#!/usr/bin/env python3

"""
Test the variable-coefficient MG solver with periodic data.

Here we solve::

   div . ( alpha grad phi ) = f

with::

   alpha = 2.0 + cos(2.0*pi*x)*cos(2.0*pi*y)

   f = -16.0*pi**2*(cos(2*pi*x)*cos(2*pi*y) + 1)*sin(2*pi*x)*sin(2*pi*y)

This has the exact solution::

   phi = sin(2.0*pi*x)*sin(2.0*pi*y)

on [0,1] x [0,1]

We use Dirichlet BCs on phi.  For alpha, we do not have to impose the
same BCs, since that may represent a different physical quantity.
Here we take alpha to have Neumann BCs.  (Dirichlet BCs for alpha will
force it to 0 on the boundary, which is not correct here)

"""


import matplotlib.pyplot as plt
import numpy as np

import pyro.mesh.boundary as bnd
import pyro.multigrid.variable_coeff_MG as MG
import pyro.util.io_pyro as io
from pyro.mesh import patch
from pyro.util import compare, msg


# the analytic solution

[docs]
def true(x, y):
    return np.sin(2.0*np.pi*x)*np.sin(2.0*np.pi*y)



# the coefficients

[docs]
def alpha(x, y):
    return 2.0 + np.cos(2.0*np.pi*x)*np.cos(2.0*np.pi*y)



# the righthand side

[docs]
def f(x, y):
    return -16.0*np.pi**2*(np.cos(2*np.pi*x)*np.cos(2*np.pi*y) + 1) * \
        np.sin(2*np.pi*x)*np.sin(2*np.pi*y)




[docs]
def test_vc_poisson_periodic(N, store_bench=False, comp_bench=False, bench_dir="tests/",
                             make_plot=False, verbose=1, rtol=1.e-12):
    """
    test the variable-coefficient MG solver.  The return value
    here is the error compared to the exact solution, UNLESS
    comp_bench=True, in which case the return value is the
    error compared to the stored benchmark
    """

    # test the multigrid solver
    nx = N
    ny = nx

    # create the coefficient variable
    g = patch.Grid2d(nx, ny, ng=1)
    d = patch.CellCenterData2d(g)
    bc_c = bnd.BC(xlb="periodic", xrb="periodic",
                  ylb="periodic", yrb="periodic")
    d.register_var("c", bc_c)
    d.create()

    c = d.get_var("c")
    c[:, :] = alpha(g.x2d, g.y2d)

    # check whether the RHS sums to zero (necessary for periodic data)
    rhs = f(g.x2d, g.y2d)
    print(f"rhs sum: {np.sum(rhs[g.ilo:g.ihi+1, g.jlo:g.jhi+1])}")

    # create the multigrid object
    a = MG.VarCoeffCCMG2d(nx, ny,
                          xl_BC_type="periodic", yl_BC_type="periodic",
                          xr_BC_type="periodic", yr_BC_type="periodic",
                          coeffs=c, coeffs_bc=bc_c,
                          verbose=verbose, vis=0, true_function=true)

    # initialize the solution to 0
    a.init_zeros()

    # initialize the RHS using the function f
    rhs = f(a.x2d, a.y2d)
    a.init_RHS(rhs)

    # solve to a relative tolerance of 1.e-11
    a.solve(rtol=1.e-11)

    # alternately, we can just use smoothing by uncommenting the following
    # a.smooth(a.nlevels-1,10000)

    # get the solution
    v = a.get_solution()

    # get the true solution
    b = true(a.x2d, a.y2d)

    # compute the error from the analytic solution -- note that with
    # periodic BCs all around, there is nothing to normalize the
    # solution.  We subtract off the average of phi from the MG
    # solution (we do the same for the true solution to put them on
    # the same footing)
    e = v - np.sum(v.v())/(nx*ny) - (b - np.sum(b[a.ilo:a.ihi+1, a.jlo:a.jhi+1])/(nx*ny))

    enorm = e.norm()
    print(" L2 error from true solution = %g\n rel. err from previous cycle = %g\n num. cycles = %d" %
          (enorm, a.relative_error, a.num_cycles))

    # plot the solution
    if make_plot:
        plt.clf()

        plt.figure(figsize=(10.0, 4.0), dpi=100, facecolor='w')

        plt.subplot(121)

        img1 = plt.imshow(np.transpose(v.v()),
                   interpolation="nearest", origin="lower",
                   extent=[a.xmin, a.xmax, a.ymin, a.ymax])

        plt.xlabel("x")
        plt.ylabel("y")
        plt.title(f"nx = {nx}")

        plt.colorbar(img1)

        plt.subplot(122)

        img2 = plt.imshow(np.transpose(e.v()),
                   interpolation="nearest", origin="lower",
                   extent=[a.xmin, a.xmax, a.ymin, a.ymax])

        plt.xlabel("x")
        plt.ylabel("y")
        plt.title("error")

        plt.colorbar(img2)

        plt.tight_layout()

        plt.savefig("mg_vc_periodic_test.png")

    # store the output for later comparison
    bench = "mg_vc_poisson_periodic"

    my_data = a.get_solution_object()

    if store_bench:
        my_data.write(f"{bench_dir}/{bench}")

    # do we do a comparison?
    if comp_bench:
        compare_file = f"{bench_dir}/{bench}"
        msg.warning(f"comparing to {compare_file}")
        bench = io.read(compare_file)

        result = compare.compare(my_data, bench, rtol)

        if result == 0:
            msg.success(f"results match benchmark to within relative tolerance of {rtol}\n")
        else:
            msg.warning(f"ERROR: {compare.errors[result]}\n")

        return result

    # normal return -- error wrt true solution
    return enorm




[docs]
def main():
    N = [16, 32, 64, 128, 256, 512]
    err = []

    plot = False
    store = False
    do_compare = False

    for nx in N:
        if nx == max(N):
            plot = True

        enorm = test_vc_poisson_periodic(nx, make_plot=plot,
                                         store_bench=store, comp_bench=do_compare)
        err.append(enorm)

    # plot the convergence
    N = np.array(N, dtype=np.float64)
    err = np.array(err)

    plt.clf()
    plt.loglog(N, err, "x", color="r")
    plt.loglog(N, err[0]*(N[0]/N)**2, "--", color="k")

    plt.xlabel("N")
    plt.ylabel("error")

    fig = plt.gcf()
    fig.set_size_inches(7.0, 6.0)

    plt.tight_layout()

    plt.savefig("mg_vc_periodic_converge.png")



if __name__ == "__main__":
    main()