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Original file line number | Diff line number | Diff line change |
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# ------------- | ||
# User Instructions | ||
# | ||
# Here you will be implementing a cyclic smoothing | ||
# algorithm. This algorithm should not fix the end | ||
# points (as you did in the unit quizzes). You | ||
# should use the gradient descent equations that | ||
# you used previously. | ||
# | ||
# Your function should return the newpath that it | ||
# calculates.. | ||
# | ||
# Feel free to use the provided solution_check function | ||
# to test your code. You can find it at the bottom. | ||
# | ||
# -------------- | ||
# Testing Instructions | ||
# | ||
# To test your code, call the solution_check function with | ||
# two arguments. The first argument should be the result of your | ||
# smooth function. The second should be the corresponding answer. | ||
# For example, calling | ||
# | ||
# solution_check(smooth(testpath1), answer1) | ||
# | ||
# should return True if your answer is correct and False if | ||
# it is not. | ||
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from math import * | ||
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# Do not modify path inside your function. | ||
path=[[0, 0], | ||
[1, 0], | ||
[2, 0], | ||
[3, 0], | ||
[4, 0], | ||
[5, 0], | ||
[6, 0], | ||
[6, 1], | ||
[6, 2], | ||
[6, 3], | ||
[5, 3], | ||
[4, 3], | ||
[3, 3], | ||
[2, 3], | ||
[1, 3], | ||
[0, 3], | ||
[0, 2], | ||
[0, 1]] | ||
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############# ONLY ENTER CODE BELOW THIS LINE ########## | ||
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# ------------------------------------------------ | ||
# smooth coordinates | ||
# If your code is timing out, make the tolerance parameter | ||
# larger to decrease run time. | ||
# | ||
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def smooth(path, weight_data = 0.1, weight_smooth = 0.1, tolerance = 0.00001): | ||
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# | ||
# Enter code here | ||
# | ||
# 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] | ||
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change = tolerance | ||
while (change >= tolerance): | ||
change = 0.0 | ||
for i in range(len(path)): | ||
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]) | ||
last = newpath[(i-1) % len(newpath)][j] | ||
nextone = newpath[(i+1) % len(newpath)][j] | ||
newpath[i][j] = newpath[i][j] + weight_smooth * (last + nextone - (2.0 * newpath[i][j])) | ||
change += abs(aux - newpath[i][j]) | ||
return newpath | ||
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# thank you - EnTerr - for posting this on our discussion forum | ||
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#newpath = smooth(path) | ||
#for i in range(len(path)): | ||
# print '['+ ', '.join('%.3f'%x for x in path[i]) +'] -> ['+ ', '.join('%.3f'%x for x in newpath[i]) +']' | ||
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##### TESTING ###### | ||
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# -------------------------------------------------- | ||
# check if two numbers are 'close enough,'used in | ||
# solution_check function. | ||
# | ||
def close_enough(user_answer, true_answer, epsilon = 0.001): | ||
if abs(user_answer - true_answer) > epsilon: | ||
return False | ||
return True | ||
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# -------------------------------------------------- | ||
# check your solution against our reference solution for | ||
# a variety of test cases (given below) | ||
# | ||
def solution_check(newpath, answer): | ||
if type(newpath) != type(answer): | ||
print "Error. You do not return a list." | ||
return False | ||
if len(newpath) != len(answer): | ||
print 'Error. Your newpath is not the correct length.' | ||
return False | ||
if len(newpath[0]) != len(answer[0]): | ||
print 'Error. Your entries do not contain an (x, y) coordinate pair.' | ||
return False | ||
for i in range(len(newpath)): | ||
for j in range(len(newpath[0])): | ||
if not close_enough(newpath[i][j], answer[i][j]): | ||
print 'Error, at least one of your entries is not correct.' | ||
return False | ||
print "Test case correct!" | ||
return True | ||
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# -------------- | ||
# Testing Instructions | ||
# | ||
# To test your code, call the solution_check function with | ||
# two arguments. The first argument should be the result of your | ||
# smooth function. The second should be the corresponding answer. | ||
# For example, calling | ||
# | ||
# solution_check(smooth(testpath1), answer1) | ||
# | ||
# should return True if your answer is correct and False if | ||
# it is not. | ||
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testpath1 = [[0, 0], | ||
[1, 0], | ||
[2, 0], | ||
[3, 0], | ||
[4, 0], | ||
[5, 0], | ||
[6, 0], | ||
[6, 1], | ||
[6, 2], | ||
[6, 3], | ||
[5, 3], | ||
[4, 3], | ||
[3, 3], | ||
[2, 3], | ||
[1, 3], | ||
[0, 3], | ||
[0, 2], | ||
[0, 1]] | ||
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answer1 = [[0.5449300156668018, 0.47485226780102946], | ||
[1.2230705677535505, 0.2046277687200752], | ||
[2.079668890615267, 0.09810778721159963], | ||
[3.0000020176660755, 0.07007646364781912], | ||
[3.9203348821839112, 0.09810853832382399], | ||
[4.7769324511170455, 0.20462917195702085], | ||
[5.455071854686622, 0.4748541381544533], | ||
[5.697264197153936, 1.1249625336275617], | ||
[5.697263485026567, 1.8750401628534337], | ||
[5.455069810373743, 2.5251482916876378], | ||
[4.776929339068159, 2.795372759575895], | ||
[3.92033110541304, 2.9018927284871063], | ||
[2.999998066091118, 2.929924058932193], | ||
[2.0796652780381826, 2.90189200881968], | ||
[1.2230677654766597, 2.7953714133566603], | ||
[0.544928391271399, 2.5251464933327794], | ||
[0.3027360471605494, 1.875038145804603], | ||
[0.302736726373967, 1.1249605602741133]] | ||
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## [0.000, 0.000] -> [0.545, 0.475] | ||
## [1.000, 0.000] -> [1.223, 0.205] | ||
## [2.000, 0.000] -> [2.080, 0.098] | ||
## [3.000, 0.000] -> [3.000, 0.070] | ||
## [4.000, 0.000] -> [3.920, 0.098] | ||
## [5.000, 0.000] -> [4.777, 0.205] | ||
## [6.000, 0.000] -> [5.455, 0.475] | ||
## [6.000, 1.000] -> [5.697, 1.125] | ||
## [6.000, 2.000] -> [5.697, 1.875] | ||
## [6.000, 3.000] -> [5.455, 2.525] | ||
## [5.000, 3.000] -> [4.777, 2.795] | ||
## [4.000, 3.000] -> [3.920, 2.902] | ||
## [3.000, 3.000] -> [3.000, 2.930] | ||
## [2.000, 3.000] -> [2.080, 2.902] | ||
## [1.000, 3.000] -> [1.223, 2.795] | ||
## [0.000, 3.000] -> [0.545, 2.525] | ||
## [0.000, 2.000] -> [0.303, 1.875] | ||
## [0.000, 1.000] -> [0.303, 1.125] | ||
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testpath2 = [[1, 0], # Move in the shape of a plus sign | ||
[2, 0], | ||
[2, 1], | ||
[3, 1], | ||
[3, 2], | ||
[2, 2], | ||
[2, 3], | ||
[1, 3], | ||
[1, 2], | ||
[0, 2], | ||
[0, 1], | ||
[1, 1]] | ||
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answer2 = [[1.239080543767428, 0.5047204351187283], | ||
[1.7609243903912781, 0.5047216452560908], | ||
[2.0915039821562416, 0.9085017167753027], | ||
[2.495281862032503, 1.2390825203587184], | ||
[2.4952805300504783, 1.7609262468826048], | ||
[2.0915003641706296, 2.0915058211575475], | ||
[1.7609195135622062, 2.4952837841027695], | ||
[1.2390757942466555, 2.4952826072236918], | ||
[0.9084962737918979, 2.091502621431358], | ||
[0.5047183914625598, 1.7609219230352355], | ||
[0.504719649257698, 1.2390782835562297], | ||
[0.9084996902674257, 0.9084987462432871]] | ||
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## [1.000, 0.000] -> [1.239, 0.505] | ||
## [2.000, 0.000] -> [1.761, 0.505] | ||
## [2.000, 1.000] -> [2.092, 0.909] | ||
## [3.000, 1.000] -> [2.495, 1.239] | ||
## [3.000, 2.000] -> [2.495, 1.761] | ||
## [2.000, 2.000] -> [2.092, 2.092] | ||
## [2.000, 3.000] -> [1.761, 2.495] | ||
## [1.000, 3.000] -> [1.239, 2.495] | ||
## [1.000, 2.000] -> [0.908, 2.092] | ||
## [0.000, 2.000] -> [0.505, 1.761] | ||
## [0.000, 1.000] -> [0.505, 1.239] | ||
## [1.000, 1.000] -> [0.908, 0.908] | ||
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solution_check(smooth(testpath1), answer1) | ||
solution_check(smooth(testpath2), answer2) | ||
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