In R, linear programming using the lpsolve library requires an extensive amount of manually typed values for the needed matrices and vectors for the objective function coefficients, left-hand side coefficients, constraints, etc. Messing up even one value or one comma will make the script error or worse, the program will find a solution but it will be the wrong one due to incorrect setup. For large, real-world problems like network flow, simply typing the program itself is time prohibitive. What am I missing about R's capabilities in this space? Or, is there an alternate tool better fit for the job? Open source preferred due to budget.
Here is an example of the type of code needed in R for a relatively simple optimization problem:
# fleet size optimization, with an added computation of total miles driven
library(lpSolve)
# Objective function coefficients
ObjCoeff<-c(1300, 690, 421.5, 531, 690, 427.50, 277.50, 421.5, 427.50, 303, 531, 277.50, 303,
460, 281, 354, 460, 285, 185, 281, 285, 202, 354, 185, 202, 0)
# Constraint matrix
Amatrix<-matrix(c(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 1, 1, -1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 1, 1, -1, 0, 0, -1, 0, 0, -1, 0, 0,0,
0, -1,0, 0, 1, 1, 1, 0, -1, 0, 0,-1, 0,-1, 0, 0, 1, 1, 1, 0, -1, 0, 0, -1, 0,0,
0, 0,-1, 0, 0,-1, 0, 1, 1, 1, 0, 0,-1, 0,-1, 0, 0, -1, 0, 1, 1, 1, 0, 0,-1,0,
0, 0, 0, -1, 0, 0,-1, 0, 0,-1, 1, 1, 1, 0, 0,-1, 0, 0,-1, 0, 0,-1, 1, 1, 1,0,
-1300, 460, 281,354,460,285,185,281,285,202,354,185,202,460,281,354, 460, 285,185, 281, 285,202, 354, 185, 202, 0,
0, 460, 281,354,460,285,185,281,285,202,354,185,202,460,281,354, 460, 285,185, 281, 285,202, 354, 185, 202,-1), nrow=18, byrow=TRUE)
# Right hand side constraint vector
Bvector<-c(10, 10, 10, 20, 10, 10, 10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 0,0 )
# Constraint inequality direction vector
constrainttype<- c(">=", ">=",">=", ">=",">=", ">=",">=", ">=",">=", ">=",">=", ">=","=", "=" , "=" , "=" ,"<=", "=" )
# Solve the specified integer program by setting all.int=TRUE
optimum<-lp(direction="min", objective.in=ObjCoeff, const.mat = Amatrix, const.dir = constrainttype, const.rhs = Bvector, all.int =TRUE)
# Print constraint matrix to verify it was specified correctly
print(optimum$constraints)
# Check to see if the solver reached optimality (0 means yes)
print(optimum$status)
# Print values of each variable in the optimal solution
# note that they are all integer valued
print(optimum$solution)
# Print the optimal objective function value
print(optimum$objval)
R has its strengths for sure, but formulation of non-trivial LP's is not one of them.
There are several other open source frameworks that are much more expressive. If you are a python user, you can pick from many including:
pyomo, gekko, cvxpy, pulp, or-tools and others I'm sure.
I'm a fan of pyomo for model building, but it requires installation of a separate solver, which isn't too difficult. There are several open-source free solvers that are excellent and in common use with different capabilities such as cbc, glpk, ipopt and others, and of course many excellent licensed solvers.
If you want to start with an "all in one" the pulp framework includes a solver with the build--I forget which one.
There are many examples on this site for all the pkgs above if you search by tag.
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R: add alpha-value to png-image
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I have a two-dimensional density plot which I need to overlay onto a photograph. I can read-in the picture with the package rtiff:
install.packages("rtiff")
library(rtiff)
x <- readTiff('F01_screenshot.tiff')
plot(x)
The data for the density plot is a very large dataframe called eet2 (see reproducible data below); the code for the density plot is this:
library(ggplot2)
ggplot(eet2, aes(x=X, y= Y)) +
geom_point() + stat_density2d()
I can easily produce both plots separately but don't know how to overlay the density plot onto the photograph in such a way that the density plot is scaled down proportionately to fit the picture. Any help is much appreciated!
Reproducible data:
eet2 <- dput(eet1[1:1000, 2:3])
structure(list(X = c(0, 177.378, 27.289, 0, 852.719, 0, 852.813,
71.068, 0, 144.875, 0, 140.385, 21.598, 0, 170.325, 0, 136.746,
21.038, 0, 146.279, 0, 141.86, 11.822, 0, 146.078, 0, 137.681,
21.182, 0, 148.867, 0, 132.886, 20.444, 0, 146.129, 0, 80.251,
6.688, 0, 141.08, 0, 149.789, 23.044, 0, 74.097, 0, 141.182,
21.72, 0, 83.075, 0, 81.192, 6.766, 0, 849.784, 0, 153.96, 23.686,
0, 78.374, 0, 142.782, 21.967, 0, 72.929, 0, 142.922, 11.91,
0, 83.639, 0, 143.912, 22.14, 0, 134.809, 0, 142.826, 21.973,
0, 132.7, 0, 85.876, 7.156, 0, 138.935, 0, 80.951, 12.454, 0,
144.385, 0, 141.716, 21.802, 0, 76.768, 0, 74.406, 6.2, 0, 134.444,
0, 155.341, 23.899, 0, 189.336, 0, 224.517, 34.541, 0, 207.46,
0, 216.122, 18.01, 0, 204.552, 0, 208.524, 32.081, 0, 207.513,
0, 203.162, 31.256, 0, 197.578, 0, 204.362, 17.03, 0, 195.223,
0, 956.396, 147.138, 0, 201.969, 0, 224.989, 34.614, 0, 214.064,
0, 140.374, 11.698, 0, 140.235, 0, 958.501, 147.462, 0, 141.898,
0, 143.337, 22.052, 0, 955.901, 0, 954.965, 79.58, 0, 131.323,
0, 223.214, 34.341, 0, 952.203, 0, 143.102, 22.016, 0, 935.525,
0, 918.238, 76.52, 0, 123.337, 0, 127.93, 19.682, 0, 915.755,
0, 128.336, 19.744, 0, 913.158, 0, 120.076, 10.006, 0, 911.196,
0, 124.387, 19.136, 0, 911.631, 0, 911.389, 140.214, 0, 910.433,
0, 119.375, 9.948, 0, 115.898, 0, 910.073, 140.011, 0, 915.461,
0, 965.025, 148.465, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1125.565,
0, 1074.389, 165.291, 0, 1061.611, 0, 1051.23, 161.728, 0, 1044.3,
0, 269.733, 22.478, 0, 245.869, 0, 206.934, 234.525, 245.609,
250.874, 251.576, 260.164, 262.974, 263.161, 269.25, 262.693,
261.818, 265.634, 266.479, 266.592, 266.39, 262.751, 262.508,
265.093, 262.666, 262.343, 1059.856, 1075.848, 1077.98, 1068.255,
1065.442, 1065.255, 1071.821, 1072.292, 1072.355, 1073.788, 1072.572,
1072.41, 1074.295, 1074.487, 1074.499, 1078.434, 1080.074, 1080.293,
1081.104, 1080.014, 1079.869, 1080.261, 1080.181, 1080.175, 1078.568,
1079.422, 1079.536, 1078.84, 1077.459, 1077.275, 1077.805, 1076.787,
1076.719, 1077.199, 1076.045, 1075.891, 1077.362, 1076.663, 1076.569,
1077.942, 1078.842, 1078.902, 1078.713, 1080.023, 1080.198, 1080.764,
1081.553, 1081.659, 1081.946, 1082.445, 1082.479, 1083.987, 1084.113,
1084.13, 1084.741, 1085.809, 1085.952, 1085.031, 1084.708, 1084.686,
1085.901, 1085.266, 1085.181, 1085.513, 1085.159, 1085.112, 1088.024,
1088.29, 1088.308, 1088.889, 1088.327, 1088.252, 1069.543, 1065.069,
1064.472, 1067.409, 1068.075, 1068.119, 1068.377, 1070.019, 1070.238,
1072.384, 1071.454, 1071.33, 1072.31, 1069.704, 1069.53, 1068.856,
1073.986, 1074.67, 1075.824, 1077.42, 1077.633, 1080.095, 1082.62,
1082.788, 1087.112, 1090.026, 1090.414, 1094.654, 1098.678, 1099.215,
1103.801, 1097.674, 1097.266, 1110.129, 1105.4, 1104.769, 1115.638,
1115.922, 1115.96, 1115.612, 1115.278, 1115.256, 1114.682, 1112.96,
1112.73, 1063.573, 948.249, 932.873, 844.512, 834.23, 833.545,
865.203, 867.402, 867.695, 838.499, 864.3, 867.74, 837.215, 864.187,
865.985, 0, 760.653, 862.073, 861.199, 860.757, 860.699, 0, 861.681,
71.807, 0, 851.287, 855.415, 855.965, 859.554, 864.523, 865.185,
868.109, 873.22, 873.561, 845.881, 882.877, 887.81, 893.391,
899.782, 900.634, 908.492, 56.781, 0, 0, 0, 0, 0, 0, 0, 319.09,
0, 0, 0, 0, 0, 0, 0, 0, 0, 696.905, 0, 704.008, 58.667, 0, 0,
0, 0, 677.276, 673.676, 673.195, 673.45, 671.209, 671.06, 672.474,
674.07, 674.283, 674.896, 656.33, 653.855, 678.654, 681.884,
682.099, 684.933, 715.507, 719.584, 735.659, 1290.244, 1364.188,
1362.632, 1366.322, 1366.568, 1371.973, 1364.1, 1363.051, 1361.383,
812.325, 739.117, 734.716, 1322.199, 1361.365, 730.422, 731.132,
731.227, 729.084, 724.164, 723.507, 726.199, 725.939, 725.922,
725.437, 1278.917, 1352.714, 726.791, 1281.431, 1355.383, 1366.558,
764.435, 724.294, 725.46, 724.544, 724.422, 724.178, 1288.932,
1364.232, 723.902, 680.495, 677.601, 724.172, 722.856, 722.681,
735.236, 743.706, 744.835, 554.779, 735.387, 747.427, 724.914,
720.25, 719.628, 721.122, 742.971, 745.884, 742.171, 737.947,
737.665, 729.207, 808.032, 818.542, 905.216, 106.496, 0, 1169.534,
0, 1195.852, 99.654, 0, 1236.396, 0, 0, 0, 0, 1190.473, 183.15,
0, 1143.686, 1132.754, 1132.025, 1123.856, 1103.6, 1100.9, 1083.716,
1079.191, 1078.588, 1083.785, 1070.395, 1069.503, 1066.885, 1065.121,
1064.885, 1064.401, 1065.285, 1065.403, 1075.009, 1076.036, 1076.105,
1086.308, 1075.821, 1074.423, 1073.282, 126.268, 0, 1092.281,
0, 1019.684, 1087.663, 286.389, 33.693, 0, 1117.064, 0, 1114.254,
171.424, 0, 1111.518, 0, 1110.347, 92.529, 0, 1077.293, 0, 1107.754,
170.424, 0, 1107.136, 0, 1076.571, 165.626, 0, 1067.475, 0, 1110.71,
92.559, 0, 274.852, 0, 280.654, 43.177, 0, 280.278, 271.773,
270.639, 0, 1060.434, 88.369, 0, 1054.964, 1047.876, 1046.931,
1052.977, 1064.93, 1066.524, 1061.181, 1069.339, 1069.883, 275.888,
970.662, 1063.299, 268.308, 974.232, 1068.355, 1044.757, 1065.286,
1066.655, 1076.68, 1085.54, 1086.721, 1088.216, 1083.409, 1082.768,
1087.272, 1087.283, 1087.283, 1086.689, 1087.19, 1087.257, 1089.988,
1087.837, 1087.55, 272.953, 1040.007, 1091.144, 1076.712, 1089.387,
1091.077, 1103.104, -360.56, -555.715, 1072.081, 1073.131, 1073.201,
1073.04, 1089.257, 1091.419, 1072.888, 1073.111, 1073.141, 1104.182,
1075.399, 1073.48, 1103.711, 1076.133, 1072.456, 1104.247, 1105.181,
1105.305, 1072.744, 1104.02, 1106.105, 1074.673, 1102.759, 1106.503,
1076.082, 1104.401, 1108.177, 1078.025, 1109.772, 1111.888, 288.949,
292.278, 292.722, 1112.981, 1123.139, 1124.493, 1127.996, 1134.943,
1135.406, 1136.071, 1141.749, 1142.506, 1148.754, 1150.764, 1151.032,
1156.093, 1154.597, 1154.497, 1150.481, 1124.218, 1120.716, 1108.646,
1095.181, 1093.385, 1113.175, 1089.783, 1088.224, 1719.795, -286.164,
-553.625, 1112.49, 1099.064, 1097.274, 1106.601, 1105.705, 1105.645,
1100.75, 1110.143, 1111.395, 1114.044, 1108.662, 1107.944, 1115.615,
1114.492, 1114.417, 296.606, 1011.559, 1106.886, 213.15, 735.037,
804.622, 643.816, 590.868, 587.338, 588.443, 591.022, 591.366,
595.437, 598.575, 598.994, -70.23, 562.977, 605.191, 608.988,
14.755, -64.476, -86.326, 490.189, 567.057, 573.015, 572.841,
572.83, 576.607, 578.243, 578.461, 579.714, 1343.595, 1445.446,
585.277, 588.153, 588.345, 588.809, 588.843, 588.848, 592.898,
591.447, 591.254, 592.538, 589.623, 589.429, 590.233, 587.901,
587.59, 589.276, 603.526, 605.426, 691.889, 810.649, 818.566,
889.948, 866.466, 863.335, 164.367, 164.895, 164.966, 158.056,
851.73, 897.975, 164.51, 806.786, 892.423, 894.069, 892.465,
892.251, 153.408, 842.909, 888.876, 151.935, 802.889, 889.683,
154.817, 146.446, 145.329, 888.428, 193.529, 147.202, 885.088,
224.817, 136.78, 147.255, 802.581, 889.958, 888.64, 889.975,
890.064, 1575.971, 968.922, 887.982, 889.232, 860.991, 857.226,
872.007, 893.987, 895.452, 859.373, 892.292, 896.681, 859.84,
859.942, 859.955, 898.274, 860.41, 857.885, 879.17, 862.76, 860.572,
856.434, 854.683, 854.45, 851.949, 174.027, 128.832, 848.35,
847.791, 847.716, 847.847, 849.008, 849.163, 133.198, 806.744,
851.647, 146.291, 773.622, 857.267, 860.622, 834.937, 831.512,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 623.517, 0, 631.712, 97.187,
0, 631.526, 0, 641.912, 98.756, 0, 648.161, 0, 654.673, 54.556,
0, 659.733, 0, 603.775, 684.278, 696.548, 689.181, 688.198, 687.25,
682.216, 681.881, 711.089, 713.482, 713.802, 713.969, 715.124,
715.278, 711.369, 709.299, 709.162, 679.428, 675.016, 674.428,
675.948, 673.724, 673.427, 675.195, 678.8, 679.041, 681.486,
686.341, 686.988, 696.445, 694.867, 694.657, 703.31, 705.003,
705.116, 0, 711.882, 109.52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1269.549, 1438.822, 0, 720.784, 60.065, 0, 721.678, 0, 713.535,
109.775, 0, 709.244, 0, 681.534, 104.851, 0, 693.092, 0, 681.394,
56.783, 0, 679.538, 0, 680.866, 104.749, 0, 675.661, 0, 668.345,
102.822, 0, 0, 0, 0, 0, -69.364, -10.671, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 677.983, 0), Y = c(0, -560.914,
-86.294, 0, 12.57, 0, 10.336, 0.861, 0, -569.851, 0, -582.641,
-89.637, 0, -513.461, 0, -582.556, -89.624, 0, -567.846, 0, -574.869,
-47.906, 0, -567.25, 0, -571.902, -87.985, 0, -554.095, 0, -574.651,
-88.408, 0, -557.127, 0, -365.662, -30.472, 0, -565.123, 0, -564.378,
-86.827, 0, -380.282, 0, -587.338, -90.36, 0, -373.494, 0, -394.186,
-32.849, 0, -15.305, 0, -586.833, -90.282, 0, -391.571, 0, -603.611,
-92.863, 0, -392.659, 0, -595.738, -49.645, 0, -369.805, 0, -585.56,
-90.086, 0, -607.653, 0, -598.77, -92.118, 0, -603.821, 0, -362.726,
-30.227, 0, -590.569, 0, -365.806, -56.278, 0, -584.274, 0, -594.203,
-91.416, 0, -378.246, 0, -385.426, -32.119, 0, -585.678, 0, -569.332,
-87.589, 0, -572.327, 0, -566.971, -87.226, 0, -586.06, 0, -584.482,
-48.707, 0, -593.944, 0, -583.298, -89.738, 0, -580.776, 0, -590.48,
-90.843, 0, -600.616, 0, -598.535, -49.878, 0, -602.826, 0, -29.44,
-4.529, 0, -618.062, 0, -592.995, -91.23, 0, -609.041, 0, -411.878,
-34.323, 0, -413.262, 0, -52.608, -8.094, 0, -411.569, 0, -415.928,
-63.989, 0, -48.63, 0, -47.12, -3.927, 0, -415.299, 0, -599.916,
-92.295, 0, -44.314, 0, -411.139, -63.252, 0, -46.124, 0, -48.509,
-4.042, 0, -407.485, 0, -413.499, -63.615, 0, -55.391, 0, -415.922,
-63.988, 0, -57.45, 0, -422.827, -35.236, 0, -54.607, 0, -414.86,
-63.825, 0, -51.45, 0, -48.986, -7.536, 0, -45.942, 0, -413.839,
-34.487, 0, -411.075, 0, -38.956, -5.993, 0, -14.525, 0, 35.454,
5.455, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 279.172, 0, 315.145,
48.484, 0, 313.523, 0, 314.854, 48.439, 0, 314.166, 0, -89.369,
-7.447, 0, -125.57, 0, -138.883, -157.401, -162.487, -158.14,
-157.561, -171.662, -160.906, -160.189, -166.883, -171.154, -171.724,
-187.379, -175.901, -174.37, -188.734, -185.215, -184.98, -189.818,
-189.088, -188.991, 283.22, 302.83, 305.444, 270.066, 289.663,
290.969, 275.119, 276.953, 277.198, 260.347, 261.677, 261.855,
246.632, 250.916, 251.202, 238.808, 246.008, 246.968, 240.285,
253.356, 255.099, 251.122, 262.086, 262.817, 258.677, 268.433,
269.734, 264.812, 273.771, 274.966, 268.696, 276.112, 276.606,
268.26, 275.135, 276.051, 265.545, 272.265, 273.161, 264.077,
268.116, 268.385, 261.015, 266.217, 266.911, 259.724, 265.892,
266.714, 259.602, 265.93, 266.352, 258.209, 265.537, 266.514,
259.411, 265.687, 266.523, 259.761, 266.978, 267.459, 260.97,
268.01, 268.949, 262.4, 271.867, 273.13, 264.803, 273.569, 274.153,
266.979, 275.25, 276.353, 268.073, 274.926, 275.84, 269.625,
279.424, 280.077, 271.785, 281.741, 283.068, 276.083, 284.162,
285.239, 279.865, 291.741, 292.533, 291.52, 302.124, 303.538,
300.685, 313.141, 314.802, 313.594, 327.048, 327.945, 325.593,
339.796, 341.69, 341.58, 355.702, 357.585, 356.602, 381.738,
383.413, 370.869, 394.752, 397.936, 391.659, 409.376, 411.739,
415.584, 433.281, 434.461, 437.478, 454.368, 456.62, 445.173,
427.865, 425.558, 383.004, 370.373, 369.531, 382.343, 399.016,
401.239, 413.831, 422.157, 423.267, 432.015, 448.845, 449.967,
0, 425.956, 482.75, 487.1, 501.178, 503.055, 0, 508.065, 42.339,
0, 492.242, 494.125, 494.376, 484.667, 484.368, 484.328, 467.742,
464.267, 464.035, 468.697, 433.854, 429.208, 400.85, 393.727,
392.777, 376.735, 23.546, 0, 0, 0, 0, 0, 0, 0, 885.955, 0, 0,
0, 0, 0, 0, 0, 0, 0, 500.323, 0, 481.941, 40.162, 0, 0, 0, 0,
530.014, 516.432, 514.621, 494.618, 478.341, 477.256, 456.114,
458.922, 459.297, 456.514, 425.5, 421.365, 462.707, 472.408,
473.055, 467.768, 454.51, 452.742, 441.741, 201.307, 169.249,
167.631, 163.795, 163.539, 160.509, 161.775, 161.943, 161.298,
397.997, 429.557, 419.546, 177.979, 161.875, 418.022, 423.34,
424.049, 413.55, 419.645, 420.457, 407.472, 415.496, 416.031,
407.006, 148.509, 114.042, 409.442, 164.128, 131.419, 109.849,
407.293, 427.122, 418.844, 426.465, 427.481, 417.779, 161.317,
127.123, 409.12, 367.918, 365.171, 395.673, 396.298, 396.381,
388.306, 392.859, 393.466, 473.545, 400.213, 395.325, 366.771,
370.934, 371.489, 339.469, 387.501, 393.905, 386.022, 390.883,
391.207, 378.721, 394.352, 396.436, 384.581, 45.245, 0, 380.042,
0, 375.485, 31.29, 0, 335.187, 0, 0, 0, 0, 323.048, 49.7, 0,
359.169, 361.068, 361.195, 348.111, 362.176, 364.051, 383.932,
392.518, 393.663, 349.699, 392.668, 395.532, 391.36, 396.741,
397.458, 387.906, 391.383, 391.846, 371.849, 378.048, 378.461,
318.908, 357.694, 362.865, 342.973, 40.35, 0, 288.149, 0, 259.291,
276.577, -102.466, -12.055, 0, 241.977, 0, 234.288, 36.044, 0,
247.849, 0, 244.967, 20.414, 0, 290.17, 0, 258.996, 39.846, 0,
269.854, 0, 259.002, 39.847, 0, 297.18, 0, 266.569, 22.214, 0,
-87.029, 0, -89.617, -13.787, 0, -95.348, -79.043, -76.869, 0,
246.968, 20.581, 0, 272.257, 289.812, 292.152, 271.933, 287.652,
289.748, 276.443, 284.481, 285.017, -116.323, 230.711, 276.983,
-141.084, 229.411, 278.81, 314.961, 280.304, 277.994, 277.686,
282.62, 283.278, 287.306, 282.107, 281.414, 290.288, 291.936,
292.045, 288.296, 302.772, 304.702, 292.15, 302.242, 303.588,
-136.669, 270.271, 297.4, 274.154, 301.517, 305.165, 290.369,
-426.184, -521.724, 321.366, 329.046, 329.558, 321.7, 306.849,
304.869, 321.009, 327.981, 328.91, 290.339, 328.378, 330.914,
289.022, 325.172, 329.992, 288.447, 295.19, 296.089, 322.57,
298.091, 296.459, 321.394, 300.861, 298.123, 320.881, 300.679,
297.985, 319.966, 296.464, 294.897, -164.893, -160.079, -159.437,
278.924, 281.357, 281.682, 269.259, 274.752, 275.118, 267.165,
265.143, 264.873, 258.509, 264.614, 265.429, 256.744, 266.259,
266.893, 263.361, 301.473, 306.555, 262.416, 313.245, 320.022,
281.712, 320.535, 323.123, -194.846, -521.034, -564.526, 274.367,
278.267, 278.787, 264.133, 268.555, 268.85, 256.818, 266.194,
267.444, 260.084, 265.714, 266.464, 262.669, 272.063, 272.689,
-175.62, 225.568, 279.06, -159.431, 216.327, 266.428, 245.597,
254.043, 254.606, 244.851, 255.798, 257.258, 248.152, 256.508,
257.622, -319.948, 219.787, 255.769, 243.947, -235.689, -299.64,
-334.288, 164.071, 230.518, 224.188, 233.409, 234.024, 228.544,
236.363, 237.405, 235.462, -116.121, -162.999, 240.889, 251.796,
252.524, 246.8, 258.72, 260.309, 257.726, 267.828, 269.175, 265.087,
277.995, 278.856, 273.876, 287.09, 288.852, 280.858, 292.608,
294.174, 246.387, 213.675, 211.494, 201.469, 209.375, 210.429,
-217.38, -218.456, -218.6, -232.09, 196.612, 225.193, -248.699,
166.3, 221.633, 213.54, 219.095, 219.836, -261.438, 192.469,
222.729, -265.48, 164.234, 221.529, -254.99, -254.199, -254.094,
209.197, -218.172, -246.663, 207.52, -196.823, -250.735, -261.477,
163.4, 220.05, 210.838, 222.305, 223.069, -196.463, 176.753,
226.515, 217.024, 249.012, 253.277, 203.798, 226.753, 228.283,
241.225, 228.683, 227.011, 235.665, 243.606, 244.664, 212.621,
240.812, 242.692, 207.285, 207.473, 207.498, 194.745, 202.346,
203.359, 191.408, -221.759, -249.304, 186.022, 192.304, 193.141,
182.101, 191.751, 193.037, -260.225, 162.901, 191.109, -252.884,
141.317, 193.877, 186.754, 220.72, 225.249, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 304.742, 0, 316.744, 48.73, 0, 334.833, 0,
352.419, 54.218, 0, 368.749, 0, 378.178, 31.515, 0, 378.548,
0, 339.912, 385.233, 406.951, 373.432, 368.963, 411.64, 362.786,
359.529, 358.897, 353.738, 353.051, 336.054, 340.344, 340.915,
335.944, 355.461, 356.762, 345.061, 372.321, 375.955, 376.513,
404.13, 407.812, 416.338, 426.28, 426.943, 432.67, 429.483, 429.058,
426.368, 425.226, 425.074, 416.298, 411.677, 411.369, 0, 345.327,
53.127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 183.69, 208.182, 0,
261.561, 21.797, 0, 298.1, 0, 281.941, 43.375, 0, 314.226, 0,
304.413, 46.833, 0, 374.171, 0, 368.525, 30.71, 0, 359.118, 0,
367.905, 56.601, 0, 287.494, 0, 285.213, 43.879, 0, 0, 0, 0,
0, 735.244, 113.115, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 304.619, 0)), row.names = 31537:32536, class = "data.frame")
This should give you a way to get the image you want. However, I don't have your original TIFF, and therefore the alignment won't be correct here since I had to use a cut-and-pasted version of the png in your question.
Anyway, the method I would use is:
Convert the image to a raster
Convert the raster to a grid::rasterGrob
Plot the rasterGrob as your first layer in ggplot using annotation_custom
Plot your other layers as normal.
Here's an example:
library(ggplot2)
library(rtiff)
library(grid)
x <- readTiff('F01_screenshot.tiff')
pic <- as.raster(array(c(x#red, x#green, x#blue), c(x#size, 3)))
picgrob <- rasterGrob(pic)
ggplot(eet2, aes(x=X, y= Y)) +
annotation_custom(picgrob) +
geom_point() +
stat_density2d() +
coord_equal()
You may need to scale your Y axis data to make it match the aspect ratio of the picture.
As an example, if we assume max(eet2$Y) is the top edge of the image, and min(eet2$Y) the bottom edge, and also assume that min(eet2$X) is the left edge and max(eet2$X) the right edge (as you have suggested is the case in your comments), we can marry the picture to the data like this:
pic_ratio <- dim(pic)[2]/dim(pic)[1]
data_ratio <- diff(range(eet2$X)) / diff(range(eet2$Y))
eet2$Y <- eet2$Y * data_ratio / pic_ratio
ggplot(eet2, aes(x=X, y= Y)) +
annotation_custom(picgrob) +
geom_point() +
stat_density2d() +
coord_equal(xlim = range(eet2$X), ylim = range(eet2$Y))
If this alignment is not correct, then we need extra calibration information not present in the data (i.e. what value of eet2$Y should represent the top and bottom of the image, and what value of eet2$X represents the left and right edges.
I'm new to bipartite network analysis and i've some trouble with basic measures.
I'm trying to work on bipartite networks without projecting in 1-mode graphs.
My problems come from the fact that the igraph package allows to create bipartite graphs but that the measures do not seem to adapt to the specificity of these graphs.
So, my general question is how do you do when you work directly on bipartite networks ?
Here a concrete exemple with density
## Working with an incidence matrix (sample) with 47 columns and 10 rows (unweighted / undirected)
# Want to compute basic global index like density with igraph
library(igraph)
g <- graph.incidence(m, directed = F )
graph.density(g) # result = 0.04636591
# Now trying to compute basic density for a bipartite graph without igraph (number of edges divided by the product of the two types of vertices)
library(Matrix)
d <- nnzero(m)/ (ncol(m)*nrow(m)) # result 0.1574468
# It seems that bipartite package does the job
library(bipartite)
networklevel(m, index=c("connectance")) # result 0.1574468
But the bipartite package is very specific to ecology fields and lot of measures are designed to food web and interaction between species (and some, like clustering coefficient, don't seem to take into account the bipartite nature of the graph : e.g compute 4-cycles).
So, are there simpler ways to work on bipartite networks with igraph ? To measure some global indexes (density, clustering coefficient with 4-cycles, I know that tnet does this but my actual networks are too large), and to normalize local indexes like degree, closeness, betweenness centralities taking into account the bipartite specificity (like in Borgatti S.P., Everett M.G., 1997, « Network analysis of 2-mode data », Social Networks) ?
Any advice will be appreciated !
Below the code to reproduce the sample of my matrix "m"
m <- structure(c(1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0,
1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0,
0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0,
0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0), .Dim = c(10L, 47L), .Dimnames = list(
c("02723", "13963", "F3238", "02194", "15051", "04477", "02164",
"06283", "04080", "08304"), c("1185241", "170063", "10350868",
"217831", "2210247", "2262963", "1816670", "1848354", "2232593",
"146214", "1880252", "2261639", "2262581", "2158177", "1850147",
"2262912", "146412", "2262957", "1566083", "1841811", "146384",
"216281", "2220957", "1846986", "1951567", "1581130", "105343",
"1580240", "170654", "1796236", "1835553", "1835848", "146400",
"1174872", "1283240", "2253354", "1283617", "146617", "160263",
"2263115", "184745", "1809858", "1496747", "10346824", "148730",
"2262582", "146268")))
Density: you already got it
Degree
degv1 <- degree(g, V(g)[type == FALSE])
degv2 <- degree(g, V(g)[type == TRUE])
Normalized degree: divise by the vcount of the other node category
degnormv1 <- degv1/length(V(g)[type == TRUE])
degnormv2 <- degv2/length(V(g)[type == FALSE])
No answer regarding closeness, betweenness nor clustering coefficient
For the normalized degree, here a solution without igraph
normalizedegreeV1 <- data.frame(ND = colSums(m)/nrow(m))
normalizedegreeV2 <- data.frame(ND = rowSums(m)/ncol(m))
but that leaves the other questions about centrality measures open...