl(xp, ext=ext), xp_zeros**3, atol=1e-16)
+                assert_allclose(cls(x, y, ext=ext)(xp), xp_zeros**3, atol=1e-16)
+            for ext in [2, 'raise']:
+                assert_raises(ValueError, spl, xp, **dict(ext=ext))
+            for ext in [3, 'const']:
+                assert_allclose(spl(xp, ext=ext), xp_clip**3, atol=1e-16)
+                assert_allclose(cls(x, y, ext=ext)(xp), xp_clip**3, atol=1e-16)
+
+        # also test LSQUnivariateSpline [which needs explicit knots]
+        t = spl.get_knots()[3:4]  # interior knots w/ default k=3
+        spl = LSQUnivariateSpline(x, y, t)
+        assert_allclose(spl(xp, ext=0), xp**3, atol=1e-16)
+        assert_allclose(spl(xp, ext=1), xp_zeros**3, atol=1e-16)
+        assert_raises(ValueError, spl, xp, **dict(ext=2))
+        assert_allclose(spl(xp, ext=3), xp_clip**3, atol=1e-16)
+
+        # also make sure that unknown values for `ext` are caught early
+        for ext in [-1, 'unknown']:
+            spl = UnivariateSpline(x, y)
+            assert_raises(ValueError, spl, xp, **dict(ext=ext))
+            assert_raises(ValueError, UnivariateSpline,
+                    **dict(x=x, y=y, ext=ext))
+
+    def test_lsq_fpchec(self):
+        xs = np.arange(100) * 1.
+        ys = np.arange(100) * 1.
+        knots = np.linspace(0, 99, 10)
+        bbox = (-1, 101)
+        assert_raises(ValueError, LSQUnivariateSpline, xs, ys, knots,
+                      bbox=bbox)
+
+    def test_derivative_and_antiderivative(self):
+        # Thin wrappers to splder/splantider, so light smoke test only.
+        x = np.linspace(0, 1, 70)**3
+        y = np.cos(x)
+
+        spl = UnivariateSpline(x, y, s=0)
+        spl2 = spl.antiderivative(2).derivative(2)
+        assert_allclose(spl(0.3), spl2(0.3))
+
+        spl2 = spl.antiderivative(1)
+        assert_allclose(spl2(0.6) - spl2(0.2),
+                        spl.integral(0.2, 0.6))
+
+    def test_nan(self):
+        # bail out early if the input data contains nans
+        x = np.arange(10, dtype=float)
+        y = x**3
+        w = np.ones_like(x)
+        # also test LSQUnivariateSpline [which needs explicit knots]
+        spl = UnivariateSpline(x, y, check_finite=True)
+        t = spl.get_knots()[3:4]  # interior knots w/ default k=3
+        y_end = y[-1]
+        for z in [np.nan, np.inf, -np.inf]:
+            y[-1] = z
+            assert_raises(ValueError, UnivariateSpline,
+                    **dict(x=x, y=y, check_finite=True))
+            assert_raises(ValueError, InterpolatedUnivariateSpline,
+                    **dict(x=x, y=y, check_finite=True))
+            assert_raises(ValueError, LSQUnivariateSpline,
+                    **dict(x=x, y=y, t=t, check_finite=True))
+            y[-1] = y_end  # check valid y but invalid w
+            w[-1] = z
+            assert_raises(ValueError, UnivariateSpline,
+                    **dict(x=x, y=y, w=w, check_finite=True))
+            assert_raises(ValueError, InterpolatedUnivariateSpline,
+                    **dict(x=x, y=y, w=w, check_finite=True))
+            assert_raises(ValueError, LSQUnivariateSpline,
+                    **dict(x=x, y=y, t=t, w=w, check_finite=True))
+
+    def test_increasing_x(self):
+        xx = np.arange(10, dtype=float)
+        yy = xx**3
+        x = np.arange(10, dtype=float)
+        x[1] = x[0]
+        y = x**3
+        w = np.ones_like(x)
+        # also test LSQUnivariateSpline [which needs explicit knots]
+        spl = UnivariateSpline(xx, yy, check_finite=True)
+        t = spl.get_knots()[3:4]  # interior knots w/ default k=3
+        assert_raises(ValueError, UnivariateSpline,
+                **dict(x=x, y=y, check_finite=True))
+        assert_raises(ValueError, InterpolatedUnivariateSpline,
+                **dict(x=x, y=y, check_finite=True))
+        assert_raises(ValueError, LSQUnivariateSpline,
+                **dict(x=x, y=y, t=t, w=w, check_finite=True))
+
+
+class TestLSQBivariateSpline(object):
+    # NOTE: The systems in this test class are rank-deficient
+    def test_linear_constant(self):
+        x = [1,1,1,2,2,2,3,3,3]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = [3,3,3,3,3,3,3,3,3]
+        s = 0.1
+        tx = [1+s,3-s]
+        ty = [1+s,3-s]
+        with suppress_warnings() as sup:
+            r = sup.record(UserWarning, "\nThe coefficients of the spline")
+            lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
+            assert_equal(len(r), 1)
+
+        assert_almost_equal(lut(2,2), 3.)
+
+    def test_bilinearity(self):
+        x = [1,1,1,2,2,2,3,3,3]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = [0,7,8,3,4,7,1,3,4]
+        s = 0.1
+        tx = [1+s,3-s]
+        ty = [1+s,3-s]
+        with suppress_warnings() as sup:
+            # This seems to fail (ier=1, see ticket 1642).
+            sup.filter(UserWarning, "\nThe coefficients of the spline")
+            lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
+
+        tx, ty = lut.get_knots()
+        for xa, xb in zip(tx[:-1], tx[1:]):
+            for ya, yb in zip(ty[:-1], ty[1:]):
+                for t in [0.1, 0.5, 0.9]:
+                    for s in [0.3, 0.4, 0.7]:
+                        xp = xa*(1-t) + xb*t
+                        yp = ya*(1-s) + yb*s
+                        zp = (+ lut(xa, ya)*(1-t)*(1-s)
+                              + lut(xb, ya)*t*(1-s)
+                              + lut(xa, yb)*(1-t)*s
+                              + lut(xb, yb)*t*s)
+                        assert_almost_equal(lut(xp,yp), zp)
+
+    def test_integral(self):
+        x = [1,1,1,2,2,2,8,8,8]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = array([0,7,8,3,4,7,1,3,4])
+
+        s = 0.1
+        tx = [1+s,3-s]
+        ty = [1+s,3-s]
+        with suppress_warnings() as sup:
+            r = sup.record(UserWarning, "\nThe coefficients of the spline")
+            lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
+            assert_equal(len(r), 1)
+        tx, ty = lut.get_knots()
+        tz = lut(tx, ty)
+        trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
+                    * (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
+
+        assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]),
+                            trpz)
+
+    def test_empty_input(self):
+        # Test whether empty inputs returns an empty output. Ticket 1014
+        x = [1,1,1,2,2,2,3,3,3]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = [3,3,3,3,3,3,3,3,3]
+        s = 0.1
+        tx = [1+s,3-s]
+        ty = [1+s,3-s]
+        with suppress_warnings() as sup:
+            r = sup.record(UserWarning, "\nThe coefficients of the spline")
+            lut = LSQBivariateSpline(x, y, z, tx, ty, kx=1, ky=1)
+            assert_equal(len(r), 1)
+
+        assert_array_equal(lut([], []), np.zeros((0,0)))
+        assert_array_equal(lut([], [], grid=False), np.zeros((0,)))
+
+
+class TestSmoothBivariateSpline(object):
+    def test_linear_constant(self):
+        x = [1,1,1,2,2,2,3,3,3]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = [3,3,3,3,3,3,3,3,3]
+        lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
+        assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
+        assert_array_almost_equal(lut.get_coeffs(),[3,3,3,3])
+        assert_almost_equal(lut.get_residual(),0.0)
+        assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[3,3],[3,3],[3,3]])
+
+    def test_linear_1d(self):
+        x = [1,1,1,2,2,2,3,3,3]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = [0,0,0,2,2,2,4,4,4]
+        lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
+        assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
+        assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4])
+        assert_almost_equal(lut.get_residual(),0.0)
+        assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[0,0],[1,1],[2,2]])
+
+    def test_integral(self):
+        x = [1,1,1,2,2,2,4,4,4]
+        y = [1,2,3,1,2,3,1,2,3]
+        z = array([0,7,8,3,4,7,1,3,4])
+
+        with suppress_warnings() as sup:
+            # This seems to fail (ier=1, see ticket 1642).
+            sup.filter(UserWarning, "\nThe required storage space")
+            lut = SmoothBivariateSpline(x, y, z, kx=1, ky=1, s=0)
+
+        tx = [1,2,4]
+        ty = [1,2,3]
+
+        tz = lut(tx, ty)
+        trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
+                    * (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
+        assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
+
+        lut2 = SmoothBivariateSpline(x, y, z, kx=2, ky=2, s=0)
+        assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
+                            decimal=0)  # the quadratures give 23.75 and 23.85
+
+        tz = lut(tx[:-1], ty[:-1])
+        trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
+                    * (tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
+        assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
+
+    def test_rerun_lwrk2_too_small(self):
+        # in this setting, lwrk2 is too small in the default run. Here we
+        # check for equality with the bisplrep/bisplev output because there,
+        # an automatic re-run of the spline representation is done if ier>10.
+        x = np.linspace(-2, 2, 80)
+        y = np.linspace(-2, 2, 80)
+        z = x + y
+        xi = np.linspace(-1, 1, 100)
+        yi = np.linspace(-2, 2, 100)
+        tck = bisplrep(x, y, z)
+        res1 = bisplev(xi, yi, tck)
+        interp_ = SmoothBivariateSpline(x, y, z)
+        res2 = interp_(xi, yi)
+        assert_almost_equal(res1, res2)
+
+
+class TestLSQSphereBivariateSpline(object):
+    def setup_method(self):
+        # define the input data and coordinates
+        ntheta, nphi = 70, 90
+        theta = linspace(0.5/(ntheta - 1), 1 - 0.5/(ntheta - 1), ntheta) * pi
+        phi = linspace(0.5/(nphi - 1), 1 - 0.5/(nphi - 1), nphi) * 2. * pi
+        data = ones((theta.shape[0], phi.shape[0]))
+        # define knots and extract data values at the knots
+        knotst = theta[::5]
+        knotsp = phi[::5]
+        knotdata = data[::5, ::5]
+        # calculate spline coefficients
+        lats, lons = meshgrid(theta, phi)
+        lut_lsq = LSQSphereBivariateSpline(lats.ravel(), lons.ravel(),
+                                           data.T.ravel(), knotst, knotsp)
+        self.lut_lsq = lut_lsq
+        self.data = knotdata
+        self.new_lons, self.new_lats = knotsp, knotst
+
+    def test_linear_constant(self):
+        assert_almost_equal(self.lut_lsq.get_residual(), 0.0)
+        assert_array_almost_equal(self.lut_lsq(self.new_lats, self.new_lons),
+                                  self.data)
+
+    def test_empty_input(self):
+        assert_array_almost_equal(self.lut_lsq([], []), np.zeros((0,0)))
+        assert_array_almost_equal(self.lut_lsq([], [], grid=False), np.zeros((0,)))
+
+
+class TestSmoothSphereBivariateSpline(object):
+    def setup_method(self):
+        theta = array([.25*pi, .25*pi, .25*pi, .5*pi, .5*pi, .5*pi, .75*pi,
+                       .75*pi, .75*pi])
+        phi = array([.5 * pi, pi, 1.5 * pi, .5 * pi, pi, 1.5 * pi, .5 * pi, pi,
+                     1.5 * pi])
+        r = array([3, 3, 3, 3, 3, 3, 3, 3, 3])
+        self.lut = SmoothSphereBivariateSpline(theta, phi, r, s=1E10)
+
+    def test_linear_constant(self):
+        assert_almost_equal(self.lut.get_residual(), 0.)
+        assert_array_almost_equal(self.lut([1, 1.5, 2],[1, 1.5]),
+                                  [[3, 3], [3, 3], [3, 3]])
+
+    def test_empty_input(self):
+        assert_array_almost_equal(self.lut([], []), np.zeros((0,0)))
+        assert_array_almost_equal(self.lut([], [], grid=False), np.zeros((0,)))
+
+
+class TestRectBivariateSpline(object):
+    def test_defaults(self):
+        x = array([1,2,3,4,5])
+        y = array([1,2,3,4,5])
+        z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
+        lut = RectBivariateSpline(x,y,z)
+        assert_array_almost_equal(lut(x,y),z)
+
+    def test_evaluate(self):
+        x = array([1,2,3,4,5])
+        y = array([1,2,3,4,5])
+        z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
+        lut = RectBivariateSpline(x,y,z)
+
+        xi = [1, 2.3, 5.3, 0.5, 3.3, 1.2, 3]
+        yi = [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]
+        zi = lut.ev(xi, yi)
+        zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)])
+
+        assert_almost_equal(zi, zi2)
+
+    def test_derivatives_grid(self):
+        x = array([1,2,3,4,5])
+        y = array([1,2,3,4,5])
+        z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
+        dx = array([[0,0,-20,0,0],[0,0,13,0,0],[0,0,4,0,0],
+            [0,0,-11,0,0],[0,0,4,0,0]])/6.
+        dy = array([[4,-1,0,1,-4],[4,-1,0,1,-4],[0,1.5,0,-1.5,0],
+            [2,.25,0,-.25,-2],[4,-1,0,1,-4]])
+        dxdy = array([[40,-25,0,25,-40],[-26,16.25,0,-16.25,26],
+            [-8,5,0,-5,8],[22,-13.75,0,13.75,-22],[-8,5,0,-5,8]])/6.
+        lut = RectBivariateSpline(x,y,z)
+        assert_array_almost_equal(lut(x,y,dx=1),dx)
+        assert_array_almost_equal(lut(x,y,dy=1),dy)
+        assert_array_almost_equal(lut(x,y,dx=1,dy=1),dxdy)
+
+    def test_derivatives(self):
+        x = array([1,2,3,4,5])
+        y = array([1,2,3,4,5])
+        z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
+        dx = array([0,0,2./3,0,0])
+        dy = array([4,-1,0,-.25,-4])
+        dxdy = array([160,65,0,55,32])/24.
+        lut = RectBivariateSpline(x,y,z)
+        assert_array_almost_equal(lut(x,y,dx=1,grid=False),dx)
+        assert_array_almost_equal(lut(x,y,dy=1,grid=False),dy)
+        assert_array_almost_equal(lut(x,y,dx=1,dy=1,grid=False),dxdy)
+
+    def test_broadcast(self):
+        x = array([1,2,3,4,5])
+        y = array([1,2,3,4,5])
+        z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
+        lut = RectBivariateSpline(x,y,z)
+        assert_allclose(lut(x, y), lut(x[:,None], y[None,:], grid=False))
+
+
+class TestRectSphereBivariateSpline(object):
+    def test_defaults(self):
+        y = linspace(0.01, 2*pi-0.01, 7)
+        x = linspace(0.01, pi-0.01, 7)
+        z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
+                   [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
+                   [1,2,1,2,1,2,1]])
+        lut = RectSphereBivariateSpline(x,y,z)
+        assert_array_almost_equal(lut(x,y),z)
+
+    def test_evaluate(self):
+        y = linspace(0.01, 2*pi-0.01, 7)
+        x = linspace(0.01, pi-0.01, 7)
+        z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
+                   [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
+                   [1,2,1,2,1,2,1]])
+        lut = RectSphereBivariateSpline(x,y,z)
+        yi = [0.2, 1, 2.3, 2.35, 3.0, 3.99, 5.25]
+        xi = [1.5, 0.4, 1.1, 0.45, 0.2345, 1., 0.0001]
+        zi = lut.ev(xi, yi)
+        zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)])
+        assert_almost_equal(zi, zi2)
+
+    def test_derivatives_grid(self):
+        y = linspace(0.01, 2*pi-0.01, 7)
+        x = linspace(0.01, pi-0.01, 7)
+        z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
+                   [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
+                   [1,2,1,2,1,2,1]])
+
+        lut = RectSphereBivariateSpline(x,y,z)
+
+        y = linspace(0.02, 2*pi-0.02, 7)
+        x = linspace(0.02, pi-0.02, 7)
+
+        assert_allclose(lut(x, y, dtheta=1), _numdiff_2d(lut, x, y, dx=1),
+                        rtol=1e-4, atol=1e-4)
+        assert_allclose(lut(x, y, dphi=1), _numdiff_2d(lut, x, y, dy=1),
+                        rtol=1e-4, atol=1e-4)
+        assert_allclose(lut(x, y, dtheta=1, dphi=1), _numdiff_2d(lut, x, y, dx=1, dy=1, eps=1e-6),
+                        rtol=1e-3, atol=1e-3)
+
+    def test_derivatives(self):
+        y = linspace(0.01, 2*pi-0.01, 7)
+        x = linspace(0.01, pi-0.01, 7)
+        z = array([[1,2,1,2,1,2,1],[1,2,1,2,1,2,1],[1,2,3,2,1,2,1],
+                   [1,2,2,2,1,2,1],[1,2,1,2,1,2,1],[1,2,2,2,1,2,1],
+                   [1,2,1,2,1,2,1]])
+
+        lut = RectSphereBivariateSpline(x,y,z)
+
+        y = linspace(0.02, 2*pi-0.02, 7)
+        x = linspace(0.02, pi-0.02, 7)
+
+        assert_equal(lut(x, y, dtheta=1, grid=False).shape, x.shape)
+        assert_allclose(lut(x, y, dtheta=1, grid=False),
+                        _numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dx=1),
+                        rtol=1e-4, atol=1e-4)
+        assert_allclose(lut(x, y, dphi=1, grid=False),
+                        _numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dy=1),
+                        rtol=1e-4, atol=1e-4)
+        assert_allclose(lut(x, y, dtheta=1, dphi=1, grid=False),
+                        _numdiff_2d(lambda x,y: lut(x,y,grid=False), x, y, dx=1, dy=1, eps=1e-6),
+                        rtol=1e-3, atol=1e-3)
+
+
+def _numdiff_2d(func, x, y, dx=0, dy=0, eps=1e-8):
+    if dx == 0 and dy == 0:
+        return func(x, y)
+    elif dx == 1 and dy == 0:
+        return (func(x + eps, y) - func(x - eps, y)) / (2*eps)
+    elif dx == 0 and dy == 1:
+        return (func(x, y + eps) - func(x, y - eps)) / (2*eps)
+    elif dx == 1 and dy == 1:
+        return (func(x + eps, y + eps) - func(x - eps, y + eps)
+                - func(x + eps, y - eps) + func(x - eps, y - eps)) / (2*eps)**2
+    else:
+        raise ValueError("invalid derivative order")

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_gil.py

@@ -0,0 +1,67 @@
+from __future__ import division, print_function, absolute_import
+
+import itertools
+import threading
+import time
+
+import numpy as np
+from numpy.testing import assert_equal
+import pytest
+import scipy.interpolate
+
+
+class TestGIL(object):
+    """Check if the GIL is properly released by scipy.interpolate functions."""
+
+    def setup_method(self):
+        self.messages = []
+
+    def log(self, message):
+        self.messages.append(message)
+
+    def make_worker_thread(self, target, args):
+        log = self.log
+
+        class WorkerThread(threading.Thread):
+            def run(self):
+                log('interpolation started')
+                target(*args)
+                log('interpolation complete')
+
+        return WorkerThread()
+
+    @pytest.mark.slow
+    @pytest.mark.xfail(reason='race conditions, may depend on system load')
+    def test_rectbivariatespline(self):
+        def generate_params(n_points):
+            x = y = np.linspace(0, 1000, n_points)
+            x_grid, y_grid = np.meshgrid(x, y)
+            z = x_grid * y_grid
+            return x, y, z
+
+        def calibrate_delay(requested_time):
+            for n_points in itertools.count(5000, 1000):
+                args = generate_params(n_points)
+                time_started = time.time()
+                interpolate(*args)
+                if time.time() - time_started > requested_time:
+                    return args
+
+        def interpolate(x, y, z):
+            scipy.interpolate.RectBivariateSpline(x, y, z)
+
+        args = calibrate_delay(requested_time=3)
+        worker_thread = self.make_worker_thread(interpolate, args)
+        worker_thread.start()
+        for i in range(3):
+            time.sleep(0.5)
+            self.log('working')
+        worker_thread.join()
+        assert_equal(self.messages, [
+            'interpolation started',
+            'working',
+            'working',
+            'working',
+            'interpolation complete',
+        ])
+

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_interpnd.py

@@ -0,0 +1,388 @@
+from __future__ import division, print_function, absolute_import
+
+import os
+
+import numpy as np
+from numpy.testing import assert_equal, assert_allclose, assert_almost_equal
+from pytest import raises as assert_raises
+import pytest
+from scipy._lib._numpy_compat import suppress_warnings
+
+import scipy.interpolate.interpnd as interpnd
+import scipy.spatial.qhull as qhull
+
+import pickle
+
+
+def data_file(basename):
+    return os.path.join(os.path.abspath(os.path.dirname(__file__)),
+                        'data', basename)
+
+
+class TestLinearNDInterpolation(object):
+    def test_smoketest(self):
+        # Test at single points
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+
+        yi = interpnd.LinearNDInterpolator(x, y)(x)
+        assert_almost_equal(y, yi)
+
+    def test_smoketest_alternate(self):
+        # Test at single points, alternate calling convention
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+
+        yi = interpnd.LinearNDInterpolator((x[:,0], x[:,1]), y)(x[:,0], x[:,1])
+        assert_almost_equal(y, yi)
+
+    def test_complex_smoketest(self):
+        # Test at single points
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        yi = interpnd.LinearNDInterpolator(x, y)(x)
+        assert_almost_equal(y, yi)
+
+    def test_tri_input(self):
+        # Test at single points
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        tri = qhull.Delaunay(x)
+        yi = interpnd.LinearNDInterpolator(tri, y)(x)
+        assert_almost_equal(y, yi)
+
+    def test_square(self):
+        # Test barycentric interpolation on a square against a manual
+        # implementation
+
+        points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.double)
+        values = np.array([1., 2., -3., 5.], dtype=np.double)
+
+        # NB: assume triangles (0, 1, 3) and (1, 2, 3)
+        #
+        #  1----2
+        #  | \  |
+        #  |  \ |
+        #  0----3
+
+        def ip(x, y):
+            t1 = (x + y <= 1)
+            t2 = ~t1
+
+            x1 = x[t1]
+            y1 = y[t1]
+
+            x2 = x[t2]
+            y2 = y[t2]
+
+            z = 0*x
+
+            z[t1] = (values[0]*(1 - x1 - y1)
+                     + values[1]*y1
+                     + values[3]*x1)
+
+            z[t2] = (values[2]*(x2 + y2 - 1)
+                     + values[1]*(1 - x2)
+                     + values[3]*(1 - y2))
+            return z
+
+        xx, yy = np.broadcast_arrays(np.linspace(0, 1, 14)[:,None],
+                                     np.linspace(0, 1, 14)[None,:])
+        xx = xx.ravel()
+        yy = yy.ravel()
+
+        xi = np.array([xx, yy]).T.copy()
+        zi = interpnd.LinearNDInterpolator(points, values)(xi)
+
+        assert_almost_equal(zi, ip(xx, yy))
+
+    def test_smoketest_rescale(self):
+        # Test at single points
+        x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+
+        yi = interpnd.LinearNDInterpolator(x, y, rescale=True)(x)
+        assert_almost_equal(y, yi)
+
+    def test_square_rescale(self):
+        # Test barycentric interpolation on a rectangle with rescaling
+        # agaings the same implementation without rescaling
+
+        points = np.array([(0,0), (0,100), (10,100), (10,0)], dtype=np.double)
+        values = np.array([1., 2., -3., 5.], dtype=np.double)
+
+        xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None],
+                                     np.linspace(0, 100, 14)[None,:])
+        xx = xx.ravel()
+        yy = yy.ravel()
+        xi = np.array([xx, yy]).T.copy()
+        zi = interpnd.LinearNDInterpolator(points, values)(xi)
+        zi_rescaled = interpnd.LinearNDInterpolator(points, values,
+                rescale=True)(xi)
+
+        assert_almost_equal(zi, zi_rescaled)
+
+    def test_tripoints_input_rescale(self):
+        # Test at single points
+        x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        tri = qhull.Delaunay(x)
+        yi = interpnd.LinearNDInterpolator(tri.points, y)(x)
+        yi_rescale = interpnd.LinearNDInterpolator(tri.points, y,
+                rescale=True)(x)
+        assert_almost_equal(yi, yi_rescale)
+
+    def test_tri_input_rescale(self):
+        # Test at single points
+        x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        tri = qhull.Delaunay(x)
+        match = ("Rescaling is not supported when passing a "
+                 "Delaunay triangulation as ``points``.")
+        with pytest.raises(ValueError, match=match):
+            interpnd.LinearNDInterpolator(tri, y, rescale=True)(x)
+
+    def test_pickle(self):
+        # Test at single points
+        np.random.seed(1234)
+        x = np.random.rand(30, 2)
+        y = np.random.rand(30) + 1j*np.random.rand(30)
+
+        ip = interpnd.LinearNDInterpolator(x, y)
+        ip2 = pickle.loads(pickle.dumps(ip))
+
+        assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
+
+
+class TestEstimateGradients2DGlobal(object):
+    def test_smoketest(self):
+        x = np.array([(0, 0), (0, 2),
+                      (1, 0), (1, 2), (0.25, 0.75), (0.6, 0.8)], dtype=float)
+        tri = qhull.Delaunay(x)
+
+        # Should be exact for linear functions, independent of triangulation
+
+        funcs = [
+            (lambda x, y: 0*x + 1, (0, 0)),
+            (lambda x, y: 0 + x, (1, 0)),
+            (lambda x, y: -2 + y, (0, 1)),
+            (lambda x, y: 3 + 3*x + 14.15*y, (3, 14.15))
+        ]
+
+        for j, (func, grad) in enumerate(funcs):
+            z = func(x[:,0], x[:,1])
+            dz = interpnd.estimate_gradients_2d_global(tri, z, tol=1e-6)
+
+            assert_equal(dz.shape, (6, 2))
+            assert_allclose(dz, np.array(grad)[None,:] + 0*dz,
+                            rtol=1e-5, atol=1e-5, err_msg="item %d" % j)
+
+    def test_regression_2359(self):
+        # Check regression --- for certain point sets, gradient
+        # estimation could end up in an infinite loop
+        points = np.load(data_file('estimate_gradients_hang.npy'))
+        values = np.random.rand(points.shape[0])
+        tri = qhull.Delaunay(points)
+
+        # This should not hang
+        with suppress_warnings() as sup:
+            sup.filter(interpnd.GradientEstimationWarning,
+                       "Gradient estimation did not converge")
+            interpnd.estimate_gradients_2d_global(tri, values, maxiter=1)
+
+
+class TestCloughTocher2DInterpolator(object):
+
+    def _check_accuracy(self, func, x=None, tol=1e-6, alternate=False, rescale=False, **kw):
+        np.random.seed(1234)
+        if x is None:
+            x = np.array([(0, 0), (0, 1),
+                          (1, 0), (1, 1), (0.25, 0.75), (0.6, 0.8),
+                          (0.5, 0.2)],
+                         dtype=float)
+
+        if not alternate:
+            ip = interpnd.CloughTocher2DInterpolator(x, func(x[:,0], x[:,1]),
+                                                     tol=1e-6, rescale=rescale)
+        else:
+            ip = interpnd.CloughTocher2DInterpolator((x[:,0], x[:,1]),
+                                                     func(x[:,0], x[:,1]),
+                                                     tol=1e-6, rescale=rescale)
+
+        p = np.random.rand(50, 2)
+
+        if not alternate:
+            a = ip(p)
+        else:
+            a = ip(p[:,0], p[:,1])
+        b = func(p[:,0], p[:,1])
+
+        try:
+            assert_allclose(a, b, **kw)
+        except AssertionError:
+            print(abs(a - b))
+            print(ip.grad)
+            raise
+
+    def test_linear_smoketest(self):
+        # Should be exact for linear functions, independent of triangulation
+        funcs = [
+            lambda x, y: 0*x + 1,
+            lambda x, y: 0 + x,
+            lambda x, y: -2 + y,
+            lambda x, y: 3 + 3*x + 14.15*y,
+        ]
+
+        for j, func in enumerate(funcs):
+            self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
+                                 err_msg="Function %d" % j)
+            self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
+                                 alternate=True,
+                                 err_msg="Function (alternate) %d" % j)
+            # check rescaling
+            self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
+                                 err_msg="Function (rescaled) %d" % j, rescale=True)
+            self._check_accuracy(func, tol=1e-13, atol=1e-7, rtol=1e-7,
+                                 alternate=True, rescale=True,
+                                 err_msg="Function (alternate, rescaled) %d" % j)
+
+    def test_quadratic_smoketest(self):
+        # Should be reasonably accurate for quadratic functions
+        funcs = [
+            lambda x, y: x**2,
+            lambda x, y: y**2,
+            lambda x, y: x**2 - y**2,
+            lambda x, y: x*y,
+        ]
+
+        for j, func in enumerate(funcs):
+            self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0,
+                                 err_msg="Function %d" % j)
+            self._check_accuracy(func, tol=1e-9, atol=0.22, rtol=0,
+                                 err_msg="Function %d" % j, rescale=True)
+
+    def test_tri_input(self):
+        # Test at single points
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        tri = qhull.Delaunay(x)
+        yi = interpnd.CloughTocher2DInterpolator(tri, y)(x)
+        assert_almost_equal(y, yi)
+
+    def test_tri_input_rescale(self):
+        # Test at single points
+        x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        tri = qhull.Delaunay(x)
+        match = ("Rescaling is not supported when passing a "
+                 "Delaunay triangulation as ``points``.")
+        with pytest.raises(ValueError, match=match):
+            interpnd.CloughTocher2DInterpolator(tri, y, rescale=True)(x)
+
+    def test_tripoints_input_rescale(self):
+        # Test at single points
+        x = np.array([(0,0), (-5,-5), (-5,5), (5, 5), (2.5, 3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 3j*y
+
+        tri = qhull.Delaunay(x)
+        yi = interpnd.CloughTocher2DInterpolator(tri.points, y)(x)
+        yi_rescale = interpnd.CloughTocher2DInterpolator(tri.points, y, rescale=True)(x)
+        assert_almost_equal(yi, yi_rescale)
+
+    def test_dense(self):
+        # Should be more accurate for dense meshes
+        funcs = [
+            lambda x, y: x**2,
+            lambda x, y: y**2,
+            lambda x, y: x**2 - y**2,
+            lambda x, y: x*y,
+            lambda x, y: np.cos(2*np.pi*x)*np.sin(2*np.pi*y)
+        ]
+
+        np.random.seed(4321)  # use a different seed than the check!
+        grid = np.r_[np.array([(0,0), (0,1), (1,0), (1,1)], dtype=float),
+                     np.random.rand(30*30, 2)]
+
+        for j, func in enumerate(funcs):
+            self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2,
+                                 err_msg="Function %d" % j)
+            self._check_accuracy(func, x=grid, tol=1e-9, atol=5e-3, rtol=1e-2,
+                                 err_msg="Function %d" % j, rescale=True)
+
+    def test_wrong_ndim(self):
+        x = np.random.randn(30, 3)
+        y = np.random.randn(30)
+        assert_raises(ValueError, interpnd.CloughTocher2DInterpolator, x, y)
+
+    def test_pickle(self):
+        # Test at single points
+        np.random.seed(1234)
+        x = np.random.rand(30, 2)
+        y = np.random.rand(30) + 1j*np.random.rand(30)
+
+        ip = interpnd.CloughTocher2DInterpolator(x, y)
+        ip2 = pickle.loads(pickle.dumps(ip))
+
+        assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
+
+    def test_boundary_tri_symmetry(self):
+        # Interpolation at neighbourless triangles should retain
+        # symmetry with mirroring the triangle.
+
+        # Equilateral triangle
+        points = np.array([(0, 0), (1, 0), (0.5, np.sqrt(3)/2)])
+        values = np.array([1, 0, 0])
+
+        ip = interpnd.CloughTocher2DInterpolator(points, values)
+
+        # Set gradient to zero at vertices
+        ip.grad[...] = 0
+
+        # Interpolation should be symmetric vs. bisector
+        alpha = 0.3
+        p1 = np.array([0.5 * np.cos(alpha), 0.5 * np.sin(alpha)])
+        p2 = np.array([0.5 * np.cos(np.pi/3 - alpha), 0.5 * np.sin(np.pi/3 - alpha)])
+
+        v1 = ip(p1)
+        v2 = ip(p2)
+        assert_allclose(v1, v2)
+
+        # ... and affine invariant
+        np.random.seed(1)
+        A = np.random.randn(2, 2)
+        b = np.random.randn(2)
+
+        points = A.dot(points.T).T + b[None,:]
+        p1 = A.dot(p1) + b
+        p2 = A.dot(p2) + b
+
+        ip = interpnd.CloughTocher2DInterpolator(points, values)
+        ip.grad[...] = 0
+
+        w1 = ip(p1)
+        w2 = ip(p2)
+        assert_allclose(w1, v1)
+        assert_allclose(w2, v2)

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_interpolate_wrapper.py

@@ -0,0 +1,81 @@
+""" module to test interpolate_wrapper.py
+"""
+from __future__ import division, print_function, absolute_import
+
+from numpy import arange, allclose, ones, isnan
+import numpy as np
+from numpy.testing import (assert_, assert_allclose)
+from scipy._lib._numpy_compat import suppress_warnings
+
+# functionality to be tested
+from scipy.interpolate.interpolate_wrapper import (linear, logarithmic,
+    block_average_above, nearest)
+
+
+class Test(object):
+
+    def assertAllclose(self, x, y, rtol=1.0e-5):
+        for i, xi in enumerate(x):
+            assert_(allclose(xi, y[i], rtol) or (isnan(xi) and isnan(y[i])))
+
+    def test_nearest(self):
+        N = 5
+        x = arange(N)
+        y = arange(N)
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning, "`nearest` is deprecated")
+            assert_allclose(y, nearest(x, y, x+.1))
+            assert_allclose(y, nearest(x, y, x-.1))
+
+    def test_linear(self):
+        N = 3000.
+        x = arange(N)
+        y = arange(N)
+        new_x = arange(N)+0.5
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning, "`linear` is deprecated")
+            new_y = linear(x, y, new_x)
+
+        assert_allclose(new_y[:5], [0.5, 1.5, 2.5, 3.5, 4.5])
+
+    def test_block_average_above(self):
+        N = 3000
+        x = arange(N, dtype=float)
+        y = arange(N, dtype=float)
+
+        new_x = arange(N // 2) * 2
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning, "`block_average_above` is deprecated")
+            new_y = block_average_above(x, y, new_x)
+        assert_allclose(new_y[:5], [0.0, 0.5, 2.5, 4.5, 6.5])
+
+    def test_linear2(self):
+        N = 3000
+        x = arange(N, dtype=float)
+        y = ones((100,N)) * arange(N)
+        new_x = arange(N) + 0.5
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning, "`linear` is deprecated")
+            new_y = linear(x, y, new_x)
+        assert_allclose(new_y[:5,:5],
+                            [[0.5, 1.5, 2.5, 3.5, 4.5],
+                             [0.5, 1.5, 2.5, 3.5, 4.5],
+                             [0.5, 1.5, 2.5, 3.5, 4.5],
+                             [0.5, 1.5, 2.5, 3.5, 4.5],
+                             [0.5, 1.5, 2.5, 3.5, 4.5]])
+
+    def test_logarithmic(self):
+        N = 4000.
+        x = arange(N)
+        y = arange(N)
+        new_x = arange(N)+0.5
+        with suppress_warnings() as sup:
+            sup.filter(DeprecationWarning, "`logarithmic` is deprecated")
+            new_y = logarithmic(x, y, new_x)
+        correct_y = [np.NaN, 1.41421356, 2.44948974, 3.46410162, 4.47213595]
+        assert_allclose(new_y[:5], correct_y)
+
+    def runTest(self):
+        test_list = [name for name in dir(self) if name.find('test_') == 0]
+        for test_name in test_list:
+            exec("self.%s()" % test_name)

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_ndgriddata.py

@@ -0,0 +1,177 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_equal, assert_array_equal, assert_allclose
+from pytest import raises as assert_raises
+
+from scipy.interpolate import griddata, NearestNDInterpolator
+
+
+class TestGriddata(object):
+    def test_fill_value(self):
+        x = [(0,0), (0,1), (1,0)]
+        y = [1, 2, 3]
+
+        yi = griddata(x, y, [(1,1), (1,2), (0,0)], fill_value=-1)
+        assert_array_equal(yi, [-1., -1, 1])
+
+        yi = griddata(x, y, [(1,1), (1,2), (0,0)])
+        assert_array_equal(yi, [np.nan, np.nan, 1])
+
+    def test_alternative_call(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = (np.arange(x.shape[0], dtype=np.double)[:,None]
+             + np.array([0,1])[None,:])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            for rescale in (True, False):
+                msg = repr((method, rescale))
+                yi = griddata((x[:,0], x[:,1]), y, (x[:,0], x[:,1]), method=method,
+                              rescale=rescale)
+                assert_allclose(y, yi, atol=1e-14, err_msg=msg)
+
+    def test_multivalue_2d(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = (np.arange(x.shape[0], dtype=np.double)[:,None]
+             + np.array([0,1])[None,:])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            for rescale in (True, False):
+                msg = repr((method, rescale))
+                yi = griddata(x, y, x, method=method, rescale=rescale)
+                assert_allclose(y, yi, atol=1e-14, err_msg=msg)
+
+    def test_multipoint_2d(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+
+        xi = x[:,None,:] + np.array([0,0,0])[None,:,None]
+
+        for method in ('nearest', 'linear', 'cubic'):
+            for rescale in (True, False):
+                msg = repr((method, rescale))
+                yi = griddata(x, y, xi, method=method, rescale=rescale)
+
+                assert_equal(yi.shape, (5, 3), err_msg=msg)
+                assert_allclose(yi, np.tile(y[:,None], (1, 3)),
+                                atol=1e-14, err_msg=msg)
+
+    def test_complex_2d(self):
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 2j*y[::-1]
+
+        xi = x[:,None,:] + np.array([0,0,0])[None,:,None]
+
+        for method in ('nearest', 'linear', 'cubic'):
+            for rescale in (True, False):
+                msg = repr((method, rescale))
+                yi = griddata(x, y, xi, method=method, rescale=rescale)
+
+                assert_equal(yi.shape, (5, 3), err_msg=msg)
+                assert_allclose(yi, np.tile(y[:,None], (1, 3)),
+                                atol=1e-14, err_msg=msg)
+
+    def test_1d(self):
+        x = np.array([1, 2.5, 3, 4.5, 5, 6])
+        y = np.array([1, 2, 0, 3.9, 2, 1])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            assert_allclose(griddata(x, y, x, method=method), y,
+                            err_msg=method, atol=1e-14)
+            assert_allclose(griddata(x.reshape(6, 1), y, x, method=method), y,
+                            err_msg=method, atol=1e-14)
+            assert_allclose(griddata((x,), y, (x,), method=method), y,
+                            err_msg=method, atol=1e-14)
+
+    def test_1d_borders(self):
+        # Test for nearest neighbor case with xi outside
+        # the range of the values.
+        x = np.array([1, 2.5, 3, 4.5, 5, 6])
+        y = np.array([1, 2, 0, 3.9, 2, 1])
+        xi = np.array([0.9, 6.5])
+        yi_should = np.array([1.0, 1.0])
+
+        method = 'nearest'
+        assert_allclose(griddata(x, y, xi,
+                                 method=method), yi_should,
+                        err_msg=method,
+                        atol=1e-14)
+        assert_allclose(griddata(x.reshape(6, 1), y, xi,
+                                 method=method), yi_should,
+                        err_msg=method,
+                        atol=1e-14)
+        assert_allclose(griddata((x, ), y, (xi, ),
+                                 method=method), yi_should,
+                        err_msg=method,
+                        atol=1e-14)
+
+    def test_1d_unsorted(self):
+        x = np.array([2.5, 1, 4.5, 5, 6, 3])
+        y = np.array([1, 2, 0, 3.9, 2, 1])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            assert_allclose(griddata(x, y, x, method=method), y,
+                            err_msg=method, atol=1e-10)
+            assert_allclose(griddata(x.reshape(6, 1), y, x, method=method), y,
+                            err_msg=method, atol=1e-10)
+            assert_allclose(griddata((x,), y, (x,), method=method), y,
+                            err_msg=method, atol=1e-10)
+
+    def test_square_rescale_manual(self):
+        points = np.array([(0,0), (0,100), (10,100), (10,0), (1, 5)], dtype=np.double)
+        points_rescaled = np.array([(0,0), (0,1), (1,1), (1,0), (0.1, 0.05)], dtype=np.double)
+        values = np.array([1., 2., -3., 5., 9.], dtype=np.double)
+
+        xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None],
+                                     np.linspace(0, 100, 14)[None,:])
+        xx = xx.ravel()
+        yy = yy.ravel()
+        xi = np.array([xx, yy]).T.copy()
+
+        for method in ('nearest', 'linear', 'cubic'):
+            msg = method
+            zi = griddata(points_rescaled, values, xi/np.array([10, 100.]),
+                          method=method)
+            zi_rescaled = griddata(points, values, xi, method=method,
+                                   rescale=True)
+            assert_allclose(zi, zi_rescaled, err_msg=msg,
+                            atol=1e-12)
+
+    def test_xi_1d(self):
+        # Check that 1-D xi is interpreted as a coordinate
+        x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
+                     dtype=np.double)
+        y = np.arange(x.shape[0], dtype=np.double)
+        y = y - 2j*y[::-1]
+
+        xi = np.array([0.5, 0.5])
+
+        for method in ('nearest', 'linear', 'cubic'):
+            p1 = griddata(x, y, xi, method=method)
+            p2 = griddata(x, y, xi[None,:], method=method)
+            assert_allclose(p1, p2, err_msg=method)
+
+            xi1 = np.array([0.5])
+            xi3 = np.array([0.5, 0.5, 0.5])
+            assert_raises(ValueError, griddata, x, y, xi1,
+                          method=method)
+            assert_raises(ValueError, griddata, x, y, xi3,
+                          method=method)
+        
+
+def test_nearest_options():
+    # smoke test that NearestNDInterpolator accept cKDTree options
+    npts, nd = 4, 3
+    x = np.arange(npts*nd).reshape((npts, nd))
+    y = np.arange(npts)
+    nndi = NearestNDInterpolator(x, y)
+
+    opts = {'balanced_tree': False, 'compact_nodes': False}
+    nndi_o = NearestNDInterpolator(x, y, tree_options=opts)
+    assert_allclose(nndi(x), nndi_o(x), atol=1e-14)
+

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_pade.py

@@ -0,0 +1,66 @@
+from __future__ import division, print_function, absolute_import
+
+from numpy.testing import (assert_array_equal, assert_array_almost_equal)
+from scipy.interpolate import pade
+
+def test_pade_trivial():
+    nump, denomp = pade([1.0], 0)
+    assert_array_equal(nump.c, [1.0])
+    assert_array_equal(denomp.c, [1.0])
+    
+    nump, denomp = pade([1.0], 0, 0)
+    assert_array_equal(nump.c, [1.0])
+    assert_array_equal(denomp.c, [1.0])
+
+
+def test_pade_4term_exp():
+    # First four Taylor coefficients of exp(x).
+    # Unlike poly1d, the first array element is the zero-order term.
+    an = [1.0, 1.0, 0.5, 1.0/6]
+
+    nump, denomp = pade(an, 0)
+    assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0])
+    assert_array_almost_equal(denomp.c, [1.0])
+
+    nump, denomp = pade(an, 1)
+    assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0])
+    assert_array_almost_equal(denomp.c, [-1.0/3, 1.0])
+
+    nump, denomp = pade(an, 2)
+    assert_array_almost_equal(nump.c, [1.0/3, 1.0])
+    assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0])
+
+    nump, denomp = pade(an, 3)
+    assert_array_almost_equal(nump.c, [1.0])
+    assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0])
+   
+    # Testing inclusion of optional parameter
+    nump, denomp = pade(an, 0, 3)
+    assert_array_almost_equal(nump.c, [1.0/6, 0.5, 1.0, 1.0])
+    assert_array_almost_equal(denomp.c, [1.0])
+
+    nump, denomp = pade(an, 1, 2)
+    assert_array_almost_equal(nump.c, [1.0/6, 2.0/3, 1.0])
+    assert_array_almost_equal(denomp.c, [-1.0/3, 1.0])
+
+    nump, denomp = pade(an, 2, 1)
+    assert_array_almost_equal(nump.c, [1.0/3, 1.0])
+    assert_array_almost_equal(denomp.c, [1.0/6, -2.0/3, 1.0])
+
+    nump, denomp = pade(an, 3, 0)
+    assert_array_almost_equal(nump.c, [1.0])
+    assert_array_almost_equal(denomp.c, [-1.0/6, 0.5, -1.0, 1.0])
+   
+    # Testing reducing array
+    nump, denomp = pade(an, 0, 2)
+    assert_array_almost_equal(nump.c, [0.5, 1.0, 1.0])
+    assert_array_almost_equal(denomp.c, [1.0])
+
+    nump, denomp = pade(an, 1, 1)
+    assert_array_almost_equal(nump.c, [1.0/2, 1.0])
+    assert_array_almost_equal(denomp.c, [-1.0/2, 1.0])
+
+    nump, denomp = pade(an, 2, 0)
+    assert_array_almost_equal(nump.c, [1.0])
+    assert_array_almost_equal(denomp.c, [1.0/2, -1.0, 1.0])
+

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_polyint.py

@@ -0,0 +1,664 @@
+from __future__ import division, print_function, absolute_import
+
+import warnings
+
+import numpy as np
+
+from numpy.testing import (
+    assert_almost_equal, assert_array_equal, assert_array_almost_equal,
+    assert_allclose, assert_equal, assert_)
+from pytest import raises as assert_raises
+
+from scipy.interpolate import (
+    KroghInterpolator, krogh_interpolate,
+    BarycentricInterpolator, barycentric_interpolate,
+    approximate_taylor_polynomial, pchip, PchipInterpolator,
+    pchip_interpolate, Akima1DInterpolator, CubicSpline, make_interp_spline)
+
+from scipy._lib.six import xrange
+
+
+def check_shape(interpolator_cls, x_shape, y_shape, deriv_shape=None, axis=0,
+                extra_args={}):
+    np.random.seed(1234)
+
+    x = [-1, 0, 1, 2, 3, 4]
+    s = list(range(1, len(y_shape)+1))
+    s.insert(axis % (len(y_shape)+1), 0)
+    y = np.random.rand(*((6,) + y_shape)).transpose(s)
+
+    # Cython code chokes on y.shape = (0, 3) etc, skip them
+    if y.size == 0:
+        return
+
+    xi = np.zeros(x_shape)
+    yi = interpolator_cls(x, y, axis=axis, **extra_args)(xi)
+
+    target_shape = ((deriv_shape or ()) + y.shape[:axis]
+                    + x_shape + y.shape[axis:][1:])
+    assert_equal(yi.shape, target_shape)
+
+    # check it works also with lists
+    if x_shape and y.size > 0:
+        interpolator_cls(list(x), list(y), axis=axis, **extra_args)(list(xi))
+
+    # check also values
+    if xi.size > 0 and deriv_shape is None:
+        bs_shape = y.shape[:axis] + (1,)*len(x_shape) + y.shape[axis:][1:]
+        yv = y[((slice(None,),)*(axis % y.ndim)) + (1,)]
+        yv = yv.reshape(bs_shape)
+
+        yi, y = np.broadcast_arrays(yi, yv)
+        assert_allclose(yi, y)
+
+
+SHAPES = [(), (0,), (1,), (6, 2, 5)]
+
+
+def test_shapes():
+
+    def spl_interp(x, y, axis):
+        return make_interp_spline(x, y, axis=axis)
+
+    for ip in [KroghInterpolator, BarycentricInterpolator, pchip,
+               Akima1DInterpolator, CubicSpline, spl_interp]:
+        for s1 in SHAPES:
+            for s2 in SHAPES:
+                for axis in range(-len(s2), len(s2)):
+                    if ip != CubicSpline:
+                        check_shape(ip, s1, s2, None, axis)
+                    else:
+                        for bc in ['natural', 'clamped']:
+                            extra = {'bc_type': bc}
+                            check_shape(ip, s1, s2, None, axis, extra)
+
+def test_derivs_shapes():
+    def krogh_derivs(x, y, axis=0):
+        return KroghInterpolator(x, y, axis).derivatives
+
+    for s1 in SHAPES:
+        for s2 in SHAPES:
+            for axis in range(-len(s2), len(s2)):
+                check_shape(krogh_derivs, s1, s2, (6,), axis)
+
+
+def test_deriv_shapes():
+    def krogh_deriv(x, y, axis=0):
+        return KroghInterpolator(x, y, axis).derivative
+
+    def pchip_deriv(x, y, axis=0):
+        return pchip(x, y, axis).derivative()
+
+    def pchip_deriv2(x, y, axis=0):
+        return pchip(x, y, axis).derivative(2)
+
+    def pchip_antideriv(x, y, axis=0):
+        return pchip(x, y, axis).derivative()
+
+    def pchip_antideriv2(x, y, axis=0):
+        return pchip(x, y, axis).derivative(2)
+
+    def pchip_deriv_inplace(x, y, axis=0):
+        class P(PchipInterpolator):
+            def __call__(self, x):
+                return PchipInterpolator.__call__(self, x, 1)
+            pass
+        return P(x, y, axis)
+
+    def akima_deriv(x, y, axis=0):
+        return Akima1DInterpolator(x, y, axis).derivative()
+
+    def akima_antideriv(x, y, axis=0):
+        return Akima1DInterpolator(x, y, axis).antiderivative()
+
+    def cspline_deriv(x, y, axis=0):
+        return CubicSpline(x, y, axis).derivative()
+
+    def cspline_antideriv(x, y, axis=0):
+        return CubicSpline(x, y, axis).antiderivative()
+
+    def bspl_deriv(x, y, axis=0):
+        return make_interp_spline(x, y, axis=axis).derivative()
+
+    def bspl_antideriv(x, y, axis=0):
+        return make_interp_spline(x, y, axis=axis).antiderivative()
+
+    for ip in [krogh_deriv, pchip_deriv, pchip_deriv2, pchip_deriv_inplace,
+               pchip_antideriv, pchip_antideriv2, akima_deriv, akima_antideriv,
+               cspline_deriv, cspline_antideriv, bspl_deriv, bspl_antideriv]:
+        for s1 in SHAPES:
+            for s2 in SHAPES:
+                for axis in range(-len(s2), len(s2)):
+                    check_shape(ip, s1, s2, (), axis)
+
+
+def _check_complex(ip):
+    x = [1, 2, 3, 4]
+    y = [1, 2, 1j, 3]
+    p = ip(x, y)
+    assert_allclose(y, p(x))
+
+
+def test_complex():
+    for ip in [KroghInterpolator, BarycentricInterpolator, pchip, CubicSpline]:
+        _check_complex(ip)
+
+
+class TestKrogh(object):
+    def setup_method(self):
+        self.true_poly = np.poly1d([-2,3,1,5,-4])
+        self.test_xs = np.linspace(-1,1,100)
+        self.xs = np.linspace(-1,1,5)
+        self.ys = self.true_poly(self.xs)
+
+    def test_lagrange(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
+
+    def test_scalar(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        assert_almost_equal(self.true_poly(7),P(7))
+        assert_almost_equal(self.true_poly(np.array(7)), P(np.array(7)))
+
+    def test_derivatives(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        D = P.derivatives(self.test_xs)
+        for i in xrange(D.shape[0]):
+            assert_almost_equal(self.true_poly.deriv(i)(self.test_xs),
+                                D[i])
+
+    def test_low_derivatives(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        D = P.derivatives(self.test_xs,len(self.xs)+2)
+        for i in xrange(D.shape[0]):
+            assert_almost_equal(self.true_poly.deriv(i)(self.test_xs),
+                                D[i])
+
+    def test_derivative(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        m = 10
+        r = P.derivatives(self.test_xs,m)
+        for i in xrange(m):
+            assert_almost_equal(P.derivative(self.test_xs,i),r[i])
+
+    def test_high_derivative(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        for i in xrange(len(self.xs),2*len(self.xs)):
+            assert_almost_equal(P.derivative(self.test_xs,i),
+                                np.zeros(len(self.test_xs)))
+
+    def test_hermite(self):
+        xs = [0,0,0,1,1,1,2]
+        ys = [self.true_poly(0),
+              self.true_poly.deriv(1)(0),
+              self.true_poly.deriv(2)(0),
+              self.true_poly(1),
+              self.true_poly.deriv(1)(1),
+              self.true_poly.deriv(2)(1),
+              self.true_poly(2)]
+        P = KroghInterpolator(self.xs,self.ys)
+        assert_almost_equal(self.true_poly(self.test_xs),P(self.test_xs))
+
+    def test_vector(self):
+        xs = [0, 1, 2]
+        ys = np.array([[0,1],[1,0],[2,1]])
+        P = KroghInterpolator(xs,ys)
+        Pi = [KroghInterpolator(xs,ys[:,i]) for i in xrange(ys.shape[1])]
+        test_xs = np.linspace(-1,3,100)
+        assert_almost_equal(P(test_xs),
+                np.rollaxis(np.asarray([p(test_xs) for p in Pi]),-1))
+        assert_almost_equal(P.derivatives(test_xs),
+                np.transpose(np.asarray([p.derivatives(test_xs) for p in Pi]),
+                    (1,2,0)))
+
+    def test_empty(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        assert_array_equal(P([]), [])
+
+    def test_shapes_scalarvalue(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        assert_array_equal(np.shape(P(0)), ())
+        assert_array_equal(np.shape(P(np.array(0))), ())
+        assert_array_equal(np.shape(P([0])), (1,))
+        assert_array_equal(np.shape(P([0,1])), (2,))
+
+    def test_shapes_scalarvalue_derivative(self):
+        P = KroghInterpolator(self.xs,self.ys)
+        n = P.n
+        assert_array_equal(np.shape(P.derivatives(0)), (n,))
+        assert_array_equal(np.shape(P.derivatives(np.array(0))), (n,))
+        assert_array_equal(np.shape(P.derivatives([0])), (n,1))
+        assert_array_equal(np.shape(P.derivatives([0,1])), (n,2))
+
+    def test_shapes_vectorvalue(self):
+        P = KroghInterpolator(self.xs,np.outer(self.ys,np.arange(3)))
+        assert_array_equal(np.shape(P(0)), (3,))
+        assert_array_equal(np.shape(P([0])), (1,3))
+        assert_array_equal(np.shape(P([0,1])), (2,3))
+
+    def test_shapes_1d_vectorvalue(self):
+        P = KroghInterpolator(self.xs,np.outer(self.ys,[1]))
+        assert_array_equal(np.shape(P(0)), (1,))
+        assert_array_equal(np.shape(P([0])), (1,1))
+        assert_array_equal(np.shape(P([0,1])), (2,1))
+
+    def test_shapes_vectorvalue_derivative(self):
+        P = KroghInterpolator(self.xs,np.outer(self.ys,np.arange(3)))
+        n = P.n
+        assert_array_equal(np.shape(P.derivatives(0)), (n,3))
+        assert_array_equal(np.shape(P.derivatives([0])), (n,1,3))
+        assert_array_equal(np.shape(P.derivatives([0,1])), (n,2,3))
+
+    def test_wrapper(self):
+        P = KroghInterpolator(self.xs, self.ys)
+        ki = krogh_interpolate
+        assert_almost_equal(P(self.test_xs), ki(self.xs, self.ys, self.test_xs))
+        assert_almost_equal(P.derivative(self.test_xs, 2),
+                            ki(self.xs, self.ys, self.test_xs, der=2))
+        assert_almost_equal(P.derivatives(self.test_xs, 2),
+                            ki(self.xs, self.ys, self.test_xs, der=[0, 1]))
+
+    def test_int_inputs(self):
+        # Check input args are cast correctly to floats, gh-3669
+        x = [0, 234, 468, 702, 936, 1170, 1404, 2340, 3744, 6084, 8424,
+             13104, 60000]
+        offset_cdf = np.array([-0.95, -0.86114777, -0.8147762, -0.64072425,
+                               -0.48002351, -0.34925329, -0.26503107,
+                               -0.13148093, -0.12988833, -0.12979296,
+                               -0.12973574, -0.08582937, 0.05])
+        f = KroghInterpolator(x, offset_cdf)
+
+        assert_allclose(abs((f(x) - offset_cdf) / f.derivative(x, 1)),
+                        0, atol=1e-10)
+
+    def test_derivatives_complex(self):
+        # regression test for gh-7381: krogh.derivatives(0) fails complex y
+        x, y = np.array([-1, -1, 0, 1, 1]), np.array([1, 1.0j, 0, -1, 1.0j])
+        func = KroghInterpolator(x, y)
+        cmplx = func.derivatives(0)
+
+        cmplx2 = (KroghInterpolator(x, y.real).derivatives(0) +
+                  1j*KroghInterpolator(x, y.imag).derivatives(0))
+        assert_allclose(cmplx, cmplx2, atol=1e-15)
+
+
+class TestTaylor(object):
+    def test_exponential(self):
+        degree = 5
+        p = approximate_taylor_polynomial(np.exp, 0, degree, 1, 15)
+        for i in xrange(degree+1):
+            assert_almost_equal(p(0),1)
+            p = p.deriv()
+        assert_almost_equal(p(0),0)
+
+
+class TestBarycentric(object):
+    def setup_method(self):
+        self.true_poly = np.poly1d([-2, 3, 1, 5, -4])
+        self.test_xs = np.linspace(-1, 1, 100)
+        self.xs = np.linspace(-1, 1, 5)
+        self.ys = self.true_poly(self.xs)
+
+    def test_lagrange(self):
+        P = BarycentricInterpolator(self.xs, self.ys)
+        assert_almost_equal(self.true_poly(self.test_xs), P(self.test_xs))
+
+    def test_scalar(self):
+        P = BarycentricInterpolator(self.xs, self.ys)
+        assert_almost_equal(self.true_poly(7), P(7))
+        assert_almost_equal(self.true_poly(np.array(7)), P(np.array(7)))
+
+    def test_delayed(self):
+        P = BarycentricInterpolator(self.xs)
+        P.set_yi(self.ys)
+        assert_almost_equal(self.true_poly(self.test_xs), P(self.test_xs))
+
+    def test_append(self):
+        P = BarycentricInterpolator(self.xs[:3], self.ys[:3])
+        P.add_xi(self.xs[3:], self.ys[3:])
+        assert_almost_equal(self.true_poly(self.test_xs), P(self.test_xs))
+
+    def test_vector(self):
+        xs = [0, 1, 2]
+        ys = np.array([[0, 1], [1, 0], [2, 1]])
+        BI = BarycentricInterpolator 
+        P = BI(xs, ys)
+        Pi = [BI(xs, ys[:, i]) for i in xrange(ys.shape[1])]
+        test_xs = np.linspace(-1, 3, 100)
+        assert_almost_equal(P(test_xs),
+                np.rollaxis(np.asarray([p(test_xs) for p in Pi]), -1))
+
+    def test_shapes_scalarvalue(self):
+        P = BarycentricInterpolator(self.xs, self.ys)
+        assert_array_equal(np.shape(P(0)), ())
+        assert_array_equal(np.shape(P(np.array(0))), ())
+        assert_array_equal(np.shape(P([0])), (1,))
+        assert_array_equal(np.shape(P([0, 1])), (2,))
+
+    def test_shapes_vectorvalue(self):
+        P = BarycentricInterpolator(self.xs, np.outer(self.ys, np.arange(3)))
+        assert_array_equal(np.shape(P(0)), (3,))
+        assert_array_equal(np.shape(P([0])), (1, 3))
+        assert_array_equal(np.shape(P([0, 1])), (2, 3))
+
+    def test_shapes_1d_vectorvalue(self):
+        P = BarycentricInterpolator(self.xs, np.outer(self.ys, [1]))
+        assert_array_equal(np.shape(P(0)), (1,))
+        assert_array_equal(np.shape(P([0])), (1, 1))
+        assert_array_equal(np.shape(P([0,1])), (2, 1))
+
+    def test_wrapper(self):
+        P = BarycentricInterpolator(self.xs, self.ys)
+        values = barycentric_interpolate(self.xs, self.ys, self.test_xs)
+        assert_almost_equal(P(self.test_xs), values)
+
+
+class TestPCHIP(object):
+    def _make_random(self, npts=20):
+        np.random.seed(1234)
+        xi = np.sort(np.random.random(npts))
+        yi = np.random.random(npts)
+        return pchip(xi, yi), xi, yi
+
+    def test_overshoot(self):
+        # PCHIP should not overshoot
+        p, xi, yi = self._make_random()
+        for i in range(len(xi)-1):
+            x1, x2 = xi[i], xi[i+1]
+            y1, y2 = yi[i], yi[i+1]
+            if y1 > y2:
+                y1, y2 = y2, y1
+            xp = np.linspace(x1, x2, 10)
+            yp = p(xp)
+            assert_(((y1 <= yp) & (yp <= y2)).all())
+
+    def test_monotone(self):
+        # PCHIP should preserve monotonicty
+        p, xi, yi = self._make_random()
+        for i in range(len(xi)-1):
+            x1, x2 = xi[i], xi[i+1]
+            y1, y2 = yi[i], yi[i+1]
+            xp = np.linspace(x1, x2, 10)
+            yp = p(xp)
+            assert_(((y2-y1) * (yp[1:] - yp[:1]) > 0).all())
+
+    def test_cast(self):
+        # regression test for integer input data, see gh-3453
+        data = np.array([[0, 4, 12, 27, 47, 60, 79, 87, 99, 100],
+                         [-33, -33, -19, -2, 12, 26, 38, 45, 53, 55]])
+        xx = np.arange(100)
+        curve = pchip(data[0], data[1])(xx)
+
+        data1 = data * 1.0
+        curve1 = pchip(data1[0], data1[1])(xx)
+
+        assert_allclose(curve, curve1, atol=1e-14, rtol=1e-14)
+
+    def test_nag(self):
+        # Example from NAG C implementation,
+        # http://nag.com/numeric/cl/nagdoc_cl25/html/e01/e01bec.html
+        # suggested in gh-5326 as a smoke test for the way the derivatives
+        # are computed (see also gh-3453)
+        from scipy._lib.six import StringIO
+        dataStr = '''
+          7.99   0.00000E+0
+          8.09   0.27643E-4
+          8.19   0.43750E-1
+          8.70   0.16918E+0
+          9.20   0.46943E+0
+         10.00   0.94374E+0
+         12.00   0.99864E+0
+         15.00   0.99992E+0
+         20.00   0.99999E+0
+        '''
+        data = np.loadtxt(StringIO(dataStr))
+        pch = pchip(data[:,0], data[:,1])
+
+        resultStr = '''
+           7.9900       0.0000
+           9.1910       0.4640
+          10.3920       0.9645
+          11.5930       0.9965
+          12.7940       0.9992
+          13.9950       0.9998
+          15.1960       0.9999
+          16.3970       1.0000
+          17.5980       1.0000
+          18.7990       1.0000
+          20.0000       1.0000
+        '''
+        result = np.loadtxt(StringIO(resultStr))
+        assert_allclose(result[:,1], pch(result[:,0]), rtol=0., atol=5e-5)
+
+    def test_endslopes(self):
+        # this is a smoke test for gh-3453: PCHIP interpolator should not
+        # set edge slopes to zero if the data do not suggest zero edge derivatives
+        x = np.array([0.0, 0.1, 0.25, 0.35])
+        y1 = np.array([279.35, 0.5e3, 1.0e3, 2.5e3])
+        y2 = np.array([279.35, 2.5e3, 1.50e3, 1.0e3])
+        for pp in (pchip(x, y1), pchip(x, y2)):
+            for t in (x[0], x[-1]):
+                assert_(pp(t, 1) != 0)
+
+    def test_all_zeros(self):
+        x = np.arange(10)
+        y = np.zeros_like(x)
+
+        # this should work and not generate any warnings
+        with warnings.catch_warnings():
+            warnings.filterwarnings('error')
+            pch = pchip(x, y)
+
+        xx = np.linspace(0, 9, 101)
+        assert_equal(pch(xx), 0.)
+
+    def test_two_points(self):
+        # regression test for gh-6222: pchip([0, 1], [0, 1]) fails because
+        # it tries to use a three-point scheme to estimate edge derivatives,
+        # while there are only two points available.
+        # Instead, it should construct a linear interpolator.
+        x = np.linspace(0, 1, 11)
+        p = pchip([0, 1], [0, 2])
+        assert_allclose(p(x), 2*x, atol=1e-15)
+
+    def test_pchip_interpolate(self):
+        assert_array_almost_equal(
+            pchip_interpolate([1,2,3], [4,5,6], [0.5], der=1),
+            [1.])
+
+        assert_array_almost_equal(
+            pchip_interpolate([1,2,3], [4,5,6], [0.5], der=0),
+            [3.5])
+
+        assert_array_almost_equal(
+            pchip_interpolate([1,2,3], [4,5,6], [0.5], der=[0, 1]),
+            [[3.5], [1]])
+
+    def test_roots(self):
+        # regression test for gh-6357: .roots method should work
+        p = pchip([0, 1], [-1, 1])
+        r = p.roots()
+        assert_allclose(r, 0.5)
+
+class TestCubicSpline(object):
+    @staticmethod
+    def check_correctness(S, bc_start='not-a-knot', bc_end='not-a-knot',
+                          tol=1e-14):
+        """Check that spline coefficients satisfy the continuity and boundary
+        conditions."""
+        x = S.x
+        c = S.c
+        dx = np.diff(x)
+        dx = dx.reshape([dx.shape[0]] + [1] * (c.ndim - 2))
+        dxi = dx[:-1]
+
+        # Check C2 continuity.
+        assert_allclose(c[3, 1:], c[0, :-1] * dxi**3 + c[1, :-1] * dxi**2 +
+                        c[2, :-1] * dxi + c[3, :-1], rtol=tol, atol=tol)
+        assert_allclose(c[2, 1:], 3 * c[0, :-1] * dxi**2 +
+                        2 * c[1, :-1] * dxi + c[2, :-1], rtol=tol, atol=tol)
+        assert_allclose(c[1, 1:], 3 * c[0, :-1] * dxi + c[1, :-1],
+                        rtol=tol, atol=tol)
+
+        # Check that we found a parabola, the third derivative is 0.
+        if x.size == 3 and bc_start == 'not-a-knot' and bc_end == 'not-a-knot':
+            assert_allclose(c[0], 0, rtol=tol, atol=tol)
+            return
+
+        # Check periodic boundary conditions.
+        if bc_start == 'periodic':
+            assert_allclose(S(x[0], 0), S(x[-1], 0), rtol=tol, atol=tol)
+            assert_allclose(S(x[0], 1), S(x[-1], 1), rtol=tol, atol=tol)
+            assert_allclose(S(x[0], 2), S(x[-1], 2), rtol=tol, atol=tol)
+            return
+
+        # Check other boundary conditions.
+        if bc_start == 'not-a-knot':
+            if x.size == 2:
+                slope = (S(x[1]) - S(x[0])) / dx[0]
+                assert_allclose(S(x[0], 1), slope, rtol=tol, atol=tol)
+            else:
+                assert_allclose(c[0, 0], c[0, 1], rtol=tol, atol=tol)
+        elif bc_start == 'clamped':
+            assert_allclose(S(x[0], 1), 0, rtol=tol, atol=tol)
+        elif bc_start == 'natural':
+            assert_allclose(S(x[0], 2), 0, rtol=tol, atol=tol)
+        else:
+            order, value = bc_start
+            assert_allclose(S(x[0], order), value, rtol=tol, atol=tol)
+
+        if bc_end == 'not-a-knot':
+            if x.size == 2:
+                slope = (S(x[1]) - S(x[0])) / dx[0]
+                assert_allclose(S(x[1], 1), slope, rtol=tol, atol=tol)
+            else:
+                assert_allclose(c[0, -1], c[0, -2], rtol=tol, atol=tol)
+        elif bc_end == 'clamped':
+            assert_allclose(S(x[-1], 1), 0, rtol=tol, atol=tol)
+        elif bc_end == 'natural':
+            assert_allclose(S(x[-1], 2), 0, rtol=2*tol, atol=2*tol)
+        else:
+            order, value = bc_end
+            assert_allclose(S(x[-1], order), value, rtol=tol, atol=tol)
+
+    def check_all_bc(self, x, y, axis):
+        deriv_shape = list(y.shape)
+        del deriv_shape[axis]
+        first_deriv = np.empty(deriv_shape)
+        first_deriv.fill(2)
+        second_deriv = np.empty(deriv_shape)
+        second_deriv.fill(-1)
+        bc_all = [
+            'not-a-knot',
+            'natural',
+            'clamped',
+            (1, first_deriv),
+            (2, second_deriv)
+        ]
+        for bc in bc_all[:3]:
+            S = CubicSpline(x, y, axis=axis, bc_type=bc)
+            self.check_correctness(S, bc, bc)
+
+        for bc_start in bc_all:
+            for bc_end in bc_all:
+                S = CubicSpline(x, y, axis=axis, bc_type=(bc_start, bc_end))
+                self.check_correctness(S, bc_start, bc_end, tol=2e-14)
+
+    def test_general(self):
+        x = np.array([-1, 0, 0.5, 2, 4, 4.5, 5.5, 9])
+        y = np.array([0, -0.5, 2, 3, 2.5, 1, 1, 0.5])
+        for n in [2, 3, x.size]:
+            self.check_all_bc(x[:n], y[:n], 0)
+
+            Y = np.empty((2, n, 2))
+            Y[0, :, 0] = y[:n]
+            Y[0, :, 1] = y[:n] - 1
+            Y[1, :, 0] = y[:n] + 2
+            Y[1, :, 1] = y[:n] + 3
+            self.check_all_bc(x[:n], Y, 1)
+
+    def test_periodic(self):
+        for n in [2, 3, 5]:
+            x = np.linspace(0, 2 * np.pi, n)
+            y = np.cos(x)
+            S = CubicSpline(x, y, bc_type='periodic')
+            self.check_correctness(S, 'periodic', 'periodic')
+
+            Y = np.empty((2, n, 2))
+            Y[0, :, 0] = y
+            Y[0, :, 1] = y + 2
+            Y[1, :, 0] = y - 1
+            Y[1, :, 1] = y + 5
+            S = CubicSpline(x, Y, axis=1, bc_type='periodic')
+            self.check_correctness(S, 'periodic', 'periodic')
+
+    def test_periodic_eval(self):
+        x = np.linspace(0, 2 * np.pi, 10)
+        y = np.cos(x)
+        S = CubicSpline(x, y, bc_type='periodic')
+        assert_almost_equal(S(1), S(1 + 2 * np.pi), decimal=15)
+
+    def test_dtypes(self):
+        x = np.array([0, 1, 2, 3], dtype=int)
+        y = np.array([-5, 2, 3, 1], dtype=int)
+        S = CubicSpline(x, y)
+        self.check_correctness(S)
+
+        y = np.array([-1+1j, 0.0, 1-1j, 0.5-1.5j])
+        S = CubicSpline(x, y)
+        self.check_correctness(S)
+
+        S = CubicSpline(x, x ** 3, bc_type=("natural", (1, 2j)))
+        self.check_correctness(S, "natural", (1, 2j))
+
+        y = np.array([-5, 2, 3, 1])
+        S = CubicSpline(x, y, bc_type=[(1, 2 + 0.5j), (2, 0.5 - 1j)])
+        self.check_correctness(S, (1, 2 + 0.5j), (2, 0.5 - 1j))
+
+    def test_small_dx(self):
+        rng = np.random.RandomState(0)
+        x = np.sort(rng.uniform(size=100))
+        y = 1e4 + rng.uniform(size=100)
+        S = CubicSpline(x, y)
+        self.check_correctness(S, tol=1e-13)
+
+    def test_incorrect_inputs(self):
+        x = np.array([1, 2, 3, 4])
+        y = np.array([1, 2, 3, 4])
+        xc = np.array([1 + 1j, 2, 3, 4])
+        xn = np.array([np.nan, 2, 3, 4])
+        xo = np.array([2, 1, 3, 4])
+        yn = np.array([np.nan, 2, 3, 4])
+        y3 = [1, 2, 3]
+        x1 = [1]
+        y1 = [1]
+
+        assert_raises(ValueError, CubicSpline, xc, y)
+        assert_raises(ValueError, CubicSpline, xn, y)
+        assert_raises(ValueError, CubicSpline, x, yn)
+        assert_raises(ValueError, CubicSpline, xo, y)
+        assert_raises(ValueError, CubicSpline, x, y3)
+        assert_raises(ValueError, CubicSpline, x[:, np.newaxis], y)
+        assert_raises(ValueError, CubicSpline, x1, y1)
+
+        wrong_bc = [('periodic', 'clamped'),
+                    ((2, 0), (3, 10)),
+                    ((1, 0), ),
+                    (0., 0.),
+                    'not-a-typo']
+
+        for bc_type in wrong_bc:
+            assert_raises(ValueError, CubicSpline, x, y, 0, bc_type, True)
+
+        # Shapes mismatch when giving arbitrary derivative values:
+        Y = np.c_[y, y]
+        bc1 = ('clamped', (1, 0))
+        bc2 = ('clamped', (1, [0, 0, 0]))
+        bc3 = ('clamped', (1, [[0, 0]]))
+        assert_raises(ValueError, CubicSpline, x, Y, 0, bc1, True)
+        assert_raises(ValueError, CubicSpline, x, Y, 0, bc2, True)
+        assert_raises(ValueError, CubicSpline, x, Y, 0, bc3, True)
+
+        # periodic condition, y[-1] must be equal to y[0]:
+        assert_raises(ValueError, CubicSpline, x, y, 0, 'periodic', True)
+

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_rbf.py

@@ -0,0 +1,155 @@
+# Created by John Travers, Robert Hetland, 2007
+""" Test functions for rbf module """
+from __future__ import division, print_function, absolute_import
+
+
+import numpy as np
+from numpy.testing import (assert_, assert_array_almost_equal,
+                           assert_almost_equal)
+from numpy import linspace, sin, random, exp, allclose
+from scipy.interpolate.rbf import Rbf
+
+FUNCTIONS = ('multiquadric', 'inverse multiquadric', 'gaussian',
+             'cubic', 'quintic', 'thin-plate', 'linear')
+
+
+def check_rbf1d_interpolation(function):
+    # Check that the Rbf function interpolates through the nodes (1D)
+    x = linspace(0,10,9)
+    y = sin(x)
+    rbf = Rbf(x, y, function=function)
+    yi = rbf(x)
+    assert_array_almost_equal(y, yi)
+    assert_almost_equal(rbf(float(x[0])), y[0])
+
+
+def check_rbf2d_interpolation(function):
+    # Check that the Rbf function interpolates through the nodes (2D).
+    x = random.rand(50,1)*4-2
+    y = random.rand(50,1)*4-2
+    z = x*exp(-x**2-1j*y**2)
+    rbf = Rbf(x, y, z, epsilon=2, function=function)
+    zi = rbf(x, y)
+    zi.shape = x.shape
+    assert_array_almost_equal(z, zi)
+
+
+def check_rbf3d_interpolation(function):
+    # Check that the Rbf function interpolates through the nodes (3D).
+    x = random.rand(50, 1)*4 - 2
+    y = random.rand(50, 1)*4 - 2
+    z = random.rand(50, 1)*4 - 2
+    d = x*exp(-x**2 - y**2)
+    rbf = Rbf(x, y, z, d, epsilon=2, function=function)
+    di = rbf(x, y, z)
+    di.shape = x.shape
+    assert_array_almost_equal(di, d)
+
+
+def test_rbf_interpolation():
+    for function in FUNCTIONS:
+        check_rbf1d_interpolation(function)
+        check_rbf2d_interpolation(function)
+        check_rbf3d_interpolation(function)
+
+
+def check_rbf1d_regularity(function, atol):
+    # Check that the Rbf function approximates a smooth function well away
+    # from the nodes.
+    x = linspace(0, 10, 9)
+    y = sin(x)
+    rbf = Rbf(x, y, function=function)
+    xi = linspace(0, 10, 100)
+    yi = rbf(xi)
+    # import matplotlib.pyplot as plt
+    # plt.figure()
+    # plt.plot(x, y, 'o', xi, sin(xi), ':', xi, yi, '-')
+    # plt.plot(x, y, 'o', xi, yi-sin(xi), ':')
+    # plt.title(function)
+    # plt.show()
+    msg = "abs-diff: %f" % abs(yi - sin(xi)).max()
+    assert_(allclose(yi, sin(xi), atol=atol), msg)
+
+
+def test_rbf_regularity():
+    tolerances = {
+        'multiquadric': 0.1,
+        'inverse multiquadric': 0.15,
+        'gaussian': 0.15,
+        'cubic': 0.15,
+        'quintic': 0.1,
+        'thin-plate': 0.1,
+        'linear': 0.2
+    }
+    for function in FUNCTIONS:
+        check_rbf1d_regularity(function, tolerances.get(function, 1e-2))
+
+
+def check_rbf1d_stability(function):
+    # Check that the Rbf function with default epsilon is not subject 
+    # to overshoot.  Regression for issue #4523.
+    #
+    # Generate some data (fixed random seed hence deterministic) 
+    np.random.seed(1234)
+    x = np.linspace(0, 10, 50)
+    z = x + 4.0 * np.random.randn(len(x))
+
+    rbf = Rbf(x, z, function=function)
+    xi = np.linspace(0, 10, 1000)
+    yi = rbf(xi)
+
+    # subtract the linear trend and make sure there no spikes
+    assert_(np.abs(yi-xi).max() / np.abs(z-x).max() < 1.1)
+
+def test_rbf_stability():
+    for function in FUNCTIONS:
+        check_rbf1d_stability(function)
+
+
+def test_default_construction():
+    # Check that the Rbf class can be constructed with the default
+    # multiquadric basis function. Regression test for ticket #1228.
+    x = linspace(0,10,9)
+    y = sin(x)
+    rbf = Rbf(x, y)
+    yi = rbf(x)
+    assert_array_almost_equal(y, yi)
+
+
+def test_function_is_callable():
+    # Check that the Rbf class can be constructed with function=callable.
+    x = linspace(0,10,9)
+    y = sin(x)
+    linfunc = lambda x:x
+    rbf = Rbf(x, y, function=linfunc)
+    yi = rbf(x)
+    assert_array_almost_equal(y, yi)
+
+
+def test_two_arg_function_is_callable():
+    # Check that the Rbf class can be constructed with a two argument
+    # function=callable.
+    def _func(self, r):
+        return self.epsilon + r
+
+    x = linspace(0,10,9)
+    y = sin(x)
+    rbf = Rbf(x, y, function=_func)
+    yi = rbf(x)
+    assert_array_almost_equal(y, yi)
+
+
+def test_rbf_epsilon_none():
+    x = linspace(0, 10, 9)
+    y = sin(x)
+    rbf = Rbf(x, y, epsilon=None)
+
+
+def test_rbf_epsilon_none_collinear():
+    # Check that collinear points in one dimension doesn't cause an error
+    # due to epsilon = 0
+    x = [1, 2, 3]
+    y = [4, 4, 4]
+    z = [5, 6, 7]
+    rbf = Rbf(x, y, z, epsilon=None)
+    assert_(rbf.epsilon > 0)

utils/venv/lib/python3.6/site-packages/scipy/interpolate/tests/test_regression.py

@@ -0,0 +1,16 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+import scipy.interpolate as interp
+from numpy.testing import assert_almost_equal
+
+
+class TestRegression(object):
+    def test_spalde_scalar_input(self):
+        """Ticket #629"""
+        x = np.linspace(0,10)
+        y = x**3
+        tck = interp.splrep(x, y, k=3, t=[5])
+        res = interp.spalde(np.float64(1), tck)
+        des = np.array([1., 3., 6., 6.])
+        assert_almost_equal(res, des)