import time
import platform
print('Last updated: %s' %time.strftime('%d/%m/%Y'))
print('Created using Python', platform.python_version())

%%file hello.py
def func_inside_script(x, y):
    return x + y
print('Hello World')

%run hello.py

func_inside_script(1, 2)

%timeit [x**2 for x in range(100)] 

%timeit -r 5 -n 100 [x**2 for x in range(100)] 

my_dir = 'new_dir'
!mkdir $my_dir
!pwd
!touch $my_dir'/some.txt'
!ls -l './new_dir'
!ls -l $my_dir | wc -l

def some_func():
    var = 'hello world'
    for i in range(5):
        print(i)
    i / 0
    return 'finished'

%debug
some_func()

%matplotlib inline

import numpy as np
from matplotlib import pyplot as plt
import math

def pdf(x, mu=0, sigma=1):
    """Calculates the normal distribution's probability density 
        function (PDF).  
        
    """
    term1 = 1.0 / ( math.sqrt(2*np.pi) * sigma )
    term2 = np.exp( -0.5 * ( (x-mu)/sigma )**2 )
    return term1 * term2


x = np.arange(0, 100, 0.05)

pdf1 = pdf(x, mu=5, sigma=2.5**0.5)
pdf2 = pdf(x, mu=10, sigma=6**0.5)

plt.plot(x, pdf1)
plt.plot(x, pdf2)
plt.title('Probability Density Functions')
plt.ylabel('p(x)')
plt.xlabel('random variable x')
plt.legend(['pdf1 ~ N($\mu=5$, $\sigma=2.5$)', 'pdf2 ~ N($\mu=10$, $\sigma=6$)'], loc='upper right')
plt.ylim([0,0.5])
plt.xlim([0,20])

plt.show()

%load_ext cythonmagic

%%cython
import numpy as np
cimport numpy as np
cimport cython
@cython.boundscheck(False) 
@cython.wraparound(False)
@cython.cdivision(True)
cpdef cython_lstsqr(x_ary, y_ary):
    """ Computes the least-squares solution to a linear matrix equation. """
    cdef double x_avg, y_avg, var_x, cov_xy,\
         slope, y_interc, temp
    cdef double[:] x = x_ary # memoryview
    cdef double[:] y = y_ary
    cdef unsigned long N, i
    
    N = x.shape[0]
    x_avg = 0
    y_avg = 0
    for i in range(N):
        x_avg += x[i]
        y_avg += y[i]
    x_avg = x_avg/N
    y_avg = y_avg/N
    var_x = 0
    cov_xy = 0
    for i in range(N):
        temp = (x[i] - x_avg)
        var_x += temp**2
        cov_xy += temp*(y[i] - y_avg)
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg
    return (slope, y_interc)

import numpy as np

x_ary = np.array([x_i*np.random.randint(8,12)/10 for x_i in range(100)])
y_ary = np.array([y_i*np.random.randint(10,14)/10 for y_i in range(100)])

cython_lstsqr(x_ary, y_ary)

%install_ext https://raw.github.com/mgaitan/fortran_magic/master/fortranmagic.py

%load_ext fortranmagic

%%fortran
SUBROUTINE fortran_lstsqr(ary_x, ary_y, slope, y_interc)
    ! Computes the least-squares solution to a linear matrix equation. """
    IMPLICIT NONE
    REAL(8), INTENT(in), DIMENSION(:) :: ary_x, ary_y
    REAL(8), INTENT(out) :: slope, y_interc
    REAL(8) :: x_avg, y_avg, var_x, cov_xy, temp
    INTEGER(8) :: N, i
    
    N = SIZE(ary_x)

    x_avg = SUM(ary_x) / N
    y_avg = SUM(ary_y) / N
    var_x = 0
    cov_xy = 0
    
    DO i = 1, N
        temp = ary_x(i) - x_avg
        var_x = var_x + temp**2
        cov_xy = cov_xy + (temp*(ary_y(i) - y_avg))
    END DO
    
    slope = cov_xy / var_x
    y_interc = y_avg - slope*x_avg

END SUBROUTINE fortran_lstsqr

import numpy as np

x_ary = np.array([x_i*np.random.randint(8,12)/10 for x_i in range(100)])
y_ary = np.array([y_i*np.random.randint(10,14)/10 for y_i in range(100)])

fortran_lstsqr(x_ary, y_ary)

%%script perl
print 'Hello, World!';

%%perl
print 'Hello, World!';

%%ruby
puts "Hello, World!"

%%bash
echo "Hello World!"

%%script R --no-save
cat("Goodbye, World!\n")

def hello_world():
    """This is a hello world example function."""
    print('Hello, World!')

%pdoc hello_world

%pdef hello_world

%psource math.mean()

from math import sqrt