CoCalc Public FilesPM_2_5 / wave_equation / worksheets / volume_integral_test.sagewsOpen in CoCalc with one click!
Author: Balavarun P
var('x, y, xi') import numpy as np from scipy import special as sp x_nodes = [-1, 1]
(x, y, xi)
def LGL_points(N): ''' ''' xi = np.poly1d([1, 0]) legendre_N_minus_1 = N * (xi * sp.legendre(N - 1) - sp.legendre(N)) lgl_points = legendre_N_minus_1.r lgl_points.sort() return lgl_points
def lagrange_polynomials(x): ''' ''' X = np.array(x) lagrange_basis_poly = [] lagrange_basis_coeffs = np.zeros([X.shape[0], X.shape[0]]) for j in np.arange(X.shape[0]): lagrange_basis_j = np.poly1d([1]) for m in np.arange(X.shape[0]): if m != j: lagrange_basis_j *= np.poly1d([1, -X[m]]) \ / (X[j] - X[m]) lagrange_basis_poly.append(lagrange_basis_j) return lagrange_basis_poly
N_LGL = 16
N_LGL_lagrange_polynomials = lagrange_polynomials(LGL_points(N_LGL))
e = np.e
x_element = e ** (((-0.9 + 0.1 * xi) ** 2) / 0.4 ** 2)
var(x, xi, eta)
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 995, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> NameError: name 'xi' is not defined
def L_0(): ''' ''' for i in range(N_LGL): for j in range(N_LGL):