.. _sphx_glr_auto_examples_plot_sine_wave.py: ============================= Plotting simple sine function ============================= A simple example plotting a fit of the sine function. .. image:: /auto_examples/images/sphx_glr_plot_sine_wave_001.png :align: center .. rst-class:: sphx-glr-script-out Out:: Beginning forward pass --------------------------------------------------------------------- iter parent var knot mse terms gcv rsq grsq --------------------------------------------------------------------- 0 - - - 5244.476631 1 5245.526 0.000 0.000 1 0 6 9961 5067.564966 3 5073.652 0.034 0.033 2 2 6 3206 4861.646322 5 4872.360 0.073 0.071 3 4 6 7844 4639.910399 7 4654.794 0.115 0.113 4 0 6 7260 4468.624616 9 4487.452 0.148 0.145 5 7 6 8157 4244.467266 11 4266.625 0.191 0.187 6 9 6 2242 3900.087914 13 3924.381 0.256 0.252 7 10 6 5832 3770.802883 15 3798.100 0.281 0.276 8 7 6 1644 3534.771940 17 3563.936 0.326 0.321 9 15 6 3475 3314.407980 19 3345.112 0.368 0.362 10 15 6 2648 3162.265769 21 3194.769 0.397 0.391 11 9 6 1923 3028.741358 23 3062.950 0.422 0.416 12 7 6 3624 2880.064377 25 2915.525 0.451 0.444 13 23 6 3486 2702.824122 27 2738.858 0.485 0.478 14 23 6 116 2545.534016 29 2582.069 0.515 0.508 15 4 6 8773 2422.575970 31 2459.823 0.538 0.531 16 2 6 803 2262.126670 33 2299.223 0.569 0.562 17 32 6 5864 2122.594794 35 2159.580 0.595 0.588 18 4 6 7610 1836.777669 37 1870.669 0.650 0.643 19 0 6 2035 1641.898343 39 1673.883 0.687 0.681 20 38 6 7332 1428.554810 41 1457.855 0.728 0.722 21 40 6 9013 1053.447265 43 1076.141 0.799 0.795 22 37 6 1206 758.322249 45 775.442 0.855 0.852 23 7 6 593 636.565160 47 651.594 0.879 0.876 24 43 6 6001 532.755707 49 545.886 0.898 0.896 25 23 6 1488 451.992938 51 463.602 0.914 0.912 26 37 6 6122 385.157239 53 395.450 0.927 0.925 27 7 6 6946 335.936149 55 345.263 0.936 0.934 28 32 6 3381 287.101417 57 295.372 0.945 0.944 29 24 6 1440 235.668475 59 242.704 0.955 0.954 30 32 6 8375 209.747432 61 216.228 0.960 0.959 31 45 6 500 196.500438 63 202.778 0.963 0.961 32 2 6 3553 184.151662 65 190.228 0.965 0.964 33 39 6 9809 173.669012 67 179.582 0.967 0.966 34 52 6 1334 161.396838 69 167.061 0.969 0.968 35 9 6 1940 154.513111 71 160.099 0.971 0.969 36 7 6 9087 147.735445 73 153.232 0.972 0.971 37 53 6 3475 141.226286 75 146.630 0.973 0.972 38 40 6 1097 135.344070 77 140.666 0.974 0.973 39 40 6 7450 129.288718 79 134.510 0.975 0.974 40 64 6 1948 124.662704 81 129.829 0.976 0.975 ------------------------------------------------------------------- Stopping Condition 2: Improvement below threshold Beginning pruning pass ------------------------------------------------ iter bf terms mse gcv rsq grsq ------------------------------------------------ 0 - 81 124.94 130.113 0.976 0.975 1 43 80 124.94 130.047 0.976 0.975 2 31 79 124.94 129.981 0.976 0.975 3 35 78 124.94 129.915 0.976 0.975 4 1 77 124.94 129.848 0.976 0.975 5 58 76 124.94 129.782 0.976 0.975 6 17 75 124.94 129.716 0.976 0.975 7 40 74 124.94 129.650 0.976 0.975 8 63 73 124.94 129.584 0.976 0.975 9 69 72 124.94 129.518 0.976 0.975 10 42 71 124.94 129.452 0.976 0.975 11 46 70 124.94 129.386 0.976 0.975 12 26 69 124.94 129.320 0.976 0.975 13 23 68 124.94 129.255 0.976 0.975 14 71 67 124.94 129.189 0.976 0.975 15 55 66 124.94 129.123 0.976 0.975 16 15 65 124.94 129.058 0.976 0.975 17 60 64 124.94 128.992 0.976 0.975 18 54 63 124.94 128.927 0.976 0.975 19 9 62 124.94 128.861 0.976 0.975 20 6 61 124.94 128.796 0.976 0.975 21 10 60 124.93 128.723 0.976 0.975 22 13 59 124.93 128.662 0.976 0.975 23 8 58 124.94 128.604 0.976 0.975 24 16 57 124.99 128.586 0.976 0.975 25 4 56 125.10 128.642 0.976 0.975 26 32 55 125.61 129.095 0.976 0.975 27 33 54 127.52 130.994 0.976 0.975 28 74 53 128.99 132.437 0.975 0.975 29 80 52 131.21 134.645 0.975 0.974 30 22 51 132.74 136.150 0.975 0.974 31 21 50 133.34 136.691 0.975 0.974 32 75 49 133.99 137.295 0.974 0.974 33 36 48 138.74 142.089 0.974 0.973 34 79 47 144.86 148.276 0.972 0.972 35 72 46 151.28 154.769 0.971 0.970 36 70 45 160.51 164.129 0.969 0.969 37 66 44 170.02 173.767 0.968 0.967 38 65 43 178.52 182.365 0.966 0.965 39 25 42 188.91 192.887 0.964 0.963 40 68 41 199.78 203.874 0.962 0.961 41 7 40 211.71 215.947 0.960 0.959 42 59 39 223.54 227.893 0.957 0.957 43 45 38 240.03 244.579 0.954 0.953 44 76 37 252.64 257.300 0.952 0.951 45 67 36 277.68 282.664 0.947 0.946 46 5 35 307.60 312.958 0.941 0.940 47 62 34 339.68 345.429 0.935 0.934 48 61 33 349.66 355.399 0.933 0.932 49 56 32 406.73 413.191 0.922 0.921 50 53 31 476.86 484.187 0.909 0.908 51 73 30 531.86 539.769 0.899 0.897 52 19 29 565.68 573.801 0.892 0.891 53 3 28 724.42 734.443 0.862 0.860 54 20 27 974.98 987.983 0.814 0.812 55 57 26 1241.03 1256.947 0.763 0.760 56 18 25 1547.42 1566.472 0.705 0.701 57 14 24 1934.24 1957.075 0.631 0.627 58 44 23 2135.76 2159.880 0.593 0.588 59 38 22 2283.01 2307.631 0.565 0.560 60 49 21 2339.81 2363.860 0.554 0.549 61 27 20 2504.83 2529.307 0.522 0.518 62 12 19 2702.93 2727.972 0.485 0.480 63 24 18 2955.40 2981.280 0.436 0.432 64 50 17 3260.70 3287.600 0.378 0.373 65 28 16 3372.40 3398.523 0.357 0.352 66 41 15 3598.03 3624.073 0.314 0.309 67 51 14 3906.02 3932.321 0.255 0.250 68 37 13 3982.16 4006.966 0.241 0.236 69 2 12 4090.99 4114.409 0.220 0.216 70 78 11 4427.86 4450.979 0.156 0.151 71 47 10 4472.96 4494.060 0.147 0.143 72 77 9 4524.47 4543.529 0.137 0.134 73 29 8 4682.77 4700.141 0.107 0.104 74 34 7 4792.20 4807.568 0.086 0.083 75 11 6 4921.47 4934.784 0.062 0.059 76 30 5 4951.47 4962.377 0.056 0.054 77 64 4 4963.49 4971.937 0.054 0.052 78 52 3 5024.68 5030.718 0.042 0.041 79 39 2 5095.04 5098.605 0.028 0.028 80 48 1 5244.48 5245.526 0.000 0.000 -------------------------------------------------- Selected iteration: 24 Forward Pass --------------------------------------------------------------------- iter parent var knot mse terms gcv rsq grsq --------------------------------------------------------------------- 0 - - - 5244.476631 1 5245.526 0.000 0.000 1 0 6 9961 5067.564966 3 5073.652 0.034 0.033 2 2 6 3206 4861.646322 5 4872.360 0.073 0.071 3 4 6 7844 4639.910399 7 4654.794 0.115 0.113 4 0 6 7260 4468.624616 9 4487.452 0.148 0.145 5 7 6 8157 4244.467266 11 4266.625 0.191 0.187 6 9 6 2242 3900.087914 13 3924.381 0.256 0.252 7 10 6 5832 3770.802883 15 3798.100 0.281 0.276 8 7 6 1644 3534.771940 17 3563.936 0.326 0.321 9 15 6 3475 3314.407980 19 3345.112 0.368 0.362 10 15 6 2648 3162.265769 21 3194.769 0.397 0.391 11 9 6 1923 3028.741358 23 3062.950 0.422 0.416 12 7 6 3624 2880.064377 25 2915.525 0.451 0.444 13 23 6 3486 2702.824122 27 2738.858 0.485 0.478 14 23 6 116 2545.534016 29 2582.069 0.515 0.508 15 4 6 8773 2422.575970 31 2459.823 0.538 0.531 16 2 6 803 2262.126670 33 2299.223 0.569 0.562 17 32 6 5864 2122.594794 35 2159.580 0.595 0.588 18 4 6 7610 1836.777669 37 1870.669 0.650 0.643 19 0 6 2035 1641.898343 39 1673.883 0.687 0.681 20 38 6 7332 1428.554810 41 1457.855 0.728 0.722 21 40 6 9013 1053.447265 43 1076.141 0.799 0.795 22 37 6 1206 758.322249 45 775.442 0.855 0.852 23 7 6 593 636.565160 47 651.594 0.879 0.876 24 43 6 6001 532.755707 49 545.886 0.898 0.896 25 23 6 1488 451.992938 51 463.602 0.914 0.912 26 37 6 6122 385.157239 53 395.450 0.927 0.925 27 7 6 6946 335.936149 55 345.263 0.936 0.934 28 32 6 3381 287.101417 57 295.372 0.945 0.944 29 24 6 1440 235.668475 59 242.704 0.955 0.954 30 32 6 8375 209.747432 61 216.228 0.960 0.959 31 45 6 500 196.500438 63 202.778 0.963 0.961 32 2 6 3553 184.151662 65 190.228 0.965 0.964 33 39 6 9809 173.669012 67 179.582 0.967 0.966 34 52 6 1334 161.396838 69 167.061 0.969 0.968 35 9 6 1940 154.513111 71 160.099 0.971 0.969 36 7 6 9087 147.735445 73 153.232 0.972 0.971 37 53 6 3475 141.226286 75 146.630 0.973 0.972 38 40 6 1097 135.344070 77 140.666 0.974 0.973 39 40 6 7450 129.288718 79 134.510 0.975 0.974 40 64 6 1948 124.662704 81 129.829 0.976 0.975 --------------------------------------------------------------------- Stopping Condition 2: Improvement below threshold Pruning Pass -------------------------------------------------- iter bf terms mse gcv rsq grsq -------------------------------------------------- 0 - 81 124.94 130.113 0.976 0.975 1 43 80 124.94 130.047 0.976 0.975 2 31 79 124.94 129.981 0.976 0.975 3 35 78 124.94 129.915 0.976 0.975 4 1 77 124.94 129.848 0.976 0.975 5 58 76 124.94 129.782 0.976 0.975 6 17 75 124.94 129.716 0.976 0.975 7 40 74 124.94 129.650 0.976 0.975 8 63 73 124.94 129.584 0.976 0.975 9 69 72 124.94 129.518 0.976 0.975 10 42 71 124.94 129.452 0.976 0.975 11 46 70 124.94 129.386 0.976 0.975 12 26 69 124.94 129.320 0.976 0.975 13 23 68 124.94 129.255 0.976 0.975 14 71 67 124.94 129.189 0.976 0.975 15 55 66 124.94 129.123 0.976 0.975 16 15 65 124.94 129.058 0.976 0.975 17 60 64 124.94 128.992 0.976 0.975 18 54 63 124.94 128.927 0.976 0.975 19 9 62 124.94 128.861 0.976 0.975 20 6 61 124.94 128.796 0.976 0.975 21 10 60 124.93 128.723 0.976 0.975 22 13 59 124.93 128.662 0.976 0.975 23 8 58 124.94 128.604 0.976 0.975 24 16 57 124.99 128.586 0.976 0.975 25 4 56 125.10 128.642 0.976 0.975 26 32 55 125.61 129.095 0.976 0.975 27 33 54 127.52 130.994 0.976 0.975 28 74 53 128.99 132.437 0.975 0.975 29 80 52 131.21 134.645 0.975 0.974 30 22 51 132.74 136.150 0.975 0.974 31 21 50 133.34 136.691 0.975 0.974 32 75 49 133.99 137.295 0.974 0.974 33 36 48 138.74 142.089 0.974 0.973 34 79 47 144.86 148.276 0.972 0.972 35 72 46 151.28 154.769 0.971 0.970 36 70 45 160.51 164.129 0.969 0.969 37 66 44 170.02 173.767 0.968 0.967 38 65 43 178.52 182.365 0.966 0.965 39 25 42 188.91 192.887 0.964 0.963 40 68 41 199.78 203.874 0.962 0.961 41 7 40 211.71 215.947 0.960 0.959 42 59 39 223.54 227.893 0.957 0.957 43 45 38 240.03 244.579 0.954 0.953 44 76 37 252.64 257.300 0.952 0.951 45 67 36 277.68 282.664 0.947 0.946 46 5 35 307.60 312.958 0.941 0.940 47 62 34 339.68 345.429 0.935 0.934 48 61 33 349.66 355.399 0.933 0.932 49 56 32 406.73 413.191 0.922 0.921 50 53 31 476.86 484.187 0.909 0.908 51 73 30 531.86 539.769 0.899 0.897 52 19 29 565.68 573.801 0.892 0.891 53 3 28 724.42 734.443 0.862 0.860 54 20 27 974.98 987.983 0.814 0.812 55 57 26 1241.03 1256.947 0.763 0.760 56 18 25 1547.42 1566.472 0.705 0.701 57 14 24 1934.24 1957.075 0.631 0.627 58 44 23 2135.76 2159.880 0.593 0.588 59 38 22 2283.01 2307.631 0.565 0.560 60 49 21 2339.81 2363.860 0.554 0.549 61 27 20 2504.83 2529.307 0.522 0.518 62 12 19 2702.93 2727.972 0.485 0.480 63 24 18 2955.40 2981.280 0.436 0.432 64 50 17 3260.70 3287.600 0.378 0.373 65 28 16 3372.40 3398.523 0.357 0.352 66 41 15 3598.03 3624.073 0.314 0.309 67 51 14 3906.02 3932.321 0.255 0.250 68 37 13 3982.16 4006.966 0.241 0.236 69 2 12 4090.99 4114.409 0.220 0.216 70 78 11 4427.86 4450.979 0.156 0.151 71 47 10 4472.96 4494.060 0.147 0.143 72 77 9 4524.47 4543.529 0.137 0.134 73 29 8 4682.77 4700.141 0.107 0.104 74 34 7 4792.20 4807.568 0.086 0.083 75 11 6 4921.47 4934.784 0.062 0.059 76 30 5 4951.47 4962.377 0.056 0.054 77 64 4 4963.49 4971.937 0.054 0.052 78 52 3 5024.68 5030.718 0.042 0.041 79 39 2 5095.04 5098.605 0.028 0.028 80 48 1 5244.48 5245.526 0.000 0.000 -------------------------------------------------- Selected iteration: 24 Earth Model ------------------------------------------------------------------ Basis Function Pruned Coefficient ------------------------------------------------------------------ (Intercept) No -803005 h(x6-37.2487) Yes None h(37.2487-x6) No 188.026 h(x6-34.6929)*h(37.2487-x6) No -57.3172 h(34.6929-x6)*h(37.2487-x6) No -14.598 h(x6-31.4766)*h(34.6929-x6)*h(37.2487-x6) No 7.22891 h(31.4766-x6)*h(34.6929-x6)*h(37.2487-x6) Yes None h(x6+37.1733) No 2791.92 h(-37.1733-x6) Yes None h(x6+30.3035)*h(x6+37.1733) Yes None h(-30.3035-x6)*h(x6+37.1733) Yes None h(x6+24.4224)*h(x6+30.3035)*h(x6+37.1733) No 6.74221 h(-24.4224-x6)*h(x6+30.3035)*h(x6+37.1733) No -8.02723 h(x6+32.6468)*h(-30.3035-x6)*h(x6+37.1733) Yes None h(-32.6468-x6)*h(-30.3035-x6)*h(x6+37.1733) No 17.9338 h(x6+21.4336)*h(x6+37.1733) Yes None h(-21.4336-x6)*h(x6+37.1733) Yes None h(x6+18.9904)*h(x6+21.4336)*h(x6+37.1733) Yes None h(-18.9904-x6)*h(x6+21.4336)*h(x6+37.1733) No -5.59185 h(x6+15.1619)*h(x6+21.4336)*h(x6+37.1733) No -2.09208 h(-15.1619-x6)*h(x6+21.4336)*h(x6+37.1733) No 2.522 h(x6+11.6831)*h(x6+30.3035)*h(x6+37.1733) No -1.52138 h(-11.6831-x6)*h(x6+30.3035)*h(x6+37.1733) No 1.45609 h(x6+8.85579)*h(x6+37.1733) Yes None h(-8.85579-x6)*h(x6+37.1733) No -114.6 h(x6+6.44975)*h(x6+8.85579)*h(x6+37.1733) No -1.13963 h(-6.44975-x6)*h(x6+8.85579)*h(x6+37.1733) Yes None h(x6+2.53505)*h(x6+8.85579)*h(x6+37.1733) No -48.1755 h(-2.53505-x6)*h(x6+8.85579)*h(x6+37.1733) No 48.6257 h(x6-27.8323)*h(34.6929-x6)*h(37.2487-x6) No 4.21319 h(27.8323-x6)*h(34.6929-x6)*h(37.2487-x6) No -5.01954 h(x6-24.2978)*h(37.2487-x6) Yes None h(24.2978-x6)*h(37.2487-x6) No -7.6801 h(x6-17.967)*h(24.2978-x6)*h(37.2487-x6) No -2.12423 h(17.967-x6)*h(24.2978-x6)*h(37.2487-x6) No 4.57391 h(x6-14.9965)*h(34.6929-x6)*h(37.2487-x6) Yes None h(14.9965-x6)*h(34.6929-x6)*h(37.2487-x6) No 0.751507 h(x6-11.4815) No -59690.4 h(11.4815-x6) No 46789.7 h(x6-5.48349)*h(11.4815-x6) No 1021.09 h(5.48349-x6)*h(11.4815-x6) Yes None h(x6+1.02101)*h(5.48349-x6)*h(11.4815-x6) No 2.90161 h(-1.02101-x6)*h(5.48349-x6)*h(11.4815-x6) Yes None h(x6-24.4123)*h(x6-11.4815) Yes None h(24.4123-x6)*h(x6-11.4815) No -32.4221 h(x6+16.989)*h(x6+37.1733) No 23.3009 h(-16.989-x6)*h(x6+37.1733) Yes None h(x6-29.1534)*h(x6-24.4123)*h(x6-11.4815) No -9.5744 h(29.1534-x6)*h(x6-24.4123)*h(x6-11.4815) No 10.0986 h(x6+4.90451)*h(x6+8.85579)*h(x6+37.1733) No 48.9149 h(-4.90451-x6)*h(x6+8.85579)*h(x6+37.1733) No -49.8358 h(x6-17.8314)*h(x6-11.4815) No -1186.75 h(17.8314-x6)*h(x6-11.4815) No 1193.17 h(x6+26.7124)*h(x6+37.1733) No 18.2946 h(-26.7124-x6)*h(x6+37.1733) Yes None h(x6-3.83896)*h(24.2978-x6)*h(37.2487-x6) Yes None h(3.83896-x6)*h(24.2978-x6)*h(37.2487-x6) No 0.223623 h(x6+13.5093)*h(-8.85579-x6)*h(x6+37.1733) No 1.36938 h(-13.5093-x6)*h(-8.85579-x6)*h(x6+37.1733) Yes None h(x6-19.0415)*h(24.2978-x6)*h(37.2487-x6) No 1.72457 h(19.0415-x6)*h(24.2978-x6)*h(37.2487-x6) Yes None h(x6-0.224416)*h(x6+16.989)*h(x6+37.1733) No 1.68078 h(0.224416-x6)*h(x6+16.989)*h(x6+37.1733) No -1.6004 h(x6-30.2116)*h(37.2487-x6) Yes None h(30.2116-x6)*h(37.2487-x6) No 27.0289 h(x6-8.16867)*h(x6-5.48349)*h(11.4815-x6) No -3.1417 h(8.16867-x6)*h(x6-5.48349)*h(11.4815-x6) No -5.95814 h(x6-14.9373)*h(17.8314-x6)*h(x6-11.4815) No -16.2685 h(14.9373-x6)*h(17.8314-x6)*h(x6-11.4815) No -12.5622 h(x6+28.1102)*h(x6+30.3035)*h(x6+37.1733) Yes None h(-28.1102-x6)*h(x6+30.3035)*h(x6+37.1733) No 5.21693 h(x6+23.3288)*h(x6+37.1733) Yes None h(-23.3288-x6)*h(x6+37.1733) No -5.72154 h(x6+18.9904)*h(x6+26.7124)*h(x6+37.1733) No 2.81992 h(-18.9904-x6)*h(x6+26.7124)*h(x6+37.1733) No -1.14742 h(x6-3.90363)*h(5.48349-x6)*h(11.4815-x6) No 12.6573 h(3.90363-x6)*h(5.48349-x6)*h(11.4815-x6) No -21.5864 h(x6+32.6274)*h(5.48349-x6)*h(11.4815-x6) No -27.0684 h(-32.6274-x6)*h(5.48349-x6)*h(11.4815-x6) No 26.9698 h(x6-26.9536)*h(30.2116-x6)*h(37.2487-x6) No -3.53026 h(26.9536-x6)*h(30.2116-x6)*h(37.2487-x6) No 1.29164 ------------------------------------------------------------------ MSE: 124.9852, GCV: 128.5858, RSQ: 0.9762, GRSQ: 0.9755 | .. code-block:: python import numpy import matplotlib.pyplot as plt from pyearth import Earth # Create some fake data numpy.random.seed(2) m = 10000 n = 10 X = 80 * numpy.random.uniform(size=(m, n)) - 40 y = 100 * \ (numpy.sin((X[:, 6])) - 4.0) + \ 10 * numpy.random.normal(size=m) # Fit an Earth model model = Earth(max_degree=3, minspan_alpha=.5, verbose=True) model.fit(X, y) # Print the model print(model.trace()) print(model.summary()) # Plot the model y_hat = model.predict(X) plt.plot(X[:, 6], y, 'r.') plt.plot(X[:, 6], y_hat, 'b.') plt.show() **Total running time of the script:** (4 minutes 14.485 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_sine_wave.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_sine_wave.ipynb `