# udacity373_code / unit5 / u5-hw3_constrainedsmoothing.py

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196``` ```# ------------- # User Instructions # # Now you will be incorporating fixed points into # your smoother. # # You will need to use the equations from gradient # descent AND the new equations presented in the # previous lecture to implement smoothing with # fixed points. # # 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. from math import * # Do not modify path inside your function. path=[[0, 0], #fix [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], #fix [6, 1], [6, 2], [6, 3], #fix [5, 3], [4, 3], [3, 3], [2, 3], [1, 3], [0, 3], #fix [0, 2], [0, 1]] # Do not modify fix inside your function fix = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0] ######################## ENTER CODE BELOW HERE ######################### def smooth(path, fix, weight_data = 0.0, weight_smooth = 0.1, tolerance = 0.00001): # # Enter code here. # The weight for each of the two new equations should be 0.5 * weight_smooth # # Enter code here newpath = [[float(col) for col in row] for row in path] change = tolerance while change >= tolerance: change = 0.0 for i in range(len(path)): if fix[i]: continue #else update coordinates for j in range(len(path[0])): aux = newpath[i][j] x = path[i][j] xn1 = (i+1) % len(path) xn2 = (i+2) % len(path) xp1 = (i-1) % len(path) xp2 = (i-2) % len(path) newpath[i][j] += weight_data * (x - newpath[i][j]) newpath[i][j] += weight_smooth * ( newpath[xn1][j] + newpath[xp1][j] - 2.0*newpath[i][j]) newpath[i][j] += 0.5 * weight_smooth * ( 2.0* newpath[xp1][j] - newpath[xp2][j] - newpath[i][j]) newpath[i][j] += 0.5 * weight_smooth * ( 2.0 * newpath[xn1][j] - newpath[xn2][j] - newpath[i][j]) change += abs(aux - newpath[i][j]) return newpath #thank you - EnTerr - for posting this on our discussion forum ##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]) +']' # -------------------------------------------------- # check if two numbers are 'close enough,'used in # solution_check function. # def close_enough(user_answer, true_answer, epsilon = 0.03): if abs(user_answer - true_answer) > epsilon: return False return True # -------------------------------------------------- # 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 # -------------- # 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. testpath1=[[0, 0], #fix [1, 0], [2, 0], [3, 0], [4, 0], [5, 0], [6, 0], #fix [6, 1], [6, 2], [6, 3], #fix [5, 3], [4, 3], [3, 3], [2, 3], [1, 3], [0, 3], #fix [0, 2], [0, 1]] testfix1 = [1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0] answer1 = [[0, 0], [0.7938620981547201, -0.8311168821106101], [1.8579052986461084, -1.3834788165869276], [3.053905318597796, -1.5745863173084], [4.23141390533387, -1.3784271816058231], [5.250184859723701, -0.8264215958231558], [6, 0], [6.415150091996651, 0.9836951698796843], [6.41942442687092, 2.019512290770163], [6, 3], [5.206131365604606, 3.831104483245191], [4.142082497497067, 4.383455704596517], [2.9460804122779813, 4.5745592975708105], [1.768574219397359, 4.378404668718541], [0.7498089205417316, 3.826409771585794], [0, 3], [-0.4151464728194156, 2.016311854977891], [-0.4194207879552198, 0.9804948340550833]] testpath2 = [[0, 0], # fix [2, 0], [4, 0], # fix [4, 2], [4, 4], # fix [2, 4], [0, 4], # fix [0, 2]] testfix2 = [1, 0, 1, 0, 1, 0, 1, 0] answer2 = [[0, 0], [2.0116767115496095, -0.7015439080661671], [4, 0], [4.701543905420104, 2.0116768147460418], [4, 4], [1.9883231877640861, 4.701543807525115], [0, 4], [-0.7015438099112995, 1.9883232808252207]] #solution_check(smooth(testpath1, testfix1), answer1) ```
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