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September 12, 2014 16:28
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sqRtAprox.py
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# Kristi Short | |
# Math 180 Numerical Analysis | |
# Fall 2014 | |
# Square Root Approximation | |
# Pythonista Version | |
import math | |
# prompt user for radicand | |
n = float(raw_input("Please enter an integer value for the radicand: ")) | |
toleranceVal = float(raw_input("Please enter a positive integer value for the power of the tolerance: ")) | |
tolerance = math.pow(10, -toleranceVal) | |
sqRt = math.sqrt(n) | |
err = 0 | |
print "Note: Computer memory is system dependent, floats are limited in accuracy. So unless you are running something seriously badass dont ask for a tolerance value larger than 6 or so." | |
def findRoot(n, tolerance): | |
itr = 0 | |
with open('SquareRootAprxData', 'w') as f: | |
f.write('#itr,floor, celing, prevMid, mid\n') | |
sqRt = math.sqrt(n) | |
floor = 0 | |
ceiling = n | |
mid = n | |
prevMid = -1 | |
err = 0 | |
while (math.fabs(mid - prevMid) >= tolerance): | |
f.write('{0},{1},{2},{3}\n'.format(itr,floor,ceiling,prevMid,mid)) | |
prevMid = mid | |
mid = float((floor+ceiling)/2) | |
if mid**2 > n: | |
ceiling = mid | |
else: | |
floor = mid | |
itr = itr + 1 | |
return mid | |
root = findRoot(n, tolerance) | |
err = math.fabs(root - sqRt) | |
print "The approximated root of " + str(n) + " is " + str(root) | |
print "The error in Approximation is: " + str(err) | |
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