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test_waveform.dat

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  • Forked from einsteinathome / libclfft
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    A_test_with_n=1.py 5.11 KiB
    """
    In this script I use a mock data generated from combining n=0 and n=1 overtones together, and sample it with the ptemcee sampler under the n=1 scenario. It seems that either there are some fundamental internal problems that prevent us from separating alpha_0 from alpha_1, or that ptemcee doesn't work as well for this problem. Either way, there should be something going on with our approach for this entire project...
    
    --- R^a_{yne} L^i_u
    """
    
    import numpy as np
    import corner
    import matplotlib.pyplot as plt
    from matplotlib.ticker import MaxNLocator
    from matplotlib import rc
    plt.rcParams['font.family'] = 'DejaVu Sans'
    rc('text', usetex=True)
    plt.rcParams.update({'font.size': 19})
    import pandas as pd
    import ptemcee
    import qnm
    import random
    
    
    ntemps = 20
    nwalkers = 100
    npoints = 150
    ndim = 8
    burnin = 75
    numbins = 42
    datacolor = '#105670' #'#4fa3a7'
    pkcolor = '#f2c977' #'#ffb45f'
    mediancolor = '#f7695c' #'#9b2814'
    rootpath = "/Users/RayneLiu"
    
    
    t = np.arange(0, 80, 0.1)
    w0, tau0, x0, y0 = [0.55578191, 11.74090006, 0.978518, -2.11289] 
    #Can get the w and tau from example nb and amplitude and phase from the 1910 paper
    w1, tau1, x1, y1 = [0.54351639, 3.88312743, 4.29435, 1.38519]
    mockdata = x0*np.exp(1j*y0)*np.exp(-t/(tau0)) * (np.cos(w0*t)-1j*np.sin(w0*t)) + \
                x1*np.exp(1j*y1)*np.exp(-t/(tau1)) * (np.cos(w1*t)-1j*np.sin(w1*t))
    
    
    def modelmock(theta):
        """
        theta: comprised of alpha0, alpha1, beta0, beta1, x0, x1, and y0, y1
        """ 
        
        alpha0, alpha1, beta0, beta1, xvar0, xvar1, yvar0, yvar1 = theta
        tauvar0 = tau0*(1+beta0)
        wvar0 = w0*(1+alpha0)
        tauvar1 = tau1*(1+beta1)
        wvar1 = w1*(1+alpha1)
        ansatz = (xvar0*np.exp(1j*yvar0))*np.exp(-t/tauvar0)*(np.cos(wvar0*t)-1j*np.sin(wvar0*t))+\
                 (xvar1*np.exp(1j*yvar1))*np.exp(-t/tauvar1)*(np.cos(wvar1*t)-1j*np.sin(wvar1*t))
        # -1j to agree with SXS convention
        return ansatz
    
    def log_prior(theta): 
        alpha0, alpha1, beta0, beta1, xvar0, xvar1, yvar0, yvar1 = theta
        
        if all([-0.4 <= alpha0 <= 0.4, -1.0 <= beta0 <= 2.0, 0 <= xvar0 <= 2.4, -2*np.pi <= yvar0 <= 0, \
                -0.4 <= alpha1 <= 0.4, -1.0 <= beta1 <= 2.0, 0 <= xvar1 <= 6.0, -np.pi <= yvar1 <= np.pi]):        
                return 0.0
        return -np.inf
    
    # LogLikelihood function. It is just a Gaussian loglikelihood based on computing the residuals^2
    def log_likelihood(theta):
        model_mock = modelmock(theta)
        
        return  -np.sum((mockdata.real - model_mock.real)**2+(mockdata.imag - model_mock.imag)**2)
    
    # Logposterior distribution for the residuals case.
    # The evidence is just a normalization factor
    def log_probability(theta):
        lp = log_prior(theta)
        if not np.isfinite(lp):
            return -np.inf
        return lp + log_likelihood(theta)
    
    
    #Define labels used in plotting
    paramlabels_a = [r'$\alpha_0$', r'$\alpha_1$']
    paramlabels_b = [r'$\beta_0$', r'$\beta_1$']
    paramlabels_x = [r'$x_0$', r'$x_1$']
    paramlabels_y = [r'$y_0$', r'$y_1$']
    paramlabels = paramlabels_a + paramlabels_b + paramlabels_x + paramlabels_y
    
    
    np.random.seed(42)
    pos = [random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), \
           random.uniform(0.8, 1.0), random.uniform(4, 5), random.uniform(-3, -2), random.uniform(1, 2)]
    pos += 1e-5 * np.random.randn(ntemps, nwalkers, ndim)
    
    sampler = ptemcee.Sampler(nwalkers, ndim, log_likelihood, log_prior, ntemps=ntemps)
    sampler.run_mcmc(pos,npoints);
    
    
    #Chain plot
    fig, axes = plt.subplots(ndim, 1, sharex=True, figsize=(12, 4*(4)))
    for i in range(ndim):
        axes[i].plot(sampler.chain[0,:, :, i].T, color="k", alpha=0.4, rasterized=True)
        axes[i].yaxis.set_major_locator(MaxNLocator(5))
        axes[i].set_ylabel(paramlabels[i])
    axes[-1].set_xlabel('Iterations')
    
    fig.savefig(rootpath+'/git/rdstackingproject/plotsmc/Test_with_mockdatan=1'+ str(npoints)+'pts_chainplot.png', format = 'png', bbox_inches = 'tight')
    
    
    #Output chain
    samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
    df0 = pd.DataFrame(samples, columns=paramlabels)
    df0.to_csv(rootpath+'/git/rdstackingproject/plotsmc/Test_with_mockdatan=1'+ str(npoints)+'pts_chain.csv', index = False)
    
    
    #Corner plot
    lglk = np.array([log_likelihood(samples[i]) for i in range(len(samples))])
    pk = samples[np.argmax(lglk)]
    median = np.median(samples, axis=0)
    
    figcorn = corner.corner(samples, bins = numbins, hist_bin_factor = 5, color = datacolor, truths=pk, truth_color = pkcolor, plot_contours = True, labels = paramlabels, quantiles=(0.05, 0.16, 0.5, 0.84, 0.95), levels=[1-np.exp(-0.5), 1-np.exp(-1.64 ** 2/2)], show_titles=True)
    
    #Extract the axes in order to add more important line plots
    naxes = len(pk)
    axes = np.array(figcorn.axes).reshape((naxes, naxes))
    
    # Loop over the diagonal
    for i in range(naxes):
        ax = axes[i, i]
        ax.axvline(median[i], color=mediancolor)
    
    # Loop over the histograms
    for yi in range(naxes):
        for xi in range(yi):
            ax = axes[yi, xi]
            ax.axvline(median[xi], color=mediancolor)
            ax.axhline(median[yi], color=mediancolor)
            ax.plot(median[xi], median[yi], color = mediancolor, marker = 's')
    
    figcorn.savefig(rootpath+'/git/rdstackingproject/plotsmc/Test_with_mockdatan=1'+ str(npoints)+'pts_corner.pdf', format = 'pdf')