#!/usr/bin/env python
# coding: utf-8

# In[16]:


# Iam very sorry because I had to copy the problems given below directly from the textbook, because it is a redundant process.
# Moreover the concept of numpy library is a never ending process, because there are a ton of different methods and functions.
# I think this is more than enough to learn about numpy.
import numpy as np
x = np.arange(4)
print("x =", x)
print("x + 5 =", x + 5)
print("x - 5 =", x - 5)
print("x * 2 =", x * 2)
print("x / 2 =", x / 2)
print("x // 2 =", x // 2) # floor division
print("-x = ", -x)
print("x ** 2 = ", x ** 2)
print("x % 2 = ", x % 2)
print(np.add(x, 2))


# In[18]:


# Absolute value
x = np.array([-2, -1, 0, 1, 2])
print(abs(x))
print("---------------------------")
x = np.array([3 - 4j, 4 - 3j, 2 + 0j, 0 + 1j])
print(np.abs(x))


# In[22]:


# Trigonometric functions

theta = np.linspace(0, np.pi, 3)
print("---------------------------")
print("theta = ", theta)
print("sin(theta) = ", np.sin(theta))
print("cos(theta) = ", np.cos(theta))
print("tan(theta) = ", np.tan(theta))
print("---------------------------")

x = [-1, 0, 1]
print("x = ", x)
print("arcsin(x) = ", np.arcsin(x))
print("arccos(x) = ", np.arccos(x))
print("arctan(x) = ", np.arctan(x))


# In[25]:


# Exponents and logarithms
x = [1, 2, 3]
print("x =", x)
print("e^x =", np.exp(x))
print("2^x =", np.exp2(x))
print("3^x =", np.power(3, x))
print("---------------------------")

x = [1, 2, 4, 10]
print("x =", x)
print("ln(x) =", np.log(x))
print("log2(x) =", np.log2(x))
print("log10(x) =", np.log10(x))
print("---------------------------")

x = [0, 0.001, 0.01, 0.1]
print("exp(x) - 1 =", np.expm1(x))
print("log(1 + x) =", np.log1p(x))


# In[29]:


# Another excellent source for more specialized and obscure ufuncs is the submodule
# scipy.special. If you want to compute some obscure mathematical function on
# your data, chances are it is implemented in scipy.special.

from scipy import special
x = [1, 5, 10]
print("gamma(x) =", special.gamma(x))
print("ln|gamma(x)| =", special.gammaln(x))
print("beta(x, 2) =", special.beta(x, 2))
print("---------------------------")

# Error function (integral of Gaussian)
# its complement, and its inverse
x = np.array([0, 0.3, 0.7, 1.0])
print("erf(x) =", special.erf(x))
print("erfc(x) =", special.erfc(x))
print("erfinv(x) =", special.erfinv(x))


# In[31]:


# Advanced Ufunc Features
# Specifying output

x = np.arange(5)
y = np.empty(5)
np.multiply(x, 10, out=y)
print(y)
print("---------------------------")

y = np.zeros(10)
np.power(2, x, out=y[::2])
print(y)


# In[35]:


# Aggregates
x = np.arange(1, 6)
print(np.add.reduce(x))
print("---------------------------")

print(np.multiply.reduce(x))
print("---------------------------")

print(np.add.accumulate(x))
print("---------------------------")

print(np.multiply.accumulate(x))