├── .gitignore ├── Makefile ├── README.md ├── bandwidth.json ├── dmap.json ├── examples ├── cluster │ ├── cluster.dat │ ├── cluster.pdf │ ├── cluster.png │ ├── dmap-1.dat │ ├── dmap-1.pdf │ ├── dmap-1.png │ ├── dmap-10.dat │ ├── dmap-10.pdf │ ├── dmap-10.png │ ├── dmap-100.dat │ ├── dmap-100.pdf │ ├── dmap-100.png │ ├── dmap-evalues-1.dat │ ├── dmap-evalues-10.dat │ ├── dmap-evalues-100.dat │ ├── dmap-evects-1.dat │ ├── dmap-evects-10.dat │ ├── dmap-evects-100.dat │ ├── pca-evalues.dat │ ├── pca-evects.dat │ ├── pca.dat │ ├── pca.pdf │ └── pca.png ├── clusters │ ├── clusters.pdf │ ├── clusters.png │ ├── dmap-1.dat │ ├── dmap-1.pdf │ ├── dmap-1.png │ ├── dmap-10.dat │ ├── dmap-10.pdf │ ├── dmap-10.png │ ├── dmap-100.dat │ ├── dmap-100.pdf │ ├── dmap-100.png │ ├── dmap-evalues-1.dat │ ├── dmap-evalues-10.dat │ ├── dmap-evalues-100.dat │ ├── dmap-evects-1.dat │ ├── dmap-evects-10.dat │ ├── dmap-evects-100.dat │ ├── pca-evalues.dat │ ├── pca-evects.dat │ ├── pca.dat │ ├── pca.pdf │ └── pca.png ├── octane │ ├── dmap.png │ ├── pca.png │ └── prd.tpr ├── punctured-sphere │ ├── dmap-1.dat │ ├── dmap-1.pdf │ ├── dmap-1.png │ ├── dmap-10.dat │ ├── dmap-10.pdf │ ├── dmap-10.png │ ├── dmap-100.dat │ ├── dmap-100.pdf │ ├── dmap-100.png │ ├── dmap-evalues-1.dat │ ├── dmap-evalues-10.dat │ ├── dmap-evalues-100.dat │ ├── dmap-evects-1.dat │ ├── dmap-evects-10.dat │ ├── dmap-evects-100.dat │ ├── pca-evalues.dat │ ├── pca-evects.dat │ ├── pca.dat │ ├── pca.pdf │ ├── pca.png │ ├── puncsphere.dat │ ├── puncsphere.pdf │ └── puncsphere.png └── swiss-roll │ ├── dmap-1.dat │ ├── dmap-1.pdf │ ├── dmap-1.png │ ├── dmap-10.dat │ ├── dmap-10.pdf │ ├── dmap-10.png │ ├── dmap-100.dat │ ├── dmap-100.pdf │ ├── dmap-100.png │ ├── dmap-evalues-1.dat │ ├── dmap-evalues-10.dat │ ├── dmap-evalues-100.dat │ ├── dmap-evects-1.dat │ ├── dmap-evects-10.dat │ ├── dmap-evects-100.dat │ ├── pca-evalues.dat │ ├── pca-evects.dat │ ├── pca.dat │ ├── pca.pdf │ ├── pca.png │ ├── swissroll.dat │ ├── swissroll.pdf │ └── swissroll.png ├── extra ├── gen-cluster.f90 ├── gen-clusters.f90 ├── gen-punc-sphere.f90 ├── gen-swiss-roll.f90 └── plot-dmap.plt ├── pca.json └── src ├── diffusion_map.f90 ├── main.f90 └── princ_comp.f90 /.gitignore: -------------------------------------------------------------------------------- 1 | *.dat 2 | *.mod 3 | *.out 4 | *.o 5 | *.so 6 | *.swp 7 | run 8 | -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- 1 | .PHONY: clean 2 | 3 | PREREQ = lapack 4 | SOURCES := $(wildcard src/*.f90) 5 | SOURCES := $(filter-out src/main.f90, $(SOURCES)) 6 | OBJECTS := $(SOURCES:src/%.f90=%.o) 7 | LDFLAGS += `pkg-config --libs ${PREREQ}` 8 | CFLAGS += -shared -fPIC -Wall `pkg-config --cflags ${PREREQ}` 9 | 10 | run: machlearn.so 11 | @gfortran -o $@ lib/$< src/main.f90 -ljsonfortran -I/usr/include -Jinclude 12 | 13 | machlearn.so: ${OBJECTS} 14 | @mkdir -p include 15 | @mkdir -p lib 16 | @gfortran -o lib/$@ src/*.o ${LDFLAGS} ${CFLAGS} 17 | 18 | %.o: src/%.f90 19 | @mkdir -p include 20 | @gfortran -c -o src/$@ $< -Jinclude ${LDFLAGS} ${CFLAGS} 21 | 22 | clean: 23 | @rm -f *.mod 24 | @rm -f src/*.o 25 | @rm -rf include 26 | @rm -rf lib 27 | @rm -f run 28 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | Personal code for principal component analysis and diffusion map 2 | [examples](#examples). Specifically made to test the idea on some well-known 3 | types of data, but it wouldn't take much to modify the source for use with whatever 4 | data set or distance metric you desire. 5 | 6 | ## Compilation 7 | 8 | $ make 9 | 10 | A library is compiled with the classes needed for the main program and the main 11 | program links to that. The main program requires 12 | [json-fortran](https://github.com/jacobwilliams/json-fortran). LAPACK is 13 | required for the library to calculate the eigenvectors and eigenvalues of 14 | various matrices. 15 | 16 | ## Running 17 | 18 | Modify `dmap.json`. Then do: 19 | 20 | $ ./run dmap.json 21 | 22 | You can also run principal component analysis using the following file: 23 | 24 | $ ./run pca.json 25 | 26 | `bandwidth.json` is for running the program iteratively over different bandwidth 27 | values. See Figure S1 in [this 28 | document](https://www.pnas.org/cgi/doi/10.1073/pnas.1003293107) for what I was 29 | going for with this. This would more helpful for analyzing simulation data, but 30 | the main program is not set up for that. 31 | 32 | ## Extras 33 | 34 | The `extras` folder contains the source code of two programs to aid in 35 | generating example data sets. No configuration files are provided, so you will 36 | need to edit the source. 37 | 38 | ## Examples 39 | 40 | A few examples using this program. 41 | 42 | Compare the swiss roll and punctured sphere results with those found [in this 43 | paper](http://wireilla.com/papers/ijfcst/V4N6/4614ijfcst06.pdf), specifically in 44 | Section 3.1. Note that my value of `bandwidth` is the square of what they 45 | call `sigma` (I am not squaring the denominator of the Gaussian kernel in my 46 | code). 47 | 48 | ### Cluster of points 49 | 50 | Colors indicate where points are in relationship to axis with greatest variance. 51 | 52 | #### Original data 53 | ![Cluster dataset](examples/cluster/cluster.png) 54 | 55 | #### Principal component analysis 56 | ![PCA](examples/cluster/pca.png) 57 | 58 | #### Diffusion maps 59 | ![Diffusion map (eps = 1)](examples/cluster/dmap-1.png) 60 | ![Diffusion map (eps = 10)](examples/cluster/dmap-10.png) 61 | ![Diffusion map (eps = 100)](examples/cluster/dmap-100.png) 62 | 63 | ### Multiple clusters 64 | 65 | Colors indicate original cluster. 66 | 67 | #### Original data 68 | ![Cluster dataset](examples/clusters/clusters.png) 69 | 70 | #### Principal component analysis 71 | ![PCA](examples/clusters/pca.png) 72 | 73 | #### Diffusion maps 74 | ![Diffusion map (eps = 1)](examples/clusters/dmap-1.png) 75 | ![Diffusion map (eps = 10)](examples/clusters/dmap-10.png) 76 | ![Diffusion map (eps = 100)](examples/clusters/dmap-100.png) 77 | 78 | ### Swiss roll 79 | 80 | Colors indicate where points are in relationship to the center of the swiss 81 | roll. 82 | 83 | #### Original data 84 | ![Swiss roll dataset](examples/swiss-roll/swissroll.png) 85 | 86 | #### Principal component analysis 87 | ![PCA](examples/swiss-roll/pca.png) 88 | 89 | #### Diffusion maps 90 | ![Diffusion map (eps = 1)](examples/swiss-roll/dmap-1.png) 91 | ![Diffusion map (eps = 10)](examples/swiss-roll/dmap-10.png) 92 | ![Diffusion map (eps = 100)](examples/swiss-roll/dmap-100.png) 93 | 94 | ### Punctured sphere 95 | 96 | Colors indicate where points are in relationship to axis that goes through the 97 | holes in the sphere. 98 | 99 | #### Original data 100 | ![Punctured sphere dataset](examples/punctured-sphere/puncsphere.png) 101 | 102 | #### Principal component analysis 103 | ![PCA](examples/punctured-sphere/pca.png) 104 | 105 | #### Diffusion maps 106 | ![Diffusion map (eps = 1)](examples/punctured-sphere/dmap-1.png) 107 | ![Diffusion map (eps = 10)](examples/punctured-sphere/dmap-10.png) 108 | ![Diffusion map (eps = 100)](examples/punctured-sphere/dmap-100.png) 109 | 110 | ### Simulation of octane in water 111 | 112 | The original data is from a Molecular Dynamics simulation I performed of a 113 | single octane in water. I used the RMSD between each pair of simulation 114 | snapshots of the octane as the distance metric for the diffusion map 115 | calculation (1,000 snapshots total). For the principal components analysis I 116 | used the dihedral angles as the metric. The colors indicate the radius of 117 | gyration of the octane. Compare these results with Figure S2.C from [this 118 | paper's SI 119 | (PDF)](http://www.pnas.org/content/suppl/2010/07/14/1003293107.DCSupplemental/pnas.1003293107_SI.pdf). 120 | 121 | The branch `alkane` has the modified code that performs these calculations. The 122 | original simulation trajectory is too large to post here. To reproduce the data, 123 | use [this input](examples/octane/prd.tpr) file with GROMACS and run the 124 | simulation. Then use `gmx trjconv` to fit the octane's translational and 125 | rotational motion, saving only the octane's coordinates. Use the output 126 | coordinate file (xtc) as the input for this analysis. By default the simulation 127 | will output 10,000 frames, so you may want to reduce this some for the diffusion 128 | map analysis, since it is very memory intensive. 129 | 130 | #### Principal component analysis 131 | ![PCA](examples/octane/pca.png) 132 | 133 | #### Diffusion map 134 | ![Diffusion map](examples/octane/dmap.png) 135 | -------------------------------------------------------------------------------- /bandwidth.json: -------------------------------------------------------------------------------- 1 | { 2 | "input": { 3 | "file": "swissroll.dat", 4 | "dimensions": 3 5 | }, 6 | "bandwidth_calc": { 7 | "get": true, 8 | "log_l": -20, 9 | "log_u": 20, 10 | "file": "eps.dat" 11 | }, 12 | } 13 | -------------------------------------------------------------------------------- /dmap.json: -------------------------------------------------------------------------------- 1 | { 2 | "infile": "swissroll.dat", 3 | "dimensions": 3, 4 | "dmap": { 5 | "run": true, 6 | "evalues": "dmap-evalues-1.dat", 7 | "evects": "dmap-evects-1.dat", 8 | "outfile": "dmap-1.dat", 9 | "bandwidth": 1.0, 10 | "time": 0.0 11 | } 12 | } 13 | -------------------------------------------------------------------------------- /examples/cluster/cluster.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wesbarnett/diffusion-map/e85dfafac05494e553ca59f3bed71b790a6bafe3/examples/cluster/cluster.pdf -------------------------------------------------------------------------------- /examples/cluster/cluster.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wesbarnett/diffusion-map/e85dfafac05494e553ca59f3bed71b790a6bafe3/examples/cluster/cluster.png -------------------------------------------------------------------------------- /examples/cluster/dmap-1.pdf: -------------------------------------------------------------------------------- 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0.290556 3 | 0.115851 4 | 0.111420 5 | -------------------------------------------------------------------------------- /examples/cluster/dmap-evalues-10.dat: -------------------------------------------------------------------------------- 1 | 1.000000 2 | 0.042472 3 | 0.012976 4 | 0.010628 5 | -------------------------------------------------------------------------------- /examples/cluster/dmap-evalues-100.dat: -------------------------------------------------------------------------------- 1 | 1.000000 2 | 0.004448 3 | 0.001318 4 | 0.001077 5 | -------------------------------------------------------------------------------- /examples/cluster/pca-evalues.dat: -------------------------------------------------------------------------------- 1 | # Eigenvalues 2 | 0.447383 3 | 0.132110 4 | 0.107940 5 | # Contribution 6 | 0.650802 7 | 0.192178 8 | 0.157019 9 | # Cumulative contribution 10 | 0.650802 11 | 0.842981 12 | 1.000000 13 | 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/examples/clusters/dmap-evalues-10.dat: -------------------------------------------------------------------------------- 1 | 1.000000 2 | 0.668760 3 | 0.419687 4 | 0.063561 5 | -------------------------------------------------------------------------------- /examples/clusters/dmap-evalues-100.dat: -------------------------------------------------------------------------------- 1 | 1.000000 2 | 0.081449 3 | 0.039301 4 | 0.005428 5 | -------------------------------------------------------------------------------- /examples/clusters/dmap-evects-1.dat: -------------------------------------------------------------------------------- 1 | 0.025820 -0.023203 0.000403 -0.000003 2 | 0.025820 -0.023191 0.000393 -0.000047 3 | 0.025820 -0.023213 0.000411 0.000046 4 | 0.025820 -0.023212 0.000410 0.000039 5 | 0.025820 -0.023200 0.000400 -0.000027 6 | 0.025820 -0.023216 0.000413 0.000060 7 | 0.025820 -0.023214 0.000412 0.000052 8 | 0.025820 -0.023215 0.000413 0.000058 9 | 0.025820 -0.023215 0.000412 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1282 | 0.025820 0.026260 -0.039689 0.009927 1283 | 0.025820 0.026442 -0.033285 0.076239 1284 | 0.025820 0.026211 -0.036197 -0.001518 1285 | 0.025820 0.026223 -0.040332 0.001310 1286 | 0.025820 0.026204 -0.039309 -0.083739 1287 | 0.025820 0.026253 -0.040096 0.020946 1288 | 0.025820 0.025547 -0.034704 -0.112305 1289 | 0.025820 0.026220 -0.040878 0.073213 1290 | 0.025820 0.026319 -0.033796 -0.010065 1291 | 0.025820 0.026242 -0.040042 0.007124 1292 | 0.025820 0.026253 -0.039942 0.012030 1293 | 0.025820 0.026204 -0.041050 0.029561 1294 | 0.025820 0.025980 -0.038510 -0.085614 1295 | 0.025820 0.026169 -0.041149 -0.083829 1296 | 0.025820 0.026487 -0.028177 -0.010971 1297 | 0.025820 0.026389 -0.035794 0.073215 1298 | 0.025820 0.026232 -0.040369 0.001832 1299 | 0.025820 0.026237 -0.040602 0.012962 1300 | 0.025820 0.026960 -0.006003 -0.024723 1301 | 0.025820 0.026272 -0.038499 -0.027189 1302 | 0.025820 0.026247 -0.040546 0.053939 1303 | 0.025820 0.026654 -0.021845 -0.042603 1304 | 0.025820 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0.026242 -0.040212 0.003636 1395 | 0.025820 0.026238 -0.040537 0.007638 1396 | 0.025820 0.026050 -0.039794 -0.055707 1397 | 0.025820 0.027208 -0.002909 0.012815 1398 | 0.025820 0.026242 -0.040098 0.017312 1399 | 0.025820 0.026238 -0.040373 0.019548 1400 | 0.025820 0.026164 -0.040186 -0.040751 1401 | 0.025820 0.026235 -0.040441 0.001346 1402 | 0.025820 0.026239 -0.040035 0.002034 1403 | 0.025820 0.026236 -0.040425 0.007696 1404 | 0.025820 0.026208 -0.040405 0.003598 1405 | 0.025820 0.026243 -0.040762 0.028506 1406 | 0.025820 0.026253 -0.039842 0.009802 1407 | 0.025820 0.025557 -0.037107 -0.044266 1408 | 0.025820 0.026152 -0.039228 -0.068281 1409 | 0.025820 0.026232 -0.039678 -0.000110 1410 | 0.025820 0.024598 -0.038651 -0.150213 1411 | 0.025820 0.026236 -0.040091 0.004239 1412 | 0.025820 0.026314 -0.038185 0.048555 1413 | 0.025820 0.026180 -0.039325 0.001721 1414 | 0.025820 0.026248 -0.040685 0.039451 1415 | 0.025820 0.026251 -0.040267 -0.077235 1416 | 0.025820 0.026234 -0.040868 -0.008117 1417 | 0.025820 0.026395 -0.035596 0.064327 1418 | 0.025820 0.026234 -0.040132 0.003205 1419 | 0.025820 0.026247 -0.040133 0.020346 1420 | 0.025820 0.026225 -0.039792 -0.009351 1421 | 0.025820 0.026276 -0.040192 0.111688 1422 | 0.025820 0.026227 -0.040363 0.003858 1423 | 0.025820 0.026207 -0.040121 -0.012385 1424 | 0.025820 0.026238 -0.040271 0.013070 1425 | 0.025820 0.026165 -0.040430 -0.105659 1426 | 0.025820 0.026228 -0.040108 0.002063 1427 | 0.025820 0.026235 -0.040097 0.002995 1428 | 0.025820 0.026250 -0.039279 0.007056 1429 | 0.025820 0.026121 -0.037755 -0.055295 1430 | 0.025820 0.026216 -0.039912 -0.003726 1431 | 0.025820 0.026190 -0.041025 -0.080437 1432 | 0.025820 0.026248 -0.040116 0.017287 1433 | 0.025820 0.026282 -0.039700 0.073222 1434 | 0.025820 0.026220 -0.040145 0.001737 1435 | 0.025820 0.023740 -0.036851 -0.165618 1436 | 0.025820 0.026248 -0.039643 -0.004642 1437 | 0.025820 0.026216 -0.040706 0.005479 1438 | 0.025820 0.026519 -0.030204 0.011627 1439 | 0.025820 0.026212 -0.038928 -0.023110 1440 | 0.025820 0.026284 -0.038723 0.033277 1441 | 0.025820 0.026211 -0.040439 -0.005971 1442 | 0.025820 0.026225 -0.041129 0.022059 1443 | 0.025820 0.026228 -0.038478 -0.094348 1444 | 0.025820 0.026251 -0.040228 0.015684 1445 | 0.025820 0.026270 -0.040325 0.020037 1446 | 0.025820 0.026248 -0.040507 0.009507 1447 | 0.025820 0.026246 -0.039560 -0.019854 1448 | 0.025820 0.026216 -0.039988 -0.012420 1449 | 0.025820 0.026241 -0.040149 0.006130 1450 | 0.025820 0.026182 -0.040910 -0.028093 1451 | 0.025820 0.026196 -0.039570 -0.005150 1452 | 0.025820 0.026082 -0.040329 -0.134757 1453 | 0.025820 0.026239 -0.040043 0.005031 1454 | 0.025820 0.026234 -0.039871 0.003874 1455 | 0.025820 0.026274 -0.040046 0.079636 1456 | 0.025820 0.026332 -0.037101 0.004830 1457 | 0.025820 0.026225 -0.040181 -0.000898 1458 | 0.025820 0.026241 -0.040082 0.010136 1459 | 0.025820 0.026087 -0.040017 0.018754 1460 | 0.025820 0.026287 -0.039088 0.039200 1461 | 0.025820 0.026237 -0.040117 0.006186 1462 | 0.025820 0.026263 -0.038285 -0.001106 1463 | 0.025820 0.026274 -0.038917 0.004187 1464 | 0.025820 0.026368 -0.024504 -0.000464 1465 | 0.025820 0.026229 -0.040168 -0.002598 1466 | 0.025820 0.026237 -0.040584 -0.062118 1467 | 0.025820 0.026362 -0.033750 0.030819 1468 | 0.025820 0.026255 -0.039724 0.008587 1469 | 0.025820 0.026218 -0.039940 -0.007336 1470 | 0.025820 0.026247 -0.040161 0.001803 1471 | 0.025820 0.026238 -0.040075 0.004922 1472 | 0.025820 0.026237 -0.040043 0.005172 1473 | 0.025820 0.027132 -0.005781 0.003110 1474 | 0.025820 0.022152 -0.035771 -0.105871 1475 | 0.025820 0.026256 -0.040552 0.009298 1476 | 0.025820 0.026250 -0.040114 0.015035 1477 | 0.025820 0.026127 -0.039990 -0.019654 1478 | 0.025820 0.026280 -0.039061 0.011293 1479 | 0.025820 0.026246 -0.040084 0.003893 1480 | 0.025820 0.026896 -0.006923 -0.029084 1481 | 0.025820 0.026240 -0.040453 0.012021 1482 | 0.025820 0.026124 -0.040444 -0.107120 1483 | 0.025820 0.026219 -0.040490 -0.007641 1484 | 0.025820 0.026474 -0.031546 0.009217 1485 | 0.025820 0.026233 -0.040126 0.006332 1486 | 0.025820 0.026236 -0.040061 0.004130 1487 | 0.025820 0.026227 -0.039389 -0.005193 1488 | 0.025820 0.026190 -0.040194 -0.007839 1489 | 0.025820 0.026244 -0.040395 0.010839 1490 | 0.025820 0.026160 -0.040821 -0.044423 1491 | 0.025820 0.026398 -0.035576 0.065605 1492 | 0.025820 0.026303 -0.038675 0.028933 1493 | 0.025820 0.026271 -0.039933 0.022706 1494 | 0.025820 0.026239 -0.040359 0.011401 1495 | 0.025820 0.026245 -0.040186 0.000879 1496 | 0.025820 0.026263 -0.039414 0.025466 1497 | 0.025820 0.026339 -0.036603 0.021331 1498 | 0.025820 0.026207 -0.039680 0.011538 1499 | 0.025820 0.026238 -0.039214 0.006187 1500 | 0.025820 0.026681 -0.021709 -0.027030 1501 | -------------------------------------------------------------------------------- /examples/clusters/pca-evalues.dat: -------------------------------------------------------------------------------- 1 | # Eigenvalues 2 | 8.149675 3 | 3.819040 4 | 0.531479 5 | # Contribution 6 | 0.651964 7 | 0.305518 8 | 0.042518 9 | # Cumulative contribution 10 | 0.651964 11 | 0.957482 12 | 1.000000 13 | -------------------------------------------------------------------------------- /examples/clusters/pca-evects.dat: -------------------------------------------------------------------------------- 1 | -0.335954 -0.150137 -0.929835 2 | 0.742434 -0.649701 -0.163340 3 | 0.579591 0.745217 -0.329737 4 | -------------------------------------------------------------------------------- /examples/clusters/pca.dat: -------------------------------------------------------------------------------- 1 | 1.000000 3.243798 0.863615 0.217589 2 | 1.000000 3.526553 -0.017383 -0.527405 3 | 1.000000 3.888738 0.639069 -0.096399 4 | 1.000000 3.834610 0.587080 0.133738 5 | 1.000000 3.814075 -0.098902 0.467012 6 | 1.000000 4.314123 0.749394 0.388124 7 | 1.000000 3.905491 0.797428 -0.221587 8 | 1.000000 4.183972 0.812072 0.379858 9 | 1.000000 3.805847 1.112383 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3.000000 -2.795153 -2.500456 0.114218 1493 | 3.000000 -2.600629 -3.213634 0.351597 1494 | 3.000000 -1.171903 -2.922025 -0.356881 1495 | 3.000000 -1.474831 -2.835639 0.579629 1496 | 3.000000 -1.542457 -2.152551 -1.097912 1497 | 3.000000 -2.072323 -1.664836 -0.487281 1498 | 3.000000 -0.620680 -2.033675 -1.231831 1499 | 3.000000 -1.022054 -1.846451 -0.525541 1500 | 3.000000 -1.778982 -0.717482 1.614401 1501 | -------------------------------------------------------------------------------- /examples/clusters/pca.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/wesbarnett/diffusion-map/e85dfafac05494e553ca59f3bed71b790a6bafe3/examples/clusters/pca.pdf -------------------------------------------------------------------------------- /examples/clusters/pca.png: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- 1 | 1.000000 2 | 0.001012 3 | 0.001005 4 | 0.000416 5 | -------------------------------------------------------------------------------- /examples/punctured-sphere/pca-evalues.dat: -------------------------------------------------------------------------------- 1 | # Eigenvalues 2 | 0.101258 3 | 0.100511 4 | 0.041580 5 | # Contribution 6 | 0.416102 7 | 0.413033 8 | 0.170865 9 | # Cumulative contribution 10 | 0.416102 11 | 0.829135 12 | 1.000000 13 | -------------------------------------------------------------------------------- /examples/punctured-sphere/pca-evects.dat: -------------------------------------------------------------------------------- 1 | -0.109238 -0.947279 -0.301214 2 | -0.954162 0.184873 -0.235365 3 | -0.278642 -0.261696 0.924053 4 | -------------------------------------------------------------------------------- /examples/punctured-sphere/pca.pdf: 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| 0.131770 4 | 0.078196 5 | -------------------------------------------------------------------------------- /examples/swiss-roll/pca-evalues.dat: -------------------------------------------------------------------------------- 1 | # Eigenvalues 2 | 18.445280 3 | 14.258507 4 | 8.103496 5 | # Contribution 6 | 0.452010 7 | 0.349411 8 | 0.198580 9 | # Cumulative contribution 10 | 0.452010 11 | 0.801420 12 | 1.000000 13 | -------------------------------------------------------------------------------- /examples/swiss-roll/pca-evects.dat: -------------------------------------------------------------------------------- 1 | -0.275042 0.377752 0.884113 2 | -0.560772 0.683924 -0.466671 3 | 0.780952 0.624140 -0.023725 4 | -------------------------------------------------------------------------------- /examples/swiss-roll/pca.pdf: -------------------------------------------------------------------------------- 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| zeta2 = 100.0d0 33 | 34 | do while (zeta2 .gt. 1.0d0) 35 | call random_number(xi) 36 | zeta = 1.0d0 - 2.0d0*xi 37 | zeta2 = sum(zeta**2) 38 | end do 39 | 40 | gen_sphere_point = [ 2.0d0 * zeta(1) * sqrt(1.0d0 - zeta2), & 41 | 2.0d0 * zeta(2) * sqrt(1.0d0 - zeta2), & 42 | 1.0d0 - 2.0d0*zeta2 ] 43 | gen_sphere_point = gen_sphere_point * r + center 44 | 45 | end function gen_sphere_point 46 | 47 | end module subs 48 | 49 | program main 50 | 51 | use subs 52 | 53 | implicit none 54 | integer :: i, n, u 55 | real(8), allocatable :: z(:), data3d(:,:) 56 | real(8) :: Rx(3,3), Ry(3,3), Rz(3,3), angles(3), mindim, point(3), a, b, g, center(3), r, rotate(3,3), rand(3) 57 | logical :: do_rotate 58 | character (len=:), allocatable :: outfile 59 | 60 | ! TODO: Read in from config file 61 | do_rotate = .true. 62 | outfile = "cluster.dat" 63 | n = 2000 64 | 65 | call init_seed() 66 | 67 | allocate(data3d(3,n)) 68 | allocate(z(n)) 69 | do i = 1, n 70 | call random_number(rand) 71 | point = gen_sphere_point([0.0d0,0.0d0,0.0d0], rand(1)) 72 | point(3) = point(3)*2.0d0 73 | point(2) = point(2)*1.1d0 74 | data3d(:,i) = point 75 | z(i) = point(3) 76 | end do 77 | 78 | ! Add some noise 79 | mindim = min(maxval(data3d(3,:)) - minval(data3d(3,:)), maxval(data3d(2,:)) - minval(data3d(2,:)), & 80 | maxval(data3d(1,:)) - minval(data3d(1,:))) 81 | do i = 1, n 82 | call random_number(rand) 83 | data3d(:,i) = data3d(:,i) + 0.02*rand*sqrt(mindim) 84 | end do 85 | 86 | ! Rotate all the points 87 | if (do_rotate) then 88 | call random_number(angles) 89 | 90 | a = angles(1) * pi 91 | b = angles(2) * pi 92 | g = angles(3) * pi 93 | 94 | Rx = reshape((/ 1.0d0, 0.0d0, 0.0d0, 0.0d0, cos(a), -sin(a), 0.0d0, sin(a), cos(a) /), shape(Rx)) 95 | Ry = reshape((/cos(b), 0.0d0, sin(b), 0.0d0, 1.0d0, 0.0d0, -sin(b), 0.0d0, cos(b) /), shape(Ry)) 96 | Rz = reshape((/cos(g), -sin(g), 0.0d0, sin(g), cos(g), 0.0d0, 0.0d0, 0.0d0, 1.0d0 /), shape(Rz)) 97 | 98 | rotate = matmul(Rz, matmul(Ry, Rx)) 99 | data3d = matmul(rotate, data3d) 100 | end if 101 | 102 | open(newunit=u, file=trim(outfile)) 103 | write(u, "(i0)") n 104 | do i = 1, n 105 | write(u, "(4f24.3)") data3d(:,i), z(i) 106 | end do 107 | close(u) 108 | 109 | end program main 110 | -------------------------------------------------------------------------------- /extra/gen-clusters.f90: -------------------------------------------------------------------------------- 1 | module subs 2 | 3 | implicit none 4 | real(8), parameter :: pi = 2.0d0*acos(0.0d0) 5 | 6 | contains 7 | 8 | subroutine init_seed() 9 | 10 | implicit none 11 | integer :: n, u 12 | integer, allocatable :: seed(:) 13 | 14 | call random_seed(size=n) 15 | 16 | allocate(seed(n)) 17 | open(newunit=u, file="/dev/urandom", access="stream", form="unformatted", & 18 | action="read", status="old") 19 | read(u) seed(:) 20 | close(u) 21 | 22 | call random_seed(put=seed) 23 | 24 | end subroutine init_seed 25 | 26 | function gen_sphere_point(center, r) 27 | 28 | implicit none 29 | real(8) :: xi(2), zeta(2), zeta2, gen_sphere_point(3) 30 | real(8), intent(in) :: center(3), r 31 | 32 | zeta2 = 100.0d0 33 | 34 | do while (zeta2 .gt. 1.0d0) 35 | call random_number(xi) 36 | zeta = 1.0d0 - 2.0d0*xi 37 | zeta2 = sum(zeta**2) 38 | end do 39 | 40 | gen_sphere_point = [ 2.0d0 * zeta(1) * sqrt(1.0d0 - zeta2), & 41 | 2.0d0 * zeta(2) * sqrt(1.0d0 - zeta2), & 42 | 1.0d0 - 2.0d0*zeta2 ] 43 | gen_sphere_point = gen_sphere_point * r + center 44 | 45 | end function gen_sphere_point 46 | 47 | end module subs 48 | 49 | program main 50 | 51 | use subs 52 | 53 | implicit none 54 | integer :: i, n, u, nclust, j, k 55 | real(8), allocatable :: z(:), data3d(:,:) 56 | real(8) :: Rx(3,3), Ry(3,3), Rz(3,3), angles(3), mindim, point(3), a, b, g, center(3), r, rotate(3,3), rand(3), rand2(3), & 57 | rand3(3) 58 | logical :: do_rotate 59 | character (len=:), allocatable :: outfile 60 | 61 | ! TODO: Read in from config file 62 | do_rotate = .true. 63 | outfile = "clusters.dat" 64 | n = 500 65 | nclust = 3 66 | 67 | call init_seed() 68 | 69 | allocate(data3d(3,n*nclust)) 70 | allocate(z(n*nclust)) 71 | k = 1 72 | do i = 1, nclust 73 | call random_number(rand) 74 | call random_number(rand3) 75 | rand = rand*10.0 76 | do j = 1, n 77 | call random_number(rand2) 78 | point = gen_sphere_point(rand, rand2(1)*dble(i)) 79 | data3d(:,k) = point 80 | z(k) = i 81 | k = k + 1 82 | end do 83 | end do 84 | 85 | ! Add some noise 86 | mindim = min(maxval(data3d(3,:)) - minval(data3d(3,:)), maxval(data3d(2,:)) - minval(data3d(2,:)), & 87 | maxval(data3d(1,:)) - minval(data3d(1,:))) 88 | do i = 1, n 89 | call random_number(rand) 90 | data3d(:,i) = data3d(:,i) + 0.10*rand*sqrt(mindim) 91 | end do 92 | 93 | ! Rotate all the points 94 | if (do_rotate) then 95 | call random_number(angles) 96 | 97 | a = angles(1) * pi 98 | b = angles(2) * pi 99 | g = angles(3) * pi 100 | 101 | Rx = reshape((/ 1.0d0, 0.0d0, 0.0d0, 0.0d0, cos(a), -sin(a), 0.0d0, sin(a), cos(a) /), shape(Rx)) 102 | Ry = reshape((/cos(b), 0.0d0, sin(b), 0.0d0, 1.0d0, 0.0d0, -sin(b), 0.0d0, cos(b) /), shape(Ry)) 103 | Rz = reshape((/cos(g), -sin(g), 0.0d0, sin(g), cos(g), 0.0d0, 0.0d0, 0.0d0, 1.0d0 /), shape(Rz)) 104 | 105 | rotate = matmul(Rz, matmul(Ry, Rx)) 106 | data3d = matmul(rotate, data3d) 107 | end if 108 | 109 | open(newunit=u, file=trim(outfile)) 110 | write(u, "(i0)") n*nclust 111 | do i = 1, n*nclust 112 | write(u, "(4f24.3)") data3d(:,i), z(i) 113 | end do 114 | close(u) 115 | 116 | end program main 117 | -------------------------------------------------------------------------------- /extra/gen-punc-sphere.f90: -------------------------------------------------------------------------------- 1 | module subs 2 | 3 | implicit none 4 | real(8), parameter :: pi = 2.0d0*acos(0.0d0) 5 | 6 | contains 7 | 8 | subroutine init_seed() 9 | 10 | implicit none 11 | integer :: n, u 12 | integer, allocatable :: seed(:) 13 | 14 | call random_seed(size=n) 15 | 16 | allocate(seed(n)) 17 | open(newunit=u, file="/dev/urandom", access="stream", form="unformatted", & 18 | action="read", status="old") 19 | read(u) seed(:) 20 | close(u) 21 | 22 | call random_seed(put=seed) 23 | 24 | end subroutine init_seed 25 | 26 | function gen_sphere_point(center, r) 27 | 28 | implicit none 29 | real(8) :: xi(2), zeta(2), zeta2, gen_sphere_point(3) 30 | real(8), intent(in) :: center(3), r 31 | 32 | zeta2 = 100.0d0 33 | 34 | do while (zeta2 .gt. 1.0d0) 35 | call random_number(xi) 36 | zeta = 1.0d0 - 2.0d0*xi 37 | zeta2 = sum(zeta**2) 38 | end do 39 | 40 | gen_sphere_point = [ 2.0d0 * zeta(1) * sqrt(1.0d0 - zeta2), & 41 | 2.0d0 * zeta(2) * sqrt(1.0d0 - zeta2), & 42 | 1.0d0 - 2.0d0*zeta2 ] 43 | gen_sphere_point = gen_sphere_point * r + center 44 | 45 | end function gen_sphere_point 46 | 47 | end module subs 48 | 49 | program main 50 | 51 | use subs 52 | 53 | implicit none 54 | integer :: i, n, u 55 | real(8), allocatable :: z(:), data3d(:,:) 56 | real(8) :: Rx(3,3), Ry(3,3), Rz(3,3), angles(3), mindim, point(3), a, b, g, center(3), r, rotate(3,3), rand(3) 57 | logical :: do_rotate 58 | character (len=:), allocatable :: outfile 59 | 60 | ! TODO: Read in from config file 61 | do_rotate = .true. 62 | outfile = "puncsphere.dat" 63 | n = 2000 64 | center = [ 0.0, 0.0, 0.0 ] 65 | r = 0.5 66 | 67 | call init_seed() 68 | 69 | ! top of sphere is cut off 70 | ! points become less dense as they go further down the sphere 71 | allocate(data3d(3,n)) 72 | allocate(z(n)) 73 | do i = 1, n 74 | do while (.true.) 75 | point = gen_sphere_point(center, r) 76 | call random_number(rand) 77 | if ((rand(1)-0.5d0) .le. point(3) .and. point(3) .lt. (center(3)+0.75*r)) then 78 | exit 79 | end if 80 | end do 81 | data3d(:,i) = point 82 | z(i) = point(3) 83 | end do 84 | 85 | ! Add some noise 86 | mindim = min(maxval(data3d(3,:)) - minval(data3d(3,:)), maxval(data3d(2,:)) - minval(data3d(2,:)), & 87 | maxval(data3d(1,:)) - minval(data3d(1,:))) 88 | do i = 1, n 89 | call random_number(rand) 90 | data3d(:,i) = data3d(:,i) + 0.02*rand*sqrt(mindim) 91 | end do 92 | 93 | ! Rotate all the points 94 | if (do_rotate) then 95 | call random_number(angles) 96 | 97 | a = angles(1) * pi 98 | b = angles(2) * pi 99 | g = angles(3) * pi 100 | 101 | Rx = reshape((/ 1.0d0, 0.0d0, 0.0d0, 0.0d0, cos(a), -sin(a), 0.0d0, sin(a), cos(a) /), shape(Rx)) 102 | Ry = reshape((/cos(b), 0.0d0, sin(b), 0.0d0, 1.0d0, 0.0d0, -sin(b), 0.0d0, cos(b) /), shape(Ry)) 103 | Rz = reshape((/cos(g), -sin(g), 0.0d0, sin(g), cos(g), 0.0d0, 0.0d0, 0.0d0, 1.0d0 /), shape(Rz)) 104 | 105 | rotate = matmul(Rz, matmul(Ry, Rx)) 106 | data3d = matmul(rotate, data3d) 107 | end if 108 | 109 | open(newunit=u, file=trim(outfile)) 110 | write(u, "(i0)") n 111 | do i = 1, n 112 | write(u, "(4f24.3)") data3d(:,i), z(i) 113 | end do 114 | close(u) 115 | 116 | end program main 117 | -------------------------------------------------------------------------------- /extra/gen-swiss-roll.f90: -------------------------------------------------------------------------------- 1 | module subs 2 | 3 | implicit none 4 | real(8), parameter :: pi = 2.0d0*acos(0.0d0) 5 | 6 | contains 7 | 8 | subroutine init_seed() 9 | 10 | implicit none 11 | integer :: n, u 12 | integer, allocatable :: seed(:) 13 | 14 | call random_seed(size=n) 15 | 16 | allocate(seed(n)) 17 | open(newunit=u, file="/dev/urandom", access="stream", form="unformatted", & 18 | action="read", status="old") 19 | read(u) seed(:) 20 | close(u) 21 | 22 | call random_seed(put=seed) 23 | 24 | end subroutine init_seed 25 | 26 | end module subs 27 | 28 | program main 29 | 30 | use subs 31 | 32 | implicit none 33 | integer :: i, n, u 34 | real(8), allocatable :: data2d(:,:), data3d(:,:) 35 | real(8) :: rand(2), width, height, hole_x1, hole_x2, hole_y1, hole_y2, x, y, rotate(3,3), a, b, g, r 36 | real(8) :: Rx(3,3), Ry(3,3), Rz(3,3), angles(3), mindim 37 | logical :: do_rotate 38 | character (len=:), allocatable :: outfile 39 | 40 | ! TODO: Read in from config file 41 | do_rotate = .true. 42 | outfile = "swissroll.dat" 43 | n = 2000 44 | height = 10.0 45 | 46 | call init_seed() 47 | 48 | ! Generate a plane of numbers randomly 49 | allocate(data2d(2,n)) 50 | allocate(data3d(3,n)) 51 | do i = 1, n 52 | call random_number(rand) 53 | ! TODO 54 | !r = dble(i)-1.0d0 55 | !x = pi*(1.5d0+3.0d0*r) 56 | x = rand(1)*height 57 | y = rand(2)*height 58 | data2d(1,i) = x 59 | data2d(2,i) = y 60 | data3d(:,i) = [ x*dcos(x), x*dsin(x), y ] 61 | end do 62 | 63 | ! Add some noise 64 | mindim = min(maxval(data3d(2,:)) - minval(data3d(2,:)), maxval(data3d(1,:)) - minval(data3d(1,:))) 65 | do i = 1, n 66 | call random_number(rand) 67 | data3d(1:2,i) = data3d(1:2,i) + 0.02*rand*sqrt(mindim) 68 | end do 69 | 70 | ! Rotate all the points 71 | if (do_rotate) then 72 | call random_number(angles) 73 | 74 | a = angles(1) * pi 75 | b = angles(2) * pi 76 | g = angles(3) * pi 77 | 78 | Rx = reshape((/ 1.0d0, 0.0d0, 0.0d0, 0.0d0, cos(a), -sin(a), 0.0d0, sin(a), cos(a) /), shape(Rx)) 79 | Ry = reshape((/cos(b), 0.0d0, sin(b), 0.0d0, 1.0d0, 0.0d0, -sin(b), 0.0d0, cos(b) /), shape(Ry)) 80 | Rz = reshape((/cos(g), -sin(g), 0.0d0, sin(g), cos(g), 0.0d0, 0.0d0, 0.0d0, 1.0d0 /), shape(Rz)) 81 | 82 | rotate = matmul(Rz, matmul(Ry, Rx)) 83 | data3d = matmul(rotate, data3d) 84 | end if 85 | 86 | open(newunit=u, file=trim(outfile)) 87 | write(u, "(i0)") n 88 | do i = 1, n 89 | write(U, "(4f24.3)") data3d(:,i), data2d(1,i) 90 | end do 91 | close(U) 92 | 93 | end program main 94 | -------------------------------------------------------------------------------- /extra/plot-dmap.plt: -------------------------------------------------------------------------------- 1 | # MATLAB jet color pallete 2 | 3 | # line styles 4 | set style line 1 lt 1 lc rgb '#000080' # 5 | set style line 2 lt 1 lc rgb '#0000ff' # 6 | set style line 3 lt 1 lc rgb '#0080ff' # 7 | set style line 4 lt 1 lc rgb '#00ffff' # 8 | set style line 5 lt 1 lc rgb '#80ff80' # 9 | set style line 6 lt 1 lc rgb '#ffff00' # 10 | set style line 7 lt 1 lc rgb '#ff8000' # 11 | set style line 8 lt 1 lc rgb '#ff0000' # 12 | set style line 9 lt 1 lc rgb '#800000' # 13 | # line style used together with jet (<2014b) 14 | set style line 11 lt 1 lc rgb '#0000ff' # blue 15 | set style line 12 lt 1 lc rgb '#007f00' # green 16 | set style line 13 lt 1 lc rgb '#ff0000' # red 17 | set style line 14 lt 1 lc rgb '#00bfbf' # cyan 18 | set style line 15 lt 1 lc rgb '#bf00bf' # pink 19 | set style line 16 lt 1 lc rgb '#bfbf00' # yellow 20 | set style line 17 lt 1 lc rgb '#3f3f3f' # black 21 | 22 | # palette 23 | set palette defined (0 0.0 0.0 0.5, \ 24 | 1 0.0 0.0 1.0, \ 25 | 2 0.0 0.5 1.0, \ 26 | 3 0.0 1.0 1.0, \ 27 | 4 0.5 1.0 0.5, \ 28 | 5 1.0 1.0 0.0, \ 29 | 6 1.0 0.5 0.0, \ 30 | 7 1.0 0.0 0.0, \ 31 | 8 0.5 0.0 0.0 ) 32 | 33 | set term tikz standalone color size 3.5in, 3.5in 34 | 35 | unset key 36 | unset colorbox 37 | set xlabel 'x' 38 | set ylabel 'y' 39 | set zlabel 'z' 40 | set view equal xyz 41 | set tics out 42 | set mxtics 43 | set mytics 44 | set mztics 45 | set out 'cluster.tex' 46 | splot 'cluster.dat' u 1:2:3:4 w points palette 47 | 48 | set xlabel '$PC_{1}$' 49 | set ylabel '$PC_{2}$' 50 | set out 'pca.tex' 51 | plot 'pca.dat' u 2:3:1 w points palette 52 | 53 | set xlabel '$\lambda_{2}$' 54 | set ylabel '$\lambda_{3}$' 55 | set title "time = 0, bandwidth = 1" 56 | set out 'dmap-1.tex' 57 | plot 'dmap-1.dat' u 2:3:1 w points palette 58 | 59 | set title "time = 0, bandwidth = 10" 60 | set out 'dmap-10.tex' 61 | plot 'dmap-10.dat' u 2:3:1 w points palette 62 | 63 | set title "time = 0, bandwidth = 100" 64 | set out 'dmap-100.tex' 65 | plot 'dmap-100.dat' u 2:3:1 w points palette 66 | -------------------------------------------------------------------------------- /pca.json: -------------------------------------------------------------------------------- 1 | { 2 | "infile": "puncsphere.dat", 3 | "dimensions": 3, 4 | "pca": { 5 | "run": true, 6 | "evalues": "pca-evalues.dat", 7 | "evects": "pca-evects.dat", 8 | "outfile": "pca.dat" 9 | }, 10 | } 11 | -------------------------------------------------------------------------------- /src/diffusion_map.f90: -------------------------------------------------------------------------------- 1 | module diffusion_map 2 | 3 | implicit none 4 | type, public :: diffusion_map_type 5 | real(8), dimension(:,:), allocatable :: evec, map 6 | real(8), dimension(:), allocatable :: eval 7 | contains 8 | procedure :: run => diffusion_map_run 9 | end type 10 | 11 | contains 12 | 13 | subroutine get_evect(p, evect, evalues) 14 | 15 | ! SLOW 16 | implicit none 17 | integer :: n, info, i, lwork, lda, ldvl, ldvr 18 | real(8), dimension(:), allocatable :: wr, wi, work 19 | real(8), dimension(:,:), allocatable :: a, vl, vr 20 | real(8), dimension(:), allocatable, intent(inout) :: evalues(:), evect(:,:), p(:,:) 21 | integer, allocatable :: order(:) 22 | logical, allocatable :: mask(:) 23 | character :: jobvl = 'N', jobvr = 'V' 24 | 25 | interface 26 | subroutine dgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info) 27 | character, intent(in) :: jobvl, jobvr 28 | integer, intent(in) :: n, lda, ldvl, ldvr, lwork 29 | integer, intent(out) :: info 30 | real(8), intent(inout) :: a(lda,*) 31 | real(8), intent(out) :: wr(*), wi(*), vl(ldvl,*), vr(ldvr,*), work(*) 32 | end subroutine 33 | end interface 34 | 35 | a = p 36 | n = size(a,1) 37 | lwork = 26*n 38 | lda = n 39 | ldvl = n 40 | ldvr = n 41 | allocate(work(lwork), vl(ldvl, n), vr(ldvr, n), wr(n), wi(n)) 42 | 43 | ! Get eigenvectors and eigenvalues (LAPACK) 44 | call dgeev(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr, work, lwork, info) 45 | if(info .ne. 0) then 46 | write(*,*) "ERROR: Eigenvector calculation failed." 47 | end if 48 | 49 | ! Sort the evalues in descending so we can use the top components for 50 | ! later calcs 51 | allocate(order(n), mask(n)) 52 | mask = .true. 53 | do i = lbound(wr,1), ubound(wr,1) 54 | order(i) = maxloc(wr,1,mask) 55 | mask(order(i)) = .false. 56 | end do 57 | 58 | allocate(evect(ldvr, n), evalues(n)) 59 | evalues = wr(order) 60 | evect = vr(:,order) 61 | 62 | end subroutine get_evect 63 | 64 | function gauss_similarity(distance, bandwidth) 65 | 66 | implicit none 67 | real(8) :: bandwidth 68 | real(8), dimension(:,:), allocatable, intent(in) :: distance 69 | real(8), dimension(:,:), allocatable :: gauss_similarity 70 | 71 | allocate(gauss_similarity(size(distance,1),size(distance,2))) 72 | gauss_similarity = exp( - ( (distance**2) / (2.0d0*bandwidth) ) ) 73 | 74 | end function gauss_similarity 75 | 76 | subroutine diffusion_map_run(this, distance, bandwidth, time, dimensions) 77 | 78 | implicit none 79 | integer :: i, j, n 80 | integer, intent(in), optional :: dimensions 81 | real(8), dimension(:,:), allocatable :: similarity, markov_transition, evec 82 | real(8), dimension(:), allocatable :: eval 83 | real(8), dimension(:,:), allocatable, intent(in) :: distance 84 | real(8), intent(in) :: time, bandwidth 85 | class(diffusion_map_type), intent(inout) :: this 86 | 87 | n = size(distance,1) 88 | 89 | ! Using a Gaussian kernel 90 | similarity = gauss_similarity(distance, bandwidth) 91 | 92 | ! Normalize the diffusion / similarity matrix 93 | allocate(markov_transition(n,n)) 94 | do i = 1, n 95 | markov_transition(i,:) = similarity(i,:) / sum(similarity(i,:)) 96 | end do 97 | 98 | call get_evect(markov_transition, evec, eval) 99 | 100 | allocate(this%eval(1:dimensions+1)) 101 | this%eval = eval(1:dimensions+1) 102 | allocate(this%evec(size(evec,1),1:dimensions+1)) 103 | this%evec = evec(:,1:dimensions+1) 104 | 105 | ! Note that we do not save the first eigenvector to the map since it is trivial (all 1's) 106 | ! We do keep it in "evect" just as a check 107 | allocate(this%map(n,dimensions)) 108 | do j = 2, dimensions+1 109 | this%map(:,j-1) = this%evec(:,j)*this%eval(j)**time 110 | end do 111 | 112 | end subroutine diffusion_map_run 113 | 114 | end module diffusion_map 115 | -------------------------------------------------------------------------------- /src/main.f90: -------------------------------------------------------------------------------- 1 | ! Diffusion map code example 2 | ! James W. Barnett 3 | 4 | module subs 5 | 6 | contains 7 | 8 | subroutine check_file(myfile) 9 | 10 | implicit none 11 | character (len=*), intent(in) :: myfile 12 | logical ex 13 | 14 | inquire(file=trim(myfile), exist=ex) 15 | if (ex .eqv. .false.) then 16 | write(*,"(a)") "ERROR: "//trim(myfile)//" does not exist." 17 | stop 18 | end if 19 | 20 | end subroutine 21 | 22 | ! kept separate from diffusion_map module since distance metric is determined depending only the application 23 | function get_distance(indata) 24 | 25 | implicit none 26 | real(8), allocatable :: get_distance(:,:) 27 | real(8), allocatable, intent(in) :: indata(:,:) 28 | real(8) :: s 29 | integer :: ndata, ndim, i, j, k 30 | 31 | ndim = size(indata,1) 32 | ndata = size(indata,2) 33 | 34 | ! only appropriate for cartesian data. Real world use we would use a different metric here 35 | allocate(get_distance(ndata,ndata)) 36 | 37 | do i = 1, ndata-1 38 | do j = i+1, ndata 39 | s = 0.0d0 40 | do k = 1, ndim 41 | s = s + (indata(k,i)-indata(k,j))**2 42 | end do 43 | get_distance(i,j) = dsqrt(s) 44 | get_distance(j,i) = get_distance(i,j) 45 | end do 46 | end do 47 | 48 | end function get_distance 49 | 50 | end module subs 51 | 52 | program main 53 | 54 | use diffusion_map 55 | use princ_comp 56 | use json_module 57 | use subs 58 | 59 | implicit none 60 | integer :: i, j, n, u, logbandwidth_l, logbandwidth_u, max_output, dimensions 61 | real(8), dimension(:,:), allocatable :: distance, similarity, point 62 | real(8), dimension(:), allocatable :: val 63 | real(8) :: bandwidth 64 | logical :: get_bandwidth, found, run_pca, run_dmap 65 | character (len=256), allocatable :: config_file 66 | character (len=32) :: arg, n_char 67 | character (len=:), allocatable :: infile, bandwidth_file, evects_file, evalues_file, diffusionmap_file, pca_evects_file, & 68 | pca_evalues_file, pca_file 69 | character (len=1024) :: format_string 70 | type(json_file) :: config 71 | real(8) :: time ! diffusion "time", not simulation time 72 | type(diffusion_map_type) :: dm 73 | type(princ_comp_type) :: pca 74 | 75 | if (command_argument_count() .ne. 1) then 76 | write(0,*) "ERROR: First argument should be config file." 77 | stop 78 | end if 79 | 80 | call get_command_argument(1, arg) 81 | 82 | config_file = trim(arg) 83 | write(*,*) "Reading in configuration from "//trim(config_file)//"..." 84 | call check_file(config_file) 85 | call config%initialize() 86 | call config%load_file(filename=config_file) 87 | call config%print_file() 88 | call config%get('bandwidth_calc.get',get_bandwidth,found) 89 | if (.not. found) then 90 | get_bandwidth=.false. 91 | end if 92 | call config%get("bandwidth_calc.log_l",logbandwidth_l,found) 93 | if (.not. found) then 94 | logbandwidth_l = -10 95 | end if 96 | call config%get("bandwidth_calc.log_u",logbandwidth_u,found) 97 | if (.not. found) then 98 | logbandwidth_l = 10 99 | end if 100 | call config%get("bandwidth_calc.file",bandwidth_file,found) 101 | if (.not. found) then 102 | bandwidth_file = "eps.dat" 103 | end if 104 | call config%get('dmap.run',run_dmap,found) 105 | if (.not. found) then 106 | run_dmap = .false. 107 | end if 108 | call config%get("dmap.outfile",diffusionmap_file,found) 109 | if (.not. found) then 110 | diffusionmap_file = "dmap.dat" 111 | end if 112 | call config%get("dmap.bandwidth",bandwidth,found) 113 | if (.not. found) then 114 | bandwidth = 1.0 115 | end if 116 | call config%get("dimensions",dimensions,found) 117 | if (.not. found) then 118 | dimensions = 3 119 | end if 120 | ! Default is 4 because we are using 3d data for this example (and first eigenvector is all 1's and is ignored) 121 | max_output = dimensions + 1 122 | call config%get("infile",infile,found) 123 | if (.not. found) then 124 | infile = "infile.dat" 125 | end if 126 | call config%get("dmap.time",time,found) 127 | if (.not. found) then 128 | time = 0.0 129 | end if 130 | call check_file(infile) 131 | call config%get("dmap.evects",evects_file,found) 132 | if (.not. found) then 133 | evects_file = "evects.dat" 134 | end if 135 | call config%get("dmap.evalues",evalues_file,found) 136 | if (.not. found) then 137 | evalues_file = "evalues.dat" 138 | end if 139 | call config%get('pca.run',run_pca,found) 140 | if (.not. found) then 141 | run_pca = .false. 142 | end if 143 | call config%get("pca.evects",pca_evects_file,found) 144 | if (.not. found) then 145 | pca_evects_file = "evects.dat" 146 | end if 147 | call config%get("pca.evalues",pca_evalues_file,found) 148 | if (.not. found) then 149 | pca_evalues_file = "evalues.dat" 150 | end if 151 | call config%get("pca.outfile",pca_file,found) 152 | if (.not. found) then 153 | pca_file = "pca.dat" 154 | end if 155 | call config%destroy() 156 | 157 | ! val is the original data's position on the swiss roll 158 | write(*,*) "Reading in data from "//trim(infile)//"..." 159 | open(newunit=u, file=trim(infile), status="old") 160 | read(u,*) n 161 | allocate(point(dimensions,n)) 162 | allocate(val(n)) 163 | 164 | ! Each point is stored in a row 165 | ! Data is stored in columns (x, y, and z) 166 | do i = 1, n 167 | read(u,*) point(:,i), val(i) 168 | end do 169 | close(u) 170 | 171 | if (run_dmap .or. get_bandwidth) then 172 | 173 | distance = get_distance(point) 174 | 175 | if (get_bandwidth) then 176 | 177 | write(*,*) "Writing diffusion map bandwidth analysis to "//trim(bandwidth_file)//"..." 178 | ! Cycle through different values of the bandwidth. See Fig. S1 in https://www.pnas.org/cgi/doi/10.1073/pnas.1003293107 179 | open(newunit=u, file=trim(bandwidth_file)) 180 | do i = logbandwidth_l, logbandwidth_u 181 | bandwidth = exp(dble(i)) 182 | similarity = gauss_similarity(distance, bandwidth) 183 | write(u,"(i0,f12.6)") i, log(sum(similarity)) 184 | end do 185 | close(u) 186 | 187 | else 188 | 189 | write(*,*) "Performing diffusion map calculation..." 190 | write(*,*) "bandwidth = ", bandwidth 191 | write(*,*) "time = ", time 192 | write(*,*) "dimensions = ", dimensions 193 | call dm%run(distance, bandwidth, time, dimensions) 194 | 195 | write(*,*) "Writing diffusion map eigenvalues to "//trim(evalues_file)//"..." 196 | open(newunit=u, file=trim(evalues_file)) 197 | write(u,"(f12.6)") dm%eval 198 | close(u) 199 | 200 | write(*,*) "Writing diffusion map eigenectors to "//trim(evects_file)//"..." 201 | open(newunit=u, file=trim(evects_file)) 202 | write(n_char,'(i0)') max_output 203 | format_string = "("//trim(n_char)//"f12.6)" 204 | write(u,format_string) transpose(dm%evec) 205 | close(u) 206 | 207 | write(*,*) "Writing diffusion map to "//trim(diffusionmap_file)//"..." 208 | open(newunit=u, file=trim(diffusionmap_file)) 209 | write(u,"(a)") "# First column is original location on swiss roll" 210 | write(u,"(a)") "# Next columns are points in diffusion space" 211 | write(u,"(a)") "# Note that first (trivial) eigenvector not used." 212 | write(u,"(a)") "# In gnuplot to plot the first dimensions try:" 213 | write(u,"(a)") "# plot 'dmap.dat' u 2:3:1 w points palette" 214 | write(u,"(a,f12.6)") "# time = ", time 215 | write(u,"(a,f12.6)") "# bandwidth = ", bandwidth 216 | format_string = "("//trim(n_char)//"f12.6)" 217 | do i = 1, n 218 | write(u,"(f12.6)", advance="no") val(i) 219 | do j = 1, dimensions 220 | write(u,"(f12.6)", advance="no") dm%map(i,j) 221 | end do 222 | write(u,*) 223 | end do 224 | close(u) 225 | 226 | end if 227 | 228 | end if 229 | 230 | if (run_pca) then 231 | 232 | write(*,*) "Performing PCA..." 233 | call pca%run(point) 234 | 235 | write(*,*) "Writing PCA eigenvalues to "//trim(pca_evalues_file)//"..." 236 | open(newunit=u, file=trim(pca_evalues_file)) 237 | write(u,"(a)") "# Eigenvalues" 238 | write(u,"(f12.6)") pca%eval 239 | write(u,"(a)") "# Contribution" 240 | write(u,"(f12.6)") pca%contrib 241 | write(u,"(a)") "# Cumulative contribution" 242 | write(u,"(f12.6)") pca%cumul_contrib 243 | close(u) 244 | 245 | write(*,*) "Writing PCA eigenvectors to "//trim(pca_evects_file)//"..." 246 | open(newunit=u, file=trim(pca_evects_file)) 247 | write(n_char,'(i0)') dimensions 248 | format_string = "("//trim(n_char)//"f12.6)" 249 | write(u,format_string) transpose(pca%evec) 250 | close(u) 251 | 252 | write(*,*) "Writing PCA data to "//trim(pca_file)//"..." 253 | open(newunit=u, file=trim(pca_file)) 254 | ! NOTE: dimensions for pca data are reversed from those of the diffusion map 255 | do j = 1, n 256 | write(u,"(f12.6)", advance="no") val(j) 257 | do i = 1, dimensions 258 | write(u,"(f12.6)", advance="no") pca%x(i,j) 259 | end do 260 | write(u,*) 261 | end do 262 | close(u) 263 | 264 | end if 265 | 266 | end program main 267 | -------------------------------------------------------------------------------- /src/princ_comp.f90: -------------------------------------------------------------------------------- 1 | module princ_comp 2 | 3 | implicit none 4 | type, public :: princ_comp_type 5 | real(8), allocatable :: cov(:,:), contrib(:), cumul_contrib(:), evec(:,:), eval(:), x(:,:) 6 | contains 7 | procedure :: run => princ_comp_run 8 | end type 9 | 10 | contains 11 | 12 | subroutine get_evect_sym(cov, evect, evalues) 13 | 14 | implicit none 15 | character :: jobz = 'V', uplo = 'U' 16 | real(8), allocatable :: work(:), a(:,:) 17 | real(8), allocatable, intent(inout) :: evalues(:), evect(:,:), cov(:,:) 18 | integer, allocatable :: order(:) 19 | integer :: i, lwork, lda, n, info 20 | logical, allocatable :: mask(:) 21 | 22 | interface 23 | subroutine dsyev(jobz, uplo, n, a, lda, w, work, lwork, info) 24 | character, intent(in) :: jobz, uplo 25 | integer, intent(in) :: n, lda, lwork 26 | integer, intent(out) :: info 27 | real(8), intent(inout) :: a(lda,*) 28 | real(8), intent(out) :: w(*), work(*) 29 | end subroutine 30 | end interface 31 | 32 | a = cov 33 | n = size(a,1) 34 | lwork = 26*n 35 | lda = n 36 | allocate(work(lwork), evect(n,n), evalues(n)) 37 | 38 | ! Get eigenvectors and eigenvalues (LAPACK) 39 | ! matrix "a" is returned as the eigenvectors 40 | call dsyev(jobz, uplo, n, a, lda, evalues, work, lwork, info) 41 | if(info .ne. 0) then 42 | write(*,*) "ERROR: Eigenvector calculation failed." 43 | end if 44 | 45 | ! Sort the evalues in descending so we can use the top components for later calcs 46 | allocate(order(N), mask(n)) 47 | mask = .true. 48 | do i = lbound(evalues,1), ubound(evalues,1) 49 | order(i) = maxloc(evalues,1,mask) 50 | mask(order(i)) = .false. 51 | end do 52 | 53 | evalues = evalues(order) 54 | evect = a(:,order) 55 | 56 | end subroutine get_evect_sym 57 | 58 | subroutine princ_comp_run(this, indata) 59 | 60 | integer :: ncomp, ndata, i, j 61 | real(8), allocatable, intent(inout) :: indata(:,:) 62 | class(princ_comp_type), intent(inout) :: this 63 | 64 | ncomp = size(indata,1) 65 | ndata = size(indata,2) 66 | 67 | ! mean adjust 68 | do i = 1, ncomp 69 | indata(i,:) = indata(i,:) - sum(indata(i,:))/dble(ndata) 70 | end do 71 | 72 | allocate(this%cov(ncomp, ncomp)) 73 | allocate(this%contrib(ncomp)) 74 | allocate(this%cumul_contrib(ncomp)) 75 | 76 | ! get covariance matrix 77 | do i = 1, ncomp 78 | do j = 1, ncomp 79 | this%cov(i,j) = dot_product(indata(j,:), indata(i,:)) 80 | this%cov(j,i) = this%cov(i,j) 81 | end do 82 | end do 83 | 84 | this%cov = this%cov / dble(ndata - 1) 85 | 86 | call get_evect_sym(this%cov, this%evec, this%eval) 87 | 88 | this%contrib = this%eval / sum(this%eval) 89 | 90 | do i = 1, ncomp 91 | this%cumul_contrib(i) = sum(this%contrib(1:i)) 92 | end do 93 | 94 | this%x = matmul(transpose(this%evec), indata) 95 | 96 | end subroutine princ_comp_run 97 | 98 | end module princ_comp 99 | --------------------------------------------------------------------------------