from gekko import gekko 
import numpy as np
import matplotlib.pyplot as plt

"""
minimize y
s.t.     y = f(x)

using cubic spline with random sampling of data
"""

# Function to generate data for cspline
def f(x):
    return 3*np.sin(x) - (x-3) 

# Create model
c = gekko()

# Cubic spline
x = c.Var(value=15)
y = c.Var()
x_data = np.random.rand(50)*10+10
y_data = f(x_data)
c.cspline(x,y,x_data,y_data,True)
c.Obj(y)

# Options
c.options.IMODE = 3
c.options.CSV_READ = 0
c.options.SOLVER = 3
c.solve()

# Generate continuous trend for plot
z = np.linspace(10,20,100)

# Check if solved successfully
if c.options.SOLVESTATUS == 1:
    plt.figure()
    plt.plot(z,f(z),'r-',label='original')
    plt.scatter(x_data,y_data,5,'b',label='data')
    plt.scatter(x.value,y.value,200,'k','x',label='minimum')
    plt.legend(loc='best')
else:
    print ('Failed to converge!')
    plt.figure()
    plt.plot(z,f(z),'r-',label='original')
    plt.scatter(x_data,y_data,5,'b')
    plt.legend(loc='best')
plt.show()