#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Double gyre Hyperbolic LCS
==========================

Compute hyperbolic LCS using the variational theory for the double gyre.
"""

# Author: ajarvis

import numpy as np
from math import copysign
from numbacs.flows import get_predefined_flow
from numbacs.integration import flowmap_aux_grid_2D
from numbacs.diagnostics import C_eig_aux_2D, ftle_from_eig
from numbacs.extraction import hyperbolic_lcs
import matplotlib.pyplot as plt
# %%
# Get flow
# --------------
# Set the integration span and direction, retrieve the flow, and set up domain.

# set initial time, integration time, and integration direction
t0 = 0.
T = -10.
int_direction = copysign(1,T)

# retrieve function pointer and parameters for double gyre flow.
funcptr, params, domain = get_predefined_flow('double_gyre', int_direction = int_direction)

# set up domain
nx,ny = 401,201
x = np.linspace(domain[0][0],domain[0][1],nx)
y = np.linspace(domain[1][0],domain[1][1],ny)
dx = x[1]-x[0]
dy = y[1]-y[0]

# %%
# Integrate
# ---------
# Integrate grid of particles and auxillary grid with spacing h, return final positions

# computes final position of particle trajectories over grid + auxillary grid
# with spacing h
h = 1e-5
flowmap = flowmap_aux_grid_2D(funcptr, t0, T, x, y, params,h=h)

# %%
# CG eigenvalues, eigenvectors, and FTLE
# ----------------------------------------------
# Compute eigenvalues/vectors of CG tensor from final particle positions and compute FTLE.

# compute eigenvalues/vectors of Cauchy Green tensor
eigvals,eigvecs = C_eig_aux_2D(flowmap, dx, dy, h=h)
eigval_max = eigvals[:,:,1]
eigvec_max = eigvecs[:,:,:,1]

# copmute FTLE from max eigenvalue
ftle = ftle_from_eig(eigval_max,T)
# %%
# Hyperbolic LCS
# --------------
# Compute hyperbolic LCS using the variational theory.

# set parameters for hyperbolic lcs extraction,
# see function description for more details
step_size = 1e-3
steps = 3000
lf = 0.1
lmin = 1.5
r = 0.1
nmax = -1
dtol = 1e-1
nlines = 10
percentile=40
ep_dist_tol=1e-2
lambda_avg_min = 600
arclen_flag=True

# extract hyperbolic lcs
lcs = hyperbolic_lcs(eigval_max, eigvecs, x, y, step_size, steps, lf, lmin, r, nmax, 
                     dist_tol=dtol, 
                     nlines=nlines,
                     ep_dist_tol=ep_dist_tol,
                     percentile=percentile,
                     lambda_avg_min=lambda_avg_min,
                     arclen_flag=arclen_flag)

# %%
# Plot
# ----
# Plot the results.
fig,ax = plt.subplots(dpi=200)
ax.contourf(x,y,ftle.T,levels=80)
for l in lcs:
    ax.plot(l[:,0],l[:,1],'r',lw=1)
ax.set_aspect('equal')
plt.show()