{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Correlator Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are often dealing with lists of observables defined at every time slice. For a more convenient analysis, those can be represented using the \"correlators.Corr\" class.\n", "This is especially useful, if there is not one Obs per time slice, but a whole smearing matrix. We will load an example of such an object." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "64 4\n" ] } ], "source": [ "import pyerrors as pe\n", "import autograd.numpy as np\n", "P5P5=pe.load_object(\"data/Example_Corr_P5P5.p\")\n", "print(P5P5.T, P5P5.N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What we just printed out, are the only parameters a Corr has. T represents the number of time slices and N the rank of the NxN smearing matrix. \n", "The content is accessible with P5P5.content and gives a list of np.arrays of obs. There is no formal difference between correlators, which contain a single observable per time slice \n", "and those, which hold a smearing matrix. \n", "To initialize a Corr, we only need to pass the content or in the case of N=1, we might pass a list of obs.\n", "Lets run some code!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P5P5.symmetric().projected().show(logscale=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will go over this line the way it is executed, left to right. \n", "The correlator has a method called **symmetric()**, which returns a time symmetrized version of itself. \n", "We did not need to redo the error estimation. While a Corr has a **.gamma_method()** defined, which simply applies the Obs.gamma_method() to every Obs in the correlator, \n", "this is done automatically, whenever a new corr is initiated. This is a little slow, but convenient. The next method called is **.projected()**. \n", "This methods *projects* the smearing matrices $G(t)$ with a set of vectors, returning a single value at every $t$. $$v_l^T G(t) v_r$$ Since we did not pass an argument, it defaulted to $v_l=v_r=(1,0,...,0)$, giving us $G(t)[0,0]$ . The method returns another Corr, but this time with N=1. \n", " The last method **.show()** just allows us to quickly inspect a correlator. \n", "Let us now look at the GEVP. \n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-6.26306805e-04 1.64198098e-01 -5.99926044e-01 7.83024479e-01]\n" ] } ], "source": [ "eigenvector=P5P5.symmetric().GEVP(t0=3,ts=6)\n", "print(eigenvector)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**.GEVP()** Needs two time indices as arguments. It then solves:\n", "\n", "$$G(t_s)v=\\lambda G(t_0)v$$\n", "\n", "and returns the vector $v$ for the largest eigenvalue. It uses a *Scipy* method, which itself is based on a *LAPACK* method. \n", "To really see the difference this makes, we can visualize the effective mass, which we also have a method for." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P5P5.symmetric().projected().m_eff().show([0,32])\n", "P5P5.symmetric().projected(eigenvector).m_eff().show([0,32])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plateau is definetely larger now. We can use it to extract the pseudoscalar mass. All we need is a plateau range. \n", "Finding those can be time consuming, if we are dealing with many correlators and we need to zoom in to the plot, to see the range properly.\n", "~We can call a GUI method to help us to visualize the range. Play around with the checkboxes at the bottom of the window to make the program adjust plot to your selected range.~" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [] }, "outputs": [], "source": [ "# m_eff=P5P5.symmetric().projected(eigenvector).m_eff() # Our lines were getting a little long, so we just assign a new Corr. \n", "# plateau_range=pe.correlators.GUI_range_finder(m_eff)\n", "# m_p=m_eff.plateau(plateau_range)\n", "# print(\"The pseudoscalar mass is: \",m_p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "~For fun you can compare your result with https://arxiv.org/abs/1912.09937v1 Table XV (the first value for $am_{H_{is}}$).~\n", "Before we wrap up, we should look at Corrs and math operations. They can be multiplied by and added to other Corrs (of same N,T), or scaled by an Obs or float. \n", "Usually the operation is just done for every value at the same time and smearing. \n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "64 4\n" ] } ], "source": [ "new_correlator=0.5*P5P5+np.sqrt(P5P5)/np.sin(P5P5**2)+np.arcsinh(P5P5)\n", "print(new_correlator.T, new_correlator.N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a senseless but valid expression, which does exactly, what one would expect. It returns a Corr of the same shape as P5P5. \n", " It is really important, that there is never any confusion about the appropriate time slices. Lets look at *m_eff* once again. \n", " By default it is calculated as $$ m_{eff}(t)=\\ln(\\frac{Corr[t]}{Corr[t+1]})$$ \n", " Therefore m_eff is only defined up to the second to last time slice. But the method appends a **None** object, so that m_eff.T=64. \n", " If we add m_eff to P5P5.projected(), the resulting Corr would still have T=64, with the last item being **None**. \n", "Another reason for a Corr being **None** at one time slice, is a division by zero or other undefined operation. \n", "Even if a Corr is partially undefined, math operations still work, as long as T and N are identical.\n", " " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# print((m_eff+P5P5.projected()).T)" ] }, { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }