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docs: Plots
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@jngrad @biermanncarl
jngrad authored and biermanncarl committed Jun 2, 2021
1 parent 5df5dc9 commit cfb14f0
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43 changes: 37 additions & 6 deletions doc/tutorials/error_analysis/error_analysis_part1.ipynb
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"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams.update({'font.size': 18})\n",
"\n",
"np.random.seed(43)\n",
"\n",
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"time_series_2 = ar_1_process(N_SAMPLES, C_2, PHI_2, EPS_2)\n",
"\n",
"\n",
"print(\"Done\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"fig = plt.figure(figsize=(10, 6))\n",
"plt.title(\"The first 1000 samples of both time series\")\n",
"plt.plot(time_series_1[0:1000], label=\"time series 1\")\n",
"plt.plot(time_series_2[0:1000], label=\"time series 2\")\n",
"plt.xlabel(\"$i$\")\n",
"plt.ylabel(\"$X_i$\")\n",
"plt.legend()\n",
"plt.show()"
]
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"metadata": {},
"outputs": [],
"source": [
"plt.plot(time_series_1[1000:1050],\"x\")\n",
"plt.ylim((7,20))\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.plot(time_series_1[1000:1050], \"x\")\n",
"fig.axes[0].margins(y=0.1)\n",
"plt.xlabel(\"$i$\")\n",
"plt.ylabel(\"$X_i$\")\n",
"plt.show()"
]
},
Expand All @@ -166,8 +184,12 @@
"metadata": {},
"outputs": [],
"source": [
"plt.plot(time_series_1[2000:42000:800],\"x\")\n",
"plt.ylim((7,20))\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.plot(np.arange(2000, 42000, 800), time_series_1[2000:42000:800], \"x\")\n",
"fig.axes[0].margins(y=0.1)\n",
"plt.xlabel(\"$i$\")\n",
"plt.ylabel(\"$X_i$\")\n",
"fig.axes[0].xaxis.set_major_locator(plt.MultipleLocator(base=8000))\n",
"plt.show()"
]
},
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"for s in range(len(sizes)):\n",
" sems[s] = do_binning_analysis(time_series_1,sizes[s])\n",
"\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(sizes,sems, \"x\")\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(\"$N_B$\")\n",
"plt.ylabel(\"SEM\")\n",
"plt.show()\n",
"```"
]
Expand Down Expand Up @@ -380,9 +405,12 @@
"\n",
"fit_sems = fit_fn(sizes,*fit_params)\n",
"\n",
"plt.plot(sizes,sems[:CUTOFF], \"x\")\n",
"plt.plot(sizes,fit_sems,\"-\")\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(sizes, sems[:CUTOFF], \"x\")\n",
"plt.plot(sizes, fit_sems, \"-\")\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(\"$N_B$\")\n",
"plt.ylabel(\"SEM\")\n",
"plt.show()\n",
"\n",
"print(\"Final Standard Error of the Mean: {:.3f}\".format(fit_params[2]))"
Expand Down Expand Up @@ -412,8 +440,11 @@
"for s in range(len(sizes)):\n",
" sems[s] = do_binning_analysis(time_series_2,sizes[s])\n",
"\n",
"plt.figure(figsize=(10, 6))\n",
"plt.plot(sizes,sems, \"x\")\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(\"$N_B$\")\n",
"plt.ylabel(\"SEM\")\n",
"plt.show()"
]
},
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38 changes: 29 additions & 9 deletions doc/tutorials/error_analysis/error_analysis_part2.ipynb
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Expand Up @@ -36,6 +36,7 @@
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.rcParams.update({'font.size': 18})\n",
"\n",
"np.random.seed(43)\n",
"\n",
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"time_series_2 = ar_1_process(N_SAMPLES, C_2, PHI_2, EPS_2)\n",
"\n",
"\n",
"print(\"Done\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"fig = plt.figure(figsize=(10, 6))\n",
"plt.title(\"The first 1000 samples of both time series\")\n",
"plt.plot(time_series_1[0:1000], label=\"time series 1\")\n",
"plt.plot(time_series_2[0:1000], label=\"time series 2\")\n",
"plt.xlabel(\"$i$\")\n",
"plt.ylabel(\"$X_i$\")\n",
"plt.legend()\n",
"plt.show()"
]
Expand Down Expand Up @@ -166,9 +179,10 @@
" temp += (time_series_1[i]-avg)*(time_series_1[i+j]-avg)\n",
" autocov[j] = temp / N_SAMPLES\n",
"\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.plot(autocov)\n",
"plt.xlabel(\"lag time\")\n",
"plt.ylabel(\"auto-covariance\")\n",
"plt.xlabel(\"lag time $j$\")\n",
"plt.ylabel(\"$\\hat{R}^{XX}_j$\")\n",
"plt.show()\n",
"```"
]
Expand Down Expand Up @@ -203,10 +217,11 @@
" autocov[j] = np.dot(time_series_1_centered[:N_SAMPLES-j], time_series_1_centered[j:])\n",
"autocov /= N_SAMPLES\n",
"\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.gca().axhline(0, color=\"gray\",linewidth=1)\n",
"plt.plot(autocov)\n",
"plt.xlabel(\"lag time\")\n",
"plt.ylabel(\"auto-covariance\")\n",
"plt.xlabel(\"lag time $j$\")\n",
"plt.ylabel(\"$\\hat{R}^{XX}_j$\")\n",
"plt.show()"
]
},
Expand Down Expand Up @@ -243,12 +258,13 @@
"j = np.linspace(0,N_MAX-1,N_MAX)\n",
"popt, pcov = curve_fit(exp_fnc, j, autocov[:N_MAX], p0=[15,10])\n",
"\n",
"plt.plot(j,autocov[:N_MAX])\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.plot(j,autocov[:N_MAX], 'x')\n",
"plt.plot(j,exp_fnc(j,popt[0],popt[1]))\n",
"plt.xlim((1,N_MAX))\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(\"lag time\")\n",
"plt.ylabel(\"auto-covariance\")\n",
"plt.xlabel(\"lag time $j$\")\n",
"plt.ylabel(\"$\\hat{R}^{XX}_j$\")\n",
"plt.show()\n",
"\n",
"print(\"Exponential autocorrelation time: {:.2f} sampling intervals\".format(popt[1]))"
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" tau_int_v[j_max] = 0.5 + np.sum(acf[1:j_max+1])\n",
"\n",
"# plot\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.plot(j_max_v,tau_int_v)\n",
"plt.xscale(\"log\")\n",
"plt.xlabel(r\"sum length $j_\\mathrm{max}$\")\n",
Expand Down Expand Up @@ -317,6 +334,7 @@
" j_max += 1\n",
"\n",
"# plot\n",
"fig = plt.figure(figsize=(10, 6))\n",
"plt.plot(j_max_v,C*tau_int_v)\n",
"plt.plot(j_max_v, j_max_v)\n",
"plt.plot([j_max],[j_max],\"ro\")\n",
Expand Down Expand Up @@ -419,13 +437,15 @@
" sem = np.sqrt(autocov[0]/N_eff)\n",
"\n",
" # create ACF plot\n",
" fig = plt.figure(figsize=(10, 6))\n",
" plt.gca().axhline(0, color=\"gray\",linewidth=1)\n",
" plt.plot(acf)\n",
" plt.title(\"Autocorrelation function\")\n",
" plt.xlabel(\"lag time\")\n",
" plt.xlabel(\"lag time $j$\")\n",
" plt.ylabel(\"$\\hat{R}^{XX}_j$\")\n",
" plt.show()\n",
" \n",
" # create integrated ACF plot\n",
" fig = plt.figure(figsize=(10, 6))\n",
" plt.plot(j_max_v,C*tau_int_v)\n",
" plt.ylim(plt.gca().get_ylim()) # explicitly keep the limits of the first plot\n",
" plt.plot(j_max_v, j_max_v)\n",
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