Python interpolate.make_interp_spline函数代码示例

    def test_sliced_input(self):
        # cython code chokes on non C contiguous arrays
        xx = np.linspace(-1, 1, 100)

        x = xx[::5]
        y = xx[::5]

        make_interp_spline(x, y, k=1)

    def test_quadratic_deriv(self):
        der = [(1, 8.)]  # order, value: f'(x) = 8.

        # derivative at right-hand edge
        b = make_interp_spline(self.xx, self.yy, k=2, bc_type=(None, der))
        assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14)
        assert_allclose(b(self.xx[-1], 1), der[0][1], atol=1e-14, rtol=1e-14)

        # derivative at left-hand edge
        b = make_interp_spline(self.xx, self.yy, k=2, bc_type=(der, None))
        assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14)
        assert_allclose(b(self.xx[0], 1), der[0][1], atol=1e-14, rtol=1e-14)

    def test_cubic_deriv(self):
        k = 3

        # first derivatives at left & right edges:
        der_l, der_r = [(1, 3.)], [(1, 4.)]
        b = make_interp_spline(self.xx, self.yy, k, bc_type=(der_l, der_r))
        assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14)
        assert_allclose([b(self.xx[0], 1), b(self.xx[-1], 1)],
                        [der_l[0][1], der_r[0][1]], atol=1e-14, rtol=1e-14)

        # 'natural' cubic spline, zero out 2nd derivatives at the boundaries
        der_l, der_r = [(2, 0)], [(2, 0)]
        b = make_interp_spline(self.xx, self.yy, k, bc_type=(der_l, der_r))
        assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14)

    def test_shapes(self):
        np.random.seed(1234)
        k, n = 3, 22
        x = np.sort(np.random.random(size=n))
        y = np.random.random(size=(n, 5, 6, 7))

        b = make_interp_spline(x, y, k)
        assert_equal(b.c.shape, (n, 5, 6, 7))

        # now throw in some derivatives
        d_l = [(1, np.random.random((5, 6, 7)))]
        d_r = [(1, np.random.random((5, 6, 7)))]
        b = make_interp_spline(x, y, k, bc_type=(d_l, d_r))
        assert_equal(b.c.shape, (n + k - 1, 5, 6, 7))

    def test_complex(self):
        k = 3
        xx = self.xx
        yy = self.yy + 1.j*self.yy

        # first derivatives at left & right edges:
        der_l, der_r = [(1, 3.j)], [(1, 4.+2.j)]
        b = make_interp_spline(xx, yy, k, bc_type=(der_l, der_r))
        assert_allclose(b(xx), yy, atol=1e-14, rtol=1e-14)
        assert_allclose([b(xx[0], 1), b(xx[-1], 1)],
                        [der_l[0][1], der_r[0][1]], atol=1e-14, rtol=1e-14)

        # also test zero and first order
        for k in (0, 1):
            b = make_interp_spline(xx, yy, k=k)
            assert_allclose(b(xx), yy, atol=1e-14, rtol=1e-14)

    def test_int_xy(self):
        x = np.arange(10).astype(np.int_)
        y = np.arange(10).astype(np.int_)

        # cython chokes on "buffer type mismatch" (construction) or
        # "no matching signature found" (evaluation)
        for k in (0, 1, 2, 3):
            b = make_interp_spline(x, y, k=k)
            b(x)

    def test_multiple_rhs(self):
        yy = np.c_[np.sin(self.xx), np.cos(self.xx)]
        der_l = [(1, [1., 2.])]
        der_r = [(1, [3., 4.])]

        b = make_interp_spline(self.xx, yy, k=3, bc_type=(der_l, der_r))
        assert_allclose(b(self.xx), yy, atol=1e-14, rtol=1e-14)
        assert_allclose(b(self.xx[0], 1), der_l[0][1], atol=1e-14, rtol=1e-14)
        assert_allclose(b(self.xx[-1], 1), der_r[0][1], atol=1e-14, rtol=1e-14)

    def test_full_matrix(self):
        np.random.seed(1234)
        k, n = 3, 7
        x = np.sort(np.random.random(size=n))
        y = np.random.random(size=n)
        t = _not_a_knot(x, k)

        b = make_interp_spline(x, y, k, t)
        cf = make_interp_full_matr(x, y, t, k)
        assert_allclose(b.c, cf, atol=1e-14, rtol=1e-14)

    def test_integrate_ppoly(self):
        # test .integrate method to be consistent with PPoly.integrate
        x = [0, 1, 2, 3, 4]
        b = make_interp_spline(x, x)
        b.extrapolate = 'periodic'
        p = PPoly.from_spline(b)

        for x0, x1 in [(-5, 0.5), (0.5, 5), (-4, 13)]:
            assert_allclose(b.integrate(x0, x1),
                            p.integrate(x0, x1))

 def test_minimum_points_and_deriv(self):
     # interpolation of f(x) = x**3 between 0 and 1. f'(x) = 3 * xx**2 and 
     # f'(0) = 0, f'(1) = 3.
     k = 3
     x = [0., 1.]
     y = [0., 1.]
     b = make_interp_spline(x, y, k, bc_type=([(1, 0.)], [(1, 3.)]))
     
     xx = np.linspace(0., 1.)
     yy = xx**3
     assert_allclose(b(xx), yy, atol=1e-14, rtol=1e-14)

 def test_quintic_derivs(self):
     k, n = 5, 7
     x = np.arange(n).astype(np.float_)
     y = np.sin(x)
     der_l = [(1, -12.), (2, 1)]
     der_r = [(1, 8.), (2, 3.)]
     b = make_interp_spline(x, y, k=k, bc_type=(der_l, der_r))
     assert_allclose(b(x), y, atol=1e-14, rtol=1e-14)
     assert_allclose([b(x[0], 1), b(x[0], 2)],
                     [val for (nu, val) in der_l])
     assert_allclose([b(x[-1], 1), b(x[-1], 2)],
                     [val for (nu, val) in der_r])

    def setup_method(self):
        xx = np.linspace(0, 4.*np.pi, 41)
        yy = np.cos(xx)
        b = make_interp_spline(xx, yy)
        self.tck = (b.t, b.c, b.k)
        self.xx, self.yy, self.b = xx, yy, b

        self.xnew = np.linspace(0, 4.*np.pi, 21)

        c2 = np.c_[b.c, b.c, b.c]
        self.c2 = np.dstack((c2, c2))
        self.b2 = BSpline(b.t, self.c2, b.k)

    def test_cubic_deriv_unstable(self):
        # 1st and 2nd derivative at x[0], no derivative information at x[-1]
        # The problem is not that it fails [who would use this anyway],
        # the problem is that it fails *silently*, and I've no idea
        # how to detect this sort of instability.
        # In this particular case: it's OK for len(t) < 20, goes haywire
        # at larger `len(t)`.
        k = 3
        t = _augknt(self.xx, k)

        der_l = [(1, 3.), (2, 4.)]
        b = make_interp_spline(self.xx, self.yy, k, t, bc_type=(der_l, None))
        assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14)

    def test_deriv_spec(self):
        # If one of the derivatives is omitted, the spline definition is 
        # incomplete.
        x = y = [1.0, 2, 3, 4, 5, 6]

        with assert_raises(ValueError):
            make_interp_spline(x, y, bc_type=([(1, 0.)], None))

        with assert_raises(ValueError):
            make_interp_spline(x, y, bc_type=(1, 0.))

        with assert_raises(ValueError):
            make_interp_spline(x, y, bc_type=[(1, 0.)])

        with assert_raises(ValueError):
            make_interp_spline(x, y, bc_type=42)

        # CubicSpline expects`bc_type=(left_pair, right_pair)`, while
        # here we expect `bc_type=(iterable, iterable)`.
        l, r = (1, 0.0), (1, 0.0)
        with assert_raises(ValueError):
            make_interp_spline(x, y, bc_type=(l, r))

    def test_knots_not_data_sites(self):
        # Knots need not coincide with the data sites.
        # use a quadratic spline, knots are at data averages,
        # two additional constraints are zero 2nd derivs at edges
        k = 2
        t = np.r_[(self.xx[0],)*(k+1),
                  (self.xx[1:] + self.xx[:-1]) / 2.,
                  (self.xx[-1],)*(k+1)]
        b = make_interp_spline(self.xx, self.yy, k, t,
                               bc_type=([(2, 0)], [(2, 0)]))

        assert_allclose(b(self.xx), self.yy, atol=1e-14, rtol=1e-14)
        assert_allclose([b(self.xx[0], 2), b(self.xx[-1], 2)], [0., 0.],
                atol=1e-14)