# ipython magic
%matplotlib notebook
%load_ext autoreload
%autoreload 2

# plot configuration
import matplotlib
import matplotlib.pyplot as plt
plt.style.use("ggplot")
# import seaborn as sns # sets another style
matplotlib.rcParams['lines.linewidth'] = 3
fig_width, fig_height = (7.0,5.0)
matplotlib.rcParams['figure.figsize'] = (fig_width, fig_height)

# font = {'family' : 'sans-serif',
#         'weight' : 'normal',
#         'size'   : 18.0}
# matplotlib.rc('font', **font)  # pass in the font dict as kwar

import chaospy as cp
import numpy as np
from numpy import linalg as LA

def ishigami_function(sample):
    q1 = sample[0]
    q2 = sample[1]
    q3 = sample[2]
    a = 7.
    b = 0.1
    return np.sin(q1) + a*np.sin(q2)**2 + b* q3**4 * np.sin(q1)

def ishigami_analytic():
    #Analytical values
    #Total variance
    measures = {}
    a = 7.
    measures["mean"] = a/2.0
    b = 0.1
    D = a**2./8 + b*np.pi**4./5 + b**2*np.pi**8./18 + 1./2
    measures 
    measures["var"] = D
    # Conditional variances
    D1 = b*np.pi**4./5 + b**2*np.pi**8./50. + 1./2
    D2 = a**2/8.
    D3 = 0
    
    D12  = 0
    D13  = b**2. * np.pi**8 / 18 - b**2*np.pi**8./50.
    D23  = 0
    D123 = 0
    
    # Main and total sensitivity indices
    measures["sens_m"] = {}
    measures["sens_m"][0] = D1/D
    measures["sens_m"][1] = D2/D
    measures["sens_m"][2] = D3/D
   

    measures["sens_t"] = {}
    measures["sens_t"][0] = (D1 + D12 + D13 + D123)/D
    measures["sens_t"][1] = (D2 + D12 + D23 + D123)/D
    measures["sens_t"][2] = (D3 + D13 + D23 + D123)/D
    return measures