Commit 572f5382 by Uddeepta Deka

Ft_contour bug fixed and Ft_approx added

parent b21a2777
Showing with 69 additions and 24 deletions
......@@ -15,7 +15,10 @@
"## Table of contents:\n",
"- [Histogram method](#Ft_histogram)\n",
"- [Contour method](#Ft_contour)\n",
"- [Testing $\\widetilde{F}(t)$](#Ft_test)"
"- [Approximate Ft](#Ft_approx)\n",
"- [Testing $\\widetilde{F}(t)$](#Ft_test)\n",
"\n",
"This is implemented in [generate_Ft.py](../utils/generate_Ft.py)"
]
},
{
......@@ -41,7 +44,6 @@
"from plotsettings import *\n",
"import warnings\n",
"import time\n",
"from tqdm import tqdm\n",
"from cycler import cycler\n",
"from matplotlib import colors\n",
"from lenses import ChargedLens\n",
......@@ -85,7 +87,8 @@
" t_max: maximum time delay to be resolved (relative to global minima)\n",
" dt: bin width of histogram\n",
" \"\"\"\n",
" #!FIXME we assume that atleast one image exists\n",
" # We assume that atleast one image exists\n",
" assert len(lens.img)!=0\n",
" minima_td = min(lens.img_td)\n",
" t_max += minima_td\n",
" x_max = 1.2 * np.sqrt(2 * t_max) \n",
......@@ -139,7 +142,8 @@
" t_max: maximum time delay to be resolved (relative to global minima)\n",
" dt: bin width of histogram\n",
" \"\"\"\n",
" #!FIXME: We assume that atleast one image exists\n",
" # We assume that atleast one image exists\n",
" assert len(lens.img)!=0\n",
" minima_td = min(lens.img_td)\n",
" t_max += minima_td\n",
" x_max = 1.2 * np.sqrt(2 * t_max)\n",
......@@ -162,12 +166,13 @@
" for level in level_coords:\n",
" res_sum = 0\n",
" for i in range(len(level)):\n",
" x_coord, y_coord = np.vstack(level[i]).T\n",
" ds = np.sqrt(np.diff(x_coord)**2 + np.diff(y_coord)**2)\n",
" gtd = lens.gradTimeDelay(x_coord, y_coord)\n",
" gradnorm = np.linalg.norm([gtd[0],gtd[1]], axis = 0)[:-1]\n",
" res = np.divide(ds, gradnorm)\n",
" res_sum += np.sum(res) / 2. / np.pi\n",
" if len(level[i])!=0:\n",
" x_coord, y_coord = np.vstack(level[i]).T\n",
" ds = np.sqrt(np.diff(x_coord)**2 + np.diff(y_coord)**2)\n",
" gtd = lens.gradTimeDelay(x_coord, y_coord)\n",
" gradnorm = np.linalg.norm([gtd[0],gtd[1]], axis = 0)[:-1]\n",
" res = np.divide(ds, gradnorm)\n",
" res_sum += np.sum(res) / 2. / np.pi\n",
" Ft.append(res_sum)\n",
" plt.close()\n",
" Tarray-=minima_td\n",
......@@ -180,6 +185,41 @@
},
{
"cell_type": "markdown",
"id": "732fb49f-c634-4228-80f3-2ea22231eb57",
"metadata": {},
"source": [
"## Approximate $\\widetilde{F}(t)$ <a class=\"anchor\" id=\"Ft_approx\"></a>"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e819b1b6-c405-46cc-87c0-feee4e4f4ffe",
"metadata": {},
"outputs": [],
"source": [
"def approx_Ft(lens, t_max, dt):\n",
" \"\"\" \n",
" Computing F(t) due to the stationary points.\n",
" Ref: Eq. 5.5, Nakamura, Deguchi, 1999\n",
" \"\"\"\n",
" assert len(lens.img)!=0\n",
" image_timedelays = lens.img_td - min(lens.img_td)\n",
" t_arr = np.arange(0, t_max+dt, dt)\n",
" Ft = np.zeros_like(t_arr)\n",
" for ii in range(len(lens.img_td)):\n",
" img_morse_idx = lens.img_midx[ii]\n",
" if img_morse_idx == 0.5:\n",
" Ft -= (np.sqrt(np.abs(lens.img_mag[ii])) * \n",
" np.log(np.abs(image_timedelays[ii]-t_arr)) / np.pi)\n",
" elif (img_morse_idx==0) or (img_morse_idx==1):\n",
" sel_idxs = t_arr > image_timedelays[ii]\n",
" Ft[sel_idxs] += (-1)**(img_morse_idx) * np.sqrt(lens.img_mag[ii])\n",
" return t_arr, np.asarray(Ft)"
]
},
{
"cell_type": "markdown",
"id": "ca738bde-3fe1-4e8f-a96d-b69b76ca3086",
"metadata": {},
"source": [
......@@ -188,7 +228,7 @@
},
{
"cell_type": "code",
"execution_count": 9,
"execution_count": 7,
"id": "9a43cfbe-15a6-482b-a611-b3af5571132a",
"metadata": {},
"outputs": [
......@@ -196,17 +236,18 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Tmax = 29.97804294466326 | dt = 0.020943951023931952 | xmax = 9.291757835879613 | dx1 = 0.002396783848278275 | dx2 = 0.0022670646756315508\n",
"Number of td samples = 63566886\n",
"x_max = 9.291757835879613 | t_max = 29.97804294466326 | dx1 = 0.025, dx2 = 0.025\n",
"Tmax = 28.835924899983453 | dt = 0.020943951023931952 | xmax = 9.113038116454486 | dx1 = 0.0034570190957158614 | dx2 = 0.002312106639417798\n",
"Number of td samples = 41567051\n",
"x_max = 9.113038116454486 | t_max = 28.835924899983453 | dx1 = 0.025, dx2 = 0.025\n",
"Number of td samples = 1432\n",
"Time taken to compute Ft_hist 8.691 s. and time taken to compute Ft_cont 9.664 s\n"
"\n",
"Time taken to compute Ft_hist 6.553 s. and time taken to compute Ft_cont 10.116 s\n"
]
}
],
"source": [
"qtest = 0.1\n",
"ytest = 0.5\n",
"qtest = 0.05\n",
"ytest = 3\n",
"\n",
"lens =ChargedLens(qeff=qtest, y1=ytest)\n",
"T_MAX =30\n",
......@@ -219,19 +260,20 @@
"t2 = time.perf_counter()\n",
"t_cont, Ft_cont = Ftilde_contour(lens, T_MAX, dt, dx1=0.025, dx2=0.025, verbose=True)\n",
"t3 = time.perf_counter()\n",
"t_approx, Ft_approx = approx_Ft(lens, T_MAX, dt)\n",
"\n",
"print(\"Time taken to compute Ft_hist %.3f s. and time taken to compute Ft_cont %.3f s\"%(t2-t1, t3-t2))"
"print(\"\\nTime taken to compute Ft_hist %.3f s. and time taken to compute Ft_cont %.3f s\"%(t2-t1, t3-t2))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": 9,
"id": "21f428d3-2346-4d5c-b94c-0fd503e51900",
"metadata": {},
"outputs": [
{
"data": {
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",
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
......@@ -243,20 +285,23 @@
"source": [
"plt.plot(t_hist, Ft_hist, label='histogram')\n",
"plt.plot(t_cont, Ft_cont, label='contour')\n",
"\n",
"for imtd in lens.img_td:\n",
"plt.plot(t_approx, Ft_approx, label='approx')\n",
"images_rel_td = lens.img_td - min(lens.img_td)\n",
"for imtd in images_rel_td:\n",
" plt.axvline(imtd, ls='--', c='r')\n",
"plt.legend()\n",
"plt.xlabel(r'$t$')\n",
"plt.ylabel(r'$\\widetilde{F}(t)$')\n",
"plt.xscale('log')\n",
"plt.ylim(bottom=0.8)\n",
"# plt.xlim(6, 8)\n",
"# plt.xscale('log')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5df8eb60-c0f6-48a3-b8d5-0099c492f224",
"id": "9a4922b1-e8b5-435b-9dad-ca3ec80b1692",
"metadata": {},
"outputs": [],
"source": []
......
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