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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pyerrors as pe"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"plt.style.use('./base_style.mplstyle')\n",
"plt.rc('text', usetex=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"In this example we look at the analysis of the current quark mass (PCAC mass) on a test gauge field ensemble with fixed Schrödinger functional boundary conditions in the temporal direction."
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"## Loading data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"We can load data from preprocessed files which contains lists of `pyerror` `Obs` and convert them to `Corr` objects as explained in the previous example. We use the parameter `padding` to keep track of the fixed boundary conditions at both temporal ends of the lattice. This allows us to specify absolut temporal positions without having to keep track of any shifts in the data."
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]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Data has been written using pyerrors 2.0.0.\n",
"Format version 0.1\n",
"Written by fjosw on 2022-01-06 11:27:27 +0100 on host XPS139305, Linux-5.11.0-44-generic-x86_64-with-glibc2.29\n",
"\n",
"Description: SF correlation function f_A on a test ensemble\n",
"Data has been written using pyerrors 2.0.0.\n",
"Format version 0.1\n",
"Written by fjosw on 2022-01-06 11:27:34 +0100 on host XPS139305, Linux-5.11.0-44-generic-x86_64-with-glibc2.29\n",
"\n",
"Description: SF correlation function f_P on a test ensemble\n"
]
}
],
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"source": [
"p_obs_names = [r'f_A', r'f_P']\n",
"\n",
"p_obs = {}\n",
"for i, item in enumerate(p_obs_names):\n",
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" tmp_data = pe.input.json.load_json(\"./data/\" + item)\n",
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" p_obs[item] = pe.Corr(tmp_data, padding=[1, 1])\n",
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" p_obs[item].tag = item"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"We can now use the method `Corr.show` to have a quick look at the data we just read in "
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]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"p_obs['f_A'].show(comp=p_obs['f_P'], y_range=[-0.8, 8])"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"## Constructing the PCAC mass"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"The PCAC mass is defined as\n",
"\\begin{align*}\n",
"am(x_0)=\\frac{a\\tilde{\\partial}_0 f_\\mathrm{A}(x_0)+a^2c_\\mathrm{A}\\partial_0^{\\ast}\\partial_0^{}f_\\mathrm{P}(x_0)}{2f_\\mathrm{P}(x_0)}+\\mathrm{O}(a^2)\\,.\n",
"\\end{align*}\n",
"\n",
"We now need to obtain the first derivative of f_A and the second derivative of f_P"
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]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
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"first_deriv_fA = p_obs['f_A'].deriv()\n",
"first_deriv_fA.tag = r\"First derivative of f_A\""
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]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
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"second_deriv_fP = p_obs['f_P'].second_deriv()\n",
"second_deriv_fP.tag = r\"Second derivative of f_P\""
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"We can use these to obtain the unimproved PCAC mass:"
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]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
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"am_pcac = first_deriv_fA / 2 / p_obs['f_P']\n",
"am_pcac.tag = \"Unimproved PCAC mass\""
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"And with the inclusion of the improvement coefficient $c_\\mathrm{A}$ also the $\\mathrm{O}(a)$ improved PCAC mass:"
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]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
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"cA = -0.03888694628624465\n",
"am_pcac_impr = (first_deriv_fA + cA * second_deriv_fP) / 2 / p_obs['f_P']\n",
"am_pcac_impr.tag = \"Improved PCAC mass\""
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"We can take a look at the time dependence of the PCAC mass with the method `Corr.show`:"
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]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
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"outputs": [
{
"data": {
"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"am_pcac_impr.show(comp=am_pcac)"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"## Plateau values"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"We can now construct a plateau as a derived observable from the masses."
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]
},
{
"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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"Fit with 1 parameters\n",
"Method: Levenberg-Marquardt\n",
"`ftol` termination condition is satisfied.\n",
"chisquare/d.o.f.: 0.2704765091136813\n",
"Result\t 5.03431904e-03 +/- 5.38835422e-04 +/- 8.24919899e-05 (10.703%)\n",
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" t_int\t 5.15384615e-01 +/- 1.25000000e-01 S = 2.00\n",
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"64 samples in 1 ensemble:\n",
" · Ensemble 'test_ensemble' : 64 configurations (from 1 to 64)\n"
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]
}
],
"source": [
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"pcac_plateau = am_pcac_impr.plateau([7, 16]) # We manually specify the plateau range here\n",
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"pcac_plateau.gamma_method()\n",
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"pcac_plateau.details()"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now plot the data with the two plateaus"
]
},
{
"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
"outputs": [
{
"data": {
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"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
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"am_pcac_impr.show(comp=am_pcac, plateau=pcac_plateau)"
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]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Monte Carlo history of the observable can be accessed with `plot_history` to identify possible outliers or have a look at the shape of the distribution"
]
},
{
"cell_type": "code",
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"execution_count": 12,
"metadata": {
"scrolled": false
},
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"outputs": [
{
"data": {
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"image/png": "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"text/plain": [
"<Figure size 640x395.55 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pcac_plateau.plot_history()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
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"If everything is satisfactory we can save the `Obs` in a file for future use. The `Obs` `pcac_plateau` conatains all relevant information for any follow up analyses."
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]
},
{
"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
"outputs": [],
"source": [
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"pcac_plateau.tag = \"O(a) improved PCAC mass extracted on the test ensemble\"\n",
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"pcac_plateau.dump(\"pcac_plateau_test_ensemble\", datatype=\"json.gz\")"
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]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"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",
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"version": "3.8.10"
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}
},
"nbformat": 4,
"nbformat_minor": 4
}
