def test_spli_shape(self):
n, a, b = 35, -3, 3
basis = BasisSpline(n, a, b)
assert_equal(basis.nodes.size, n)
assert_equal(basis.Phi().shape, (n, n))
assert_equal(basis._diff(0, 2).shape, (n - 2, n))
assert_equal(basis._diff(0, -3).shape, (n + 3, n))
assert_equal(basis().shape, (n, ))
nx = 24
x = np.linspace(a, b, nx)
assert_equal(basis.Phi(x).shape, (nx, n))
assert_equal(basis.Phi(x, 1).shape, (nx, n))
assert_equal(basis.Phi(x, -1).shape, (nx, n))
assert_equal(basis(x).shape, (nx, ))
def test_cheb_2d(self):
n, a, b = [5, 9], -3, 3
s = 2
nn = n[0] * n[1]
basis = BasisSpline(n, a, b, s=s)
assert_equal(basis.nodes.shape, (len(n), nn))
assert_equal(basis.Phi().shape, (nn, nn))
assert_equal(basis._diff(0, 2).shape, (n[0] - 2, n[0]))
assert_equal(basis._diff(1, -3).shape, (n[1] + 3, n[1]))
assert_equal(basis().shape, (s, nn))
nx = [15, 16]
nnx = nx[0] * nx[1]
x = gridmake([np.linspace(a, b, j) for j in nx])
assert_equal(basis.Phi(x).shape, (nnx, nn))
assert_equal(basis.Phi(x, [[1], [0]]).shape, (nnx, nn))
assert_equal(basis.Phi(x, [[0], [-1]]).shape, (nnx, nn))
assert_equal(basis(x).shape, (s, nnx))
Phi = np.array([x**j for j in np.arange(n)]) basisplot(x, Phi, 'Monomial Basis Functions on [0,1]') # ### % Plot Chebychev basis functions and nodes # In[7]: B = BasisChebyshev(n, a, b) basisplot(x, B.Phi(x).T, 'Chebychev Polynomial Basis Functions on [0,1]') nodeplot(B.nodes, 'Chebychev Nodes on [0,1]') # ### % Plot linear spline basis functions and nodes # In[8]: L = BasisSpline(n, a, b, k=1) basisplot(x, L.Phi(x).T.toarray(), 'Linear Spline Basis Functions on [0,1]') nodeplot(L.nodes, 'Linear Spline Standard Nodes on [0,1]') # ### % Plot cubic spline basis functions and nodes # In[9]: C = BasisSpline(n, a, b, k=3) basisplot(x, C.Phi(x).T.toarray(), 'Cubic Spline Basis Functions on [0,1]') nodeplot(C.nodes, 'Cubic Spline Standard Nodes on [0,1]') # In[10]: demo.savefig(figures)