import pandas as pd
import numpy as np
from scipy import optimize, linalg
import scipy
from scipy import spatial
import re
import math
import pandas as pd
from numpy import zeros, dot, savetxt
import matplotlib
from matplotlib import pylab as plt
%matplotlib inline

plt.style.use('ggplot')
print(plt.style.available)

def Lin_func(vector):
    znach_v = []
    for znach in vector:
        znach_v += [math.sin(znach / 5) * math.exp(znach / 10) + 5 * math.exp(-znach / 2)]
    return znach_v 
def EDin_func(znach):
    return math.sin(znach / 5) * math.exp(znach / 10) + 5 * math.exp(-znach / 2)

a = np.linspace(1, 15, num = 100)
#a, len(a)
#print Lin_func(a),
b = Lin_func(a)

b = [EDin_func(1.), EDin_func(15.)]
b

izn3 = [1., 4., 10., 15.]        #ввод точек 
fzn3 = Lin_func(izn3)

izn3 = [0.24, 0.26, 0.27, 0.29, 0.30, 0.32]
fzn3 = [1/2711, 1.297, 1.310, 1.336, 1.350, 1.377]

koeff = []
def koeff_search(izn3 = izn3, fzn3 = fzn3):
    work_m = izn3
    znach_func = fzn3
    for i in range(len(work_m)):            #из списка в матрицу
        work_m[i] = [work_m[i]]
    for i in range(len(work_m)):            #умножения количества элементов 
        work_m[i] = work_m[i] * (len(work_m))
    N = 0
    for i in range(len(work_m)):            #создание матрицы квадратов
        for j in range(len(work_m)):
            work_m[i][j] = work_m[i][j] ** N
            N += 1
        N = 0
    koeff = np.linalg.solve(work_m, znach_func) #Находим решение системы
    print koeff
    return koeff

def Polin_func1(vector, koeff = koeff):
    znach_f = []
    for znach in vector:
        znach_f += [koeff[0] + ((koeff[1]) * znach) + (koeff[2] * (znach ** 2)) + ((koeff[3]) * (znach ** 3))]
    return znach_f

def Polin_func2(vector, koeff = koeff):              #функция нахождения полинома
    znach_v = []
    shab = []
    for znach in vector:
        for i in range(len(koeff)):
            shab += [koeff[i] * (znach ** i)]
        znach_v += [float(sum(shab))]
        shab = []
    return znach_v

c =  koeff_search()

dis = np.linspace(0.238, 0.329, num = 20)
var = Lin_func(dis)
for i in range(len(var)):
    var[i] = (var[i])

x = [0.24, 0.26, 0.27, 0.29, 0.30, 0.32]
y = [1/2711, 1.297, 1.310, 1.336, 1.350, 1.377]

plt.plot(x, y, '*', dis, Polin_func2(dis, koeff=c),'-b')
plt.show

print(abs(np.array(y)) - abs(np.array(Polin_func2(x, koeff=c))))
print(np.sqrt(sum([i - sum(y)/len(y) for i in Polin_func2(x, koeff=c)])/(len(x)*(len(x)-1))))
print(y)
print(Polin_func2(x, koeff=c))

def Int_EDin_func(znach):
    return int(math.sin(znach / 5) * math.exp(znach / 10) + 5 * math.exp(-znach / 2))

% time res = scipy.optimize.minimize(EDin_func, 2 ) 
print res,'\n',res.x,'\n', res.message,'\n', res.hess_inv 
%time res = scipy.optimize.minimize(EDin_func, 30, method='BFGS' ) 
print res,'\n',res.x,'\n', res.message,'\n', res.hess_inv 
%time res = scipy.optimize.differential_evolution(EDin_func, [(0, 30)])
print res.x, res.fun
%time res = scipy.optimize.minimize(Int_EDin_func, 30, method='BFGS' ) 
print res,'\n',res.x,'\n', res.message,'\n', res.hess_inv

koeff

import random
a = []
b = range(10)
for i in range(10):
    a += [random.randint(1, 30)]

print a, len(a), '\n', b, len(b)

c =  koeff_search(b, a)