# alexband/Udacity-373

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 # ----------- # User Instructions # # Define a function smooth that takes a path as its input # (with optional parameters for weight_data, weight_smooth) # and returns a smooth path. # # Smoothing should be implemented by iteratively updating # each entry in newpath until some desired level of accuracy # is reached. The update should be done according to the # gradient descent equations given in the previous video: # # If your function isn't submitting it is possible that the # runtime is too long. Try sacrificing accuracy for speed. # ----------- #gradient descent to make #(Xi-Yi)**2 --> min #(Yi-Yi+1)**2 --> min # # Xi means the element in old path path[i][j] # Yi means the element in new path newpath[i][j] Yi-1 Yi+1 means newpath[i-1][j] # newpath[i+1][j] # j means for x cordinate and y cordiante we use the same method # tolerance means until the change would not make a difference big than that from math import * # Don't modify path inside your function. path = [[0, 0], [0, 1], [0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [4, 3], [4, 4]] # ------------------------------------------------ # smooth coordinates # def smooth(path, weight_data = 0.5, weight_smooth = 0.1): # Make a deep copy of path into newpath #newpath = [[0 for col in range(len(path[0]))] for row in range(len(path))] #for i in range(len(path)): # for j in range(len(path[0])): # newpath[i][j] = path[i][j] from copy import deepcopy newpath = deepcopy(path) #### ENTER CODE BELOW THIS LINE ### tolerance = 0.00001 change = tolerance while (change >= tolerance): change = 0.0 #a new round runs gradiant descent for i in range(1,len(path)-1): for j in range(len(path[0])): aux = newpath[i][j] newpath[i][j] = newpath[i][j] + weight_data * ( path[i][j] - newpath[i][j]) newpath[i][j] = newpath[i][j] + weight_smooth * (newpath[i-1][j] + newpath[i+1][j] - (2.0 * newpath[i][j])) #how's the change compare with tolerance? change += abs(aux - newpath[i][j]) return newpath # Leave this line for the grader! # feel free to leave this and the following lines if you want to print. newpath = smooth(path) # thank you - EnTerr - for posting this on our discussion forum for i in range(len(path)): print '['+ ', '.join('%.3f'%x for x in path[i]) +'] -> ['+ ', '.join('%.3f'%x for x in newpath[i]) +']'