#!/usr/bin/env python
"""
A simple python program of solving a 2D wave equation in parallel.
Domain partitioning and inter-processor communication
are done by an object of class MPIRectPartitioner2D
(which is a subclass of RectPartitioner2D and uses MPI via mpi4py)

An example of running the program is (8 processors, 4x2 partition,
400x100 grid cells)::

   $ ipcluster start --engines=MPIExec -n 8 # start 8 engines with mpiexec
   $ python parallelwave-mpi.py --grid 400 100 --partition 4 2

See also parallelwave-mpi, which runs the same program, but uses MPI
(via mpi4py) for the inter-engine communication.

Authors
-------

 * Xing Cai
 * Min Ragan-Kelley

"""

import argparse
import time

from numpy import sqrt

import ipyparallel as ipp


def setup_partitioner(index, num_procs, gnum_cells, parts):
    """create a partitioner in the engine namespace"""
    global partitioner
    p = MPIRectPartitioner2D(my_id=index, num_procs=num_procs)  # noqa: F821
    p.redim(global_num_cells=gnum_cells, num_parts=parts)
    p.prepare_communication()
    # put the partitioner into the global namespace:
    partitioner = p


def setup_solver(*args, **kwargs):
    """create a WaveSolver in the engine namespace"""
    global solver
    solver = WaveSolver(*args, **kwargs)  # noqa: F821


def wave_saver(u, x, y, t):
    """save the wave log"""
    global u_hist
    global t_hist
    t_hist.append(t)
    u_hist.append(1.0 * u)


# main program:
if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    paa = parser.add_argument
    paa(
        '--grid',
        '-g',
        type=int,
        nargs=2,
        default=[100, 100],
        dest='grid',
        help="Cells in the grid, e.g. --grid 100 200",
    )
    paa(
        '--partition',
        '-p',
        type=int,
        nargs=2,
        default=None,
        help="Process partition grid, e.g. --partition 4 2 for 4x2",
    )
    paa('-c', type=float, default=1.0, help="Wave speed (I think)")
    paa('-Ly', type=float, default=1.0, help="system size (in y)")
    paa('-Lx', type=float, default=1.0, help="system size (in x)")
    paa('-t', '--tstop', type=float, default=1.0, help="Time units to run")
    paa(
        '--profile',
        type=str,
        default='default',
        help="Specify the ipcluster profile for the client to connect to.",
    )
    paa(
        '--save',
        action='store_true',
        help="Add this flag to save the time/wave history during the run.",
    )
    paa(
        '--scalar',
        action='store_true',
        help="Also run with scalar interior implementation, to see vector speedup.",
    )

    ns = parser.parse_args()
    # set up arguments
    grid = ns.grid
    partition = ns.partition
    Lx = ns.Lx
    Ly = ns.Ly
    c = ns.c
    tstop = ns.tstop
    if ns.save:
        user_action = wave_saver
    else:
        user_action = None

    num_cells = 1.0 * (grid[0] - 1) * (grid[1] - 1)
    final_test = True

    # create the Client
    rc = ipp.Client(profile=ns.profile)
    num_procs = len(rc.ids)

    if partition is None:
        partition = [1, num_procs]

    assert partition[0] * partition[1] == num_procs, (
        "can't map partition %s to %i engines"
        % (
            partition,
            num_procs,
        )
    )

    view = rc[:]
    print(f"Running {grid} system on {partition} processes until {tstop:f}")

    # functions defining initial/boundary/source conditions
    def I(x, y):
        from numpy import exp

        return 1.5 * exp(-100 * ((x - 0.5) ** 2 + (y - 0.5) ** 2))

    def f(x, y, t):
        return 0.0
        # from numpy import exp,sin
        # return 10*exp(-(x - sin(100*t))**2)

    def bc(x, y, t):
        return 0.0

    # initial imports, setup rank
    view.execute(
        '\n'.join(
            [
                "from mpi4py import MPI",
                "import numpy",
                "mpi = MPI.COMM_WORLD",
                "my_id = MPI.COMM_WORLD.Get_rank()",
            ]
        ),
        block=True,
    )

    # initialize t_hist/u_hist for saving the state at each step (optional)
    view['t_hist'] = []
    view['u_hist'] = []

    # set vector/scalar implementation details
    impl = {}
    impl['ic'] = 'vectorized'
    impl['inner'] = 'scalar'
    impl['bc'] = 'vectorized'

    # execute some files so that the classes we need will be defined on the engines:
    view.run('RectPartitioner.py')
    view.run('wavesolver.py')

    # setup remote partitioner
    # note that Reference means that the argument passed to setup_partitioner will be the
    # object named 'my_id' in the engine's namespace
    view.apply_sync(
        setup_partitioner, ipp.Reference('my_id'), num_procs, grid, partition
    )
    # wait for initial communication to complete
    view.execute('mpi.barrier()')
    # setup remote solvers
    view.apply_sync(
        setup_solver,
        I,
        f,
        c,
        bc,
        Lx,
        Ly,
        partitioner=ipp.Reference('partitioner'),
        dt=0,
        implementation=impl,
    )

    # lambda for calling solver.solve:
    def _solve(*args, **kwargs):
        return solver.solve(*args, **kwargs)

    if ns.scalar:
        impl['inner'] = 'scalar'
        # run first with element-wise Python operations for each cell
        t0 = time.time()
        ar = view.apply_async(
            _solve,
            tstop,
            dt=0,
            verbose=True,
            final_test=final_test,
            user_action=user_action,
        )
        if final_test:
            # this sum is performed element-wise as results finish
            s = sum(ar)
            # the L2 norm (RMS) of the result:
            norm = sqrt(s / num_cells)
        else:
            norm = -1
        t1 = time.time()
        print(f'scalar inner-version, Wtime={t1 - t0:g}, norm={norm:g}')

    impl['inner'] = 'vectorized'
    # setup new solvers
    view.apply_sync(
        setup_solver,
        I,
        f,
        c,
        bc,
        Lx,
        Ly,
        partitioner=ipp.Reference('partitioner'),
        dt=0,
        implementation=impl,
    )
    view.execute('mpi.barrier()')

    # run again with numpy vectorized inner-implementation
    t0 = time.time()
    ar = view.apply_async(
        _solve,
        tstop,
        dt=0,
        verbose=True,
        final_test=final_test,
        user_action=user_action,
    )
    if final_test:
        # this sum is performed element-wise as results finish
        s = sum(ar)
        # the L2 norm (RMS) of the result:
        norm = sqrt(s / num_cells)
    else:
        norm = -1
    t1 = time.time()
    print(f'vector inner-version, Wtime={t1 - t0:g}, norm={norm:g}')

    # if ns.save is True, then u_hist stores the history of u as a list
    # If the partion scheme is Nx1, then u can be reconstructed via 'gather':
    if ns.save and partition[-1] == 1:
        import matplotlib.pyplot as plt

        view.execute('u_last=u_hist[-1]')
        # map mpi IDs to IPython IDs, which may not match
        ranks = view['my_id']
        targets = range(len(ranks))
        for idx in range(len(ranks)):
            targets[idx] = ranks.index(idx)
        u_last = rc[targets].gather('u_last', block=True)
        plt.pcolor(u_last)
        plt.show()