Think Python 2nd Edition Exercise 7-1

“Square Roots” loop:

while True:
    y = (x+ a/x) / 2
    if y == x:
        return x
    x = y

Copy the loop from “Square Roots” and encapsulate it in a function called mysqrt that takes a as a parameter, chooses a reasonable value of x, and returns an estimate of the square root of a. To test it, write a function named test_square_root that prints a table like this:

a   mysqrt(a)     math.sqrt(a)  diff
-   ---------     ------------  ----
1.0 1.0           1.0           0.0
2.0 1.41421356237 1.41421356237 2.22044604925e-16
3.0 1.73205080757 1.73205080757 0.0
4.0 2.0           2.0           0.0
5.0 2.2360679775  2.2360679775  0.0
6.0 2.44948974278 2.44948974278 0.0
7.0 2.64575131106 2.64575131106 0.0
8.0 2.82842712475 2.82842712475 4.4408920985e-16
9.0 3.0           3.0           0.0

Here’s what I wrote:

import math

def mysqrt(a):
    x = a/5
    while True:
        y = (x+ a/x) / 2
        if y == x:
            return x
        x = y

def test_square_root():
    a = 1.0
    print('a', repr(mysqrt(a)).rjust(6), repr(math.sqrt(a)).rjust(12), 'diff'.rjust(10))
    print("-      ---------            ------------          ----")
    while a < 10.0:
        print(a, "  ", mysqrt(a), "  ", math.sqrt(a), "  ", abs(mysqrt(a)-math.sqrt(a)))
        a += 1

test_square_root()

Here’s what I got:

a    1.0          1.0       diff
-      ---------            ------------          ----
1.0    1.0    1.0    0.0
2.0    1.414213562373095    1.4142135623730951    2.220446049250313e-16
3.0    1.7320508075688772    1.7320508075688772    0.0
4.0    2.0    2.0    0.0
5.0    2.23606797749979    2.23606797749979    0.0
6.0    2.449489742783178    2.449489742783178    0.0
7.0    2.6457513110645907    2.6457513110645907    0.0
8.0    2.82842712474619    2.8284271247461903    4.440892098500626e-16
9.0    3.0    3.0    0.0

As you can see, the array is not neatly aligned. How can I print an array if the elements do not have the same length? Thank you!

Answer

Adjust the print statement to print each element to a fixed number of decimal places using {0:.8f} {0:.10f} and {0:.4f} respectively, or your desired coloumn width.