.. _sphx_glr_dimer_lattice_cthyb_plot_maxent.py:


Analytically continue a dimer GF by Maxent
==========================================

Here I continue an insulator



.. code-block:: python

    # Created Mon Jan 30 14:13:23 2017
    # Author: Óscar Nájera

    from __future__ import division, absolute_import, print_function
    import matplotlib.pyplot as plt
    import numpy as np
    import dmft.common as gf
    from dmft import dimer
    from pymaxent.maxent import Maxent
    from pymaxent.draw import gf_plot_study
    from pymaxent.tools import gaussian, hilbert_trans, differential_weight

    # Output for G_sym= G_AA+G_AB
    # G0 = w -tp - (G_sym)
    # S = w -tp - t^2 G_sym - G_sym^-1

    fac = np.arctan(10 * np.sqrt(3) / 2.5)
    omega = np.tan(np.linspace(-fac, fac, 351)) * 2.5 / np.sqrt(3)

    tp = 0.5
    BETA = 100.
    u_int = 1.67
    u_str = 'U' + str(u_int)
    workdir = "/home/oscar/orlando/dev/dmft-learn/examples/dimer_bethe/tp03f/"
    workdir = "/home/oscar/orlando/dev/dmft-learn/examples/dimer_bethe/"

    filename = workdir + 'DIMER_PM_{}_B{}_tp{}.h5'.format('ins', BETA, tp)
    giw = dimer.extract_flat_gf_iter(filename, u_int, 2)
    nfreq = giw.shape[-1]
    wn = gf.matsubara_freq(BETA, nfreq, 1 - nfreq)

    giw = giw.reshape(-1, 2, 2, nfreq)
    giw[:, 1] = -giw[:, 1].conjugate()
    giw = giw.reshape(-1, nfreq)
    gerr = giw.std(0).clip(3e-4)


    defaultM = gaussian(omega, tp, tp**2 + 0.25 + u_int**2 / 4)

    Model_gw = Maxent(omega=omega, defaultModel=defaultM, tol=1e-5,
                      minimizer='Bryan', w_n=wn, giw=giw.mean(0),
                      giw_std=gerr, max_nfreq=int(2 * BETA))
    Model_gw.getAllSpecFs(alphamin=0.6, alphamax=2, numAlpha=24)

    fig, ax = plt.subplots(1, 2, gridspec_kw=dict(
        wspace=0.05, hspace=0.1, width_ratios=[3, 1]))
    gf_plot_study(omega, Model_gw, "{AB}", ax=ax)
    ax[0].set_title(r'$U={}$, $t_\perp={}$, $\beta={}$'.format(u_int, tp, BETA))
    plt.show()

    # np.savez('AwmetB25tp0.3{}G_sym'.format(u_str), Aw = Model_gw.aveSpecFs, w = Model_gw.omega)




.. code-block:: pytb

    Traceback (most recent call last):
      File "/home/oscar/dev/sphinx-gallery/sphinx_gallery/gen_rst.py", line 453, in execute_code_block
        exec(code_block, example_globals)
      File "<string>", line 28, in <module>
      File "/home/oscar/dev/dmft-learn/dmft/dimer.py", line 374, in extract_flat_gf_iter
        with h5py.File(filename, 'r') as datarecord:
      File "/home/oscar/.virtualenvs/dev3/lib/python3.6/site-packages/h5py/_hl/files.py", line 271, in __init__
        fid = make_fid(name, mode, userblock_size, fapl, swmr=swmr)
      File "/home/oscar/.virtualenvs/dev3/lib/python3.6/site-packages/h5py/_hl/files.py", line 101, in make_fid
        fid = h5f.open(name, flags, fapl=fapl)
      File "h5py/_objects.pyx", line 54, in h5py._objects.with_phil.wrapper (/tmp/pip-build-gr7bexsy/h5py/h5py/_objects.c:2840)
      File "h5py/_objects.pyx", line 55, in h5py._objects.with_phil.wrapper (/tmp/pip-build-gr7bexsy/h5py/h5py/_objects.c:2798)
      File "h5py/h5f.pyx", line 78, in h5py.h5f.open (/tmp/pip-build-gr7bexsy/h5py/h5py/h5f.c:2125)
    OSError: Unable to open file (Unable to open file: name = '/home/oscar/orlando/dev/dmft-learn/examples/dimer_bethe/dimer_pm_ins_b100.0_tp0.5.h5', errno = 2, error message = 'no such file or directory', flags = 0, o_flags = 0)




How was the Green function fitted
---------------------------------



.. code-block:: python

    gs, gs_ax = plt.subplots(2, 1, sharex=True)
    gfit = Model_gw.restoreG(Model_gw.aveSpecFs)
    wnfit = Model_gw.wn

    gs_ax[0].plot(wn, giw.mean(0).real, 's:', label=r'$\Re e$')
    gs_ax[0].plot(wn, giw.mean(0).imag, 'o:', label=r'$\Im m$')
    gs_ax[0].plot(wnfit, gfit.real, 'xk', label=r'MEM')
    gs_ax[0].plot(wnfit, gfit.imag, 'xk')
    gs_ax[0].set_ylabel(r'$\bar{G}_{AB}$')
    gs_ax[0].legend()

    siw = 1j * wnfit - tp - 0.25 * gfit - 1 / gfit
    gs_ax[1].plot(wnfit, siw.real, 's:', label=r'$\Re e$')
    gs_ax[1].plot(wnfit, siw.imag, 'o:', label=r'$\Im m$')
    gs_ax[1].set_ylabel(r'$\bar{\Sigma}_{AB}$')
    gs_ax[1].legend()
    plt.xlabel(r'$\omega_n$')
    gs_ax[0].set_title(r'$U={}$, $t_\perp={}$, $\beta={}$'.format(u_int, tp, BETA))
    plt.xlim(-5, 5)


    plt.figure('gd')
    plt.plot(wn, gerr, label='std(G)')
    plt.plot(wnfit, np.abs(gfit - giw.mean(0)
                           [int(len(wn) / 2 - BETA):int(len(wn) / 2 + BETA)]), label='$|G-G_{MEM}|$')
    plt.legend()
    plt.xlabel(r'$\omega_n$')
    plt.ylabel('error')
    plt.title(r'$U={}$, $t_\perp={}$, $\beta={}$'.format(u_int, tp, BETA))
    plt.xlim(-5, 5)

    plt.show()

**Total running time of the script:** ( 0 minutes  0.000 seconds)



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  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_maxent.py <plot_maxent.py>`



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     :download:`Download Jupyter notebook: plot_maxent.ipynb <plot_maxent.ipynb>`

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