print 'Starting'

from mpi4py import MPI
comm = MPI.COMM_WORLD
mpi_rank, mpi_size = comm.Get_rank(), comm.Get_size()
print '%d/%d starting'%(mpi_rank,mpi_size)
prefix='fig_RSW2_MPAS_W02/%02d'%mpi_rank

print 'Loading DYNAMICO modules ...'
from dynamico import unstructured as unst
from dynamico.meshes import MPAS_Format, Unstructured_PMesh as PMesh, Local_Mesh as Mesh
from dynamico import time_step
print '...Done'

print 'Loading modules ...'
import math as math
import matplotlib.pyplot as plt
import numpy as np
print '...Done'

grid, llm, nqdyn = 2562, 1,1 # 2562, 10242, 40962
Omega, radius, g, gh0 = 2.*np.pi/86400., 6.4e6, 1., 2.94e4
N, T, courant = 40, 10400., 1.2 # simulation length = N*T

print 'Omega, planetary PV', Omega, 2*Omega/gh0

def f(lon,lat): return 2*Omega*np.sin(lat) # Coriolis parameter
print 'Reading MPAS mesh ...'
meshfile = MPAS_Format('grids/x1.%d.grid.nc'%grid)
pmesh = PMesh(comm,meshfile)
pmesh.partition_metis()
mesh = Mesh(pmesh, llm, nqdyn, radius, f)
print '...Done'
lon, lat = mesh.lon_i, mesh.lat_i
x,y,z = np.cos(lat)*np.cos(lon), np.cos(lat)*np.sin(lon), np.sin(lat)

unst.setvar('g',g)

c0 = math.sqrt(gh0) # phase speed of barotropic mode
dx = mesh.de.min()
dt = courant*dx/c0
print dx, dt
nt = int(math.ceil(T/dt))
dt = T/nt
print dx, dt, dt*c0/dx
print T, nt

scheme = time_step.RK4(None, dt)
print dt, scheme.csjl, scheme.cfjl
step = unst.caldyn_step_TRSW(mesh,scheme,nt)

u0 = Omega*radius/12. # cf Williamson (1991), p.13
gh1 = radius*Omega*u0+.5*u0**2
print 'Williamson (1991) test 2, u0=', u0
ulon = u0*np.cos(mesh.lat_e)
Phi0 = gh0 - gh1*(np.sin(mesh.lat_i)**2)
zeta0 = (2*u0/radius+2*Omega)*np.sin(mesh.lat_v)
Phi0v = gh0 - (radius*Omega*u0+.5*u0**2)*(np.sin(mesh.lat_v)**2)
q0 = zeta0/Phi0v
fu_perp = mesh.ucov2D(0.*ulon,2*Omega*np.sin(mesh.lat_e)*ulon)

# initial condition
step.mass[:]=Phi0
step.theta_rhodz[:]=Phi0
step.u[:]=mesh.ucov2D(ulon,0.*ulon)

gh,u = step.mass.copy(), step.u.copy()

print gh.shape, gh.min(), gh.max(), u.min(), u.max()
flow=gh,u

unst.ker.dynamico_update_halo(mesh.com_edges.index, 1, u.shape[0], u) 
                                  
for i in range(20):
    if True:
        step.next()
        gh,u = step.mass, step.u
        print i, gh.shape, gh.min(), gh.max(), u.min(), u.max()
        mesh.plot_i(gh-Phi0) ; plt.title('err(gh)');
        plt.savefig('%s_err_gh_%02d.png'%(prefix,i))
        plt.close()
    else:
        # advance by one time step using dynamico_ARK
        gh,u = step.mass.copy(), step.u.copy()
        print i, gh.shape, gh.min(), gh.max(), u.min(), u.max()
        step.next()
        gh_now,u_now = step.mass.copy(), step.u.copy()
        dmass,dhs,du_slow,du_fast = step.drhodz[:], step.dtheta_rhodz[:], step.du_slow[:], step.du_fast[:]
        du=du_slow+du_fast

        # do the same using caldyn, obtain fast/slow tendencies first
        gh_ref, uref=flow
        junk, fast, slow = caldyn.bwd_fast_slow(flow,0.)                                                                      
        dmass_ref, duslow_ref = slow
        junk, dufast_ref = fast
        du_ref = duslow_ref+dufast_ref
        flow=scheme.next(flow)
        gh_nowref, u_nowref=flow
#    mesh.plot_i(gh) ; plt.title('gh');
#    mesh.plot_i(Phi0) ; plt.title('gh');
        fig = plt.figure(figsize=(6, 8)) 
        f, ((ax1, ax2), (ax3, ax4), (ax5,ax6), (ax7,ax8)) = plt.subplots(4,2)
#        mesh.plot_i(dmass-dhs) ; plt.title('dt*d(gh)/dt');
        ax1.scatter(duslow_ref,du_slow-duslow_ref) ; ax1.set_title('du_slow');
        ax2.scatter(dufast_ref,du_fast-dufast_ref) ; ax2.set_title('du_fast');
        ax3.scatter(du_ref,du-du_ref) ; ax3.set_title('du');
        ax4.scatter(gh_ref,gh-gh_ref) ; ax4.set_title('gh');
        ax5.scatter(uref, u-uref) ; ax5.set_title('u');
        ax6.scatter(dmass_ref,dmass-dmass_ref) ; ax6.set_title('dmass');
        ax7.scatter(gh_nowref,gh_now-gh_nowref) ; ax7.set_title('gh_now');
        ax8.scatter(u_nowref,u_now-u_nowref) ; ax8.set_title('u_now');
        f.subplots_adjust(hspace=1.)
        plt.savefig('%s_scatter_%02d.png'%(prefix,i))
        plt.close()

print 'Time spent in DYNAMICO (s) : ', unst.getvar('elapsed')