lambda.md

Lambda function

Python includes a quick one-line construction of functions that is often convenient to make your code compact. For example:

f = lambda x: x**3 + 6
f(2)
## 14

Which is same as:

def f(x):
  return x**3 + 6
f(2)
## 14

For another example:

g = lambda x,y,z: x*y/z
g(2,3,4)
## 1.5

which is same as:

def g(x,y,z):
  return x*y/z
g(2,3,4)
## 1.5

In general,

def fun(arg1,arg2,arg3,...):
  return expression

Can be written as

fun = lambda arg1,arg2,arg3,...: expression

For example It is possible to write a single limit for the second derivative:

def deriv2nd(f,x,h=1E-6):
  r = (f(x-h) - 2*f(x) + f(x+h))/float(h**2) 
  return r
 
## Example
f = lambda x: x**3
deriv2nd(f,2)
## 12.002843163827492

We know that the second derivative of f(x) = x**3 is equal to 6*x and is equal to 12 for x = 2.

Also, we can replace an string in a mathematical formula with a number to find the answer. For example, lets find the answer for 6*x at x = 2:

re = lambda f,x,z: eval(f.replace(str(x),str(z)))
 
## Example
f = '3*x'
re(f,'x',2)
## 12

Note that we can find the derivative of functions by using SymPy package, for example:

import sympy
x = symbols('x')
f = x**3
ff = f.diff(x,2)
ff
## 6*x

ff.subs({x:2})
## 12

And for another example let's find Euclidean norm of a vector by:

pnorm = lambda v,p=2: sum([abs(x)**p for x in v])**(1/p)
 
# Example
v = [2,3,4]
pnorm(v)
## 5.385164807134504
pnorm(v,1)
## 9.0

Another fun example is finding palindrome words:

def pal(x):
  return x == x[::-1]
## Or
pal = lambda x: x == x[::-1]

pal('pop')
## True
pal('pub'):
## False
pal('madam')
## True