# coding: utf-8 # # Arithmetic on Squiggles # Let's "import" so-called "modules" that add features to our programming language ("Python"). # In[13]: import numpy as np import matplotlib.pyplot as pt # Here are two 'squiggles' represented as a bunch of numbers: # In[14]: squiggle_1 = "141.03 291.04 141.28 291.50 141.92 291.50 142.67 291.04 143.94 290.13 145.58 288.32 147.22 285.25 149.62 281.27 152.40 276.15 155.31 270.24 158.21 264.10 161.37 258.19 164.02 252.96 166.67 248.41 168.69 244.89 170.72 241.82 172.48 239.55 174.25 237.84 175.52 236.59 176.27 236.13 176.65 236.48 176.65 237.50 177.03 240.00 177.41 244.21 177.79 250.12 178.04 257.39 178.04 265.12 178.42 273.08 178.67 280.93 179.05 288.43 179.56 295.71 179.94 302.64 180.69 309.01 181.71 314.35 182.72 318.10 183.85 320.03 184.86 321.06 186.00 320.72 187.52 319.35 189.28 316.40 191.31 311.39 193.33 304.35 195.60 295.93 198.00 286.84 200.65 277.86 203.56 269.67 206.21 262.62 208.61 257.17 210.51 253.07 212.02 250.23 213.03 248.64 213.79 247.84 214.17 247.73 214.17 248.53 214.17 250.35 214.04 253.53 213.92 258.19 213.66 263.99 213.54 270.13 213.41 276.38 213.41 282.18 213.92 287.41 214.80 291.84 216.32 295.48 218.21 298.09 220.11 299.80 222.13 300.59 224.27 300.71 226.55 300.03 228.95 298.43 231.22 295.71 233.24 292.07 235.26 287.07 237.16 280.81 239.31 273.76 241.83 265.81 244.86 257.39 248.15 249.21 251.68 241.14 255.09 233.63 258.00 227.27 260.40 222.49 261.92 219.54 262.80 218.63 263.18 218.63 263.18 219.88 263.05 222.49 262.55 226.93 261.92 233.75 261.03 242.16 260.40 251.82 260.27 262.40 260.53 273.08 260.91 284.11 261.79 294.91 262.80 304.35 264.44 312.30 266.72 317.99 269.12 321.63 271.64 323.56 274.17 324.69 276.95 324.47 279.98 322.42 283.26 318.56 286.42 311.96 289.83 303.21 293.24 292.98 296.78 282.18 300.32 272.17 303.60 263.42 306.38 256.60 308.65 251.82 310.04 248.75 310.93 247.50 311.18 247.96 311.05 248.98 310.93 250.91 310.80 253.98 310.55 258.76 310.42 265.12 310.17 272.74 310.55 280.81 311.31 289.00 312.57 296.50 314.46 302.64 316.86 307.41 319.77 310.37 322.80 311.73 325.96 312.08 328.86 311.17 331.64 309.01 334.29 304.91 336.82 299.00 339.47 291.73 342.38 283.43 345.54 275.13 348.95 267.51 352.36 260.69 355.14 255.57 357.03 252.16 358.17 250.46 358.55 250.23 358.55 250.69 358.80 251.94 359.43 254.32 360.06 258.19 360.69 264.33 361.20 271.95 361.71 280.59 362.59 289.23 363.98 296.84 366.00 303.44 368.53 308.44 371.56 311.73 375.22 313.33 379.26 312.64 383.81 310.26 388.74 306.62 394.29 301.50 " squiggle_2 = "243.60 219.20 243.60 218.06 242.84 216.92 242.21 215.67 241.07 214.19 239.56 212.60 237.66 211.01 235.26 209.65 232.23 208.62 228.82 207.60 225.03 206.92 220.86 206.46 216.57 206.12 212.27 206.80 207.60 208.05 202.80 210.33 198.13 213.74 193.20 217.72 188.78 222.15 184.74 226.59 181.45 231.13 178.93 235.91 177.28 241.02 176.27 246.59 175.89 252.62 176.27 258.99 177.28 265.81 178.93 272.85 181.33 279.79 184.74 286.38 188.91 292.64 193.83 298.32 199.52 303.78 205.71 308.67 212.40 312.99 219.60 316.62 226.80 319.69 234.00 322.19 241.20 323.90 248.27 324.81 255.60 325.26 262.93 324.81 270.25 323.90 277.96 322.53 285.54 320.60 293.12 318.56 300.32 316.17 306.63 313.33 312.44 310.14 317.75 306.39 322.80 301.96 327.60 296.73 332.15 290.82 336.44 284.11 340.48 276.83 344.15 269.22 347.05 261.60 349.07 253.98 350.34 246.59 350.59 239.20 349.83 231.59 348.19 223.63 345.41 215.67 341.75 208.17 337.07 201.35 331.77 195.66 326.21 191.12 320.65 187.48 315.09 184.75 309.16 182.93 302.84 182.02 296.02 181.91 288.82 182.36 281.87 183.27 274.93 184.52 268.11 185.89 261.54 187.25 255.35 188.61 249.66 190.21 244.86 191.68 240.82 193.28 237.03 194.87 233.87 196.57 230.97 198.28 228.44 199.98 226.42 201.69 224.65 203.51 223.52 205.55 222.51 207.94 221.75 210.78 221.24 213.97 220.74 217.72 220.48 221.24 220.23 224.43 219.85 227.04 219.22 229.20 218.72 230.91 218.21 232.04 217.83 232.72 217.71 233.07 217.33 233.07 216.95 232.50 216.06 231.13 215.43 228.86 215.05 225.56 " # "Parsing" those turns them from strings into arrays of numbers: # In[17]: def parse_squiggle(s): numbers = [float(num) for num in s.split()] a = np.array(numbers) return a.reshape(-1, 2).T # In[18]: s1 = parse_squiggle(squiggle_1) s2 = parse_squiggle(squiggle_2) # Let's plot both squiggles. # In[19]: pt.plot(s1[0], s1[1]) # In[20]: pt.plot(s2[0], s2[1]) # Will this work? # In[22]: s1 + s2 # --------------- # # So we'll need to do something. # In[24]: from scipy.interpolate import interp1d _, ns1 = s1.shape _, ns2 = s2.shape s1x_interp = interp1d(np.linspace(0, 1, ns1), s1[0]) s1y_interp = interp1d(np.linspace(0, 1, ns1), s1[1]) s1_new = np.array([ s1x_interp(np.linspace(0, 1, ns2)), s1y_interp(np.linspace(0, 1, ns2))]) # In[33]: s3 = s1_new + s2 pt.plot(s3[0], s3[1])