import numpy as np

v = np.array( [3, 4] )

print( "v = ", v )

dot_product = v.dot( v )

print( "dot product = ", dot_product )

magnitude = np.sqrt( v.dot( v ) )

print( "magnitude = ", magnitude )

base_natural_log = np.e

print( "base of natural logarithms = ", base_natural_log )

print( "base of natural logarithms = ", np.exp( 1 ) )

print( "tanh( 0 ) = ", np.tanh( 0 ) )

print( "tanh( 1 ) = ", np.tanh( 1 ) )

print( "tanh( -1 ) = ", np.tanh( -1 ) )

print( "tanh( 5 ) = ", np.tanh( 5 ) )

print( "tanh( -5 ) = ", np.tanh( -5 ) )

sigmoid = lambda x: 1 / (1 + np.exp( - x ))

print( "sigmoid(0) = ", sigmoid( 0 ) )

print( "sigmoid(5) = ", sigmoid( 5 ) )

print( "sigmoid(-5) = ", sigmoid( -5 ) )

w = np.array( [np.random.random() for i in range(10)] )

print( "array of 10 random numbers = ", w )