Created
May 8, 2015 18:49
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| def get_P(n): | |
| val = [1, 2, 1] * (n / 2) | |
| col = [] | |
| for i in xrange(n / 2): | |
| col += 3*[i] | |
| row = [] | |
| for j in xrange((n-1)/2): | |
| row += range(2*j, 2*j + 3) | |
| P = scsp.csr_matrix((val, (row, col)), shape=(n, (n-1)/2)) | |
| return 0.5 * P | |
| def MG_V_1d(l, u_old, rhs, A): | |
| if (l == 0): | |
| u_new = scspla.spsolve(A, rhs) | |
| else: | |
| u = u_old.copy() | |
| P = get_P(u.shape[0]) | |
| R = 0.5 * P.T | |
| ev1, _ = scspla.eigs(A, k=3, which='LR') | |
| ev2, _ = scspla.eigs(A, k=3, which='SR') | |
| lam_max = ev1[0] | |
| lam_min = ev2[0] | |
| tau_opt = np.real(2.0/(lam_max + lam_min)) | |
| # tau_opt = -3 * 1e-5 | |
| print "Start smoother with tau", tau_opt | |
| for it in xrange(5): | |
| rr = A.dot(u) - rhs | |
| print np.linalg.norm(rr) | |
| u = u - tau_opt * rr | |
| res = R.dot(A.dot(u) - rhs) | |
| A = R.dot(A.dot(P)) | |
| e = np.zeros(u.shape[0] / 2) | |
| for i in xrange(1): | |
| e = MG_V_1d(l - 1, e, res, A) | |
| u_new = u - P.dot(e) | |
| return u_new | |
| N = 128 | |
| x = np.linspace(1.0 / N, 1, N - 1, endpoint=False) | |
| f = -np.pi**2 * np.sin(np.pi * x) | |
| ex = np.ones(N-1); | |
| A = N**2 * scsp.spdiags(np.vstack((ex, -2*ex, ex)), [-1, 0, 1], N-1, N-1, 'csr'); | |
| u0 = np.zeros(N-1) | |
| u = MG_V_1d(5, u0, f, A) | |
| print u.shape | |
| print np.linalg.norm(np.sin(np.pi * x) - u) | |
| plt.plot(x, np.sin(np.pi * x)) | |
| plt.plot(x, u) | |
| plt.legend(["Exact", r"Approx"]) |
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