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stat: added CCA

Browse Source 
merged PCA in with CCA into pca_cca.go
added the helper svdFactorizeCentered,
added Boston and Car datasets for use in tests and examples.

Comment Improvements

go fmt

More Improvements.

made BostonData bostonData

by moving it to stat_test, moved cca_test.go into stat_test as well to
accomodate this.

Merged pca and cca

into pca_cca.go

Minor fixes

Capitalisation mostly

Full Stop

CC type

also adjusted some of the calculations to require less allocation

Updated Tests

also moved around some scaling of columns,
and updated comments

left, right

and some shuffling

Mostly doc fixes

Improvements to documentation

tidied comments, and removed approxEqual
in exchange for floats.EqualApprox.

More documentation improvement

also american spelling of centre

second pass

go fmt

CCA description

View -> Slice

and PrincipalComponents doc correction.
This commit is contained in:
Armadilloa16
2016-08-29 11:08:22 +09:30
parent 2712a51eef
commit c6af72d266
6 changed files with 1543 additions and 77 deletions
Download Patch File Download Diff File Expand all files Collapse all files

531
boston_data_test.go Normal file
View File

@@ -0,0 +1,531 @@
// Copyright ©2016 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat_test
import "github.com/gonum/matrix/mat64"
// Boston Housing Data of Harrison and Rubinfeld (1978)
// http://dx.doi.org/10.1016/0095-0696(78)90006-2
// http://lib.stat.cmu.edu/datasets/boston
// Columns are;
// per capita crime rate by town,
// proportion of non-retail business acres per town,
// nitric oxide concentration (parts per 10 million),
// weighted distances to Boston employment centers,
// index of accessibility to radial highways,
// pupil-teacher ratio by town,
// proportion of blacks by town,
// average number of rooms per dwelling,
// proportion of owner-occupied units built prior to 1940,
// full-value property-tax rate per $10000,
// median value of owner-occupied homes in $1000s.
var bostonData = mat64.NewDense(506, 11, []float64{
0.00632, 2.31000, 0.53800, 4.09000, 1.00000, 15.30000, 396.90000, 6.57500, 65.20000, 296.00000, 24.00000,
0.02731, 7.07000, 0.46900, 4.96710, 2.00000, 17.80000, 396.90000, 6.42100, 78.90000, 242.00000, 21.60000,
0.02729, 7.07000, 0.46900, 4.96710, 2.00000, 17.80000, 392.83000, 7.18500, 61.10000, 242.00000, 34.70000,
0.03237, 2.18000, 0.45800, 6.06220, 3.00000, 18.70000, 394.63000, 6.99800, 45.80000, 222.00000, 33.40000,
0.06905, 2.18000, 0.45800, 6.06220, 3.00000, 18.70000, 396.90000, 7.14700, 54.20000, 222.00000, 36.20000,
0.02985, 2.18000, 0.45800, 6.06220, 3.00000, 18.70000, 394.12000, 6.43000, 58.70000, 222.00000, 28.70000,
0.08829, 7.87000, 0.52400, 5.56050, 5.00000, 15.20000, 395.60000, 6.01200, 66.60000, 311.00000, 22.90000,
0.14455, 7.87000, 0.52400, 5.95050, 5.00000, 15.20000, 396.90000, 6.17200, 96.10000, 311.00000, 27.10000,
0.21124, 7.87000, 0.52400, 6.08210, 5.00000, 15.20000, 386.63000, 5.63100, 100.00000, 311.00000, 16.50000,
0.17004, 7.87000, 0.52400, 6.59210, 5.00000, 15.20000, 386.71000, 6.00400, 85.90000, 311.00000, 18.90000,
0.22489, 7.87000, 0.52400, 6.34670, 5.00000, 15.20000, 392.52000, 6.37700, 94.30000, 311.00000, 15.00000,
0.11747, 7.87000, 0.52400, 6.22670, 5.00000, 15.20000, 396.90000, 6.00900, 82.90000, 311.00000, 18.90000,
0.09378, 7.87000, 0.52400, 5.45090, 5.00000, 15.20000, 390.50000, 5.88900, 39.00000, 311.00000, 21.70000,
0.62976, 8.14000, 0.53800, 4.70750, 4.00000, 21.00000, 396.90000, 5.94900, 61.80000, 307.00000, 20.40000,
0.63796, 8.14000, 0.53800, 4.46190, 4.00000, 21.00000, 380.02000, 6.09600, 84.50000, 307.00000, 18.20000,
0.62739, 8.14000, 0.53800, 4.49860, 4.00000, 21.00000, 395.62000, 5.83400, 56.50000, 307.00000, 19.90000,
1.05393, 8.14000, 0.53800, 4.49860, 4.00000, 21.00000, 386.85000, 5.93500, 29.30000, 307.00000, 23.10000,
0.78420, 8.14000, 0.53800, 4.25790, 4.00000, 21.00000, 386.75000, 5.99000, 81.70000, 307.00000, 17.50000,
0.80271, 8.14000, 0.53800, 3.79650, 4.00000, 21.00000, 288.99000, 5.45600, 36.60000, 307.00000, 20.20000,
0.72580, 8.14000, 0.53800, 3.79650, 4.00000, 21.00000, 390.95000, 5.72700, 69.50000, 307.00000, 18.20000,
1.25179, 8.14000, 0.53800, 3.79790, 4.00000, 21.00000, 376.57000, 5.57000, 98.10000, 307.00000, 13.60000,
0.85204, 8.14000, 0.53800, 4.01230, 4.00000, 21.00000, 392.53000, 5.96500, 89.20000, 307.00000, 19.60000,
1.23247, 8.14000, 0.53800, 3.97690, 4.00000, 21.00000, 396.90000, 6.14200, 91.70000, 307.00000, 15.20000,
0.98843, 8.14000, 0.53800, 4.09520, 4.00000, 21.00000, 394.54000, 5.81300, 100.00000, 307.00000, 14.50000,
0.75026, 8.14000, 0.53800, 4.39960, 4.00000, 21.00000, 394.33000, 5.92400, 94.10000, 307.00000, 15.60000,
0.84054, 8.14000, 0.53800, 4.45460, 4.00000, 21.00000, 303.42000, 5.59900, 85.70000, 307.00000, 13.90000,
0.67191, 8.14000, 0.53800, 4.68200, 4.00000, 21.00000, 376.88000, 5.81300, 90.30000, 307.00000, 16.60000,
0.95577, 8.14000, 0.53800, 4.45340, 4.00000, 21.00000, 306.38000, 6.04700, 88.80000, 307.00000, 14.80000,
0.77299, 8.14000, 0.53800, 4.45470, 4.00000, 21.00000, 387.94000, 6.49500, 94.40000, 307.00000, 18.40000,
1.00245, 8.14000, 0.53800, 4.23900, 4.00000, 21.00000, 380.23000, 6.67400, 87.30000, 307.00000, 21.00000,
1.13081, 8.14000, 0.53800, 4.23300, 4.00000, 21.00000, 360.17000, 5.71300, 94.10000, 307.00000, 12.70000,
1.35472, 8.14000, 0.53800, 4.17500, 4.00000, 21.00000, 376.73000, 6.07200, 100.00000, 307.00000, 14.50000,
1.38799, 8.14000, 0.53800, 3.99000, 4.00000, 21.00000, 232.60000, 5.95000, 82.00000, 307.00000, 13.20000,
1.15172, 8.14000, 0.53800, 3.78720, 4.00000, 21.00000, 358.77000, 5.70100, 95.00000, 307.00000, 13.10000,
1.61282, 8.14000, 0.53800, 3.75980, 4.00000, 21.00000, 248.31000, 6.09600, 96.90000, 307.00000, 13.50000,
0.06417, 5.96000, 0.49900, 3.36030, 5.00000, 19.20000, 396.90000, 5.93300, 68.20000, 279.00000, 18.90000,
0.09744, 5.96000, 0.49900, 3.37790, 5.00000, 19.20000, 377.56000, 5.84100, 61.40000, 279.00000, 20.00000,
0.08014, 5.96000, 0.49900, 3.93420, 5.00000, 19.20000, 396.90000, 5.85000, 41.50000, 279.00000, 21.00000,
0.17505, 5.96000, 0.49900, 3.84730, 5.00000, 19.20000, 393.43000, 5.96600, 30.20000, 279.00000, 24.70000,
0.02763, 2.95000, 0.42800, 5.40110, 3.00000, 18.30000, 395.63000, 6.59500, 21.80000, 252.00000, 30.80000,
0.03359, 2.95000, 0.42800, 5.40110, 3.00000, 18.30000, 395.62000, 7.02400, 15.80000, 252.00000, 34.90000,
0.12744, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 385.41000, 6.77000, 2.90000, 233.00000, 26.60000,
0.14150, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 383.37000, 6.16900, 6.60000, 233.00000, 25.30000,
0.15936, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 394.46000, 6.21100, 6.50000, 233.00000, 24.70000,
0.12269, 6.91000, 0.44800, 5.72090, 3.00000, 17.90000, 389.39000, 6.06900, 40.00000, 233.00000, 21.20000,
0.17142, 6.91000, 0.44800, 5.10040, 3.00000, 17.90000, 396.90000, 5.68200, 33.80000, 233.00000, 19.30000,
0.18836, 6.91000, 0.44800, 5.10040, 3.00000, 17.90000, 396.90000, 5.78600, 33.30000, 233.00000, 20.00000,
0.22927, 6.91000, 0.44800, 5.68940, 3.00000, 17.90000, 392.74000, 6.03000, 85.50000, 233.00000, 16.60000,
0.25387, 6.91000, 0.44800, 5.87000, 3.00000, 17.90000, 396.90000, 5.39900, 95.30000, 233.00000, 14.40000,
0.21977, 6.91000, 0.44800, 6.08770, 3.00000, 17.90000, 396.90000, 5.60200, 62.00000, 233.00000, 19.40000,
0.08873, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 395.56000, 5.96300, 45.70000, 243.00000, 19.70000,
0.04337, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 393.97000, 6.11500, 63.00000, 243.00000, 20.50000,
0.05360, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 396.90000, 6.51100, 21.10000, 243.00000, 25.00000,
0.04981, 5.64000, 0.43900, 6.81470, 4.00000, 16.80000, 396.90000, 5.99800, 21.40000, 243.00000, 23.40000,
0.01360, 4.00000, 0.41000, 7.31970, 3.00000, 21.10000, 396.90000, 5.88800, 47.60000, 469.00000, 18.90000,
0.01311, 1.22000, 0.40300, 8.69660, 5.00000, 17.90000, 395.93000, 7.24900, 21.90000, 226.00000, 35.40000,
0.02055, 0.74000, 0.41000, 9.18760, 2.00000, 17.30000, 396.90000, 6.38300, 35.70000, 313.00000, 24.70000,
0.01432, 1.32000, 0.41100, 8.32480, 5.00000, 15.10000, 392.90000, 6.81600, 40.50000, 256.00000, 31.60000,
0.15445, 5.13000, 0.45300, 7.81480, 8.00000, 19.70000, 390.68000, 6.14500, 29.20000, 284.00000, 23.30000,
0.10328, 5.13000, 0.45300, 6.93200, 8.00000, 19.70000, 396.90000, 5.92700, 47.20000, 284.00000, 19.60000,
0.14932, 5.13000, 0.45300, 7.22540, 8.00000, 19.70000, 395.11000, 5.74100, 66.20000, 284.00000, 18.70000,
0.17171, 5.13000, 0.45300, 6.81850, 8.00000, 19.70000, 378.08000, 5.96600, 93.40000, 284.00000, 16.00000,
0.11027, 5.13000, 0.45300, 7.22550, 8.00000, 19.70000, 396.90000, 6.45600, 67.80000, 284.00000, 22.20000,
0.12650, 5.13000, 0.45300, 7.98090, 8.00000, 19.70000, 395.58000, 6.76200, 43.40000, 284.00000, 25.00000,
0.01951, 1.38000, 0.41610, 9.22290, 3.00000, 18.60000, 393.24000, 7.10400, 59.50000, 216.00000, 33.00000,
0.03584, 3.37000, 0.39800, 6.61150, 4.00000, 16.10000, 396.90000, 6.29000, 17.80000, 337.00000, 23.50000,
0.04379, 3.37000, 0.39800, 6.61150, 4.00000, 16.10000, 396.90000, 5.78700, 31.10000, 337.00000, 19.40000,
0.05789, 6.07000, 0.40900, 6.49800, 4.00000, 18.90000, 396.21000, 5.87800, 21.40000, 345.00000, 22.00000,
0.13554, 6.07000, 0.40900, 6.49800, 4.00000, 18.90000, 396.90000, 5.59400, 36.80000, 345.00000, 17.40000,
0.12816, 6.07000, 0.40900, 6.49800, 4.00000, 18.90000, 396.90000, 5.88500, 33.00000, 345.00000, 20.90000,
0.08826, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 383.73000, 6.41700, 6.60000, 305.00000, 24.20000,
0.15876, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 376.94000, 5.96100, 17.50000, 305.00000, 21.70000,
0.09164, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 390.91000, 6.06500, 7.80000, 305.00000, 22.80000,
0.19539, 10.81000, 0.41300, 5.28730, 4.00000, 19.20000, 377.17000, 6.24500, 6.20000, 305.00000, 23.40000,
0.07896, 12.83000, 0.43700, 4.25150, 5.00000, 18.70000, 394.92000, 6.27300, 6.00000, 398.00000, 24.10000,
0.09512, 12.83000, 0.43700, 4.50260, 5.00000, 18.70000, 383.23000, 6.28600, 45.00000, 398.00000, 21.40000,
0.10153, 12.83000, 0.43700, 4.05220, 5.00000, 18.70000, 373.66000, 6.27900, 74.50000, 398.00000, 20.00000,
0.08707, 12.83000, 0.43700, 4.09050, 5.00000, 18.70000, 386.96000, 6.14000, 45.80000, 398.00000, 20.80000,
0.05646, 12.83000, 0.43700, 5.01410, 5.00000, 18.70000, 386.40000, 6.23200, 53.70000, 398.00000, 21.20000,
0.08387, 12.83000, 0.43700, 4.50260, 5.00000, 18.70000, 396.06000, 5.87400, 36.60000, 398.00000, 20.30000,
0.04113, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 396.90000, 6.72700, 33.50000, 281.00000, 28.00000,
0.04462, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 395.63000, 6.61900, 70.40000, 281.00000, 23.90000,
0.03659, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 396.90000, 6.30200, 32.20000, 281.00000, 24.80000,
0.03551, 4.86000, 0.42600, 5.40070, 4.00000, 19.00000, 390.64000, 6.16700, 46.70000, 281.00000, 22.90000,
0.05059, 4.49000, 0.44900, 4.77940, 3.00000, 18.50000, 396.90000, 6.38900, 48.00000, 247.00000, 23.90000,
0.05735, 4.49000, 0.44900, 4.43770, 3.00000, 18.50000, 392.30000, 6.63000, 56.10000, 247.00000, 26.60000,
0.05188, 4.49000, 0.44900, 4.42720, 3.00000, 18.50000, 395.99000, 6.01500, 45.10000, 247.00000, 22.50000,
0.07151, 4.49000, 0.44900, 3.74760, 3.00000, 18.50000, 395.15000, 6.12100, 56.80000, 247.00000, 22.20000,
0.05660, 3.41000, 0.48900, 3.42170, 2.00000, 17.80000, 396.90000, 7.00700, 86.30000, 270.00000, 23.60000,
0.05302, 3.41000, 0.48900, 3.41450, 2.00000, 17.80000, 396.06000, 7.07900, 63.10000, 270.00000, 28.70000,
0.04684, 3.41000, 0.48900, 3.09230, 2.00000, 17.80000, 392.18000, 6.41700, 66.10000, 270.00000, 22.60000,
0.03932, 3.41000, 0.48900, 3.09210, 2.00000, 17.80000, 393.55000, 6.40500, 73.90000, 270.00000, 22.00000,
0.04203, 15.04000, 0.46400, 3.66590, 4.00000, 18.20000, 395.01000, 6.44200, 53.60000, 270.00000, 22.90000,
0.02875, 15.04000, 0.46400, 3.66590, 4.00000, 18.20000, 396.33000, 6.21100, 28.90000, 270.00000, 25.00000,
0.04294, 15.04000, 0.46400, 3.61500, 4.00000, 18.20000, 396.90000, 6.24900, 77.30000, 270.00000, 20.60000,
0.12204, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 357.98000, 6.62500, 57.80000, 276.00000, 28.40000,
0.11504, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 391.83000, 6.16300, 69.60000, 276.00000, 21.40000,
0.12083, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 396.90000, 8.06900, 76.00000, 276.00000, 38.70000,
0.08187, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 393.53000, 7.82000, 36.90000, 276.00000, 43.80000,
0.06860, 2.89000, 0.44500, 3.49520, 2.00000, 18.00000, 396.90000, 7.41600, 62.50000, 276.00000, 33.20000,
0.14866, 8.56000, 0.52000, 2.77780, 5.00000, 20.90000, 394.76000, 6.72700, 79.90000, 384.00000, 27.50000,
0.11432, 8.56000, 0.52000, 2.85610, 5.00000, 20.90000, 395.58000, 6.78100, 71.30000, 384.00000, 26.50000,
0.22876, 8.56000, 0.52000, 2.71470, 5.00000, 20.90000, 70.80000, 6.40500, 85.40000, 384.00000, 18.60000,
0.21161, 8.56000, 0.52000, 2.71470, 5.00000, 20.90000, 394.47000, 6.13700, 87.40000, 384.00000, 19.30000,
0.13960, 8.56000, 0.52000, 2.42100, 5.00000, 20.90000, 392.69000, 6.16700, 90.00000, 384.00000, 20.10000,
0.13262, 8.56000, 0.52000, 2.10690, 5.00000, 20.90000, 394.05000, 5.85100, 96.70000, 384.00000, 19.50000,
0.17120, 8.56000, 0.52000, 2.21100, 5.00000, 20.90000, 395.67000, 5.83600, 91.90000, 384.00000, 19.50000,
0.13117, 8.56000, 0.52000, 2.12240, 5.00000, 20.90000, 387.69000, 6.12700, 85.20000, 384.00000, 20.40000,
0.12802, 8.56000, 0.52000, 2.43290, 5.00000, 20.90000, 395.24000, 6.47400, 97.10000, 384.00000, 19.80000,
0.26363, 8.56000, 0.52000, 2.54510, 5.00000, 20.90000, 391.23000, 6.22900, 91.20000, 384.00000, 19.40000,
0.10793, 8.56000, 0.52000, 2.77780, 5.00000, 20.90000, 393.49000, 6.19500, 54.40000, 384.00000, 21.70000,
0.10084, 10.01000, 0.54700, 2.67750, 6.00000, 17.80000, 395.59000, 6.71500, 81.60000, 432.00000, 22.80000,
0.12329, 10.01000, 0.54700, 2.35340, 6.00000, 17.80000, 394.95000, 5.91300, 92.90000, 432.00000, 18.80000,
0.22212, 10.01000, 0.54700, 2.54800, 6.00000, 17.80000, 396.90000, 6.09200, 95.40000, 432.00000, 18.70000,
0.14231, 10.01000, 0.54700, 2.25650, 6.00000, 17.80000, 388.74000, 6.25400, 84.20000, 432.00000, 18.50000,
0.17134, 10.01000, 0.54700, 2.46310, 6.00000, 17.80000, 344.91000, 5.92800, 88.20000, 432.00000, 18.30000,
0.13158, 10.01000, 0.54700, 2.73010, 6.00000, 17.80000, 393.30000, 6.17600, 72.50000, 432.00000, 21.20000,
0.15098, 10.01000, 0.54700, 2.74740, 6.00000, 17.80000, 394.51000, 6.02100, 82.60000, 432.00000, 19.20000,
0.13058, 10.01000, 0.54700, 2.47750, 6.00000, 17.80000, 338.63000, 5.87200, 73.10000, 432.00000, 20.40000,
0.14476, 10.01000, 0.54700, 2.75920, 6.00000, 17.80000, 391.50000, 5.73100, 65.20000, 432.00000, 19.30000,
0.06899, 25.65000, 0.58100, 2.25770, 2.00000, 19.10000, 389.15000, 5.87000, 69.70000, 188.00000, 22.00000,
0.07165, 25.65000, 0.58100, 2.19740, 2.00000, 19.10000, 377.67000, 6.00400, 84.10000, 188.00000, 20.30000,
0.09299, 25.65000, 0.58100, 2.08690, 2.00000, 19.10000, 378.09000, 5.96100, 92.90000, 188.00000, 20.50000,
0.15038, 25.65000, 0.58100, 1.94440, 2.00000, 19.10000, 370.31000, 5.85600, 97.00000, 188.00000, 17.30000,
0.09849, 25.65000, 0.58100, 2.00630, 2.00000, 19.10000, 379.38000, 5.87900, 95.80000, 188.00000, 18.80000,
0.16902, 25.65000, 0.58100, 1.99290, 2.00000, 19.10000, 385.02000, 5.98600, 88.40000, 188.00000, 21.40000,
0.38735, 25.65000, 0.58100, 1.75720, 2.00000, 19.10000, 359.29000, 5.61300, 95.60000, 188.00000, 15.70000,
0.25915, 21.89000, 0.62400, 1.78830, 4.00000, 21.20000, 392.11000, 5.69300, 96.00000, 437.00000, 16.20000,
0.32543, 21.89000, 0.62400, 1.81250, 4.00000, 21.20000, 396.90000, 6.43100, 98.80000, 437.00000, 18.00000,
0.88125, 21.89000, 0.62400, 1.97990, 4.00000, 21.20000, 396.90000, 5.63700, 94.70000, 437.00000, 14.30000,
0.34006, 21.89000, 0.62400, 2.11850, 4.00000, 21.20000, 395.04000, 6.45800, 98.90000, 437.00000, 19.20000,
1.19294, 21.89000, 0.62400, 2.27100, 4.00000, 21.20000, 396.90000, 6.32600, 97.70000, 437.00000, 19.60000,
0.59005, 21.89000, 0.62400, 2.32740, 4.00000, 21.20000, 385.76000, 6.37200, 97.90000, 437.00000, 23.00000,
0.32982, 21.89000, 0.62400, 2.46990, 4.00000, 21.20000, 388.69000, 5.82200, 95.40000, 437.00000, 18.40000,
0.97617, 21.89000, 0.62400, 2.34600, 4.00000, 21.20000, 262.76000, 5.75700, 98.40000, 437.00000, 15.60000,
0.55778, 21.89000, 0.62400, 2.11070, 4.00000, 21.20000, 394.67000, 6.33500, 98.20000, 437.00000, 18.10000,
0.32264, 21.89000, 0.62400, 1.96690, 4.00000, 21.20000, 378.25000, 5.94200, 93.50000, 437.00000, 17.40000,
0.35233, 21.89000, 0.62400, 1.84980, 4.00000, 21.20000, 394.08000, 6.45400, 98.40000, 437.00000, 17.10000,
0.24980, 21.89000, 0.62400, 1.66860, 4.00000, 21.20000, 392.04000, 5.85700, 98.20000, 437.00000, 13.30000,
0.54452, 21.89000, 0.62400, 1.66870, 4.00000, 21.20000, 396.90000, 6.15100, 97.90000, 437.00000, 17.80000,
0.29090, 21.89000, 0.62400, 1.61190, 4.00000, 21.20000, 388.08000, 6.17400, 93.60000, 437.00000, 14.00000,
1.62864, 21.89000, 0.62400, 1.43940, 4.00000, 21.20000, 396.90000, 5.01900, 100.00000, 437.00000, 14.40000,
3.32105, 19.58000, 0.87100, 1.32160, 5.00000, 14.70000, 396.90000, 5.40300, 100.00000, 403.00000, 13.40000,
4.09740, 19.58000, 0.87100, 1.41180, 5.00000, 14.70000, 396.90000, 5.46800, 100.00000, 403.00000, 15.60000,
2.77974, 19.58000, 0.87100, 1.34590, 5.00000, 14.70000, 396.90000, 4.90300, 97.80000, 403.00000, 11.80000,
2.37934, 19.58000, 0.87100, 1.41910, 5.00000, 14.70000, 172.91000, 6.13000, 100.00000, 403.00000, 13.80000,
2.15505, 19.58000, 0.87100, 1.51660, 5.00000, 14.70000, 169.27000, 5.62800, 100.00000, 403.00000, 15.60000,
2.36862, 19.58000, 0.87100, 1.46080, 5.00000, 14.70000, 391.71000, 4.92600, 95.70000, 403.00000, 14.60000,
2.33099, 19.58000, 0.87100, 1.52960, 5.00000, 14.70000, 356.99000, 5.18600, 93.80000, 403.00000, 17.80000,
2.73397, 19.58000, 0.87100, 1.52570, 5.00000, 14.70000, 351.85000, 5.59700, 94.90000, 403.00000, 15.40000,
1.65660, 19.58000, 0.87100, 1.61800, 5.00000, 14.70000, 372.80000, 6.12200, 97.30000, 403.00000, 21.50000,
1.49632, 19.58000, 0.87100, 1.59160, 5.00000, 14.70000, 341.60000, 5.40400, 100.00000, 403.00000, 19.60000,
1.12658, 19.58000, 0.87100, 1.61020, 5.00000, 14.70000, 343.28000, 5.01200, 88.00000, 403.00000, 15.30000,
2.14918, 19.58000, 0.87100, 1.62320, 5.00000, 14.70000, 261.95000, 5.70900, 98.50000, 403.00000, 19.40000,
1.41385, 19.58000, 0.87100, 1.74940, 5.00000, 14.70000, 321.02000, 6.12900, 96.00000, 403.00000, 17.00000,
3.53501, 19.58000, 0.87100, 1.74550, 5.00000, 14.70000, 88.01000, 6.15200, 82.60000, 403.00000, 15.60000,
2.44668, 19.58000, 0.87100, 1.73640, 5.00000, 14.70000, 88.63000, 5.27200, 94.00000, 403.00000, 13.10000,
1.22358, 19.58000, 0.60500, 1.87730, 5.00000, 14.70000, 363.43000, 6.94300, 97.40000, 403.00000, 41.30000,
1.34284, 19.58000, 0.60500, 1.75730, 5.00000, 14.70000, 353.89000, 6.06600, 100.00000, 403.00000, 24.30000,
1.42502, 19.58000, 0.87100, 1.76590, 5.00000, 14.70000, 364.31000, 6.51000, 100.00000, 403.00000, 23.30000,
1.27346, 19.58000, 0.60500, 1.79840, 5.00000, 14.70000, 338.92000, 6.25000, 92.60000, 403.00000, 27.00000,
1.46336, 19.58000, 0.60500, 1.97090, 5.00000, 14.70000, 374.43000, 7.48900, 90.80000, 403.00000, 50.00000,
1.83377, 19.58000, 0.60500, 2.04070, 5.00000, 14.70000, 389.61000, 7.80200, 98.20000, 403.00000, 50.00000,
1.51902, 19.58000, 0.60500, 2.16200, 5.00000, 14.70000, 388.45000, 8.37500, 93.90000, 403.00000, 50.00000,
2.24236, 19.58000, 0.60500, 2.42200, 5.00000, 14.70000, 395.11000, 5.85400, 91.80000, 403.00000, 22.70000,
2.92400, 19.58000, 0.60500, 2.28340, 5.00000, 14.70000, 240.16000, 6.10100, 93.00000, 403.00000, 25.00000,
2.01019, 19.58000, 0.60500, 2.04590, 5.00000, 14.70000, 369.30000, 7.92900, 96.20000, 403.00000, 50.00000,
1.80028, 19.58000, 0.60500, 2.42590, 5.00000, 14.70000, 227.61000, 5.87700, 79.20000, 403.00000, 23.80000,
2.30040, 19.58000, 0.60500, 2.10000, 5.00000, 14.70000, 297.09000, 6.31900, 96.10000, 403.00000, 23.80000,
2.44953, 19.58000, 0.60500, 2.26250, 5.00000, 14.70000, 330.04000, 6.40200, 95.20000, 403.00000, 22.30000,
1.20742, 19.58000, 0.60500, 2.42590, 5.00000, 14.70000, 292.29000, 5.87500, 94.60000, 403.00000, 17.40000,
2.31390, 19.58000, 0.60500, 2.38870, 5.00000, 14.70000, 348.13000, 5.88000, 97.30000, 403.00000, 19.10000,
0.13914, 4.05000, 0.51000, 2.59610, 5.00000, 16.60000, 396.90000, 5.57200, 88.50000, 296.00000, 23.10000,
0.09178, 4.05000, 0.51000, 2.64630, 5.00000, 16.60000, 395.50000, 6.41600, 84.10000, 296.00000, 23.60000,
0.08447, 4.05000, 0.51000, 2.70190, 5.00000, 16.60000, 393.23000, 5.85900, 68.70000, 296.00000, 22.60000,
0.06664, 4.05000, 0.51000, 3.13230, 5.00000, 16.60000, 390.96000, 6.54600, 33.10000, 296.00000, 29.40000,
0.07022, 4.05000, 0.51000, 3.55490, 5.00000, 16.60000, 393.23000, 6.02000, 47.20000, 296.00000, 23.20000,
0.05425, 4.05000, 0.51000, 3.31750, 5.00000, 16.60000, 395.60000, 6.31500, 73.40000, 296.00000, 24.60000,
0.06642, 4.05000, 0.51000, 2.91530, 5.00000, 16.60000, 391.27000, 6.86000, 74.40000, 296.00000, 29.90000,
0.05780, 2.46000, 0.48800, 2.82900, 3.00000, 17.80000, 396.90000, 6.98000, 58.40000, 193.00000, 37.20000,
0.06588, 2.46000, 0.48800, 2.74100, 3.00000, 17.80000, 395.56000, 7.76500, 83.30000, 193.00000, 39.80000,
0.06888, 2.46000, 0.48800, 2.59790, 3.00000, 17.80000, 396.90000, 6.14400, 62.20000, 193.00000, 36.20000,
0.09103, 2.46000, 0.48800, 2.70060, 3.00000, 17.80000, 394.12000, 7.15500, 92.20000, 193.00000, 37.90000,
0.10008, 2.46000, 0.48800, 2.84700, 3.00000, 17.80000, 396.90000, 6.56300, 95.60000, 193.00000, 32.50000,
0.08308, 2.46000, 0.48800, 2.98790, 3.00000, 17.80000, 391.00000, 5.60400, 89.80000, 193.00000, 26.40000,
0.06047, 2.46000, 0.48800, 3.27970, 3.00000, 17.80000, 387.11000, 6.15300, 68.80000, 193.00000, 29.60000,
0.05602, 2.46000, 0.48800, 3.19920, 3.00000, 17.80000, 392.63000, 7.83100, 53.60000, 193.00000, 50.00000,
0.07875, 3.44000, 0.43700, 3.78860, 5.00000, 15.20000, 393.87000, 6.78200, 41.10000, 398.00000, 32.00000,
0.12579, 3.44000, 0.43700, 4.56670, 5.00000, 15.20000, 382.84000, 6.55600, 29.10000, 398.00000, 29.80000,
0.08370, 3.44000, 0.43700, 4.56670, 5.00000, 15.20000, 396.90000, 7.18500, 38.90000, 398.00000, 34.90000,
0.09068, 3.44000, 0.43700, 6.47980, 5.00000, 15.20000, 377.68000, 6.95100, 21.50000, 398.00000, 37.00000,
0.06911, 3.44000, 0.43700, 6.47980, 5.00000, 15.20000, 389.71000, 6.73900, 30.80000, 398.00000, 30.50000,
0.08664, 3.44000, 0.43700, 6.47980, 5.00000, 15.20000, 390.49000, 7.17800, 26.30000, 398.00000, 36.40000,
0.02187, 2.93000, 0.40100, 6.21960, 1.00000, 15.60000, 393.37000, 6.80000, 9.90000, 265.00000, 31.10000,
0.01439, 2.93000, 0.40100, 6.21960, 1.00000, 15.60000, 376.70000, 6.60400, 18.80000, 265.00000, 29.10000,
0.01381, 0.46000, 0.42200, 5.64840, 4.00000, 14.40000, 394.23000, 7.87500, 32.00000, 255.00000, 50.00000,
0.04011, 1.52000, 0.40400, 7.30900, 2.00000, 12.60000, 396.90000, 7.28700, 34.10000, 329.00000, 33.30000,
0.04666, 1.52000, 0.40400, 7.30900, 2.00000, 12.60000, 354.31000, 7.10700, 36.60000, 329.00000, 30.30000,
0.03768, 1.52000, 0.40400, 7.30900, 2.00000, 12.60000, 392.20000, 7.27400, 38.30000, 329.00000, 34.60000,
0.03150, 1.47000, 0.40300, 7.65340, 3.00000, 17.00000, 396.90000, 6.97500, 15.30000, 402.00000, 34.90000,
0.01778, 1.47000, 0.40300, 7.65340, 3.00000, 17.00000, 384.30000, 7.13500, 13.90000, 402.00000, 32.90000,
0.03445, 2.03000, 0.41500, 6.27000, 2.00000, 14.70000, 393.77000, 6.16200, 38.40000, 348.00000, 24.10000,
0.02177, 2.03000, 0.41500, 6.27000, 2.00000, 14.70000, 395.38000, 7.61000, 15.70000, 348.00000, 42.30000,
0.03510, 2.68000, 0.41610, 5.11800, 4.00000, 14.70000, 392.78000, 7.85300, 33.20000, 224.00000, 48.50000,
0.02009, 2.68000, 0.41610, 5.11800, 4.00000, 14.70000, 390.55000, 8.03400, 31.90000, 224.00000, 50.00000,
0.13642, 10.59000, 0.48900, 3.94540, 4.00000, 18.60000, 396.90000, 5.89100, 22.30000, 277.00000, 22.60000,
0.22969, 10.59000, 0.48900, 4.35490, 4.00000, 18.60000, 394.87000, 6.32600, 52.50000, 277.00000, 24.40000,
0.25199, 10.59000, 0.48900, 4.35490, 4.00000, 18.60000, 389.43000, 5.78300, 72.70000, 277.00000, 22.50000,
0.13587, 10.59000, 0.48900, 4.23920, 4.00000, 18.60000, 381.32000, 6.06400, 59.10000, 277.00000, 24.40000,
0.43571, 10.59000, 0.48900, 3.87500, 4.00000, 18.60000, 396.90000, 5.34400, 100.00000, 277.00000, 20.00000,
0.17446, 10.59000, 0.48900, 3.87710, 4.00000, 18.60000, 393.25000, 5.96000, 92.10000, 277.00000, 21.70000,
0.37578, 10.59000, 0.48900, 3.66500, 4.00000, 18.60000, 395.24000, 5.40400, 88.60000, 277.00000, 19.30000,
0.21719, 10.59000, 0.48900, 3.65260, 4.00000, 18.60000, 390.94000, 5.80700, 53.80000, 277.00000, 22.40000,
0.14052, 10.59000, 0.48900, 3.94540, 4.00000, 18.60000, 385.81000, 6.37500, 32.30000, 277.00000, 28.10000,
0.28955, 10.59000, 0.48900, 3.58750, 4.00000, 18.60000, 348.93000, 5.41200, 9.80000, 277.00000, 23.70000,
0.19802, 10.59000, 0.48900, 3.94540, 4.00000, 18.60000, 393.63000, 6.18200, 42.40000, 277.00000, 25.00000,
0.04560, 13.89000, 0.55000, 3.11210, 5.00000, 16.40000, 392.80000, 5.88800, 56.00000, 276.00000, 23.30000,
0.07013, 13.89000, 0.55000, 3.42110, 5.00000, 16.40000, 392.78000, 6.64200, 85.10000, 276.00000, 28.70000,
0.11069, 13.89000, 0.55000, 2.88930, 5.00000, 16.40000, 396.90000, 5.95100, 93.80000, 276.00000, 21.50000,
0.11425, 13.89000, 0.55000, 3.36330, 5.00000, 16.40000, 393.74000, 6.37300, 92.40000, 276.00000, 23.00000,
0.35809, 6.20000, 0.50700, 2.86170, 8.00000, 17.40000, 391.70000, 6.95100, 88.50000, 307.00000, 26.70000,
0.40771, 6.20000, 0.50700, 3.04800, 8.00000, 17.40000, 395.24000, 6.16400, 91.30000, 307.00000, 21.70000,
0.62356, 6.20000, 0.50700, 3.27210, 8.00000, 17.40000, 390.39000, 6.87900, 77.70000, 307.00000, 27.50000,
0.61470, 6.20000, 0.50700, 3.27210, 8.00000, 17.40000, 396.90000, 6.61800, 80.80000, 307.00000, 30.10000,
0.31533, 6.20000, 0.50400, 2.89440, 8.00000, 17.40000, 385.05000, 8.26600, 78.30000, 307.00000, 44.80000,
0.52693, 6.20000, 0.50400, 2.89440, 8.00000, 17.40000, 382.00000, 8.72500, 83.00000, 307.00000, 50.00000,
0.38214, 6.20000, 0.50400, 3.21570, 8.00000, 17.40000, 387.38000, 8.04000, 86.50000, 307.00000, 37.60000,
0.41238, 6.20000, 0.50400, 3.21570, 8.00000, 17.40000, 372.08000, 7.16300, 79.90000, 307.00000, 31.60000,
0.29819, 6.20000, 0.50400, 3.37510, 8.00000, 17.40000, 377.51000, 7.68600, 17.00000, 307.00000, 46.70000,
0.44178, 6.20000, 0.50400, 3.37510, 8.00000, 17.40000, 380.34000, 6.55200, 21.40000, 307.00000, 31.50000,
0.53700, 6.20000, 0.50400, 3.67150, 8.00000, 17.40000, 378.35000, 5.98100, 68.10000, 307.00000, 24.30000,
0.46296, 6.20000, 0.50400, 3.67150, 8.00000, 17.40000, 376.14000, 7.41200, 76.90000, 307.00000, 31.70000,
0.57529, 6.20000, 0.50700, 3.83840, 8.00000, 17.40000, 385.91000, 8.33700, 73.30000, 307.00000, 41.70000,
0.33147, 6.20000, 0.50700, 3.65190, 8.00000, 17.40000, 378.95000, 8.24700, 70.40000, 307.00000, 48.30000,
0.44791, 6.20000, 0.50700, 3.65190, 8.00000, 17.40000, 360.20000, 6.72600, 66.50000, 307.00000, 29.00000,
0.33045, 6.20000, 0.50700, 3.65190, 8.00000, 17.40000, 376.75000, 6.08600, 61.50000, 307.00000, 24.00000,
0.52058, 6.20000, 0.50700, 4.14800, 8.00000, 17.40000, 388.45000, 6.63100, 76.50000, 307.00000, 25.10000,
0.51183, 6.20000, 0.50700, 4.14800, 8.00000, 17.40000, 390.07000, 7.35800, 71.60000, 307.00000, 31.50000,
0.08244, 4.93000, 0.42800, 6.18990, 6.00000, 16.60000, 379.41000, 6.48100, 18.50000, 300.00000, 23.70000,
0.09252, 4.93000, 0.42800, 6.18990, 6.00000, 16.60000, 383.78000, 6.60600, 42.20000, 300.00000, 23.30000,
0.11329, 4.93000, 0.42800, 6.33610, 6.00000, 16.60000, 391.25000, 6.89700, 54.30000, 300.00000, 22.00000,
0.10612, 4.93000, 0.42800, 6.33610, 6.00000, 16.60000, 394.62000, 6.09500, 65.10000, 300.00000, 20.10000,
0.10290, 4.93000, 0.42800, 7.03550, 6.00000, 16.60000, 372.75000, 6.35800, 52.90000, 300.00000, 22.20000,
0.12757, 4.93000, 0.42800, 7.03550, 6.00000, 16.60000, 374.71000, 6.39300, 7.80000, 300.00000, 23.70000,
0.20608, 5.86000, 0.43100, 7.95490, 7.00000, 19.10000, 372.49000, 5.59300, 76.50000, 330.00000, 17.60000,
0.19133, 5.86000, 0.43100, 7.95490, 7.00000, 19.10000, 389.13000, 5.60500, 70.20000, 330.00000, 18.50000,
0.33983, 5.86000, 0.43100, 8.05550, 7.00000, 19.10000, 390.18000, 6.10800, 34.90000, 330.00000, 24.30000,
0.19657, 5.86000, 0.43100, 8.05550, 7.00000, 19.10000, 376.14000, 6.22600, 79.20000, 330.00000, 20.50000,
0.16439, 5.86000, 0.43100, 7.82650, 7.00000, 19.10000, 374.71000, 6.43300, 49.10000, 330.00000, 24.50000,
0.19073, 5.86000, 0.43100, 7.82650, 7.00000, 19.10000, 393.74000, 6.71800, 17.50000, 330.00000, 26.20000,
0.14030, 5.86000, 0.43100, 7.39670, 7.00000, 19.10000, 396.28000, 6.48700, 13.00000, 330.00000, 24.40000,
0.21409, 5.86000, 0.43100, 7.39670, 7.00000, 19.10000, 377.07000, 6.43800, 8.90000, 330.00000, 24.80000,
0.08221, 5.86000, 0.43100, 8.90670, 7.00000, 19.10000, 386.09000, 6.95700, 6.80000, 330.00000, 29.60000,
0.36894, 5.86000, 0.43100, 8.90670, 7.00000, 19.10000, 396.90000, 8.25900, 8.40000, 330.00000, 42.80000,
0.04819, 3.64000, 0.39200, 9.22030, 1.00000, 16.40000, 392.89000, 6.10800, 32.00000, 315.00000, 21.90000,
0.03548, 3.64000, 0.39200, 9.22030, 1.00000, 16.40000, 395.18000, 5.87600, 19.10000, 315.00000, 20.90000,
0.01538, 3.75000, 0.39400, 6.33610, 3.00000, 15.90000, 386.34000, 7.45400, 34.20000, 244.00000, 44.00000,
0.61154, 3.97000, 0.64700, 1.80100, 5.00000, 13.00000, 389.70000, 8.70400, 86.90000, 264.00000, 50.00000,
0.66351, 3.97000, 0.64700, 1.89460, 5.00000, 13.00000, 383.29000, 7.33300, 100.00000, 264.00000, 36.00000,
0.65665, 3.97000, 0.64700, 2.01070, 5.00000, 13.00000, 391.93000, 6.84200, 100.00000, 264.00000, 30.10000,
0.54011, 3.97000, 0.64700, 2.11210, 5.00000, 13.00000, 392.80000, 7.20300, 81.80000, 264.00000, 33.80000,
0.53412, 3.97000, 0.64700, 2.13980, 5.00000, 13.00000, 388.37000, 7.52000, 89.40000, 264.00000, 43.10000,
0.52014, 3.97000, 0.64700, 2.28850, 5.00000, 13.00000, 386.86000, 8.39800, 91.50000, 264.00000, 48.80000,
0.82526, 3.97000, 0.64700, 2.07880, 5.00000, 13.00000, 393.42000, 7.32700, 94.50000, 264.00000, 31.00000,
0.55007, 3.97000, 0.64700, 1.93010, 5.00000, 13.00000, 387.89000, 7.20600, 91.60000, 264.00000, 36.50000,
0.76162, 3.97000, 0.64700, 1.98650, 5.00000, 13.00000, 392.40000, 5.56000, 62.80000, 264.00000, 22.80000,
0.78570, 3.97000, 0.64700, 2.13290, 5.00000, 13.00000, 384.07000, 7.01400, 84.60000, 264.00000, 30.70000,
0.57834, 3.97000, 0.57500, 2.42160, 5.00000, 13.00000, 384.54000, 8.29700, 67.00000, 264.00000, 50.00000,
0.54050, 3.97000, 0.57500, 2.87200, 5.00000, 13.00000, 390.30000, 7.47000, 52.60000, 264.00000, 43.50000,
0.09065, 6.96000, 0.46400, 3.91750, 3.00000, 18.60000, 391.34000, 5.92000, 61.50000, 223.00000, 20.70000,
0.29916, 6.96000, 0.46400, 4.42900, 3.00000, 18.60000, 388.65000, 5.85600, 42.10000, 223.00000, 21.10000,
0.16211, 6.96000, 0.46400, 4.42900, 3.00000, 18.60000, 396.90000, 6.24000, 16.30000, 223.00000, 25.20000,
0.11460, 6.96000, 0.46400, 3.91750, 3.00000, 18.60000, 394.96000, 6.53800, 58.70000, 223.00000, 24.40000,
0.22188, 6.96000, 0.46400, 4.36650, 3.00000, 18.60000, 390.77000, 7.69100, 51.80000, 223.00000, 35.20000,
0.05644, 6.41000, 0.44700, 4.07760, 4.00000, 17.60000, 396.90000, 6.75800, 32.90000, 254.00000, 32.40000,
0.09604, 6.41000, 0.44700, 4.26730, 4.00000, 17.60000, 396.90000, 6.85400, 42.80000, 254.00000, 32.00000,
0.10469, 6.41000, 0.44700, 4.78720, 4.00000, 17.60000, 389.25000, 7.26700, 49.00000, 254.00000, 33.20000,
0.06127, 6.41000, 0.44700, 4.86280, 4.00000, 17.60000, 393.45000, 6.82600, 27.60000, 254.00000, 33.10000,
0.07978, 6.41000, 0.44700, 4.14030, 4.00000, 17.60000, 396.90000, 6.48200, 32.10000, 254.00000, 29.10000,
0.21038, 3.33000, 0.44290, 4.10070, 5.00000, 14.90000, 396.90000, 6.81200, 32.20000, 216.00000, 35.10000,
0.03578, 3.33000, 0.44290, 4.69470, 5.00000, 14.90000, 387.31000, 7.82000, 64.50000, 216.00000, 45.40000,
0.03705, 3.33000, 0.44290, 5.24470, 5.00000, 14.90000, 392.23000, 6.96800, 37.20000, 216.00000, 35.40000,
0.06129, 3.33000, 0.44290, 5.21190, 5.00000, 14.90000, 377.07000, 7.64500, 49.70000, 216.00000, 46.00000,
0.01501, 1.21000, 0.40100, 5.88500, 1.00000, 13.60000, 395.52000, 7.92300, 24.80000, 198.00000, 50.00000,
0.00906, 2.97000, 0.40000, 7.30730, 1.00000, 15.30000, 394.72000, 7.08800, 20.80000, 285.00000, 32.20000,
0.01096, 2.25000, 0.38900, 7.30730, 1.00000, 15.30000, 394.72000, 6.45300, 31.90000, 300.00000, 22.00000,
0.01965, 1.76000, 0.38500, 9.08920, 1.00000, 18.20000, 341.60000, 6.23000, 31.50000, 241.00000, 20.10000,
0.03871, 5.32000, 0.40500, 7.31720, 6.00000, 16.60000, 396.90000, 6.20900, 31.30000, 293.00000, 23.20000,
0.04590, 5.32000, 0.40500, 7.31720, 6.00000, 16.60000, 396.90000, 6.31500, 45.60000, 293.00000, 22.30000,
0.04297, 5.32000, 0.40500, 7.31720, 6.00000, 16.60000, 371.72000, 6.56500, 22.90000, 293.00000, 24.80000,
0.03502, 4.95000, 0.41100, 5.11670, 4.00000, 19.20000, 396.90000, 6.86100, 27.90000, 245.00000, 28.50000,
0.07886, 4.95000, 0.41100, 5.11670, 4.00000, 19.20000, 396.90000, 7.14800, 27.70000, 245.00000, 37.30000,
0.03615, 4.95000, 0.41100, 5.11670, 4.00000, 19.20000, 396.90000, 6.63000, 23.40000, 245.00000, 27.90000,
0.08265, 13.92000, 0.43700, 5.50270, 4.00000, 16.00000, 396.90000, 6.12700, 18.40000, 289.00000, 23.90000,
0.08199, 13.92000, 0.43700, 5.50270, 4.00000, 16.00000, 396.90000, 6.00900, 42.30000, 289.00000, 21.70000,
0.12932, 13.92000, 0.43700, 5.96040, 4.00000, 16.00000, 396.90000, 6.67800, 31.10000, 289.00000, 28.60000,
0.05372, 13.92000, 0.43700, 5.96040, 4.00000, 16.00000, 392.85000, 6.54900, 51.00000, 289.00000, 27.10000,
0.14103, 13.92000, 0.43700, 6.32000, 4.00000, 16.00000, 396.90000, 5.79000, 58.00000, 289.00000, 20.30000,
0.06466, 2.24000, 0.40000, 7.82780, 5.00000, 14.80000, 368.24000, 6.34500, 20.10000, 358.00000, 22.50000,
0.05561, 2.24000, 0.40000, 7.82780, 5.00000, 14.80000, 371.58000, 7.04100, 10.00000, 358.00000, 29.00000,
0.04417, 2.24000, 0.40000, 7.82780, 5.00000, 14.80000, 390.86000, 6.87100, 47.40000, 358.00000, 24.80000,
0.03537, 6.09000, 0.43300, 5.49170, 7.00000, 16.10000, 395.75000, 6.59000, 40.40000, 329.00000, 22.00000,
0.09266, 6.09000, 0.43300, 5.49170, 7.00000, 16.10000, 383.61000, 6.49500, 18.40000, 329.00000, 26.40000,
0.10000, 6.09000, 0.43300, 5.49170, 7.00000, 16.10000, 390.43000, 6.98200, 17.70000, 329.00000, 33.10000,
0.05515, 2.18000, 0.47200, 4.02200, 7.00000, 18.40000, 393.68000, 7.23600, 41.10000, 222.00000, 36.10000,
0.05479, 2.18000, 0.47200, 3.37000, 7.00000, 18.40000, 393.36000, 6.61600, 58.10000, 222.00000, 28.40000,
0.07503, 2.18000, 0.47200, 3.09920, 7.00000, 18.40000, 396.90000, 7.42000, 71.90000, 222.00000, 33.40000,
0.04932, 2.18000, 0.47200, 3.18270, 7.00000, 18.40000, 396.90000, 6.84900, 70.30000, 222.00000, 28.20000,
0.49298, 9.90000, 0.54400, 3.31750, 4.00000, 18.40000, 396.90000, 6.63500, 82.50000, 304.00000, 22.80000,
0.34940, 9.90000, 0.54400, 3.10250, 4.00000, 18.40000, 396.24000, 5.97200, 76.70000, 304.00000, 20.30000,
2.63548, 9.90000, 0.54400, 2.51940, 4.00000, 18.40000, 350.45000, 4.97300, 37.80000, 304.00000, 16.10000,
0.79041, 9.90000, 0.54400, 2.64030, 4.00000, 18.40000, 396.90000, 6.12200, 52.80000, 304.00000, 22.10000,
0.26169, 9.90000, 0.54400, 2.83400, 4.00000, 18.40000, 396.30000, 6.02300, 90.40000, 304.00000, 19.40000,
0.26938, 9.90000, 0.54400, 3.26280, 4.00000, 18.40000, 393.39000, 6.26600, 82.80000, 304.00000, 21.60000,
0.36920, 9.90000, 0.54400, 3.60230, 4.00000, 18.40000, 395.69000, 6.56700, 87.30000, 304.00000, 23.80000,
0.25356, 9.90000, 0.54400, 3.94500, 4.00000, 18.40000, 396.42000, 5.70500, 77.70000, 304.00000, 16.20000,
0.31827, 9.90000, 0.54400, 3.99860, 4.00000, 18.40000, 390.70000, 5.91400, 83.20000, 304.00000, 17.80000,
0.24522, 9.90000, 0.54400, 4.03170, 4.00000, 18.40000, 396.90000, 5.78200, 71.70000, 304.00000, 19.80000,
0.40202, 9.90000, 0.54400, 3.53250, 4.00000, 18.40000, 395.21000, 6.38200, 67.20000, 304.00000, 23.10000,
0.47547, 9.90000, 0.54400, 4.00190, 4.00000, 18.40000, 396.23000, 6.11300, 58.80000, 304.00000, 21.00000,
0.16760, 7.38000, 0.49300, 4.54040, 5.00000, 19.60000, 396.90000, 6.42600, 52.30000, 287.00000, 23.80000,
0.18159, 7.38000, 0.49300, 4.54040, 5.00000, 19.60000, 396.90000, 6.37600, 54.30000, 287.00000, 23.10000,
0.35114, 7.38000, 0.49300, 4.72110, 5.00000, 19.60000, 396.90000, 6.04100, 49.90000, 287.00000, 20.40000,
0.28392, 7.38000, 0.49300, 4.72110, 5.00000, 19.60000, 391.13000, 5.70800, 74.30000, 287.00000, 18.50000,
0.34109, 7.38000, 0.49300, 4.72110, 5.00000, 19.60000, 396.90000, 6.41500, 40.10000, 287.00000, 25.00000,
0.19186, 7.38000, 0.49300, 5.41590, 5.00000, 19.60000, 393.68000, 6.43100, 14.70000, 287.00000, 24.60000,
0.30347, 7.38000, 0.49300, 5.41590, 5.00000, 19.60000, 396.90000, 6.31200, 28.90000, 287.00000, 23.00000,
0.24103, 7.38000, 0.49300, 5.41590, 5.00000, 19.60000, 396.90000, 6.08300, 43.70000, 287.00000, 22.20000,
0.06617, 3.24000, 0.46000, 5.21460, 4.00000, 16.90000, 382.44000, 5.86800, 25.80000, 430.00000, 19.30000,
0.06724, 3.24000, 0.46000, 5.21460, 4.00000, 16.90000, 375.21000, 6.33300, 17.20000, 430.00000, 22.60000,
0.04544, 3.24000, 0.46000, 5.87360, 4.00000, 16.90000, 368.57000, 6.14400, 32.20000, 430.00000, 19.80000,
0.05023, 6.06000, 0.43790, 6.64070, 1.00000, 16.90000, 394.02000, 5.70600, 28.40000, 304.00000, 17.10000,
0.03466, 6.06000, 0.43790, 6.64070, 1.00000, 16.90000, 362.25000, 6.03100, 23.30000, 304.00000, 19.40000,
0.05083, 5.19000, 0.51500, 6.45840, 5.00000, 20.20000, 389.71000, 6.31600, 38.10000, 224.00000, 22.20000,
0.03738, 5.19000, 0.51500, 6.45840, 5.00000, 20.20000, 389.40000, 6.31000, 38.50000, 224.00000, 20.70000,
0.03961, 5.19000, 0.51500, 5.98530, 5.00000, 20.20000, 396.90000, 6.03700, 34.50000, 224.00000, 21.10000,
0.03427, 5.19000, 0.51500, 5.23110, 5.00000, 20.20000, 396.90000, 5.86900, 46.30000, 224.00000, 19.50000,
0.03041, 5.19000, 0.51500, 5.61500, 5.00000, 20.20000, 394.81000, 5.89500, 59.60000, 224.00000, 18.50000,
0.03306, 5.19000, 0.51500, 4.81220, 5.00000, 20.20000, 396.14000, 6.05900, 37.30000, 224.00000, 20.60000,
0.05497, 5.19000, 0.51500, 4.81220, 5.00000, 20.20000, 396.90000, 5.98500, 45.40000, 224.00000, 19.00000,
0.06151, 5.19000, 0.51500, 4.81220, 5.00000, 20.20000, 396.90000, 5.96800, 58.50000, 224.00000, 18.70000,
0.01301, 1.52000, 0.44200, 7.03790, 1.00000, 15.50000, 394.74000, 7.24100, 49.30000, 284.00000, 32.70000,
0.02498, 1.89000, 0.51800, 6.26690, 1.00000, 15.90000, 389.96000, 6.54000, 59.70000, 422.00000, 16.50000,
0.02543, 3.78000, 0.48400, 5.73210, 5.00000, 17.60000, 396.90000, 6.69600, 56.40000, 370.00000, 23.90000,
0.03049, 3.78000, 0.48400, 6.46540, 5.00000, 17.60000, 387.97000, 6.87400, 28.10000, 370.00000, 31.20000,
0.03113, 4.39000, 0.44200, 8.01360, 3.00000, 18.80000, 385.64000, 6.01400, 48.50000, 352.00000, 17.50000,
0.06162, 4.39000, 0.44200, 8.01360, 3.00000, 18.80000, 364.61000, 5.89800, 52.30000, 352.00000, 17.20000,
0.01870, 4.15000, 0.42900, 8.53530, 4.00000, 17.90000, 392.43000, 6.51600, 27.70000, 351.00000, 23.10000,
0.01501, 2.01000, 0.43500, 8.34400, 4.00000, 17.00000, 390.94000, 6.63500, 29.70000, 280.00000, 24.50000,
0.02899, 1.25000, 0.42900, 8.79210, 1.00000, 19.70000, 389.85000, 6.93900, 34.50000, 335.00000, 26.60000,
0.06211, 1.25000, 0.42900, 8.79210, 1.00000, 19.70000, 396.90000, 6.49000, 44.40000, 335.00000, 22.90000,
0.07950, 1.69000, 0.41100, 10.71030, 4.00000, 18.30000, 370.78000, 6.57900, 35.90000, 411.00000, 24.10000,
0.07244, 1.69000, 0.41100, 10.71030, 4.00000, 18.30000, 392.33000, 5.88400, 18.50000, 411.00000, 18.60000,
0.01709, 2.02000, 0.41000, 12.12650, 5.00000, 17.00000, 384.46000, 6.72800, 36.10000, 187.00000, 30.10000,
0.04301, 1.91000, 0.41300, 10.58570, 4.00000, 22.00000, 382.80000, 5.66300, 21.90000, 334.00000, 18.20000,
0.10659, 1.91000, 0.41300, 10.58570, 4.00000, 22.00000, 376.04000, 5.93600, 19.50000, 334.00000, 20.60000,
8.98296, 18.10000, 0.77000, 2.12220, 24.00000, 20.20000, 377.73000, 6.21200, 97.40000, 666.00000, 17.80000,
3.84970, 18.10000, 0.77000, 2.50520, 24.00000, 20.20000, 391.34000, 6.39500, 91.00000, 666.00000, 21.70000,
5.20177, 18.10000, 0.77000, 2.72270, 24.00000, 20.20000, 395.43000, 6.12700, 83.40000, 666.00000, 22.70000,
4.26131, 18.10000, 0.77000, 2.50910, 24.00000, 20.20000, 390.74000, 6.11200, 81.30000, 666.00000, 22.60000,
4.54192, 18.10000, 0.77000, 2.51820, 24.00000, 20.20000, 374.56000, 6.39800, 88.00000, 666.00000, 25.00000,
3.83684, 18.10000, 0.77000, 2.29550, 24.00000, 20.20000, 350.65000, 6.25100, 91.10000, 666.00000, 19.90000,
3.67822, 18.10000, 0.77000, 2.10360, 24.00000, 20.20000, 380.79000, 5.36200, 96.20000, 666.00000, 20.80000,
4.22239, 18.10000, 0.77000, 1.90470, 24.00000, 20.20000, 353.04000, 5.80300, 89.00000, 666.00000, 16.80000,
3.47428, 18.10000, 0.71800, 1.90470, 24.00000, 20.20000, 354.55000, 8.78000, 82.90000, 666.00000, 21.90000,
4.55587, 18.10000, 0.71800, 1.61320, 24.00000, 20.20000, 354.70000, 3.56100, 87.90000, 666.00000, 27.50000,
3.69695, 18.10000, 0.71800, 1.75230, 24.00000, 20.20000, 316.03000, 4.96300, 91.40000, 666.00000, 21.90000,
13.52220, 18.10000, 0.63100, 1.51060, 24.00000, 20.20000, 131.42000, 3.86300, 100.00000, 666.00000, 23.10000,
4.89822, 18.10000, 0.63100, 1.33250, 24.00000, 20.20000, 375.52000, 4.97000, 100.00000, 666.00000, 50.00000,
5.66998, 18.10000, 0.63100, 1.35670, 24.00000, 20.20000, 375.33000, 6.68300, 96.80000, 666.00000, 50.00000,
6.53876, 18.10000, 0.63100, 1.20240, 24.00000, 20.20000, 392.05000, 7.01600, 97.50000, 666.00000, 50.00000,
9.23230, 18.10000, 0.63100, 1.16910, 24.00000, 20.20000, 366.15000, 6.21600, 100.00000, 666.00000, 50.00000,
8.26725, 18.10000, 0.66800, 1.12960, 24.00000, 20.20000, 347.88000, 5.87500, 89.60000, 666.00000, 50.00000,
11.10810, 18.10000, 0.66800, 1.17420, 24.00000, 20.20000, 396.90000, 4.90600, 100.00000, 666.00000, 13.80000,
18.49820, 18.10000, 0.66800, 1.13700, 24.00000, 20.20000, 396.90000, 4.13800, 100.00000, 666.00000, 13.80000,
19.60910, 18.10000, 0.67100, 1.31630, 24.00000, 20.20000, 396.90000, 7.31300, 97.90000, 666.00000, 15.00000,
15.28800, 18.10000, 0.67100, 1.34490, 24.00000, 20.20000, 363.02000, 6.64900, 93.30000, 666.00000, 13.90000,
9.82349, 18.10000, 0.67100, 1.35800, 24.00000, 20.20000, 396.90000, 6.79400, 98.80000, 666.00000, 13.30000,
23.64820, 18.10000, 0.67100, 1.38610, 24.00000, 20.20000, 396.90000, 6.38000, 96.20000, 666.00000, 13.10000,
17.86670, 18.10000, 0.67100, 1.38610, 24.00000, 20.20000, 393.74000, 6.22300, 100.00000, 666.00000, 10.20000,
88.97620, 18.10000, 0.67100, 1.41650, 24.00000, 20.20000, 396.90000, 6.96800, 91.90000, 666.00000, 10.40000,
15.87440, 18.10000, 0.67100, 1.51920, 24.00000, 20.20000, 396.90000, 6.54500, 99.10000, 666.00000, 10.90000,
9.18702, 18.10000, 0.70000, 1.58040, 24.00000, 20.20000, 396.90000, 5.53600, 100.00000, 666.00000, 11.30000,
7.99248, 18.10000, 0.70000, 1.53310, 24.00000, 20.20000, 396.90000, 5.52000, 100.00000, 666.00000, 12.30000,
20.08490, 18.10000, 0.70000, 1.43950, 24.00000, 20.20000, 285.83000, 4.36800, 91.20000, 666.00000, 8.80000,
16.81180, 18.10000, 0.70000, 1.42610, 24.00000, 20.20000, 396.90000, 5.27700, 98.10000, 666.00000, 7.20000,
24.39380, 18.10000, 0.70000, 1.46720, 24.00000, 20.20000, 396.90000, 4.65200, 100.00000, 666.00000, 10.50000,
22.59710, 18.10000, 0.70000, 1.51840, 24.00000, 20.20000, 396.90000, 5.00000, 89.50000, 666.00000, 7.40000,
14.33370, 18.10000, 0.70000, 1.58950, 24.00000, 20.20000, 372.92000, 4.88000, 100.00000, 666.00000, 10.20000,
8.15174, 18.10000, 0.70000, 1.72810, 24.00000, 20.20000, 396.90000, 5.39000, 98.90000, 666.00000, 11.50000,
6.96215, 18.10000, 0.70000, 1.92650, 24.00000, 20.20000, 394.43000, 5.71300, 97.00000, 666.00000, 15.10000,
5.29305, 18.10000, 0.70000, 2.16780, 24.00000, 20.20000, 378.38000, 6.05100, 82.50000, 666.00000, 23.20000,
11.57790, 18.10000, 0.70000, 1.77000, 24.00000, 20.20000, 396.90000, 5.03600, 97.00000, 666.00000, 9.70000,
8.64476, 18.10000, 0.69300, 1.79120, 24.00000, 20.20000, 396.90000, 6.19300, 92.60000, 666.00000, 13.80000,
13.35980, 18.10000, 0.69300, 1.78210, 24.00000, 20.20000, 396.90000, 5.88700, 94.70000, 666.00000, 12.70000,
8.71675, 18.10000, 0.69300, 1.72570, 24.00000, 20.20000, 391.98000, 6.47100, 98.80000, 666.00000, 13.10000,
5.87205, 18.10000, 0.69300, 1.67680, 24.00000, 20.20000, 396.90000, 6.40500, 96.00000, 666.00000, 12.50000,
7.67202, 18.10000, 0.69300, 1.63340, 24.00000, 20.20000, 393.10000, 5.74700, 98.90000, 666.00000, 8.50000,
38.35180, 18.10000, 0.69300, 1.48960, 24.00000, 20.20000, 396.90000, 5.45300, 100.00000, 666.00000, 5.00000,
9.91655, 18.10000, 0.69300, 1.50040, 24.00000, 20.20000, 338.16000, 5.85200, 77.80000, 666.00000, 6.30000,
25.04610, 18.10000, 0.69300, 1.58880, 24.00000, 20.20000, 396.90000, 5.98700, 100.00000, 666.00000, 5.60000,
14.23620, 18.10000, 0.69300, 1.57410, 24.00000, 20.20000, 396.90000, 6.34300, 100.00000, 666.00000, 7.20000,
9.59571, 18.10000, 0.69300, 1.63900, 24.00000, 20.20000, 376.11000, 6.40400, 100.00000, 666.00000, 12.10000,
24.80170, 18.10000, 0.69300, 1.70280, 24.00000, 20.20000, 396.90000, 5.34900, 96.00000, 666.00000, 8.30000,
41.52920, 18.10000, 0.69300, 1.60740, 24.00000, 20.20000, 329.46000, 5.53100, 85.40000, 666.00000, 8.50000,
67.92080, 18.10000, 0.69300, 1.42540, 24.00000, 20.20000, 384.97000, 5.68300, 100.00000, 666.00000, 5.00000,
20.71620, 18.10000, 0.65900, 1.17810, 24.00000, 20.20000, 370.22000, 4.13800, 100.00000, 666.00000, 11.90000,
11.95110, 18.10000, 0.65900, 1.28520, 24.00000, 20.20000, 332.09000, 5.60800, 100.00000, 666.00000, 27.90000,
7.40389, 18.10000, 0.59700, 1.45470, 24.00000, 20.20000, 314.64000, 5.61700, 97.90000, 666.00000, 17.20000,
14.43830, 18.10000, 0.59700, 1.46550, 24.00000, 20.20000, 179.36000, 6.85200, 100.00000, 666.00000, 27.50000,
51.13580, 18.10000, 0.59700, 1.41300, 24.00000, 20.20000, 2.60000, 5.75700, 100.00000, 666.00000, 15.00000,
14.05070, 18.10000, 0.59700, 1.52750, 24.00000, 20.20000, 35.05000, 6.65700, 100.00000, 666.00000, 17.20000,
18.81100, 18.10000, 0.59700, 1.55390, 24.00000, 20.20000, 28.79000, 4.62800, 100.00000, 666.00000, 17.90000,
28.65580, 18.10000, 0.59700, 1.58940, 24.00000, 20.20000, 210.97000, 5.15500, 100.00000, 666.00000, 16.30000,
45.74610, 18.10000, 0.69300, 1.65820, 24.00000, 20.20000, 88.27000, 4.51900, 100.00000, 666.00000, 7.00000,
18.08460, 18.10000, 0.67900, 1.83470, 24.00000, 20.20000, 27.25000, 6.43400, 100.00000, 666.00000, 7.20000,
10.83420, 18.10000, 0.67900, 1.81950, 24.00000, 20.20000, 21.57000, 6.78200, 90.80000, 666.00000, 7.50000,
25.94060, 18.10000, 0.67900, 1.64750, 24.00000, 20.20000, 127.36000, 5.30400, 89.10000, 666.00000, 10.40000,
73.53410, 18.10000, 0.67900, 1.80260, 24.00000, 20.20000, 16.45000, 5.95700, 100.00000, 666.00000, 8.80000,
11.81230, 18.10000, 0.71800, 1.79400, 24.00000, 20.20000, 48.45000, 6.82400, 76.50000, 666.00000, 8.40000,
11.08740, 18.10000, 0.71800, 1.85890, 24.00000, 20.20000, 318.75000, 6.41100, 100.00000, 666.00000, 16.70000,
7.02259, 18.10000, 0.71800, 1.87460, 24.00000, 20.20000, 319.98000, 6.00600, 95.30000, 666.00000, 14.20000,
12.04820, 18.10000, 0.61400, 1.95120, 24.00000, 20.20000, 291.55000, 5.64800, 87.60000, 666.00000, 20.80000,
7.05042, 18.10000, 0.61400, 2.02180, 24.00000, 20.20000, 2.52000, 6.10300, 85.10000, 666.00000, 13.40000,
8.79212, 18.10000, 0.58400, 2.06350, 24.00000, 20.20000, 3.65000, 5.56500, 70.60000, 666.00000, 11.70000,
15.86030, 18.10000, 0.67900, 1.90960, 24.00000, 20.20000, 7.68000, 5.89600, 95.40000, 666.00000, 8.30000,
12.24720, 18.10000, 0.58400, 1.99760, 24.00000, 20.20000, 24.65000, 5.83700, 59.70000, 666.00000, 10.20000,
37.66190, 18.10000, 0.67900, 1.86290, 24.00000, 20.20000, 18.82000, 6.20200, 78.70000, 666.00000, 10.90000,
7.36711, 18.10000, 0.67900, 1.93560, 24.00000, 20.20000, 96.73000, 6.19300, 78.10000, 666.00000, 11.00000,
9.33889, 18.10000, 0.67900, 1.96820, 24.00000, 20.20000, 60.72000, 6.38000, 95.60000, 666.00000, 9.50000,
8.49213, 18.10000, 0.58400, 2.05270, 24.00000, 20.20000, 83.45000, 6.34800, 86.10000, 666.00000, 14.50000,
10.06230, 18.10000, 0.58400, 2.08820, 24.00000, 20.20000, 81.33000, 6.83300, 94.30000, 666.00000, 14.10000,
6.44405, 18.10000, 0.58400, 2.20040, 24.00000, 20.20000, 97.95000, 6.42500, 74.80000, 666.00000, 16.10000,
5.58107, 18.10000, 0.71300, 2.31580, 24.00000, 20.20000, 100.19000, 6.43600, 87.90000, 666.00000, 14.30000,
13.91340, 18.10000, 0.71300, 2.22220, 24.00000, 20.20000, 100.63000, 6.20800, 95.00000, 666.00000, 11.70000,
11.16040, 18.10000, 0.74000, 2.12470, 24.00000, 20.20000, 109.85000, 6.62900, 94.60000, 666.00000, 13.40000,
14.42080, 18.10000, 0.74000, 2.00260, 24.00000, 20.20000, 27.49000, 6.46100, 93.30000, 666.00000, 9.60000,
15.17720, 18.10000, 0.74000, 1.91420, 24.00000, 20.20000, 9.32000, 6.15200, 100.00000, 666.00000, 8.70000,
13.67810, 18.10000, 0.74000, 1.82060, 24.00000, 20.20000, 68.95000, 5.93500, 87.90000, 666.00000, 8.40000,
9.39063, 18.10000, 0.74000, 1.81720, 24.00000, 20.20000, 396.90000, 5.62700, 93.90000, 666.00000, 12.80000,
22.05110, 18.10000, 0.74000, 1.86620, 24.00000, 20.20000, 391.45000, 5.81800, 92.40000, 666.00000, 10.50000,
9.72418, 18.10000, 0.74000, 2.06510, 24.00000, 20.20000, 385.96000, 6.40600, 97.20000, 666.00000, 17.10000,
5.66637, 18.10000, 0.74000, 2.00480, 24.00000, 20.20000, 395.69000, 6.21900, 100.00000, 666.00000, 18.40000,
9.96654, 18.10000, 0.74000, 1.97840, 24.00000, 20.20000, 386.73000, 6.48500, 100.00000, 666.00000, 15.40000,
12.80230, 18.10000, 0.74000, 1.89560, 24.00000, 20.20000, 240.52000, 5.85400, 96.60000, 666.00000, 10.80000,
10.67180, 18.10000, 0.74000, 1.98790, 24.00000, 20.20000, 43.06000, 6.45900, 94.80000, 666.00000, 11.80000,
6.28807, 18.10000, 0.74000, 2.07200, 24.00000, 20.20000, 318.01000, 6.34100, 96.40000, 666.00000, 14.90000,
9.92485, 18.10000, 0.74000, 2.19800, 24.00000, 20.20000, 388.52000, 6.25100, 96.60000, 666.00000, 12.60000,
9.32909, 18.10000, 0.71300, 2.26160, 24.00000, 20.20000, 396.90000, 6.18500, 98.70000, 666.00000, 14.10000,
7.52601, 18.10000, 0.71300, 2.18500, 24.00000, 20.20000, 304.21000, 6.41700, 98.30000, 666.00000, 13.00000,
6.71772, 18.10000, 0.71300, 2.32360, 24.00000, 20.20000, 0.32000, 6.74900, 92.60000, 666.00000, 13.40000,
5.44114, 18.10000, 0.71300, 2.35520, 24.00000, 20.20000, 355.29000, 6.65500, 98.20000, 666.00000, 15.20000,
5.09017, 18.10000, 0.71300, 2.36820, 24.00000, 20.20000, 385.09000, 6.29700, 91.80000, 666.00000, 16.10000,
8.24809, 18.10000, 0.71300, 2.45270, 24.00000, 20.20000, 375.87000, 7.39300, 99.30000, 666.00000, 17.80000,
9.51363, 18.10000, 0.71300, 2.49610, 24.00000, 20.20000, 6.68000, 6.72800, 94.10000, 666.00000, 14.90000,
4.75237, 18.10000, 0.71300, 2.43580, 24.00000, 20.20000, 50.92000, 6.52500, 86.50000, 666.00000, 14.10000,
4.66883, 18.10000, 0.71300, 2.58060, 24.00000, 20.20000, 10.48000, 5.97600, 87.90000, 666.00000, 12.70000,
8.20058, 18.10000, 0.71300, 2.77920, 24.00000, 20.20000, 3.50000, 5.93600, 80.30000, 666.00000, 13.50000,
7.75223, 18.10000, 0.71300, 2.78310, 24.00000, 20.20000, 272.21000, 6.30100, 83.70000, 666.00000, 14.90000,
6.80117, 18.10000, 0.71300, 2.71750, 24.00000, 20.20000, 396.90000, 6.08100, 84.40000, 666.00000, 20.00000,
4.81213, 18.10000, 0.71300, 2.59750, 24.00000, 20.20000, 255.23000, 6.70100, 90.00000, 666.00000, 16.40000,
3.69311, 18.10000, 0.71300, 2.56710, 24.00000, 20.20000, 391.43000, 6.37600, 88.40000, 666.00000, 17.70000,
6.65492, 18.10000, 0.71300, 2.73440, 24.00000, 20.20000, 396.90000, 6.31700, 83.00000, 666.00000, 19.50000,
5.82115, 18.10000, 0.71300, 2.80160, 24.00000, 20.20000, 393.82000, 6.51300, 89.90000, 666.00000, 20.20000,
7.83932, 18.10000, 0.65500, 2.96340, 24.00000, 20.20000, 396.90000, 6.20900, 65.40000, 666.00000, 21.40000,
3.16360, 18.10000, 0.65500, 3.06650, 24.00000, 20.20000, 334.40000, 5.75900, 48.20000, 666.00000, 19.90000,
3.77498, 18.10000, 0.65500, 2.87150, 24.00000, 20.20000, 22.01000, 5.95200, 84.70000, 666.00000, 19.00000,
4.42228, 18.10000, 0.58400, 2.54030, 24.00000, 20.20000, 331.29000, 6.00300, 94.50000, 666.00000, 19.10000,
15.57570, 18.10000, 0.58000, 2.90840, 24.00000, 20.20000, 368.74000, 5.92600, 71.00000, 666.00000, 19.10000,
13.07510, 18.10000, 0.58000, 2.82370, 24.00000, 20.20000, 396.90000, 5.71300, 56.70000, 666.00000, 20.10000,
4.34879, 18.10000, 0.58000, 3.03340, 24.00000, 20.20000, 396.90000, 6.16700, 84.00000, 666.00000, 19.90000,
4.03841, 18.10000, 0.53200, 3.09930, 24.00000, 20.20000, 395.33000, 6.22900, 90.70000, 666.00000, 19.60000,
3.56868, 18.10000, 0.58000, 2.89650, 24.00000, 20.20000, 393.37000, 6.43700, 75.00000, 666.00000, 23.20000,
4.64689, 18.10000, 0.61400, 2.53290, 24.00000, 20.20000, 374.68000, 6.98000, 67.60000, 666.00000, 29.80000,
8.05579, 18.10000, 0.58400, 2.42980, 24.00000, 20.20000, 352.58000, 5.42700, 95.40000, 666.00000, 13.80000,
6.39312, 18.10000, 0.58400, 2.20600, 24.00000, 20.20000, 302.76000, 6.16200, 97.40000, 666.00000, 13.30000,
4.87141, 18.10000, 0.61400, 2.30530, 24.00000, 20.20000, 396.21000, 6.48400, 93.60000, 666.00000, 16.70000,
15.02340, 18.10000, 0.61400, 2.10070, 24.00000, 20.20000, 349.48000, 5.30400, 97.30000, 666.00000, 12.00000,
10.23300, 18.10000, 0.61400, 2.17050, 24.00000, 20.20000, 379.70000, 6.18500, 96.70000, 666.00000, 14.60000,
14.33370, 18.10000, 0.61400, 1.95120, 24.00000, 20.20000, 383.32000, 6.22900, 88.00000, 666.00000, 21.40000,
5.82401, 18.10000, 0.53200, 3.42420, 24.00000, 20.20000, 396.90000, 6.24200, 64.70000, 666.00000, 23.00000,
5.70818, 18.10000, 0.53200, 3.33170, 24.00000, 20.20000, 393.07000, 6.75000, 74.90000, 666.00000, 23.70000,
5.73116, 18.10000, 0.53200, 3.41060, 24.00000, 20.20000, 395.28000, 7.06100, 77.00000, 666.00000, 25.00000,
2.81838, 18.10000, 0.53200, 4.09830, 24.00000, 20.20000, 392.92000, 5.76200, 40.30000, 666.00000, 21.80000,
2.37857, 18.10000, 0.58300, 3.72400, 24.00000, 20.20000, 370.73000, 5.87100, 41.90000, 666.00000, 20.60000,
3.67367, 18.10000, 0.58300, 3.99170, 24.00000, 20.20000, 388.62000, 6.31200, 51.90000, 666.00000, 21.20000,
5.69175, 18.10000, 0.58300, 3.54590, 24.00000, 20.20000, 392.68000, 6.11400, 79.80000, 666.00000, 19.10000,
4.83567, 18.10000, 0.58300, 3.15230, 24.00000, 20.20000, 388.22000, 5.90500, 53.20000, 666.00000, 20.60000,
0.15086, 27.74000, 0.60900, 1.82090, 4.00000, 20.10000, 395.09000, 5.45400, 92.70000, 711.00000, 15.20000,
0.18337, 27.74000, 0.60900, 1.75540, 4.00000, 20.10000, 344.05000, 5.41400, 98.30000, 711.00000, 7.00000,
0.20746, 27.74000, 0.60900, 1.82260, 4.00000, 20.10000, 318.43000, 5.09300, 98.00000, 711.00000, 8.10000,
0.10574, 27.74000, 0.60900, 1.86810, 4.00000, 20.10000, 390.11000, 5.98300, 98.80000, 711.00000, 13.60000,
0.11132, 27.74000, 0.60900, 2.10990, 4.00000, 20.10000, 396.90000, 5.98300, 83.50000, 711.00000, 20.10000,
0.17331, 9.69000, 0.58500, 2.38170, 6.00000, 19.20000, 396.90000, 5.70700, 54.00000, 391.00000, 21.80000,
0.27957, 9.69000, 0.58500, 2.38170, 6.00000, 19.20000, 396.90000, 5.92600, 42.60000, 391.00000, 24.50000,
0.17899, 9.69000, 0.58500, 2.79860, 6.00000, 19.20000, 393.29000, 5.67000, 28.80000, 391.00000, 23.10000,
0.28960, 9.69000, 0.58500, 2.79860, 6.00000, 19.20000, 396.90000, 5.39000, 72.90000, 391.00000, 19.70000,
0.26838, 9.69000, 0.58500, 2.89270, 6.00000, 19.20000, 396.90000, 5.79400, 70.60000, 391.00000, 18.30000,
0.23912, 9.69000, 0.58500, 2.40910, 6.00000, 19.20000, 396.90000, 6.01900, 65.30000, 391.00000, 21.20000,
0.17783, 9.69000, 0.58500, 2.39990, 6.00000, 19.20000, 395.77000, 5.56900, 73.50000, 391.00000, 17.50000,
0.22438, 9.69000, 0.58500, 2.49820, 6.00000, 19.20000, 396.90000, 6.02700, 79.70000, 391.00000, 16.80000,
0.06263, 11.93000, 0.57300, 2.47860, 1.00000, 21.00000, 391.99000, 6.59300, 69.10000, 273.00000, 22.40000,
0.04527, 11.93000, 0.57300, 2.28750, 1.00000, 21.00000, 396.90000, 6.12000, 76.70000, 273.00000, 20.60000,
0.06076, 11.93000, 0.57300, 2.16750, 1.00000, 21.00000, 396.90000, 6.97600, 91.00000, 273.00000, 23.90000,
0.10959, 11.93000, 0.57300, 2.38890, 1.00000, 21.00000, 393.45000, 6.79400, 89.30000, 273.00000, 22.00000,
0.04741, 11.93000, 0.57300, 2.50500, 1.00000, 21.00000, 396.90000, 6.03000, 80.80000, 273.00000, 11.90000,
})

406
car_data_test.go Normal file
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@@ -0,0 +1,406 @@
// Copyright ©2016 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat_test
import "github.com/gonum/matrix/mat64"
// ASA Car Exposition Data of Ramos and Donoho (1983)
// http://lib.stat.cmu.edu/datasets/cars.desc
// http://lib.stat.cmu.edu/datasets/cars.data
// Columns are: displacement, horsepower, weight, acceleration, MPG.
var carData = mat64.NewDense(392, 5, []float64{
307.0, 130.0, 3504.0, 12.0, 18.0,
350.0, 165.0, 3693.0, 11.5, 15.0,
318.0, 150.0, 3436.0, 11.0, 18.0,
304.0, 150.0, 3433.0, 12.0, 16.0,
302.0, 140.0, 3449.0, 10.5, 17.0,
429.0, 198.0, 4341.0, 10.0, 15.0,
454.0, 220.0, 4354.0, 9.0, 14.0,
440.0, 215.0, 4312.0, 8.5, 14.0,
455.0, 225.0, 4425.0, 10.0, 14.0,
390.0, 190.0, 3850.0, 8.5, 15.0,
383.0, 170.0, 3563.0, 10.0, 15.0,
340.0, 160.0, 3609.0, 8.0, 14.0,
400.0, 150.0, 3761.0, 9.5, 15.0,
455.0, 225.0, 3086.0, 10.0, 14.0,
113.0, 95.0, 2372.0, 15.0, 24.0,
198.0, 95.0, 2833.0, 15.5, 22.0,
199.0, 97.0, 2774.0, 15.5, 18.0,
200.0, 85.0, 2587.0, 16.0, 21.0,
97.0, 88.0, 2130.0, 14.5, 27.0,
97.0, 46.0, 1835.0, 20.5, 26.0,
110.0, 87.0, 2672.0, 17.5, 25.0,
107.0, 90.0, 2430.0, 14.5, 24.0,
104.0, 95.0, 2375.0, 17.5, 25.0,
121.0, 113.0, 2234.0, 12.5, 26.0,
199.0, 90.0, 2648.0, 15.0, 21.0,
360.0, 215.0, 4615.0, 14.0, 10.0,
307.0, 200.0, 4376.0, 15.0, 10.0,
318.0, 210.0, 4382.0, 13.5, 11.0,
304.0, 193.0, 4732.0, 18.5, 9.0,
97.0, 88.0, 2130.0, 14.5, 27.0,
140.0, 90.0, 2264.0, 15.5, 28.0,
113.0, 95.0, 2228.0, 14.0, 25.0,
232.0, 100.0, 2634.0, 13.0, 19.0,
225.0, 105.0, 3439.0, 15.5, 16.0,
250.0, 100.0, 3329.0, 15.5, 17.0,
250.0, 88.0, 3302.0, 15.5, 19.0,
232.0, 100.0, 3288.0, 15.5, 18.0,
350.0, 165.0, 4209.0, 12.0, 14.0,
400.0, 175.0, 4464.0, 11.5, 14.0,
351.0, 153.0, 4154.0, 13.5, 14.0,
318.0, 150.0, 4096.0, 13.0, 14.0,
383.0, 180.0, 4955.0, 11.5, 12.0,
400.0, 170.0, 4746.0, 12.0, 13.0,
400.0, 175.0, 5140.0, 12.0, 13.0,
258.0, 110.0, 2962.0, 13.5, 18.0,
140.0, 72.0, 2408.0, 19.0, 22.0,
250.0, 100.0, 3282.0, 15.0, 19.0,
250.0, 88.0, 3139.0, 14.5, 18.0,
122.0, 86.0, 2220.0, 14.0, 23.0,
116.0, 90.0, 2123.0, 14.0, 28.0,
79.0, 70.0, 2074.0, 19.5, 30.0,
88.0, 76.0, 2065.0, 14.5, 30.0,
71.0, 65.0, 1773.0, 19.0, 31.0,
72.0, 69.0, 1613.0, 18.0, 35.0,
97.0, 60.0, 1834.0, 19.0, 27.0,
91.0, 70.0, 1955.0, 20.5, 26.0,
113.0, 95.0, 2278.0, 15.5, 24.0,
97.5, 80.0, 2126.0, 17.0, 25.0,
97.0, 54.0, 2254.0, 23.5, 23.0,
140.0, 90.0, 2408.0, 19.5, 20.0,
122.0, 86.0, 2226.0, 16.5, 21.0,
350.0, 165.0, 4274.0, 12.0, 13.0,
400.0, 175.0, 4385.0, 12.0, 14.0,
318.0, 150.0, 4135.0, 13.5, 15.0,
351.0, 153.0, 4129.0, 13.0, 14.0,
304.0, 150.0, 3672.0, 11.5, 17.0,
429.0, 208.0, 4633.0, 11.0, 11.0,
350.0, 155.0, 4502.0, 13.5, 13.0,
350.0, 160.0, 4456.0, 13.5, 12.0,
400.0, 190.0, 4422.0, 12.5, 13.0,
70.0, 97.0, 2330.0, 13.5, 19.0,
304.0, 150.0, 3892.0, 12.5, 15.0,
307.0, 130.0, 4098.0, 14.0, 13.0,
302.0, 140.0, 4294.0, 16.0, 13.0,
318.0, 150.0, 4077.0, 14.0, 14.0,
121.0, 112.0, 2933.0, 14.5, 18.0,
121.0, 76.0, 2511.0, 18.0, 22.0,
120.0, 87.0, 2979.0, 19.5, 21.0,
96.0, 69.0, 2189.0, 18.0, 26.0,
122.0, 86.0, 2395.0, 16.0, 22.0,
97.0, 92.0, 2288.0, 17.0, 28.0,
120.0, 97.0, 2506.0, 14.5, 23.0,
98.0, 80.0, 2164.0, 15.0, 28.0,
97.0, 88.0, 2100.0, 16.5, 27.0,
350.0, 175.0, 4100.0, 13.0, 13.0,
304.0, 150.0, 3672.0, 11.5, 14.0,
350.0, 145.0, 3988.0, 13.0, 13.0,
302.0, 137.0, 4042.0, 14.5, 14.0,
318.0, 150.0, 3777.0, 12.5, 15.0,
429.0, 198.0, 4952.0, 11.5, 12.0,
400.0, 150.0, 4464.0, 12.0, 13.0,
351.0, 158.0, 4363.0, 13.0, 13.0,
318.0, 150.0, 4237.0, 14.5, 14.0,
440.0, 215.0, 4735.0, 11.0, 13.0,
455.0, 225.0, 4951.0, 11.0, 12.0,
360.0, 175.0, 3821.0, 11.0, 13.0,
225.0, 105.0, 3121.0, 16.5, 18.0,
250.0, 100.0, 3278.0, 18.0, 16.0,
232.0, 100.0, 2945.0, 16.0, 18.0,
250.0, 88.0, 3021.0, 16.5, 18.0,
198.0, 95.0, 2904.0, 16.0, 23.0,
97.0, 46.0, 1950.0, 21.0, 26.0,
400.0, 150.0, 4997.0, 14.0, 11.0,
400.0, 167.0, 4906.0, 12.5, 12.0,
360.0, 170.0, 4654.0, 13.0, 13.0,
350.0, 180.0, 4499.0, 12.5, 12.0,
232.0, 100.0, 2789.0, 15.0, 18.0,
97.0, 88.0, 2279.0, 19.0, 20.0,
140.0, 72.0, 2401.0, 19.5, 21.0,
108.0, 94.0, 2379.0, 16.5, 22.0,
70.0, 90.0, 2124.0, 13.5, 18.0,
122.0, 85.0, 2310.0, 18.5, 19.0,
155.0, 107.0, 2472.0, 14.0, 21.0,
98.0, 90.0, 2265.0, 15.5, 26.0,
350.0, 145.0, 4082.0, 13.0, 15.0,
400.0, 230.0, 4278.0, 9.5, 16.0,
68.0, 49.0, 1867.0, 19.5, 29.0,
116.0, 75.0, 2158.0, 15.5, 24.0,
114.0, 91.0, 2582.0, 14.0, 20.0,
121.0, 112.0, 2868.0, 15.5, 19.0,
318.0, 150.0, 3399.0, 11.0, 15.0,
121.0, 110.0, 2660.0, 14.0, 24.0,
156.0, 122.0, 2807.0, 13.5, 20.0,
350.0, 180.0, 3664.0, 11.0, 11.0,
198.0, 95.0, 3102.0, 16.5, 20.0,
232.0, 100.0, 2901.0, 16.0, 19.0,
250.0, 100.0, 3336.0, 17.0, 15.0,
79.0, 67.0, 1950.0, 19.0, 31.0,
122.0, 80.0, 2451.0, 16.5, 26.0,
71.0, 65.0, 1836.0, 21.0, 32.0,
140.0, 75.0, 2542.0, 17.0, 25.0,
250.0, 100.0, 3781.0, 17.0, 16.0,
258.0, 110.0, 3632.0, 18.0, 16.0,
225.0, 105.0, 3613.0, 16.5, 18.0,
302.0, 140.0, 4141.0, 14.0, 16.0,
350.0, 150.0, 4699.0, 14.5, 13.0,
318.0, 150.0, 4457.0, 13.5, 14.0,
302.0, 140.0, 4638.0, 16.0, 14.0,
304.0, 150.0, 4257.0, 15.5, 14.0,
98.0, 83.0, 2219.0, 16.5, 29.0,
79.0, 67.0, 1963.0, 15.5, 26.0,
97.0, 78.0, 2300.0, 14.5, 26.0,
76.0, 52.0, 1649.0, 16.5, 31.0,
83.0, 61.0, 2003.0, 19.0, 32.0,
90.0, 75.0, 2125.0, 14.5, 28.0,
90.0, 75.0, 2108.0, 15.5, 24.0,
116.0, 75.0, 2246.0, 14.0, 26.0,
120.0, 97.0, 2489.0, 15.0, 24.0,
108.0, 93.0, 2391.0, 15.5, 26.0,
79.0, 67.0, 2000.0, 16.0, 31.0,
225.0, 95.0, 3264.0, 16.0, 19.0,
250.0, 105.0, 3459.0, 16.0, 18.0,
250.0, 72.0, 3432.0, 21.0, 15.0,
250.0, 72.0, 3158.0, 19.5, 15.0,
400.0, 170.0, 4668.0, 11.5, 16.0,
350.0, 145.0, 4440.0, 14.0, 15.0,
318.0, 150.0, 4498.0, 14.5, 16.0,
351.0, 148.0, 4657.0, 13.5, 14.0,
231.0, 110.0, 3907.0, 21.0, 17.0,
250.0, 105.0, 3897.0, 18.5, 16.0,
258.0, 110.0, 3730.0, 19.0, 15.0,
225.0, 95.0, 3785.0, 19.0, 18.0,
231.0, 110.0, 3039.0, 15.0, 21.0,
262.0, 110.0, 3221.0, 13.5, 20.0,
302.0, 129.0, 3169.0, 12.0, 13.0,
97.0, 75.0, 2171.0, 16.0, 29.0,
140.0, 83.0, 2639.0, 17.0, 23.0,
232.0, 100.0, 2914.0, 16.0, 20.0,
140.0, 78.0, 2592.0, 18.5, 23.0,
134.0, 96.0, 2702.0, 13.5, 24.0,
90.0, 71.0, 2223.0, 16.5, 25.0,
119.0, 97.0, 2545.0, 17.0, 24.0,
171.0, 97.0, 2984.0, 14.5, 18.0,
90.0, 70.0, 1937.0, 14.0, 29.0,
232.0, 90.0, 3211.0, 17.0, 19.0,
115.0, 95.0, 2694.0, 15.0, 23.0,
120.0, 88.0, 2957.0, 17.0, 23.0,
121.0, 98.0, 2945.0, 14.5, 22.0,
121.0, 115.0, 2671.0, 13.5, 25.0,
91.0, 53.0, 1795.0, 17.5, 33.0,
107.0, 86.0, 2464.0, 15.5, 28.0,
116.0, 81.0, 2220.0, 16.9, 25.0,
140.0, 92.0, 2572.0, 14.9, 25.0,
98.0, 79.0, 2255.0, 17.7, 26.0,
101.0, 83.0, 2202.0, 15.3, 27.0,
305.0, 140.0, 4215.0, 13.0, 17.5,
318.0, 150.0, 4190.0, 13.0, 16.0,
304.0, 120.0, 3962.0, 13.9, 15.5,
351.0, 152.0, 4215.0, 12.8, 14.5,
225.0, 100.0, 3233.0, 15.4, 22.0,
250.0, 105.0, 3353.0, 14.5, 22.0,
200.0, 81.0, 3012.0, 17.6, 24.0,
232.0, 90.0, 3085.0, 17.6, 22.5,
85.0, 52.0, 2035.0, 22.2, 29.0,
98.0, 60.0, 2164.0, 22.1, 24.5,
90.0, 70.0, 1937.0, 14.2, 29.0,
91.0, 53.0, 1795.0, 17.4, 33.0,
225.0, 100.0, 3651.0, 17.7, 20.0,
250.0, 78.0, 3574.0, 21.0, 18.0,
250.0, 110.0, 3645.0, 16.2, 18.5,
258.0, 95.0, 3193.0, 17.8, 17.5,
97.0, 71.0, 1825.0, 12.2, 29.5,
85.0, 70.0, 1990.0, 17.0, 32.0,
97.0, 75.0, 2155.0, 16.4, 28.0,
140.0, 72.0, 2565.0, 13.6, 26.5,
130.0, 102.0, 3150.0, 15.7, 20.0,
318.0, 150.0, 3940.0, 13.2, 13.0,
120.0, 88.0, 3270.0, 21.9, 19.0,
156.0, 108.0, 2930.0, 15.5, 19.0,
168.0, 120.0, 3820.0, 16.7, 16.5,
350.0, 180.0, 4380.0, 12.1, 16.5,
350.0, 145.0, 4055.0, 12.0, 13.0,
302.0, 130.0, 3870.0, 15.0, 13.0,
318.0, 150.0, 3755.0, 14.0, 13.0,
98.0, 68.0, 2045.0, 18.5, 31.5,
111.0, 80.0, 2155.0, 14.8, 30.0,
79.0, 58.0, 1825.0, 18.6, 36.0,
122.0, 96.0, 2300.0, 15.5, 25.5,
85.0, 70.0, 1945.0, 16.8, 33.5,
305.0, 145.0, 3880.0, 12.5, 17.5,
260.0, 110.0, 4060.0, 19.0, 17.0,
318.0, 145.0, 4140.0, 13.7, 15.5,
302.0, 130.0, 4295.0, 14.9, 15.0,
250.0, 110.0, 3520.0, 16.4, 17.5,
231.0, 105.0, 3425.0, 16.9, 20.5,
225.0, 100.0, 3630.0, 17.7, 19.0,
250.0, 98.0, 3525.0, 19.0, 18.5,
400.0, 180.0, 4220.0, 11.1, 16.0,
350.0, 170.0, 4165.0, 11.4, 15.5,
400.0, 190.0, 4325.0, 12.2, 15.5,
351.0, 149.0, 4335.0, 14.5, 16.0,
97.0, 78.0, 1940.0, 14.5, 29.0,
151.0, 88.0, 2740.0, 16.0, 24.5,
97.0, 75.0, 2265.0, 18.2, 26.0,
140.0, 89.0, 2755.0, 15.8, 25.5,
98.0, 63.0, 2051.0, 17.0, 30.5,
98.0, 83.0, 2075.0, 15.9, 33.5,
97.0, 67.0, 1985.0, 16.4, 30.0,
97.0, 78.0, 2190.0, 14.1, 30.5,
146.0, 97.0, 2815.0, 14.5, 22.0,
121.0, 110.0, 2600.0, 12.8, 21.5,
80.0, 110.0, 2720.0, 13.5, 21.5,
90.0, 48.0, 1985.0, 21.5, 43.1,
98.0, 66.0, 1800.0, 14.4, 36.1,
78.0, 52.0, 1985.0, 19.4, 32.8,
85.0, 70.0, 2070.0, 18.6, 39.4,
91.0, 60.0, 1800.0, 16.4, 36.1,
260.0, 110.0, 3365.0, 15.5, 19.9,
318.0, 140.0, 3735.0, 13.2, 19.4,
302.0, 139.0, 3570.0, 12.8, 20.2,
231.0, 105.0, 3535.0, 19.2, 19.2,
200.0, 95.0, 3155.0, 18.2, 20.5,
200.0, 85.0, 2965.0, 15.8, 20.2,
140.0, 88.0, 2720.0, 15.4, 25.1,
225.0, 100.0, 3430.0, 17.2, 20.5,
232.0, 90.0, 3210.0, 17.2, 19.4,
231.0, 105.0, 3380.0, 15.8, 20.6,
200.0, 85.0, 3070.0, 16.7, 20.8,
225.0, 110.0, 3620.0, 18.7, 18.6,
258.0, 120.0, 3410.0, 15.1, 18.1,
305.0, 145.0, 3425.0, 13.2, 19.2,
231.0, 165.0, 3445.0, 13.4, 17.7,
302.0, 139.0, 3205.0, 11.2, 18.1,
318.0, 140.0, 4080.0, 13.7, 17.5,
98.0, 68.0, 2155.0, 16.5, 30.0,
134.0, 95.0, 2560.0, 14.2, 27.5,
119.0, 97.0, 2300.0, 14.7, 27.2,
105.0, 75.0, 2230.0, 14.5, 30.9,
134.0, 95.0, 2515.0, 14.8, 21.1,
156.0, 105.0, 2745.0, 16.7, 23.2,
151.0, 85.0, 2855.0, 17.6, 23.8,
119.0, 97.0, 2405.0, 14.9, 23.9,
131.0, 103.0, 2830.0, 15.9, 20.3,
163.0, 125.0, 3140.0, 13.6, 17.0,
121.0, 115.0, 2795.0, 15.7, 21.6,
163.0, 133.0, 3410.0, 15.8, 16.2,
89.0, 71.0, 1990.0, 14.9, 31.5,
98.0, 68.0, 2135.0, 16.6, 29.5,
231.0, 115.0, 3245.0, 15.4, 21.5,
200.0, 85.0, 2990.0, 18.2, 19.8,
140.0, 88.0, 2890.0, 17.3, 22.3,
232.0, 90.0, 3265.0, 18.2, 20.2,
225.0, 110.0, 3360.0, 16.6, 20.6,
305.0, 130.0, 3840.0, 15.4, 17.0,
302.0, 129.0, 3725.0, 13.4, 17.6,
351.0, 138.0, 3955.0, 13.2, 16.5,
318.0, 135.0, 3830.0, 15.2, 18.2,
350.0, 155.0, 4360.0, 14.9, 16.9,
351.0, 142.0, 4054.0, 14.3, 15.5,
267.0, 125.0, 3605.0, 15.0, 19.2,
360.0, 150.0, 3940.0, 13.0, 18.5,
89.0, 71.0, 1925.0, 14.0, 31.9,
86.0, 65.0, 1975.0, 15.2, 34.1,
98.0, 80.0, 1915.0, 14.4, 35.7,
121.0, 80.0, 2670.0, 15.0, 27.4,
183.0, 77.0, 3530.0, 20.1, 25.4,
350.0, 125.0, 3900.0, 17.4, 23.0,
141.0, 71.0, 3190.0, 24.8, 27.2,
260.0, 90.0, 3420.0, 22.2, 23.9,
105.0, 70.0, 2200.0, 13.2, 34.2,
105.0, 70.0, 2150.0, 14.9, 34.5,
85.0, 65.0, 2020.0, 19.2, 31.8,
91.0, 69.0, 2130.0, 14.7, 37.3,
151.0, 90.0, 2670.0, 16.0, 28.4,
173.0, 115.0, 2595.0, 11.3, 28.8,
173.0, 115.0, 2700.0, 12.9, 26.8,
151.0, 90.0, 2556.0, 13.2, 33.5,
98.0, 76.0, 2144.0, 14.7, 41.5,
89.0, 60.0, 1968.0, 18.8, 38.1,
98.0, 70.0, 2120.0, 15.5, 32.1,
86.0, 65.0, 2019.0, 16.4, 37.2,
151.0, 90.0, 2678.0, 16.5, 28.0,
140.0, 88.0, 2870.0, 18.1, 26.4,
151.0, 90.0, 3003.0, 20.1, 24.3,
225.0, 90.0, 3381.0, 18.7, 19.1,
97.0, 78.0, 2188.0, 15.8, 34.3,
134.0, 90.0, 2711.0, 15.5, 29.8,
120.0, 75.0, 2542.0, 17.5, 31.3,
119.0, 92.0, 2434.0, 15.0, 37.0,
108.0, 75.0, 2265.0, 15.2, 32.2,
86.0, 65.0, 2110.0, 17.9, 46.6,
156.0, 105.0, 2800.0, 14.4, 27.9,
85.0, 65.0, 2110.0, 19.2, 40.8,
90.0, 48.0, 2085.0, 21.7, 44.3,
90.0, 48.0, 2335.0, 23.7, 43.4,
121.0, 67.0, 2950.0, 19.9, 36.4,
146.0, 67.0, 3250.0, 21.8, 30.0,
91.0, 67.0, 1850.0, 13.8, 44.6,
97.0, 67.0, 2145.0, 18.0, 33.8,
89.0, 62.0, 1845.0, 15.3, 29.8,
168.0, 132.0, 2910.0, 11.4, 32.7,
70.0, 100.0, 2420.0, 12.5, 23.7,
122.0, 88.0, 2500.0, 15.1, 35.0,
107.0, 72.0, 2290.0, 17.0, 32.4,
135.0, 84.0, 2490.0, 15.7, 27.2,
151.0, 84.0, 2635.0, 16.4, 26.6,
156.0, 92.0, 2620.0, 14.4, 25.8,
173.0, 110.0, 2725.0, 12.6, 23.5,
135.0, 84.0, 2385.0, 12.9, 30.0,
79.0, 58.0, 1755.0, 16.9, 39.1,
86.0, 64.0, 1875.0, 16.4, 39.0,
81.0, 60.0, 1760.0, 16.1, 35.1,
97.0, 67.0, 2065.0, 17.8, 32.3,
85.0, 65.0, 1975.0, 19.4, 37.0,
89.0, 62.0, 2050.0, 17.3, 37.7,
91.0, 68.0, 1985.0, 16.0, 34.1,
105.0, 63.0, 2215.0, 14.9, 34.7,
98.0, 65.0, 2045.0, 16.2, 34.4,
98.0, 65.0, 2380.0, 20.7, 29.9,
105.0, 74.0, 2190.0, 14.2, 33.0,
107.0, 75.0, 2210.0, 14.4, 33.7,
108.0, 75.0, 2350.0, 16.8, 32.4,
119.0, 100.0, 2615.0, 14.8, 32.9,
120.0, 74.0, 2635.0, 18.3, 31.6,
141.0, 80.0, 3230.0, 20.4, 28.1,
145.0, 76.0, 3160.0, 19.6, 30.7,
168.0, 116.0, 2900.0, 12.6, 25.4,
146.0, 120.0, 2930.0, 13.8, 24.2,
231.0, 110.0, 3415.0, 15.8, 22.4,
350.0, 105.0, 3725.0, 19.0, 26.6,
200.0, 88.0, 3060.0, 17.1, 20.2,
225.0, 85.0, 3465.0, 16.6, 17.6,
112.0, 88.0, 2605.0, 19.6, 28.0,
112.0, 88.0, 2640.0, 18.6, 27.0,
112.0, 88.0, 2395.0, 18.0, 34.0,
112.0, 85.0, 2575.0, 16.2, 31.0,
135.0, 84.0, 2525.0, 16.0, 29.0,
151.0, 90.0, 2735.0, 18.0, 27.0,
140.0, 92.0, 2865.0, 16.4, 24.0,
105.0, 74.0, 1980.0, 15.3, 36.0,
91.0, 68.0, 2025.0, 18.2, 37.0,
91.0, 68.0, 1970.0, 17.6, 31.0,
105.0, 63.0, 2125.0, 14.7, 38.0,
98.0, 70.0, 2125.0, 17.3, 36.0,
120.0, 88.0, 2160.0, 14.5, 36.0,
107.0, 75.0, 2205.0, 14.5, 36.0,
108.0, 70.0, 2245.0, 16.9, 34.0,
91.0, 67.0, 1965.0, 15.0, 38.0,
91.0, 67.0, 1965.0, 15.7, 32.0,
91.0, 67.0, 1995.0, 16.2, 38.0,
181.0, 110.0, 2945.0, 16.4, 25.0,
262.0, 85.0, 3015.0, 17.0, 38.0,
156.0, 92.0, 2585.0, 14.5, 26.0,
232.0, 112.0, 2835.0, 14.7, 22.0,
144.0, 96.0, 2665.0, 13.9, 32.0,
135.0, 84.0, 2370.0, 13.0, 36.0,
151.0, 90.0, 2950.0, 17.3, 27.0,
140.0, 86.0, 2790.0, 15.6, 27.0,
97.0, 52.0, 2130.0, 24.6, 44.0,
135.0, 84.0, 2295.0, 11.6, 32.0,
120.0, 79.0, 2625.0, 18.6, 28.0,
119.0, 82.0, 2720.0, 19.4, 31.0,
})

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// Copyright ©2016 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat_test
import (
"fmt"
"log"
"github.com/gonum/floats"
"github.com/gonum/matrix/mat64"
"github.com/gonum/stat"
)
// symView is a helper for getting a View of a SymDense.
type symView struct {
sym *mat64.SymDense
i, j, r, c int
}
func (s symView) Dims() (r, c int) { return s.r, s.c }
func (s symView) At(i, j int) float64 {
if i < 0 || s.r <= i {
panic("i out of bounds")
}
if j < 0 || s.c <= j {
panic("j out of bounds")
}
return s.sym.At(s.i+i, s.j+j)
}
func (s symView) T() mat64.Matrix { return mat64.Transpose{s} }
func ExampleCanonicalCorrelations() {
// This example is directly analogous to Example 3.5 on page 87 of
// Koch, Inge. Analysis of multivariate and high-dimensional data.
// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
// bostonData is the Boston Housing Data of Harrison and Rubinfeld (1978)
n, _ := bostonData.Dims()
var xd, yd = 7, 4
// The variables (columns) of bostonData can be partitioned into two sets:
// those that deal with environmental/social variables (xdata), and those
// that contain information regarding the individual (ydata). Because the
// variables can be naturally partitioned in this way, these data are
// appropriate for canonical correlation analysis. The columns (variables)
// of xdata are, in order:
// per capita crime rate by town,
// proportion of non-retail business acres per town,
// nitric oxide concentration (parts per 10 million),
// weighted distances to Boston employment centres,
// index of accessibility to radial highways,
// pupil-teacher ratio by town, and
// proportion of blacks by town.
xdata := bostonData.Slice(0, n, 0, xd)
// The columns (variables) of ydata are, in order:
// average number of rooms per dwelling,
// proportion of owner-occupied units built prior to 1940,
// full-value property-tax rate per $10000, and
// median value of owner-occupied homes in $1000s.
ydata := bostonData.Slice(0, n, xd, xd+yd)
// For comparison, calculate the correlation matrix for the original data.
var cor mat64.SymDense
stat.CorrelationMatrix(&cor, bostonData, nil)
// Extract just those correlations that are between xdata and ydata.
var corRaw = symView{sym: &cor, i: 0, j: xd, r: xd, c: yd}
// Note that the strongest correlation between individual variables is 0.91
// between the 5th variable of xdata (index of accessibility to radial
// highways) and the 3rd variable of ydata (full-value property-tax rate per
// $10000).
fmt.Printf("corRaw = %.4f", mat64.Formatted(corRaw, mat64.Prefix(" ")))
// Calculate the canonical correlations.
cc, err := stat.CanonicalCorrelations(xdata, ydata, nil)
if err != nil {
log.Fatal(err)
}
// Unpack cc.
ccors := cc.Corrs(nil)
pVecs := cc.Left(true)
qVecs := cc.Right(true)
phiVs := cc.Left(false)
psiVs := cc.Right(false)
// Canonical Correlation Matrix, or the correlations between the sphered
// data.
var corSph mat64.Dense
corSph.Clone(pVecs)
col := make([]float64, xd)
for j := 0; j < yd; j++ {
mat64.Col(col, j, &corSph)
floats.Scale(ccors[j], col)
corSph.SetCol(j, col)
}
corSph.Product(&corSph, qVecs.T())
fmt.Printf("\n\ncorSph = %.4f", mat64.Formatted(&corSph, mat64.Prefix(" ")))
// Canonical Correlations. Note that the first canonical correlation is
// 0.95, stronger than the greatest correlation in the original data, and
// much stronger than the greatest correlation in the sphered data.
fmt.Printf("\n\nccors = %.4f", ccors)
// Left and right eigenvectors of the canonical correlation matrix.
fmt.Printf("\n\npVecs = %.4f", mat64.Formatted(pVecs, mat64.Prefix(" ")))
fmt.Printf("\n\nqVecs = %.4f", mat64.Formatted(qVecs, mat64.Prefix(" ")))
// Canonical Correlation Transforms. These can be useful as they represent
// the canonical variables as linear combinations of the original variables.
fmt.Printf("\n\nphiVs = %.4f", mat64.Formatted(phiVs, mat64.Prefix(" ")))
fmt.Printf("\n\npsiVs = %.4f", mat64.Formatted(psiVs, mat64.Prefix(" ")))
// Output:
// corRaw = ⎡-0.2192 0.3527 0.5828 -0.3883⎤
// ⎢-0.3917 0.6448 0.7208 -0.4837⎥
// ⎢-0.3022 0.7315 0.6680 -0.4273⎥
// ⎢ 0.2052 -0.7479 -0.5344 0.2499⎥
// ⎢-0.2098 0.4560 0.9102 -0.3816⎥
// ⎢-0.3555 0.2615 0.4609 -0.5078⎥
// ⎣ 0.1281 -0.2735 -0.4418 0.3335⎦
//
// corSph = ⎡ 0.0118 0.0525 0.2300 -0.1363⎤
// ⎢-0.1810 0.3213 0.3814 -0.1412⎥
// ⎢ 0.0166 0.2241 0.0104 -0.2235⎥
// ⎢ 0.0346 -0.5481 -0.0034 -0.1994⎥
// ⎢ 0.0303 -0.0956 0.7152 0.2039⎥
// ⎢-0.0298 -0.0022 0.0739 -0.3703⎥
// ⎣-0.1226 -0.0746 -0.3899 0.1541⎦
//
// ccors = [0.9451 0.6787 0.5714 0.2010]
//
// pVecs = ⎡-0.2574 0.0158 0.2122 -0.0946⎤
// ⎢-0.4837 0.3837 0.1474 0.6597⎥
// ⎢-0.0801 0.3494 0.3287 -0.2862⎥
// ⎢ 0.1278 -0.7337 0.4851 0.2248⎥
// ⎢-0.6969 -0.4342 -0.3603 0.0291⎥
// ⎢-0.0991 0.0503 0.6384 0.1022⎥
// ⎣ 0.4260 0.0323 -0.2290 0.6419⎦
//
// qVecs = ⎡ 0.0182 -0.1583 -0.0067 -0.9872⎤
// ⎢-0.2348 0.9483 -0.1462 -0.1554⎥
// ⎢-0.9701 -0.2406 -0.0252 0.0209⎥
// ⎣ 0.0593 -0.1330 -0.9889 0.0291⎦
//
// phiVs = ⎡-0.0027 0.0093 0.0490 -0.0155⎤
// ⎢-0.0429 -0.0242 0.0361 0.1839⎥
// ⎢-1.2248 5.6031 5.8094 -4.7927⎥
// ⎢-0.0044 -0.3424 0.4470 0.1150⎥
// ⎢-0.0742 -0.1193 -0.1116 0.0022⎥
// ⎢-0.0233 0.1046 0.3853 -0.0161⎥
// ⎣ 0.0001 0.0005 -0.0030 0.0082⎦
//
// psiVs = ⎡ 0.0302 -0.3002 0.0878 -1.9583⎤
// ⎢-0.0065 0.0392 -0.0118 -0.0061⎥
// ⎢-0.0052 -0.0046 -0.0023 0.0008⎥
// ⎣ 0.0020 0.0037 -0.1293 0.1038⎦
}

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// Copyright ©2016 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat_test
import (
"testing"
"github.com/gonum/floats"
"github.com/gonum/matrix/mat64"
"github.com/gonum/stat"
)
func TestCanonicalCorrelations(t *testing.T) {
for i, test := range []struct {
xdata mat64.Matrix
ydata mat64.Matrix
weights []float64
wantCorrs []float64
wantpVecs *mat64.Dense
wantqVecs *mat64.Dense
wantphiVs *mat64.Dense
wantpsiVs *mat64.Dense
epsilon float64
}{
// Test results verified using R.
{ // Truncated iris data, Sepal vs Petal measurements.
xdata: mat64.NewDense(10, 2, []float64{
5.1, 3.5,
4.9, 3.0,
4.7, 3.2,
4.6, 3.1,
5.0, 3.6,
5.4, 3.9,
4.6, 3.4,
5.0, 3.4,
4.4, 2.9,
4.9, 3.1,
}),
ydata: mat64.NewDense(10, 2, []float64{
1.4, 0.2,
1.4, 0.2,
1.3, 0.2,
1.5, 0.2,
1.4, 0.2,
1.7, 0.4,
1.4, 0.3,
1.5, 0.2,
1.4, 0.2,
1.5, 0.1,
}),
wantCorrs: []float64{0.7250624174504773, 0.5547679185730191},
wantpVecs: mat64.NewDense(2, 2, []float64{
0.0765914610875867, 0.9970625597666721,
0.9970625597666721, -0.0765914610875868,
}),
wantqVecs: mat64.NewDense(2, 2, []float64{
0.3075184850910837, 0.9515421069649439,
0.9515421069649439, -0.3075184850910837,
}),
wantphiVs: mat64.NewDense(2, 2, []float64{
-1.9794877596804641, 5.2016325219025124,
4.5211829944066553, -2.7263663170835697,
}),
wantpsiVs: mat64.NewDense(2, 2, []float64{
-0.0613084818030103, 10.8514169865438941,
12.7209032660734298, -7.6793888180353775,
}),
epsilon: 1e-12,
},
// Test results compared to those results presented in examples by
// Koch, Inge. Analysis of multivariate and high-dimensional data.
// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
{ // ASA Car Exposition Data of Ramos and Donoho (1983)
// Displacement, Horsepower, Weight
xdata: carData.Slice(0, 392, 0, 3),
// Acceleration, MPG
ydata: carData.Slice(0, 392, 3, 5),
wantCorrs: []float64{0.8782187384352336, 0.6328187219216761},
wantpVecs: mat64.NewDense(3, 2, []float64{
0.3218296374829181, 0.3947540257657075,
0.4162807660635797, 0.7573719053303306,
0.8503740401982725, -0.5201509936144236,
}),
wantqVecs: mat64.NewDense(2, 2, []float64{
-0.5161984172278830, -0.8564690269072364,
-0.8564690269072364, 0.5161984172278830,
}),
wantphiVs: mat64.NewDense(3, 2, []float64{
0.0025033152994308, 0.0047795464118615,
0.0201923608080173, 0.0409150208725958,
-0.0000247374128745, -0.0026766435161875,
}),
wantpsiVs: mat64.NewDense(2, 2, []float64{
-0.1666196759760772, -0.3637393866139658,
-0.0915512109649727, 0.1077863777929168,
}),
epsilon: 1e-12,
},
// Test results compared to those results presented in examples by
// Koch, Inge. Analysis of multivariate and high-dimensional data.
// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
{ // Boston Housing Data of Harrison and Rubinfeld (1978)
// Per capita crime rate by town,
// Proportion of non-retail business acres per town,
// Nitric oxide concentration (parts per 10 million),
// Weighted distances to Boston employment centres,
// Index of accessibility to radial highways,
// Pupil-teacher ratio by town, Proportion of blacks by town
xdata: bostonData.Slice(0, 506, 0, 7),
// Average number of rooms per dwelling,
// Proportion of owner-occupied units built prior to 1940,
// Full-value property-tax rate per $10000,
// Median value of owner-occupied homes in $1000s
ydata: bostonData.Slice(0, 506, 7, 11),
wantCorrs: []float64{0.9451239443886021, 0.6786622733370654, 0.5714338361583764, 0.2009739704710440},
wantpVecs: mat64.NewDense(7, 4, []float64{
-0.2574391924541903, 0.0158477516621194, 0.2122169934631024, -0.0945733803894706,
-0.4836594430018478, 0.3837101908138468, 0.1474448317415911, 0.6597324886718275,
-0.0800776365873296, 0.3493556742809252, 0.3287336458109373, -0.2862040444334655,
0.1277586360386374, -0.7337427663667596, 0.4851134819037011, 0.2247964865970192,
-0.6969432006136684, -0.4341748776002893, -0.3602872887636357, 0.0290661608626292,
-0.0990903250057199, 0.0503411215453873, 0.6384330631742202, 0.1022367136218303,
0.4260459963765036, 0.0323334351308141, -0.2289527516030810, 0.6419232947608805,
}),
wantqVecs: mat64.NewDense(4, 4, []float64{
0.0181660502363264, -0.1583489460479038, -0.0066723577642883, -0.9871935400650649,
-0.2347699045986119, 0.9483314614936594, -0.1462420505631345, -0.1554470767919033,
-0.9700704038477141, -0.2406071741000039, -0.0251838984227037, 0.0209134074358349,
0.0593000682318482, -0.1330460003097728, -0.9889057151969489, 0.0291161494720761,
}),
wantphiVs: mat64.NewDense(7, 4, []float64{
-0.0027462234108197, 0.0093444513500898, 0.0489643932714296, -0.0154967189805819,
-0.0428564455279537, -0.0241708702119420, 0.0360723472093996, 0.1838983230588095,
-1.2248435648802380, 5.6030921364723980, 5.8094144583797025, -4.7926812190419676,
-0.0043684825094649, -0.3424101164977618, 0.4469961215717917, 0.1150161814353696,
-0.0741534069521954, -0.1193135794923700, -0.1115518305471460, 0.0021638758323088,
-0.0233270323101624, 0.1046330818178399, 0.3853045975077387, -0.0160927870102877,
0.0001293051387859, 0.0004540746921446, -0.0030296315865440, 0.0081895477974654,
}),
wantpsiVs: mat64.NewDense(4, 4, []float64{
0.0301593362017375, -0.3002219289647127, 0.0878217377593682, -1.9583226531517062,
-0.0065483104073892, 0.0392212086716247, -0.0117570776209991, -0.0061113064481860,
-0.0052075523350125, -0.0045770200452960, -0.0022762313289592, 0.0008441873006821,
0.0020111735096327, 0.0037352799829930, -0.1292578071621794, 0.1037709056329765,
}),
epsilon: 1e-12,
},
} {
cc, err := stat.CanonicalCorrelations(test.xdata, test.ydata, test.weights)
if err != nil {
t.Errorf("%d: unexpected error: %v", i, err)
continue
}
corrs := cc.Corrs(nil)
pVecs := cc.Left(true)
qVecs := cc.Right(true)
phiVs := cc.Left(false)
psiVs := cc.Right(false)
if !floats.EqualApprox(corrs, test.wantCorrs, test.epsilon) {
t.Errorf("%d: unexpected variance result got:%v, want:%v", i, corrs, test.wantCorrs)
}
if !mat64.EqualApprox(pVecs, test.wantpVecs, test.epsilon) {
t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
i, mat64.Formatted(pVecs), mat64.Formatted(test.wantpVecs))
}
if !mat64.EqualApprox(qVecs, test.wantqVecs, test.epsilon) {
t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
i, mat64.Formatted(qVecs), mat64.Formatted(test.wantqVecs))
}
if !mat64.EqualApprox(phiVs, test.wantphiVs, test.epsilon) {
t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
i, mat64.Formatted(phiVs), mat64.Formatted(test.wantphiVs))
}
if !mat64.EqualApprox(psiVs, test.wantpsiVs, test.epsilon) {
t.Errorf("%d: unexpected CCA result got:\n%v\nwant:\n%v",
i, mat64.Formatted(psiVs), mat64.Formatted(test.wantpsiVs))
}
}
}

77
pca.go
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@@ -1,77 +0,0 @@
// Copyright ©2016 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat
import (
"math"
"github.com/gonum/floats"
"github.com/gonum/matrix"
"github.com/gonum/matrix/mat64"
)
// PrincipalComponents returns the principal component direction vectors and
// the column variances of the principal component scores, vecs * a, computed
// using the singular value decomposition of the input. The input a is an n×d
// matrix where each row is an observation and each column represents a variable.
//
// PrincipalComponents centers the variables but does not scale the variance.
//
// The slice weights is used to weight the observations. If weights is nil,
// each weight is considered to have a value of one, otherwise the length of
// weights must match the number of observations or PrincipalComponents will
// panic.
//
// On successful completion, the principal component direction vectors are
// returned in vecs as a d×min(n, d) matrix, and the variances are returned in
// vars as a min(n, d)-long slice in descending sort order.
//
// If no singular value decomposition is possible, vecs and vars are returned
// nil and ok is returned false.
func PrincipalComponents(a mat64.Matrix, weights []float64) (vecs *mat64.Dense, vars []float64, ok bool) {
n, d := a.Dims()
if weights != nil && len(weights) != n {
panic("stat: len(weights) != observations")
}
centered := mat64.NewDense(n, d, nil)
col := make([]float64, n)
for j := 0; j < d; j++ {
mat64.Col(col, j, a)
floats.AddConst(-Mean(col, weights), col)
centered.SetCol(j, col)
}
for i, w := range weights {
floats.Scale(math.Sqrt(w), centered.RawRowView(i))
}
kind := matrix.SVDFull
if n > d {
kind = matrix.SVDThin
}
var svd mat64.SVD
ok = svd.Factorize(centered, kind)
if !ok {
return nil, nil, false
}
vecs = &mat64.Dense{}
vecs.VFromSVD(&svd)
if n < d {
// Don't retain columns that are not valid direction vectors.
vecs.Clone(vecs.View(0, 0, d, n))
}
vars = svd.Values(nil)
var f float64
if weights == nil {
f = 1 / float64(n-1)
} else {
f = 1 / (floats.Sum(weights) - 1)
}
for i, v := range vars {
vars[i] = f * v * v
}
return vecs, vars, true
}

259
pca_cca.go Normal file
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@@ -0,0 +1,259 @@
// Copyright ©2016 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat
import (
"errors"
"math"
"github.com/gonum/floats"
"github.com/gonum/matrix"
"github.com/gonum/matrix/mat64"
)
// PrincipalComponents returns the principal component vectors and the variances
// of the principal component scores of the input data which is represented as
// an n×d matrix a where each row is an observation and each column is a
// variable.
//
// PrincipalComponents centers the variables but does not scale the variance.
//
// The slice weights is used to weight the observations. If weights is nil, each
// weight is considered to have a value of one, otherwise the length of weights
// must match the number of observations or PrincipalComponents will panic.
//
// On successful completion, the principal component vectors are returned in the
// columns of vecs as a d×min(n,d) matrix, and the column variances of the
// principal component scores, b * vecs where b is a with centered columns, are
// returned in vars as a min(n,d)-long slice in descending sort order.
//
// On failure, vecs and vars are returned nil and ok is returned false.
func PrincipalComponents(a mat64.Matrix, weights []float64) (vecs *mat64.Dense, vars []float64, ok bool) {
n, d := a.Dims()
if weights != nil && len(weights) != n {
panic("stat: len(weights) != observations")
}
svd, ok := svdFactorizeCentered(a, weights)
if !ok {
return nil, nil, false
}
vecs = &mat64.Dense{}
vecs.VFromSVD(svd)
if n < d {
// Don't retain columns that are not valid direction vectors.
vecs.Clone(vecs.Slice(0, d, 0, n))
}
vars = svd.Values(nil)
var f float64
if weights == nil {
f = 1 / float64(n-1)
} else {
f = 1 / (floats.Sum(weights) - 1)
}
for i, v := range vars {
vars[i] = f * v * v
}
return vecs, vars, true
}
// CC is the result of a canonical correlation analysis. A CC should not be used
// unless it has been returned by a successful call to CanonicalCorrelations.
type CC struct {
// n is the number of observations used to
// construct the canonical correlations.
n int
x, y, c *mat64.SVD
}
// Corrs returns the canonical correlations in dest.
func (c CC) Corrs(dest []float64) []float64 {
if c.c == nil {
panic("stat: canonical correlations missing or invalid")
}
return c.c.Values(dest)
}
// Left returns the left eigenvectors of the canonical correlation matrix if
// spheredSpace is true. If spheredSpace is false it returns these eigenvectors
// back-transformed to the original data space.
func (c CC) Left(spheredSpace bool) (vecs *mat64.Dense) {
if c.c == nil || c.x == nil || c.n < 2 {
panic("stat: canonical correlations missing or invalid")
}
var pv mat64.Dense
pv.UFromSVD(c.c)
if spheredSpace {
return &pv
}
var xv mat64.Dense
xs := c.x.Values(nil)
xv.VFromSVD(c.x)
scaleColsReciSqrt(&xv, xs)
pv.Product(&xv, xv.T(), &pv)
pv.Scale(math.Sqrt(float64(c.n-1)), &pv)
return &pv
}
// Right returns the right eigenvectors of the canonical correlation matrix if
// spheredSpace is true. If spheredSpace is false it returns these eigenvectors
// back-transformed to the original data space.
func (c CC) Right(spheredSpace bool) (vecs *mat64.Dense) {
if c.c == nil || c.y == nil || c.n < 2 {
panic("stat: canonical correlations missing or invalid")
}
var qv mat64.Dense
qv.VFromSVD(c.c)
if spheredSpace {
return &qv
}
var yv mat64.Dense
ys := c.y.Values(nil)
yv.VFromSVD(c.y)
scaleColsReciSqrt(&yv, ys)
qv.Product(&yv, yv.T(), &qv)
qv.Scale(math.Sqrt(float64(c.n-1)), &qv)
return &qv
}
// CanonicalCorrelations returns a CC which can provide the results of canonical
// correlation analysis of the input data x and y, columns of which should be
// interpretable as two sets of measurements on the same observations (rows).
// These observations are optionally weighted by weights.
//
// Canonical correlation analysis finds associations between two sets of
// variables on the same observations by finding linear combinations of the two
// sphered datasets that maximise the correlation between them.
//
// Some notation: let Xc and Yc denote the centered input data matrices x
// and y (column means subtracted from each column), let Sx and Sy denote the
// sample covariance matrices within x and y respectively, and let Sxy denote
// the covariance matrix between x and y. The sphered data can then be expressed
// as Xc * Sx^{-1/2} and Yc * Sy^{-1/2} respectively, and the correlation matrix
// between the sphered data is called the canonical correlation matrix,
// Sx^{-1/2} * Sxy * Sy^{-1/2}. In cases where S^{-1/2} is ambiguous for some
// covariance matrix S, S^{-1/2} is taken to be E * D^{-1/2} * E^T where S can
// be eigendecomposed as S = E * D * E^T.
//
// The canonical correlations are the correlations between the corresponding
// pairs of canonical variables and can be obtained with c.Corrs(). Canonical
// variables can be obtained by projecting the sphered data into the left and
// right eigenvectors of the canonical correlation matrix, and these
// eigenvectors can be obtained with c.Left(true) and c.Right(true)
// respectively. The canonical variables can also be obtained directly from the
// centered raw data by using the back-transformed eigenvectors which can be
// obtained with c.Left(false) and c.Right(false) respectively.
//
// The first pair of left and right eigenvectors of the canonical correlation
// matrix can be interpreted as directions into which the respective sphered
// data can be projected such that the correlation between the two projections
// is maximised. The second pair and onwards solve the same optimization but
// under the constraint that they are uncorrelated (orthogonal in sphered space)
// to previous projections.
//
// CanonicalCorrelations will panic if the inputs x and y do not have the same
// number of rows.
//
// The slice weights is used to weight the observations. If weights is nil, each
// weight is considered to have a value of one, otherwise the length of weights
// must match the number of observations (rows of both x and y) or CanonicalCorrelations will panic.
//
// More details can be found at
// https://en.wikipedia.org/wiki/Canonical_correlation
// or in Chapter 3 of
// Koch, Inge. Analysis of multivariate and high-dimensional data.
// Vol. 32. Cambridge University Press, 2013. ISBN: 9780521887939
func CanonicalCorrelations(x, y mat64.Matrix, weights []float64) (c CC, err error) {
n, _ := x.Dims()
yn, _ := y.Dims()
if n != yn {
panic("stat: unequal number of observations")
}
if weights != nil && len(weights) != n {
panic("stat: len(weights) != observations")
}
// Center and factorize x and y.
xsvd, ok := svdFactorizeCentered(x, weights)
if !ok {
return CC{}, errors.New("stat: failed to factorize x")
}
ysvd, ok := svdFactorizeCentered(y, weights)
if !ok {
return CC{}, errors.New("stat: failed to factorize y")
}
var xu, xv, yu, yv mat64.Dense
xu.UFromSVD(xsvd)
xv.VFromSVD(xsvd)
yu.UFromSVD(ysvd)
yv.VFromSVD(ysvd)
// Calculate and factorise the canonical correlation matrix.
var ccor mat64.Dense
ccor.Product(&xv, xu.T(), &yu, yv.T())
var csvd mat64.SVD
ok = csvd.Factorize(&ccor, svdKind(ccor.Dims()))
if !ok {
return CC{}, errors.New("stat: failed to factorize ccor")
}
return CC{n: n, x: xsvd, y: ysvd, c: &csvd}, nil
}
func svdKind(n, d int) matrix.SVDKind {
if n > d {
return matrix.SVDThin
}
return matrix.SVDFull
}
func svdFactorizeCentered(m mat64.Matrix, weights []float64) (svd *mat64.SVD, ok bool) {
n, d := m.Dims()
centered := mat64.NewDense(n, d, nil)
col := make([]float64, n)
for j := 0; j < d; j++ {
mat64.Col(col, j, m)
floats.AddConst(-Mean(col, weights), col)
centered.SetCol(j, col)
}
for i, w := range weights {
floats.Scale(math.Sqrt(w), centered.RawRowView(i))
}
svd = &mat64.SVD{}
ok = svd.Factorize(centered, svdKind(n, d))
if !ok {
svd = nil
}
return svd, ok
}
// scaleColsReciSqrt scales the columns of cols
// by the reciprocal square-root of vals.
func scaleColsReciSqrt(cols *mat64.Dense, vals []float64) {
if cols == nil {
panic("stat: input nil")
}
n, d := cols.Dims()
if len(vals) != d {
panic("stat: input length mismatch")
}
col := make([]float64, n)
for j := 0; j < d; j++ {
mat64.Col(col, j, cols)
floats.Scale(math.Sqrt(1/vals[j]), col)
cols.SetCol(j, col)
}
}