Convert for loop to while loop-CodePudding

I am working on code that uses loops and Heron's method to find an estimate of the square root, while also displaying the iteration and relative change.

I completed a function that uses for loops to achieve this:

def square_root_for(a, x0, max_iter = 10, tol=1e-14):  
    
    """ (number, integer, number) -> float

    Return an estimate of the square root of a number using the Heron's method.
        
    >>> square_root_for(5, 5)
    Iteration | Estimate         | Relative Change
    -------------------------------------------------
    1         | 3.00000000000000 | 0.4000000000000000
    2         | 2.33333333333333 | 0.2222222222222222
    3         | 2.23809523809524 | 0.0408163265306123
    4         | 2.23606889564336 | 0.0009053870529653
    5         | 2.23606797749998 | 0.0000004106060359
    6         | 2.23606797749979 | 0.0000000000000842
    7         | 2.23606797749979 | 0.0000000000000000
    2.23606797749979
    """
    
    x = [x0]
    x.append(a/x0)
  
    print('Iteration | Estimate         | Relative Change')
    print('-------------------------------------------------')
         
    
    for i in range(1,(max_iter   1),1):
      
        change = (abs(x[i] - x[i-1]) / x[i-1])
        if change > tol:
            x.append(1/2 * (x[i]   (a / x[i])))
        
        else:
            break
        print('{}         | {:.14f} | {:.16f}'.format(i, x[i], change))

    print(x[i])

Next I need to create a function that uses while loops. So far I have:

def square_root_while(a, x0, tol=1e-14):
   """ (number, number, number) -> float

   Return an estimate of the square root of a number using the Heron's method.
       
   >>> square_root_while(5, 5)
   Iteration | Estimate         | Relative Change
   -------------------------------------------------
   1         | 3.00000000000000 | 0.4000000000000000
   2         | 2.33333333333333 | 0.2222222222222222
   3         | 2.23809523809524 | 0.0408163265306123
   4         | 2.23606889564336 | 0.0009053870529653
   5         | 2.23606797749998 | 0.0000004106060359
   6         | 2.23606797749979 | 0.0000000000000842
   7         | 2.23606797749979 | 0.0000000000000000
   2.23606797749979
   """
   
   x = [x0]
   x.append(a/x0)
 
   print('Iteration | Estimate         | Relative Change')
   print('-------------------------------------------------')
   
   i = range(1,(max_iter   1),1)
       
   change = (abs(x[i] - x[i-1]) / x[i-1])
   
   while change < tol:
       x.append(1/2 * (x[i]   (a / x[i])))
       i = i   1
       
       if change > tol:
           break
   print('{}         | {:.14f} | {:.16f}'.format(i, x[i], change))

But this is pretty much completely wrong. I am very confused with how to do this. I don't understand how I could convert this for loop with a range into a while loop. Any tips are appreciated, Thank you!

CodePudding user response：

As in this way? range(start, stop, step) is just creating a sequence. You can split it into add/increment instructions:

From this:

for i in range(start, stop, step):
    ...

To this:

i = start
while start < stop:
    ...
    i  = step

And applied for your loop:

i = 1
while i < max_iter   1:
    change = (abs(x[i] - x[i-1]) / x[i-1])
    if change > tol:
        x.append(1/2 * (x[i]   (a / x[i])))

    else:
        break
    print('{}         | {:.14f} | {:.16f}'.format(i, x[i], change))
    i  = 1

CodePudding user response：

These two loops are equivalent:

for i in range(N):
    # do the work

i = 0
while i < N:
    # do the work
    i  = 1

CodePudding user response：

In a for loop you got initial value, max value, step.

for i in range(initial, maxValue, step):

On a while loop you have to define that behavior.

value = 1 # initial value
maxValue= max_iter   1 # max value
while value < maxValue:
    #do your thing
    value = value   1 //step