Download --Pseudo Code/Hints for Problem 1 of Pi Estimation HW

Pseudo Code Hint for Pi estimation Problem #1
START PROGRAM
Set Parameters for Pi estimation (radius, number of dart throws)
Set Histogram Parameters
• Lower Bound
• Upper Bound
• Bin Width (pi/100 or pi/1000)
Compute Number of bins needed (for the defined range and bin width)
• nbins = int ( (Upper Bound – Lower Bound) / Bin Width )
Initialize histogram
• Initialize empty list (e.g. histogram = [])
• loop over the number of bins and append/initialize to zero
◦ e.g. :
for k in range(nbins):
histogram.append(0)
Define the number of times to loop and compute pi esitmate (e.g. npoints = 100000)
LOOP – over npoints
Compute Pi estimate – (i.e. the major portion of the starting python code)
Test if estimate is between Lower Bound and Upper Bound
if yes, then:
• compute the relevant bin index for value of pi estimate
◦ index = (value – Lower Bound) / Bind Width
• Increment the relevent bin
◦ e.g. : histogram[index] += 1
END LOOP
Normalize Histogram
• Compute the total bin counts
• Normalize by the total ( e.g. histogram[index] = float( histogram[index] ) / float( total )
Output Normalized distribution to a file/screen ( as: bin value vs. normalized distribution value)
• Compute the current bin value
◦ e.g. : bin_val = Lower Bound + (Bin Width * float( index ) ) , where index is the current
bin index
• Output
END PROGRAM