{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Preblur for bosonic continuation\n", "\n", "Demo notebook that shows that preblur for bosonic functions is correctly implemented and has the desired effect." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sys, os\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "sys.path.insert(0, os.environ['HOME'] + '/Programs/ana_cont')\n", "from ana_cont import continuation as cont" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "nw_full = 801\n", "w_full = np.linspace(0., 8., num=nw_full, endpoint=True)\n", "spectrum = np.exp(-(w_full - 2.)**2 / 2.) + np.exp(-(w_full + 2.)**2 / 2.)\n", "spectrum /= 2. * np.trapz(spectrum, w_full)\n", "\n", "beta = 20.\n", "niw = 20\n", "wn = 2. * np.pi / beta * np.arange(niw)\n", "with np.errstate(invalid=\"ignore\"):\n", " kernel = (w_full**2)[None, :] / ((w_full**2)[None, :] + (wn**2)[:, None])\n", "kernel[0, 0] = 1.\n", "chi_exact = np.trapz(kernel * spectrum, w_full, axis=1)\n", "rng = np.random.RandomState(4712)\n", "noise_unscaled = rng.randn(niw)\n", "noise_amplitude = 1e-3\n", "chi = chi_exact + noise_amplitude * noise_unscaled\n", "\n", "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(8, 4))\n", "ax[0].plot(w_full, spectrum)\n", "ax[1].plot(wn, chi)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "nw = 801\n", "w = np.linspace(0, 8., num=nw, endpoint=True)\n", "probl = cont.AnalyticContinuationProblem(im_axis=wn, re_axis=w, im_data=chi, kernel_mode='freq_bosonic')\n", "model = np.ones_like(w)\n", "model /= np.trapz(model, w)\n", "err = np.ones_like(wn) * noise_amplitude" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "801 data points on real axis\n", "20 data points on imaginary axis\n", "16 significant singular values\n", "Precomputation of coefficient matrices...\n", "log10(alpha) = 12.00,\tchi2 = 3.044e+06, S = -1.304e-11, nfev = 1, norm = 1.000\n", "log10(alpha) = 11.30,\tchi2 = 3.044e+06, S = -3.259e-10, nfev = 5, norm = 1.000\n", "log10(alpha) = 10.60,\tchi2 = 3.043e+06, S = -8.145e-09, nfev = 7, norm = 1.000\n", "log10(alpha) = 9.90,\tchi2 = 3.038e+06, S = -2.032e-07, nfev = 9, norm = 0.999\n", "log10(alpha) = 9.20,\tchi2 = 3.012e+06, S = -5.027e-06, nfev = 12, norm = 0.997\n", "log10(alpha) = 8.51,\tchi2 = 2.889e+06, S = -1.194e-04, nfev = 14, norm = 0.986\n", "log10(alpha) = 7.81,\tchi2 = 2.391e+06, S = -2.365e-03, nfev = 16, norm = 0.936\n", "log10(alpha) = 7.11,\tchi2 = 1.225e+06, S = -2.615e-02, nfev = 18, norm = 0.794\n", "log10(alpha) = 6.41,\tchi2 = 2.801e+05, S = -1.073e-01, nfev = 19, norm = 0.604\n", "log10(alpha) = 5.71,\tchi2 = 4.677e+04, S = -1.952e-01, nfev = 19, norm = 0.508\n", "log10(alpha) = 5.01,\tchi2 = 1.016e+04, S = -2.678e-01, nfev = 19, norm = 0.507\n", "log10(alpha) = 4.31,\tchi2 = 1.938e+03, S = -3.498e-01, nfev = 29, norm = 0.509\n", "log10(alpha) = 3.61,\tchi2 = 2.674e+02, S = -4.294e-01, nfev = 30, norm = 0.502\n", "log10(alpha) = 2.91,\tchi2 = 5.381e+01, S = -4.774e-01, nfev = 21, norm = 0.500\n", "log10(alpha) = 2.21,\tchi2 = 3.279e+01, S = -5.016e-01, nfev = 21, norm = 0.499\n", "log10(alpha) = 1.52,\tchi2 = 2.875e+01, S = -5.289e-01, nfev = 23, norm = 0.499\n", "log10(alpha) = 0.82,\tchi2 = 2.682e+01, S = -5.940e-01, nfev = 25, norm = 0.499\n", "log10(alpha) = 0.12,\tchi2 = 2.621e+01, S = -6.902e-01, nfev = 26, norm = 0.499\n", "log10(alpha) = -0.58,\tchi2 = 2.604e+01, S = -8.330e-01, nfev = 28, norm = 0.499\n", "log10(alpha) = -1.28,\tchi2 = 2.597e+01, S = -1.118e+00, nfev = 30, norm = 0.499\n", "log10(alpha) = -1.98,\tchi2 = 2.595e+01, S = -1.509e+00, nfev = 32, norm = 0.499\n", "Fit parameters [1.35524589 5.17828922 4.99108767 1.02207039]\n", "Optimal log alpha 2.5450721793257154\n", "log10(alpha) = 2.55,\tchi2 = 3.776e+01, S = -4.915e-01, nfev = 17, norm = 0.499\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "801 data points on real axis\n", "20 data points on imaginary axis\n", "13 significant singular values\n", "Precomputation of coefficient matrices...\n", "log10(alpha) = 12.00,\tchi2 = 3.059e+06, S = -1.293e-11, nfev = 1, norm = 1.000\n", "log10(alpha) = 11.30,\tchi2 = 3.058e+06, S = -3.231e-10, nfev = 5, norm = 1.000\n", "log10(alpha) = 10.60,\tchi2 = 3.057e+06, S = -8.075e-09, nfev = 7, norm = 1.000\n", "log10(alpha) = 9.90,\tchi2 = 3.052e+06, S = -2.015e-07, nfev = 9, norm = 0.999\n", "log10(alpha) = 9.20,\tchi2 = 3.027e+06, S = -4.984e-06, nfev = 12, norm = 0.997\n", "log10(alpha) = 8.51,\tchi2 = 2.905e+06, S = -1.184e-04, nfev = 14, norm = 0.985\n", "log10(alpha) = 7.81,\tchi2 = 2.409e+06, S = -2.352e-03, nfev = 16, norm = 0.936\n", "log10(alpha) = 7.11,\tchi2 = 1.243e+06, S = -2.618e-02, nfev = 18, norm = 0.792\n", "log10(alpha) = 6.41,\tchi2 = 2.884e+05, S = -1.082e-01, nfev = 19, norm = 0.598\n", "log10(alpha) = 5.71,\tchi2 = 5.028e+04, S = -1.981e-01, nfev = 19, norm = 0.500\n", "log10(alpha) = 5.01,\tchi2 = 1.194e+04, S = -2.746e-01, nfev = 19, norm = 0.504\n", "log10(alpha) = 4.31,\tchi2 = 3.214e+03, S = -3.624e-01, nfev = 20, norm = 0.517\n", "log10(alpha) = 3.61,\tchi2 = 7.017e+02, S = -4.926e-01, nfev = 21, norm = 0.511\n", "log10(alpha) = 2.91,\tchi2 = 1.122e+02, S = -6.332e-01, nfev = 22, norm = 0.504\n", "log10(alpha) = 2.21,\tchi2 = 3.749e+01, S = -7.160e-01, nfev = 21, norm = 0.500\n", "log10(alpha) = 1.52,\tchi2 = 3.191e+01, S = -7.460e-01, nfev = 37, norm = 0.499\n", "log10(alpha) = 0.82,\tchi2 = 3.129e+01, S = -7.662e-01, nfev = 25, norm = 0.499\n", "log10(alpha) = 0.12,\tchi2 = 3.095e+01, S = -8.286e-01, nfev = 27, norm = 0.499\n", "log10(alpha) = -0.58,\tchi2 = 3.071e+01, S = -1.042e+00, nfev = 29, norm = 0.499\n", "log10(alpha) = -1.28,\tchi2 = 3.060e+01, S = -1.464e+00, nfev = 31, norm = 0.499\n", "log10(alpha) = -1.98,\tchi2 = 3.058e+01, S = -1.875e+00, nfev = 33, norm = 0.499\n", "Fit parameters [1.40031346 5.15544171 4.8762637 0.92190143]\n", "Optimal log alpha 2.1644770449810373\n", "log10(alpha) = 2.16,\tchi2 = 3.643e+01, S = -7.194e-01, nfev = 15, norm = 0.500\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sol_noblur, _ = probl.solve(method='maxent_svd', alpha_determination='chi2kink', optimizer='newton', \n", " stdev=err, model=model,\n", " preblur=False, blur_width=0.01,\n", " alpha_start=1e12, alpha_end=1e-2, alpha_div=5.,\n", " interactive=True, fit_position=2.5)\n", "sol_preblur, _ = probl.solve(method='maxent_svd', alpha_determination='chi2kink', optimizer='newton', \n", " stdev=err, model=model,\n", " preblur=True, blur_width=0.8,\n", " alpha_start=1e12, alpha_end=1e-2, alpha_div=5.,\n", " interactive=True, fit_position=2.5)\n", "fig, ax = plt.subplots(ncols=2, nrows=1, figsize=(12, 4))\n", "ax[0].plot(w_full, spectrum)\n", "ax[0].plot(w, sol_noblur.A_opt, label='no blur')\n", "ax[0].plot(w, sol_preblur.A_opt, label='preblur')\n", "ax[0].legend()\n", "ax[0].set_xlim(0., 4.)\n", "ax[1].plot(wn, chi - sol_noblur.backtransform, label='no blur')\n", "ax[1].plot(wn, chi - sol_preblur.backtransform, label='preblur')\n", "ax[1].legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }