kernel_helper.py 5.37 KB
 Martin Reinecke committed Jul 11, 2020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 ``````import numpy as np from scipy.optimize import leastsq def gridder_to_C(gridder, W): M = len(gridder) // W C = np.zeros((W, M), dtype=float) for r in range(0, W): ell = r - (W / 2) + 1 indx = (np.arange(M) - 2 * M * ell).astype(int) # Use symmetry to deal with negative indices indx[indx < 0] = -indx[indx < 0] - 1 C[r, :] = gridder[indx] return C def C_to_grid_correction(C, nu_C, x, optimal=True): W = C.shape[0] nx = x.shape[0] c = np.zeros(x.shape, dtype=float) d = np.zeros(x.shape, dtype=float) C = C.reshape((C.shape[0],C.shape[1],1)) nu_C = nu_C.reshape((-1,1)) x = x.reshape((1,-1)) cosarr = np.empty((W,nx)) for i in range(W): cosarr[i,:] = np.cos(2 * np.pi * i * x) for rp in range(0, W): ellp = rp - (W / 2) + 1 for r in range(0, W): ell = r - (W / 2) + 1 xmn = np.mean(C[rp, :, :]*C[r, :, :], axis=0) tmp = xmn * cosarr[abs(rp-r)] # tmp = C[rp, :, :] * C[r, :, :] * np.cos(2 * np.pi * (ellp - ell) * x) # print(np.max(np.abs(tmp-np.mean(tmp2,axis=0)))) d += tmp # d += np.mean(tmp,axis=0) tmp2 = C[rp, :, :] * np.cos(2 * np.pi * (ellp-nu_C) * x) c += np.mean(tmp2,axis=0) return c / d if optimal else 1 / c def gridder_to_grid_correction(gridder, nu, x, W, optimal=True): M = len(nu) // W C = gridder_to_C(gridder, W) return C_to_grid_correction(C, nu[:M], x, optimal) def calc_map_error_from_C(C, grid_correction, nu_C, x, W): M = len(nu_C) nx = len(x) one_app=np.zeros((nx, M), dtype=np.complex128) for r in range(0, W): ell = r - (W / 2) + 1 one_app += grid_correction.reshape((-1,1)) * C[r, :] \ * np.exp(2j * np.pi * (ell - nu_C).reshape((1,-1)) * x.reshape((-1,1))) one_app = (1.-one_app.real)**2 + one_app.imag**2 map_error = np.sum(one_app, axis=1)/M return map_error def calc_map_error(gridder, grid_correction, nu, x, W): M = len(nu) // W C = gridder_to_C(gridder, W) return calc_map_error_from_C(C, grid_correction, nu[:M], x, W) import matplotlib.pyplot as plt def eskapprox(parm, nu, x, W): nunorm=2*nu/W beta=parm[0] e1 = 0.5 if len(parm)<2 else parm[1] e2 = 2. if len(parm)<3 else parm[2] return np.exp(beta*W*((1-nunorm**e2)**e1-1)) def getmaxerr(approx, coeff, nu, x, W, M, N, x0): nu=(np.arange(W*M)+0.5)/(2*M) x=np.arange(N+1)/(2*N) krn = approx(coeff, nu, x, W) err = kernel2error(krn, nu, x, W) err = err[0:int(2*x0*N+0.9999)+1] # print(coeff, np.max(err)) return np.max(np.abs(err)) def scan_esk(rbeta, re0, nu, x, W, M, N, x0): curmin=1e30 for e0 in np.linspace(re0[0], re0[1], 10): for beta in np.linspace(rbeta[0], rbeta[1], 10): test = getmaxerr(eskapprox, [beta,e0], nu, x, W, M, N, x0) if test