import numpy as np
import matplotlib.pyplot as plt

plotLegend = []

def showPlot(xmin, xmax, xsteps):
    plt.xlim(xmin - 1, xmax + 1)
    plt.xticks(np.arange(xmin, xmax + xsteps, 1.0))
    plt.xlabel("x")
    plt.ylim(-1300, 1300)
    plt.ylabel("y")
    plt.grid(markevery=1)
    plt.legend(plotLegend)
    plt.title("Aufgabe 2")
    plt.show()

def polynom_function(a, x): #a = coefficients, x = values to calculate
    a = np.squeeze(np.asarray(a))
    p = np.array([])
    for x_value in x:
        result = 0
        for power, coefficient in enumerate(a):
            result += coefficient * x_value ** power
        p = np.append(p, result)
    return p

def derivative_f(a):
    a = np.squeeze(np.asarray(a))
    result = np.array([])
    for i in range(1, len(a)):
        result = np.append(result, a[i] * i)
    return result

def integral_f(a):
    a = np.squeeze(np.asarray(a))
    c = 0
    result = np.array([c])
    for i in range(0, len(a)):
        result = np.append(result, a[i] / (i + 1))
    return result

def plot_function(x, y, legendString):
    plt.plot(x, y)
    plotLegend.append(legendString)

def is_valid_vector(vector):
    shape = np.shape(vector)
    if(len(shape) == 2):
        return (shape[0] == 1 and shape[1] >= 1) or (shape[0] >= 1 and shape[1] == 1)
    else:
        return False

def roman_schenk_Aufg2(a, xmin, xmax):
    if not is_valid_vector(a):
        raise Exception('Fehler! a ist kein gültiger Spalten- oder Zeilenvektor!')
    xsteps =  abs(xmax/100.0)
    x = np.arange(xmin, xmax + xsteps, xsteps)
    p = polynom_function(a, x)
    dp = polynom_function(derivative_f(a), x)
    pint = polynom_function(integral_f(a), x)
    return(x,p,dp,pint)