├── .gitignore ├── LICENSE ├── README.md ├── durand-kerner-aberth └── dka.ml ├── fft └── fft.ml ├── k-means ├── dataset.ml ├── dataset.png ├── dataset.txt └── kmeans.ml ├── levinson-durbin ├── dataset.ml └── levinson.ml ├── lu-decomposition └── lu.ml ├── neural-network └── naive-multilayer │ ├── dataset.ml │ └── neuralNetwork.ml ├── qr-decomposition └── qr.ml └── wav ├── wav.ml └── wav.mli /.gitignore: -------------------------------------------------------------------------------- 1 | *.annot 2 | *.cmo 3 | *.cma 4 | *.cmi 5 | *.a 6 | *.o 7 | *.cmx 8 | *.cmxs 9 | *.cmxa 10 | *.cmt 11 | *.cmti 12 | *.out 13 | *~ 14 | 15 | # ocamlbuild working directory 16 | _build/ 17 | 18 | # ocamlbuild targets 19 | *.byte 20 | *.native 21 | 22 | # oasis generated files 23 | setup.data 24 | setup.log 25 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2015 Akinori ABE 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | 23 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Stand-alone programs for numerical analysis in OCaml 2 | 3 | Sometimes you need a small code (that has no dependency to a huge or unfamiliar 4 | library/tool) for scientific computing. In this repository, we distribute such 5 | [OCaml](http://ocaml.org/) programs under MIT license (the copyright of each 6 | data set belongs to the maker of the data). 7 | 8 | ## Linear algebra 9 | 10 | - [LU decomposition](lu-decomposition/): 11 | [LU decomposition](http://en.wikipedia.org/wiki/LU_decomposition) is 12 | factorization such that `PA = LU` (or `A = PLU`) where `A` is a matrix, `L` is 13 | a lower trapezoidal matrix, `U` is a upper trapezoidal matrix, and `P` is 14 | a permutation matrix. LU decomposition is used for solving linear equations, 15 | computing determinant, etc. This code implements Crout's method. 16 | 17 | - Compilation: `ocamlopt lu.ml` 18 | 19 | - [QR decomposition](qr-decomposition/): 20 | [QR decomposition](http://en.wikipedia.org/wiki/QR_decomposition) is to 21 | factorize matrix `A` into `QR` where `Q` is an orthogonal matrix and `R` is a 22 | right trapezoidal matrix (a.k.a., an upper trapezoidal matrix). 23 | QR decomposition is used for solving linear equations, eigenproblems, etc. 24 | This program performs QR decomposition via 25 | [Householder transformation](http://en.wikipedia.org/wiki/Householder_transformation). 26 | 27 | - Compilation: `ocamlopt qr.ml` 28 | 29 | ## Signal processing 30 | 31 | - [Fast Fourier transform](fft/): 32 | This is an implementation of radix-2 33 | [Cooley-Tukey fast Fourier transform (FFT) algorithm](http://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm), 34 | the most famous method in FFT algorithms. The naive computation according to 35 | the definition of discrete Fourier transform (DFT) takes `O(n^2)` time where 36 | `n` is the number of input points, but this FFT algorithm takes only 37 | `O(n log n)` time. Input length `n` must be equal to `2^m` (where `m` is a 38 | natural number). Fourier transform is frequently used for signal analysis, 39 | data compression, etc. 40 | 41 | - Compilation: `ocamlopt fft.ml` 42 | 43 | - [Autocorrelation & Levinson-Durbin recursion](levinson-durbin/): 44 | [Levinson-Durbin recursion](http://en.wikipedia.org/wiki/Levinson_recursion) 45 | is an algorithm to compute AR coefficients of 46 | [autoregressive (AR) model](http://en.wikipedia.org/wiki/Autoregressive_model). 47 | The most well-known application of AR model is 48 | [linear predictive coding (LPC)](http://en.wikipedia.org/wiki/Linear_predictive_coding), 49 | a classic analysis/coding/compression approach for voice. We decompose 50 | input voice into *glottal source* (buzz-like sound) and *vocal tract filter 51 | characteristics* (filter coefficients) by using Levinson-Durbin algorithm, 52 | and analyze or encode the two kinds of sound by different ways. 53 | LPC vocoder (voice coder) is applied to 54 | [FS-1015](http://en.wikipedia.org/wiki/FS-1015) (secure telephony speech 55 | encoding), [Shorten](http://en.wikipedia.org/wiki/Shorten_(file_format)), 56 | [MPEG-4 ALS](http://en.wikipedia.org/wiki/MPEG-4_ALS), 57 | [FLAC](http://en.wikipedia.org/wiki/FLAC) audio codec, etc. This program 58 | computes AR coefficients from time-domain sound and outputs them. 59 | 60 | - Compilation: `ocamlopt dataset.ml levinson.ml` 61 | - Data set: Japanese vowel sound /a/ (1957 points), /i/ (3439 points), 62 | /u/ (2644 points), /e/ (3316 points), /o/ (2793 points); 63 | sampling rate = 16000, original data is at 64 | http://www.gavo.t.u-tokyo.ac.jp/~mine/B3enshu2001/samples.html 65 | - AR order: 20 66 | 67 | ## Machine learning 68 | 69 | ### Classification 70 | 71 | - [Naive multilayer neural network](neural-network/naive-multilayer): 72 | a neural network that has two or more layers can be used for nonlinear 73 | classification, regression, etc. in machine learning. This code is a very 74 | simple implementation of multilayer neural network. This neural network tends 75 | to fall into over-fitting. (In the past, multilayer neural networks are rarely 76 | applied for practical tasks because they have some problems such as 77 | [over-fitting](http://en.wikipedia.org/wiki/Overfitting) and 78 | [vanishing gradient](http://en.wikipedia.org/wiki/Vanishing_gradient_problem). 79 | After 2006, [Hinton](http://www.cs.toronto.edu/~hinton/) et al. proposed some 80 | epoch‐making approaches to solve the problems and accomplished surprisingly 81 | high performance. The newer techniques are known as *deep learning*.) 82 | The following default setting is for classification. If you want to use this 83 | for regression, you should change the activation function of the output layer 84 | to a linear function, and the error function to sum of squared errors. 85 | 86 | - Compilation: `ocamlopt dataset.ml neuralNetwork.ml` 87 | - Data set: [Ionosphere (UCI Machine Learning Repository)](https://archive.ics.uci.edu/ml/datasets/Ionosphere) 88 | (\#features = 34, \#classes = 2) 89 | - Training: error backpropagation 90 | [[Rumelhart et al., 1986]](http://dl.acm.org/citation.cfm?id=104293) + 91 | stochastic gradient descent (with a constant learning rate) 92 | - Regularization: none 93 | - Error function: cross-entropy 94 | - Layers: 3 layers + the input layer (all neurons in each layer are connected 95 | with all neurons in the lower layer. 96 | - The 1st hidden layer: 10 units, activation function = tanh 97 | - The 2nd hidden layer: 5 units, activation function = tanh 98 | - The output layer: 2 units (binary classification, 1-of-K coding), 99 | activation function = softmax 100 | 101 | ### Clustering 102 | 103 | - [K-means](k-means/): 104 | This program implements a classic clustering approach 105 | [K-means](http://en.wikipedia.org/wiki/K-means_clustering). 106 | 107 | - Compilation: `ocamlopt dataset.ml kmeans.ml` 108 | - Data set: artificially generated according to three kinds of Gaussian 109 | distribution (dimension = 2, \#classes = 3, \#points of each class = 1000) 110 | 111 | ![The distribution of data points](k-means/dataset.png) 112 | 113 | ## Miscellaneous 114 | 115 | - [Durand-Kerner-Aberth method](durand-kerner-aberth/): 116 | [Durand-Kerner method](http://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method) 117 | is an algorithm to find all (complex) roots of a given polynominal at the same 118 | time, and [Aberth method](http://en.wikipedia.org/wiki/Aberth_method) is an 119 | approach to compute the initial values for Durand-Kerner method. 120 | 121 | - Compilation: `ocamlopt dka.ml` 122 | 123 | ## Utilities 124 | 125 | - [WAV reader/writer](wav/): 126 | A lightweight reader/writer for WAV files. This code only supports 127 | uncompressed linear PCM format. 128 | 129 | - Compilation: `ocamlopt -c wav.mli wav.ml` 130 | -------------------------------------------------------------------------------- /durand-kerner-aberth/dka.ml: -------------------------------------------------------------------------------- 1 | (** dka.ml --- Durand-Kerner-Aberth method 2 | 3 | [MIT Lisence] Copyright (C) 2015 Akinori ABE 4 | *) 5 | 6 | open Format 7 | open Complex 8 | 9 | module Array = struct 10 | include Array 11 | 12 | let fold_lefti f init x = 13 | let acc = ref init in 14 | for i = 0 to length x - 1 do acc := f i !acc x.(i) done; 15 | !acc 16 | 17 | let for_all2 f x y = 18 | assert(length x = length y); 19 | let rec aux i = 20 | if i < 0 then true 21 | else if f x.(i) y.(i) then aux (i - 1) 22 | else false 23 | in 24 | aux (length x - 1) 25 | end 26 | 27 | let ( +! ) = add 28 | let ( -! ) = sub 29 | let ( *! ) = mul 30 | let ( /! ) = div 31 | 32 | let pi = 3.14159265358979 33 | 34 | (** [roots_initvals ?r [c(n); ...; c(2); c(1); c(0)]] computes 35 | initial values for [roots] by Aberth's method. 36 | @param r a radius of a circle containing all roots on complex plane 37 | *) 38 | let roots_init_vals ?(r = 1000.) cs = 39 | let n = Array.length cs in 40 | if n < 2 then invalid_arg "roots_init_vals: #coefficients < 2"; 41 | let n = n - 1 in (* the order of a given polynominal *) 42 | let s = pi /. float n in 43 | let t = cs.(1) /! (cs.(0) *! { re = ~-. (float n); im = 0. }) in 44 | Array.init n 45 | (fun i -> 46 | let angle = s *. (2.0 *. float i +. 0.5) in 47 | t +! ({ re=r; im=0. } *! (exp { re=0.; im=angle }))) 48 | 49 | (** [roots ?epsilon ?init [c(n); ...; c(2); c(1); c(0)]] computes roots of a 50 | polynominal [c(n)*x**n + ... + c(2)*x**2 + c(1)*x + c(0)] by using the 51 | Durand-Kerner method. 52 | *) 53 | let roots ?(epsilon = 1e-6) ?init cs = 54 | let zs = match init with (* initial values of roots *) 55 | | None -> roots_init_vals cs 56 | | Some zs0 -> zs0 in 57 | let calc_poly x = Array.fold_left (fun acc ci -> acc *! x +! ci) zero cs in 58 | let cn = cs.(0) in (* c(n) *) 59 | let rec update_z zs = (* update z(0), ..., z(n-1) until they converge *) 60 | let update_zi zs i zi = (* update z(i) *) 61 | let deno = Array.fold_lefti 62 | (fun j acc zj -> if i = j then acc else acc *! (zi -! zj)) cn zs in 63 | zi -! calc_poly zi /! deno 64 | in 65 | let zs' = Array.mapi (update_zi zs) zs in (* new z(0),...,z(n-1) *) 66 | if Array.for_all2 (fun zi zi' -> norm2 (zi -! zi') < epsilon) zs zs' 67 | then zs' (* converged! *) 68 | else update_z zs' 69 | in 70 | update_z zs 71 | 72 | let main () = 73 | (* -300 + 320 x - 59 x^2 - 26 x^3 + 5 x^4 + 2 x^5 = 0 *) 74 | let cs = [| 75 | { re=2.; im=0. }; 76 | { re=5.; im=0. }; 77 | { re=(-26.); im=0. }; 78 | { re=(-59.); im=0. }; 79 | { re=(320.); im=0. }; 80 | { re=(-300.); im=0.}; 81 | |] in 82 | let roots = roots cs in 83 | Array.iter (fun { re; im } -> printf "%g %+gi@." re im) roots 84 | 85 | let () = main () 86 | -------------------------------------------------------------------------------- /fft/fft.ml: -------------------------------------------------------------------------------- 1 | (** fft.ml --- Cooley-Tukey fast Fourier transform algorithm *) 2 | 3 | open Format 4 | open Complex 5 | 6 | (** [get_n_bits n] returns the number of bits of [n]. *) 7 | let get_n_bits = 8 | let rec aux n i = 9 | if i = 1 then n 10 | else if i > 0 && i land 1 = 0 then aux (n + 1) (i lsr 1) 11 | else invalid_arg "invalid input length" 12 | in 13 | aux 0 14 | 15 | (** [bitrev n i] bit-reverses [n]-digit integer [i]. *) 16 | let bitrev = 17 | let rec aux acc n i = 18 | if n = 0 then acc else aux ((acc lsl 1) lor (i land 1)) (n - 1) (i lsr 1) 19 | in 20 | aux 0 21 | 22 | let ( +! ) = add 23 | let ( -! ) = sub 24 | let ( *! ) = mul 25 | let ( /! ) = div 26 | 27 | let make_twiddle_factors len = 28 | let pi = 3.14159265358979 in 29 | let c = ~-. 2.0 *. pi /. float len in 30 | Array.init (len / 2) (fun i -> exp { re = 0.; im = c *. float i }) 31 | 32 | let fft x = 33 | let len = Array.length x in 34 | let n_bits = get_n_bits len in 35 | let w = make_twiddle_factors len in 36 | let y = Array.init len (fun i -> x.(bitrev n_bits i)) in 37 | let butterfly m n ofs = 38 | for i = 0 to n / 2 - 1 do 39 | let j, k = ofs + i, ofs + i + n / 2 in 40 | let a, b = y.(j), y.(k) in 41 | y.(j) <- a +! w.(i * m) *! b; 42 | y.(k) <- a -! w.(i * m) *! b; 43 | done 44 | in 45 | for nb = 1 to n_bits do 46 | let n = 1 lsl nb in 47 | let m = 1 lsl (n_bits - nb) in 48 | for i = 0 to m - 1 do butterfly m n (n * i) done 49 | done; 50 | y 51 | 52 | let ifft x = 53 | let c = 1.0 /. float (Array.length x) in 54 | let normalize z = { re = c *. z.re; im = ~-. c *. z.im } in 55 | fft (Array.map normalize x) 56 | 57 | let main () = 58 | let x = [| 59 | 1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 60 | 9.0; 10.0; 11.0; 12.0; 13.0; 14.0; 15.0; 16.0; 61 | |] 62 | |> Array.map (fun x -> { re = x; im = 0.0 }) in 63 | let y = fft x in 64 | printf "FFT =@\n @["; 65 | Array.iteri (fun i yi -> printf "[%d] %f %+fi@\n" i yi.re yi.im) y; 66 | printf "@]@\n"; 67 | let z = ifft y in 68 | printf "IFFT =@\n @["; 69 | Array.iteri (fun i zi -> printf "[%d] %f %+fi@\n" i zi.re zi.im) z; 70 | printf "@]@." 71 | 72 | let () = main () 73 | -------------------------------------------------------------------------------- /k-means/dataset.ml: -------------------------------------------------------------------------------- 1 | (** Clustring data set 2 | 3 | This data set contains three classes that are generated according to 4 | two-dimensional Gaussian distribution. 5 | *) 6 | 7 | let n_classes = 3 8 | 9 | let samples = [| 10 | ([|4.92158; 7.09815|], 0); 11 | ([|5.81383; 6.01565|], 0); 12 | ([|4.36317; 6.04401|], 0); 13 | ([|4.55469; 8.99767|], 0); 14 | ([|6.12869; 7.97226|], 0); 15 | ([|4.53521; 3.12714|], 0); 16 | ([|3.54062; 4.87403|], 0); 17 | ([|5.25506; 6.94233|], 0); 18 | ([|4.9273; 5.46974|], 0); 19 | ([|4.05719; 6.75775|], 0); 20 | ([|4.45576; 4.92348|], 0); 21 | ([|5.95644; 6.62171|], 0); 22 | ([|3.46091; 6.0821|], 0); 23 | ([|4.41918; 6.45101|], 0); 24 | ([|6.32739; 7.50817|], 0); 25 | ([|2.57065; 6.60825|], 0); 26 | ([|6.47355; 5.81471|], 0); 27 | ([|5.08728; 8.50587|], 0); 28 | ([|6.39073; 7.76195|], 0); 29 | ([|5.76092; 5.98383|], 0); 30 | ([|5.24876; 6.92229|], 0); 31 | ([|3.58493; 8.45347|], 0); 32 | ([|6.48666; 6.92533|], 0); 33 | ([|3.86602; 4.08991|], 0); 34 | ([|7.3689; 6.46896|], 0); 35 | ([|5.01608; 8.58189|], 0); 36 | ([|6.15132; 8.09649|], 0); 37 | ([|6.16405; 5.81923|], 0); 38 | ([|3.07234; 7.14281|], 0); 39 | ([|4.10919; 6.38804|], 0); 40 | ([|2.9665; 5.30797|], 0); 41 | ([|4.09333; 6.63553|], 0); 42 | ([|5.62551; 5.65647|], 0); 43 | ([|4.90517; 6.27995|], 0); 44 | ([|4.8847; 7.32103|], 0); 45 | ([|5.58835; 4.60537|], 0); 46 | ([|8.09213; 7.45106|], 0); 47 | ([|4.37077; 6.94562|], 0); 48 | ([|3.71009; 6.85742|], 0); 49 | ([|4.20315; 4.60728|], 0); 50 | ([|4.72685; 7.52036|], 0); 51 | ([|6.34007; 7.83467|], 0); 52 | ([|4.07844; 5.55581|], 0); 53 | ([|2.32602; 4.95526|], 0); 54 | ([|5.66899; 8.63053|], 0); 55 | ([|7.29306; 8.05774|], 0); 56 | ([|5.68242; 5.89045|], 0); 57 | ([|4.5957; 6.65504|], 0); 58 | ([|4.83003; 4.94802|], 0); 59 | ([|5.08084; 6.04463|], 0); 60 | ([|4.04726; 4.54704|], 0); 61 | ([|4.20377; 5.54231|], 0); 62 | ([|2.51916; 6.35499|], 0); 63 | ([|6.20912; 6.89301|], 0); 64 | ([|3.27776; 6.96892|], 0); 65 | ([|1.32563; 4.8233|], 0); 66 | ([|3.40929; 6.09756|], 0); 67 | ([|6.87251; 6.30003|], 0); 68 | ([|3.83601; 7.83547|], 0); 69 | ([|5.13784; 6.33883|], 0); 70 | ([|4.88366; 6.59026|], 0); 71 | ([|5.71992; 5.04449|], 0); 72 | ([|5.67868; 7.38863|], 0); 73 | ([|3.66673; 6.3691|], 0); 74 | ([|5.11931; 4.08177|], 0); 75 | ([|4.83841; 8.24535|], 0); 76 | ([|5.30823; 7.89441|], 0); 77 | ([|6.59238; 7.08117|], 0); 78 | ([|6.50176; 7.72884|], 0); 79 | ([|2.4734; 6.5848|], 0); 80 | ([|4.89856; 5.56919|], 0); 81 | ([|6.03212; 7.6736|], 0); 82 | ([|3.36993; 4.6803|], 0); 83 | ([|6.88326; 8.0949|], 0); 84 | ([|5.6551; 8.88415|], 0); 85 | ([|6.22662; 5.55753|], 0); 86 | ([|7.24123; 7.99841|], 0); 87 | ([|5.91176; 6.39267|], 0); 88 | ([|4.73581; 6.30805|], 0); 89 | ([|3.43643; 3.68549|], 0); 90 | ([|7.89253; 5.94836|], 0); 91 | ([|5.54078; 6.4136|], 0); 92 | ([|5.71753; 6.77294|], 0); 93 | ([|3.4772; 4.73904|], 0); 94 | ([|4.63397; 6.78753|], 0); 95 | ([|6.76257; 6.9776|], 0); 96 | ([|4.60409; 7.44333|], 0); 97 | ([|3.89086; 7.05717|], 0); 98 | ([|4.23822; 6.05349|], 0); 99 | ([|5.53766; 7.12207|], 0); 100 | ([|6.51101; 7.18789|], 0); 101 | ([|3.17314; 5.97846|], 0); 102 | ([|3.45705; 6.95076|], 0); 103 | ([|6.37248; 6.34209|], 0); 104 | ([|5.7138; 8.90435|], 0); 105 | ([|5.69871; 6.82426|], 0); 106 | ([|3.5969; 6.45118|], 0); 107 | ([|7.95081; 7.2952|], 0); 108 | ([|4.96224; 7.28647|], 0); 109 | ([|6.27065; 6.61742|], 0); 110 | ([|5.91905; 5.68828|], 0); 111 | ([|6.60292; 6.7778|], 0); 112 | ([|3.4581; 6.23861|], 0); 113 | ([|5.15194; 4.0876|], 0); 114 | ([|6.37862; 7.4056|], 0); 115 | ([|4.4484; 8.08953|], 0); 116 | ([|5.34502; 7.99043|], 0); 117 | ([|5.02464; 4.73026|], 0); 118 | ([|3.14565; 7.90735|], 0); 119 | ([|4.08262; 5.90371|], 0); 120 | ([|6.74731; 6.82575|], 0); 121 | ([|4.4599; 6.38457|], 0); 122 | ([|7.18605; 10.8665|], 0); 123 | ([|5.17896; 9.41558|], 0); 124 | ([|6.40294; 7.68106|], 0); 125 | ([|3.00129; 5.31708|], 0); 126 | ([|5.29942; 7.19457|], 0); 127 | ([|8.22629; 7.89854|], 0); 128 | ([|3.74881; 5.86598|], 0); 129 | ([|4.38084; 4.90158|], 0); 130 | ([|7.72852; 7.75288|], 0); 131 | ([|2.99046; 4.82481|], 0); 132 | ([|7.36555; 8.16846|], 0); 133 | ([|4.03142; 6.56927|], 0); 134 | ([|5.39705; 6.55261|], 0); 135 | ([|2.64762; 5.77129|], 0); 136 | ([|6.30259; 8.29711|], 0); 137 | ([|2.88273; 5.19736|], 0); 138 | ([|6.45846; 6.84525|], 0); 139 | ([|5.55864; 7.58292|], 0); 140 | ([|3.7233; 5.34288|], 0); 141 | ([|4.14566; 7.23268|], 0); 142 | ([|6.73189; 8.70435|], 0); 143 | ([|6.28944; 8.03451|], 0); 144 | ([|3.70395; 4.77436|], 0); 145 | ([|3.36981; 8.52264|], 0); 146 | ([|5.03886; 7.83391|], 0); 147 | ([|3.37374; 6.42048|], 0); 148 | ([|4.38566; 5.28952|], 0); 149 | ([|7.77427; 7.8868|], 0); 150 | ([|6.41164; 5.69855|], 0); 151 | ([|5.36113; 8.71171|], 0); 152 | ([|4.59991; 4.93205|], 0); 153 | ([|6.35214; 6.1348|], 0); 154 | ([|5.35281; 8.46326|], 0); 155 | ([|6.07291; 5.30571|], 0); 156 | ([|5.14728; 6.91676|], 0); 157 | ([|6.42055; 8.90867|], 0); 158 | ([|6.63426; 7.3938|], 0); 159 | ([|4.6844; 6.50485|], 0); 160 | ([|4.73914; 7.50951|], 0); 161 | ([|3.73554; 7.69706|], 0); 162 | ([|4.83276; 5.22763|], 0); 163 | ([|4.79608; 7.22376|], 0); 164 | ([|4.38527; 8.52666|], 0); 165 | ([|5.04675; 7.1933|], 0); 166 | ([|6.94; 8.69726|], 0); 167 | ([|7.38372; 6.95213|], 0); 168 | ([|5.21512; 6.43681|], 0); 169 | ([|3.13331; 5.76696|], 0); 170 | ([|5.9184; 6.85065|], 0); 171 | ([|4.41348; 4.01028|], 0); 172 | ([|4.94589; 5.71696|], 0); 173 | ([|5.30295; 4.27131|], 0); 174 | ([|5.58847; 7.54492|], 0); 175 | ([|5.58194; 6.51169|], 0); 176 | ([|5.64032; 5.79912|], 0); 177 | ([|3.57368; 4.3421|], 0); 178 | ([|2.52102; 6.12291|], 0); 179 | ([|4.89453; 6.67626|], 0); 180 | ([|5.96083; 9.14329|], 0); 181 | ([|6.90014; 6.76825|], 0); 182 | ([|7.74593; 6.38157|], 0); 183 | ([|5.52606; 5.82756|], 0); 184 | ([|5.645; 8.04593|], 0); 185 | ([|4.15703; 5.2269|], 0); 186 | ([|5.6698; 6.0843|], 0); 187 | ([|5.16535; 6.28985|], 0); 188 | ([|4.65713; 5.04234|], 0); 189 | ([|6.97923; 8.96958|], 0); 190 | ([|4.46056; 7.57686|], 0); 191 | ([|4.07087; 7.71989|], 0); 192 | ([|6.29159; 9.17017|], 0); 193 | ([|4.43121; 5.23774|], 0); 194 | ([|4.11329; 8.39212|], 0); 195 | ([|3.97184; 4.06871|], 0); 196 | ([|3.75865; 7.20994|], 0); 197 | ([|7.06121; 7.23449|], 0); 198 | ([|6.26288; 6.62298|], 0); 199 | ([|4.63428; 6.55644|], 0); 200 | ([|4.96503; 6.72958|], 0); 201 | ([|5.24181; 5.52654|], 0); 202 | ([|3.61786; 6.56779|], 0); 203 | ([|6.32775; 7.47512|], 0); 204 | ([|3.53583; 6.47336|], 0); 205 | ([|5.92408; 5.88287|], 0); 206 | ([|5.61739; 8.63334|], 0); 207 | ([|3.70325; 4.87852|], 0); 208 | ([|3.13859; 4.65313|], 0); 209 | ([|7.1399; 6.85088|], 0); 210 | ([|6.04047; 6.88692|], 0); 211 | ([|5.68052; 7.38279|], 0); 212 | ([|3.23835; 6.29804|], 0); 213 | ([|3.53413; 5.69802|], 0); 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([|0.96558; 2.45168|], 1); 1731 | ([|-0.601448; 1.29976|], 1); 1732 | ([|2.424; 1.63351|], 1); 1733 | ([|5.13825; 1.39217|], 1); 1734 | ([|1.51904; 0.489319|], 1); 1735 | ([|3.07757; 1.31227|], 1); 1736 | ([|4.55664; 3.50617|], 1); 1737 | ([|3.02229; 1.54738|], 1); 1738 | ([|2.71552; 3.66853|], 1); 1739 | ([|-0.0925946; 0.0889657|], 1); 1740 | ([|0.49272; 1.11203|], 1); 1741 | ([|3.54343; 2.89552|], 1); 1742 | ([|4.46965; 2.14482|], 1); 1743 | ([|3.30551; 1.84733|], 1); 1744 | ([|2.42957; 1.58515|], 1); 1745 | ([|4.70261; 3.26584|], 1); 1746 | ([|4.64805; 2.40162|], 1); 1747 | ([|0.172022; 1.69594|], 1); 1748 | ([|2.41407; 2.01327|], 1); 1749 | ([|2.41687; 1.58337|], 1); 1750 | ([|4.92418; 0.867796|], 1); 1751 | ([|4.24804; 3.54864|], 1); 1752 | ([|2.3714; 2.74364|], 1); 1753 | ([|-1.68655; 1.07413|], 1); 1754 | ([|2.18954; 1.40857|], 1); 1755 | ([|0.640967; 1.04911|], 1); 1756 | ([|2.00822; 2.43401|], 1); 1757 | ([|-4.04861; 0.755786|], 1); 1758 | ([|2.27837; 1.19646|], 1); 1759 | ([|3.67554; 3.56396|], 1); 1760 | ([|-0.692943; 0.0677744|], 1); 1761 | ([|2.40111; 0.739728|], 1); 1762 | ([|-0.445121; 4.2114|], 1); 1763 | ([|2.37573; 2.77911|], 1); 1764 | ([|-0.155025; 2.8286|], 1); 1765 | ([|3.99734; 2.78583|], 1); 1766 | ([|2.25473; 1.20705|], 1); 1767 | ([|4.88237; 3.76176|], 1); 1768 | ([|2.49207; 1.72561|], 1); 1769 | ([|1.40758; 2.43782|], 1); 1770 | ([|2.83653; 2.36367|], 1); 1771 | ([|6.06144; 2.44784|], 1); 1772 | ([|1.36019; 1.53963|], 1); 1773 | ([|-3.36753; 0.468981|], 1); 1774 | ([|5.30994; 2.44231|], 1); 1775 | ([|1.9585; 1.39444|], 1); 1776 | ([|1.35863; 3.3928|], 1); 1777 | ([|2.90924; 1.58289|], 1); 1778 | ([|3.13111; 1.61013|], 1); 1779 | ([|1.46205; 2.88757|], 1); 1780 | ([|5.72814; 3.0099|], 1); 1781 | ([|-0.335738; -0.0697402|], 1); 1782 | ([|1.37473; 2.30354|], 1); 1783 | ([|3.41531; 0.849781|], 1); 1784 | ([|3.33359; 2.46935|], 1); 1785 | ([|4.87531; 2.50409|], 1); 1786 | ([|0.752074; 2.19705|], 1); 1787 | ([|1.43599; 2.96597|], 1); 1788 | ([|1.10334; 1.53263|], 1); 1789 | ([|2.82717; 2.83064|], 1); 1790 | ([|8.4505; 2.72071|], 1); 1791 | ([|2.45611; 2.76754|], 1); 1792 | ([|2.18985; 1.90816|], 1); 1793 | ([|4.81681; 4.62685|], 1); 1794 | ([|1.50281; 1.59521|], 1); 1795 | ([|1.6896; 1.0429|], 1); 1796 | ([|1.69778; 1.98133|], 1); 1797 | ([|3.75086; 2.99725|], 1); 1798 | ([|4.50136; 3.66068|], 1); 1799 | ([|2.61416; 2.97759|], 1); 1800 | ([|0.275738; 2.35971|], 1); 1801 | ([|1.1594; 3.29303|], 1); 1802 | ([|0.741869; 2.38897|], 1); 1803 | ([|0.394594; 0.83294|], 1); 1804 | ([|3.42166; 2.70704|], 1); 1805 | ([|1.13056; 2.39407|], 1); 1806 | ([|6.23129; 2.1573|], 1); 1807 | ([|0.441213; 1.64783|], 1); 1808 | ([|4.15699; 1.98632|], 1); 1809 | ([|1.92693; 3.01716|], 1); 1810 | ([|2.91001; 3.62087|], 1); 1811 | ([|2.2506; 1.71774|], 1); 1812 | ([|2.42825; 2.86187|], 1); 1813 | ([|2.94417; 1.31888|], 1); 1814 | ([|2.81449; 2.05784|], 1); 1815 | ([|3.0102; 2.13261|], 1); 1816 | ([|4.95368; 3.04207|], 1); 1817 | ([|1.66326; 1.86135|], 1); 1818 | ([|5.09456; 2.16509|], 1); 1819 | ([|5.53905; 1.65675|], 1); 1820 | ([|3.93909; 0.579044|], 1); 1821 | ([|7.29634; 2.32576|], 1); 1822 | ([|2.06456; 0.818894|], 1); 1823 | ([|2.54748; 1.56357|], 1); 1824 | ([|0.983288; 0.452984|], 1); 1825 | ([|1.45295; 1.26858|], 1); 1826 | ([|3.81907; 1.81427|], 1); 1827 | ([|1.23735; 2.35717|], 1); 1828 | ([|2.53851; 2.82708|], 1); 1829 | ([|3.44823; 0.59987|], 1); 1830 | ([|2.16266; 3.20051|], 1); 1831 | ([|0.669778; 3.10859|], 1); 1832 | ([|0.844067; 1.45419|], 1); 1833 | ([|1.91048; 0.787995|], 1); 1834 | ([|2.79874; 3.08319|], 1); 1835 | ([|0.793862; 0.146647|], 1); 1836 | ([|1.5777; 2.25313|], 1); 1837 | ([|3.33653; 3.22763|], 1); 1838 | ([|2.10251; 0.294822|], 1); 1839 | ([|0.640446; 1.39395|], 1); 1840 | ([|2.47063; 1.70246|], 1); 1841 | ([|4.87008; 1.91478|], 1); 1842 | ([|2.28299; 1.12278|], 1); 1843 | ([|3.3463; 1.01883|], 1); 1844 | ([|3.30643; 1.82397|], 1); 1845 | ([|2.28121; 2.18399|], 1); 1846 | ([|3.75541; 1.66331|], 1); 1847 | ([|2.31661; 2.82944|], 1); 1848 | ([|5.2468; 2.15583|], 1); 1849 | ([|2.50994; 3.04978|], 1); 1850 | ([|-0.0982234; 2.15726|], 1); 1851 | ([|5.39776; 1.2116|], 1); 1852 | ([|0.845123; 1.18948|], 1); 1853 | ([|1.66768; 2.85506|], 1); 1854 | ([|2.08479; 2.38391|], 1); 1855 | ([|-0.092328; 1.34018|], 1); 1856 | ([|3.92341; 1.38384|], 1); 1857 | ([|2.82547; 0.391025|], 1); 1858 | ([|0.914588; 2.01975|], 1); 1859 | ([|4.05675; 1.63785|], 1); 1860 | ([|0.642898; -0.389946|], 1); 1861 | ([|5.90428; 2.61938|], 1); 1862 | ([|0.909129; 1.5967|], 1); 1863 | ([|1.33617; 1.95265|], 1); 1864 | ([|2.22401; 1.5512|], 1); 1865 | ([|1.09653; 3.71921|], 1); 1866 | ([|1.54138; -0.142108|], 1); 1867 | ([|6.56999; 0.16839|], 1); 1868 | ([|2.78702; 3.43962|], 1); 1869 | ([|2.98214; 2.57647|], 1); 1870 | ([|5.86979; 0.825116|], 1); 1871 | ([|2.47132; 2.42819|], 1); 1872 | ([|0.787812; 2.1145|], 1); 1873 | ([|1.56837; 1.50207|], 1); 1874 | ([|1.60456; 2.68694|], 1); 1875 | ([|3.22299; 2.51003|], 1); 1876 | ([|-0.557637; 1.04583|], 1); 1877 | ([|3.08919; 3.19007|], 1); 1878 | ([|1.14911; 2.21057|], 1); 1879 | ([|2.76256; 2.106|], 1); 1880 | ([|2.76243; 0.67263|], 1); 1881 | ([|4.71277; 2.41474|], 1); 1882 | ([|3.01912; 0.945432|], 1); 1883 | ([|1.4566; 2.86121|], 1); 1884 | ([|2.34184; 0.49387|], 1); 1885 | ([|1.67186; 1.66838|], 1); 1886 | ([|1.59052; 1.52993|], 1); 1887 | ([|3.44472; 1.68544|], 1); 1888 | ([|4.14336; 2.31839|], 1); 1889 | ([|4.75823; 2.05506|], 1); 1890 | ([|2.36966; 3.28112|], 1); 1891 | ([|2.18335; 2.20515|], 1); 1892 | ([|1.59984; 3.72065|], 1); 1893 | ([|2.07503; 2.17889|], 1); 1894 | ([|-0.247773; -0.267323|], 1); 1895 | ([|4.89897; 1.33912|], 1); 1896 | ([|2.85387; 1.24807|], 1); 1897 | ([|4.51968; 2.54703|], 1); 1898 | ([|2.41589; 2.45229|], 1); 1899 | ([|1.74538; 1.82216|], 1); 1900 | ([|0.540253; -0.375884|], 1); 1901 | ([|3.78783; 3.09108|], 1); 1902 | ([|0.214959; 2.12247|], 1); 1903 | ([|3.24439; 0.272564|], 1); 1904 | ([|4.80358; 1.2433|], 1); 1905 | ([|1.62117; 1.44201|], 1); 1906 | ([|2.5875; 0.381671|], 1); 1907 | ([|3.17606; 2.86244|], 1); 1908 | ([|4.69924; 1.62393|], 1); 1909 | ([|1.71719; 0.238346|], 1); 1910 | ([|1.03096; 1.06262|], 1); 1911 | ([|-0.316772; 0.60062|], 1); 1912 | ([|0.249819; 3.54339|], 1); 1913 | ([|5.51938; 2.14505|], 1); 1914 | ([|0.664685; 0.949899|], 1); 1915 | ([|1.88236; 0.0547926|], 1); 1916 | ([|-0.453601; 3.1893|], 1); 1917 | ([|2.3809; 2.20479|], 1); 1918 | ([|5.07104; 2.62693|], 1); 1919 | ([|5.02187; 3.23632|], 1); 1920 | ([|1.82568; 1.12158|], 1); 1921 | ([|0.89364; 3.53458|], 1); 1922 | ([|1.84679; 1.47948|], 1); 1923 | ([|4.15599; 2.9876|], 1); 1924 | ([|3.69796; 1.59755|], 1); 1925 | ([|4.60376; 1.60961|], 1); 1926 | ([|2.98951; 1.35037|], 1); 1927 | ([|0.0899245; 1.67058|], 1); 1928 | ([|3.71796; 1.47521|], 1); 1929 | ([|2.3636; 0.952642|], 1); 1930 | ([|1.80972; 1.82365|], 1); 1931 | ([|-3.14878; 1.86095|], 1); 1932 | ([|2.90513; 2.90725|], 1); 1933 | ([|1.08357; 0.192489|], 1); 1934 | ([|1.31236; 2.84319|], 1); 1935 | ([|5.23099; 1.83398|], 1); 1936 | ([|1.66448; 1.86448|], 1); 1937 | ([|0.737214; 1.10394|], 1); 1938 | ([|-1.81196; 1.02203|], 1); 1939 | ([|-0.640967; 2.60805|], 1); 1940 | ([|4.89775; 2.73371|], 1); 1941 | ([|-1.462; 1.98601|], 1); 1942 | ([|2.93878; 1.87994|], 1); 1943 | ([|1.47954; 2.09552|], 1); 1944 | ([|1.53976; 2.66167|], 1); 1945 | ([|-0.402025; 0.819182|], 1); 1946 | ([|4.7377; 2.37292|], 1); 1947 | ([|0.642571; 0.953856|], 1); 1948 | ([|0.762856; 2.44125|], 1); 1949 | ([|-2.04824; 0.930713|], 1); 1950 | ([|2.21223; 1.36769|], 1); 1951 | ([|0.397345; 1.58786|], 1); 1952 | ([|4.20853; 2.06325|], 1); 1953 | ([|4.45877; 2.0655|], 1); 1954 | ([|3.47358; 2.30167|], 1); 1955 | ([|4.94209; 1.82031|], 1); 1956 | ([|2.2032; 2.85351|], 1); 1957 | ([|3.36937; 0.445313|], 1); 1958 | ([|4.2679; 2.22769|], 1); 1959 | ([|-1.18711; 2.15756|], 1); 1960 | ([|2.93336; 1.24944|], 1); 1961 | ([|0.062092; 0.295985|], 1); 1962 | ([|4.41356; 2.56558|], 1); 1963 | ([|0.536829; 2.38045|], 1); 1964 | ([|1.10022; 2.14035|], 1); 1965 | ([|3.43; 4.21547|], 1); 1966 | ([|1.97871; 2.16054|], 1); 1967 | ([|4.57; 0.90866|], 1); 1968 | ([|-0.89966; 0.534549|], 1); 1969 | ([|3.5259; 1.76584|], 1); 1970 | ([|1.12148; 2.20006|], 1); 1971 | ([|3.86739; 1.36668|], 1); 1972 | ([|0.27318; 0.0588512|], 1); 1973 | ([|2.05855; 2.98984|], 1); 1974 | ([|0.9776; -0.385405|], 1); 1975 | ([|4.7055; 0.568066|], 1); 1976 | ([|4.90433; 1.72278|], 1); 1977 | ([|-1.58103; 1.194|], 1); 1978 | ([|-0.59132; 1.56148|], 1); 1979 | ([|0.564568; 1.23745|], 1); 1980 | ([|4.60769; 1.88525|], 1); 1981 | ([|6.06677; 2.91232|], 1); 1982 | ([|4.63781; 0.301828|], 1); 1983 | ([|2.32598; 0.239851|], 1); 1984 | ([|7.62153; 3.11829|], 1); 1985 | ([|4.40073; 2.09372|], 1); 1986 | ([|2.97263; 0.677611|], 1); 1987 | ([|1.52076; 1.36239|], 1); 1988 | ([|5.83578; 2.53845|], 1); 1989 | ([|2.79217; 1.26547|], 1); 1990 | ([|5.07183; 4.388|], 1); 1991 | ([|1.64587; 0.0711668|], 1); 1992 | ([|3.49751; 3.57979|], 1); 1993 | ([|0.0302592; 1.68528|], 1); 1994 | ([|2.80617; 0.509407|], 1); 1995 | ([|-0.38187; -0.36432|], 1); 1996 | ([|7.34424; 3.4279|], 1); 1997 | ([|0.618613; 1.63949|], 1); 1998 | ([|5.77641; 1.62675|], 1); 1999 | ([|2.93404; 1.40461|], 1); 2000 | ([|2.61991; 2.61175|], 1); 2001 | ([|2.0631; 3.02274|], 1); 2002 | ([|4.02591; 2.96055|], 1); 2003 | ([|1.06214; 1.20781|], 1); 2004 | ([|3.50137; 2.68129|], 1); 2005 | ([|1.42734; 2.13079|], 1); 2006 | ([|2.62895; 1.4283|], 1); 2007 | ([|1.8446; 3.2435|], 1); 2008 | ([|2.49434; 2.64785|], 1); 2009 | ([|1.84947; 1.62372|], 1); 2010 | ([|-6.5652; 5.58045|], 2); 2011 | ([|-1.7931; 8.47715|], 2); 2012 | ([|-7.26475; 6.10444|], 2); 2013 | ([|-1.48867; 2.20874|], 2); 2014 | ([|-7.94137; 4.00289|], 2); 2015 | ([|-6.97711; 6.73683|], 2); 2016 | ([|-5.08871; 7.30454|], 2); 2017 | ([|-7.35315; 5.86926|], 2); 2018 | ([|-4.211; 8.26276|], 2); 2019 | ([|-4.44116; 8.31014|], 2); 2020 | ([|-2.8489; 3.96345|], 2); 2021 | ([|-6.47126; 4.80879|], 2); 2022 | ([|-8.08872; 10.2059|], 2); 2023 | ([|-5.9625; 3.95722|], 2); 2024 | ([|-3.58957; 5.09386|], 2); 2025 | ([|-4.36757; 8.12184|], 2); 2026 | ([|-6.28169; 5.46652|], 2); 2027 | ([|-4.35804; 4.91981|], 2); 2028 | ([|-4.32418; 8.83673|], 2); 2029 | ([|-4.24562; 7.20754|], 2); 2030 | ([|-2.25401; 7.06443|], 2); 2031 | ([|-3.63242; 4.27097|], 2); 2032 | ([|-7.17698; 6.882|], 2); 2033 | ([|-4.19224; 10.0805|], 2); 2034 | ([|-4.96213; 5.72987|], 2); 2035 | ([|-6.07793; 9.29566|], 2); 2036 | ([|-6.98173; 3.9317|], 2); 2037 | ([|-7.34416; 8.74152|], 2); 2038 | ([|-7.45102; 6.99411|], 2); 2039 | ([|-4.06175; 5.77915|], 2); 2040 | ([|-6.41329; 6.15893|], 2); 2041 | ([|-6.85824; 7.74334|], 2); 2042 | ([|-5.69957; 5.99699|], 2); 2043 | ([|-4.78411; 8.24192|], 2); 2044 | ([|-3.79375; 9.59602|], 2); 2045 | ([|-3.02152; 0.357205|], 2); 2046 | ([|-1.30739; 5.05971|], 2); 2047 | ([|-5.12787; 8.68351|], 2); 2048 | ([|-5.02429; 8.45752|], 2); 2049 | ([|-6.07492; 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6.28465|], 2); 2853 | ([|-4.28788; 7.23579|], 2); 2854 | ([|-3.57905; 8.2376|], 2); 2855 | ([|-4.38832; 5.3251|], 2); 2856 | ([|-1.22415; 10.221|], 2); 2857 | ([|-5.8602; 5.74464|], 2); 2858 | ([|-5.43487; 4.84088|], 2); 2859 | ([|-3.913; 5.45376|], 2); 2860 | ([|-5.91784; 6.21079|], 2); 2861 | ([|-6.71646; 7.7339|], 2); 2862 | ([|-2.39759; 3.33235|], 2); 2863 | ([|-7.06482; 6.83096|], 2); 2864 | ([|-6.41099; 5.4251|], 2); 2865 | ([|-7.78615; 2.61955|], 2); 2866 | ([|-3.266; 2.83608|], 2); 2867 | ([|-2.01815; 9.62511|], 2); 2868 | ([|-4.29434; 4.21135|], 2); 2869 | ([|-4.5674; 3.80913|], 2); 2870 | ([|-5.78411; 5.94671|], 2); 2871 | ([|-5.98936; 7.02881|], 2); 2872 | ([|-6.56759; 5.82637|], 2); 2873 | ([|-3.65766; 6.74593|], 2); 2874 | ([|-6.53219; 7.37197|], 2); 2875 | ([|-6.50621; 5.57314|], 2); 2876 | ([|-5.14447; 3.59889|], 2); 2877 | ([|-8.5917; 7.80722|], 2); 2878 | ([|-4.73553; 6.52709|], 2); 2879 | ([|-4.46478; 6.74924|], 2); 2880 | ([|-5.1825; 8.53281|], 2); 2881 | ([|-5.83116; 7.79505|], 2); 2882 | ([|-4.85531; 5.42215|], 2); 2883 | ([|-4.79513; 4.71153|], 2); 2884 | ([|-6.41873; 6.78488|], 2); 2885 | ([|-4.4622; 9.22739|], 2); 2886 | ([|-6.45933; 3.74613|], 2); 2887 | ([|-3.61273; 5.04555|], 2); 2888 | ([|-4.52576; 7.57669|], 2); 2889 | ([|-4.25007; 4.68044|], 2); 2890 | ([|-5.08128; 6.75822|], 2); 2891 | ([|-3.59935; 6.86637|], 2); 2892 | ([|-4.9628; 3.27958|], 2); 2893 | ([|-6.25617; 5.99882|], 2); 2894 | ([|-2.20048; 10.8279|], 2); 2895 | ([|-5.01303; 8.95673|], 2); 2896 | ([|-6.02377; 5.61463|], 2); 2897 | ([|-4.17774; 2.72648|], 2); 2898 | ([|-5.05117; 4.99233|], 2); 2899 | ([|-6.89935; 10.6623|], 2); 2900 | ([|-7.62856; 3.84566|], 2); 2901 | ([|-3.45397; 4.70839|], 2); 2902 | ([|-6.78879; 4.98074|], 2); 2903 | ([|-1.58425; 6.70006|], 2); 2904 | ([|-6.07973; 7.85083|], 2); 2905 | ([|-5.58177; 6.92142|], 2); 2906 | ([|-2.14312; 5.30484|], 2); 2907 | ([|-6.63373; 4.95843|], 2); 2908 | ([|-6.95175; 3.97014|], 2); 2909 | ([|-5.94134; 7.65695|], 2); 2910 | ([|-7.71661; 6.24764|], 2); 2911 | ([|-6.45127; 6.42972|], 2); 2912 | ([|-6.35361; 3.94841|], 2); 2913 | ([|-1.81101; 5.77642|], 2); 2914 | ([|-5.2296; 6.69206|], 2); 2915 | ([|-2.89803; 4.07155|], 2); 2916 | ([|-2.61207; 2.58911|], 2); 2917 | ([|-4.37339; 9.30304|], 2); 2918 | ([|-4.76589; 6.52323|], 2); 2919 | ([|-5.65741; 4.47584|], 2); 2920 | ([|-4.66875; 4.2501|], 2); 2921 | ([|-7.06411; 5.04499|], 2); 2922 | ([|-3.08296; 4.30915|], 2); 2923 | ([|-5.43208; 7.93135|], 2); 2924 | ([|-3.06776; 7.39178|], 2); 2925 | ([|-7.43745; 8.69408|], 2); 2926 | ([|-5.75729; 5.74072|], 2); 2927 | ([|-2.99217; 6.17172|], 2); 2928 | ([|-4.22215; 2.62878|], 2); 2929 | ([|-2.92785; 9.60068|], 2); 2930 | ([|-6.53341; 2.10419|], 2); 2931 | ([|-6.00696; 7.92335|], 2); 2932 | ([|-7.43776; 3.57276|], 2); 2933 | ([|-3.07368; 6.30853|], 2); 2934 | ([|-7.28182; 5.04656|], 2); 2935 | ([|-3.30827; 3.62144|], 2); 2936 | ([|-5.50958; 5.56139|], 2); 2937 | ([|-4.65598; 4.47158|], 2); 2938 | ([|-2.88777; 2.88976|], 2); 2939 | ([|-6.32518; 2.39407|], 2); 2940 | ([|-5.25841; 5.63575|], 2); 2941 | ([|-4.47764; 7.29779|], 2); 2942 | ([|-6.68504; 4.22832|], 2); 2943 | ([|-1.37256; 3.85351|], 2); 2944 | ([|-6.84402; 4.60523|], 2); 2945 | ([|-5.07603; 5.13321|], 2); 2946 | ([|-5.44895; 5.64971|], 2); 2947 | ([|-5.69841; 4.77745|], 2); 2948 | ([|-4.59856; 4.02684|], 2); 2949 | ([|-4.00574; 7.48658|], 2); 2950 | ([|-1.61779; 8.11319|], 2); 2951 | ([|-7.37953; 5.97997|], 2); 2952 | ([|-1.7198; 7.33184|], 2); 2953 | ([|-6.07174; 6.70095|], 2); 2954 | ([|-6.69113; 6.12444|], 2); 2955 | ([|-3.85514; 5.84539|], 2); 2956 | ([|-6.30406; 7.45031|], 2); 2957 | ([|-9.19726; 8.37503|], 2); 2958 | ([|-3.5073; 6.37546|], 2); 2959 | ([|-4.47829; 5.36664|], 2); 2960 | ([|-5.54061; 5.56154|], 2); 2961 | ([|-6.5648; 9.49851|], 2); 2962 | ([|-6.71228; 5.53977|], 2); 2963 | ([|-5.88552; 6.84619|], 2); 2964 | ([|-6.33349; 7.10611|], 2); 2965 | ([|-4.30583; 6.9519|], 2); 2966 | ([|-7.45315; 9.06546|], 2); 2967 | ([|-3.85213; 6.10952|], 2); 2968 | ([|-2.4172; 9.48642|], 2); 2969 | ([|-5.13605; 6.84785|], 2); 2970 | ([|-3.81334; 5.96087|], 2); 2971 | ([|-4.83605; 9.85183|], 2); 2972 | ([|-4.15789; 2.10834|], 2); 2973 | ([|-4.72128; 2.57746|], 2); 2974 | ([|-5.59978; 7.43053|], 2); 2975 | ([|-3.68264; 3.94125|], 2); 2976 | ([|-5.15624; 8.65458|], 2); 2977 | ([|-2.89862; 5.76214|], 2); 2978 | ([|-6.69845; 8.33471|], 2); 2979 | ([|-3.88132; 6.19263|], 2); 2980 | ([|-6.44539; 7.93699|], 2); 2981 | ([|-5.86237; 3.11049|], 2); 2982 | ([|-3.82031; 2.39898|], 2); 2983 | ([|-3.53787; 5.77444|], 2); 2984 | ([|-6.00491; 4.30014|], 2); 2985 | ([|-5.38427; 3.47457|], 2); 2986 | ([|-6.03238; 5.27164|], 2); 2987 | ([|-6.63115; 8.4781|], 2); 2988 | ([|-3.13823; 3.05961|], 2); 2989 | ([|-8.74615; 5.40528|], 2); 2990 | ([|-2.32727; 8.53384|], 2); 2991 | ([|-6.39178; 5.28469|], 2); 2992 | ([|-6.81986; 5.89189|], 2); 2993 | ([|-5.21682; 3.91439|], 2); 2994 | ([|-2.99955; 4.33034|], 2); 2995 | ([|-3.73169; 7.31051|], 2); 2996 | ([|-1.49393; 6.54182|], 2); 2997 | ([|-5.37082; 4.27285|], 2); 2998 | ([|-7.37047; 4.38035|], 2); 2999 | ([|-8.1472; 7.47845|], 2); 3000 | ([|-2.99463; 8.70985|], 2); 3001 | ([|-6.83157; 5.00825|], 2); 3002 | ([|-6.1478; 7.67577|], 2); 3003 | ([|-3.97463; 4.67541|], 2); 3004 | ([|-5.12601; 4.48207|], 2); 3005 | ([|-6.29177; 4.0089|], 2); 3006 | ([|-5.6151; 7.33603|], 2); 3007 | ([|-5.25639; 1.36401|], 2); 3008 | ([|-8.71775; 4.68956|], 2); 3009 | ([|-4.5279; 2.19389|], 2); 3010 | |] 3011 | -------------------------------------------------------------------------------- /k-means/dataset.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/akabe/ocaml-numerical-analysis/7dfe3b17d675fb73406a8e11ec0000b3489c5df5/k-means/dataset.png -------------------------------------------------------------------------------- /k-means/dataset.txt: -------------------------------------------------------------------------------- 1 | 4.92158 7.09815 2 | 5.81383 6.01565 3 | 4.36317 6.04401 4 | 4.55469 8.99767 5 | 6.12869 7.97226 6 | 4.53521 3.12714 7 | 3.54062 4.87403 8 | 5.25506 6.94233 9 | 4.9273 5.46974 10 | 4.05719 6.75775 11 | 4.45576 4.92348 12 | 5.95644 6.62171 13 | 3.46091 6.0821 14 | 4.41918 6.45101 15 | 6.32739 7.50817 16 | 2.57065 6.60825 17 | 6.47355 5.81471 18 | 5.08728 8.50587 19 | 6.39073 7.76195 20 | 5.76092 5.98383 21 | 5.24876 6.92229 22 | 3.58493 8.45347 23 | 6.48666 6.92533 24 | 3.86602 4.08991 25 | 7.3689 6.46896 26 | 5.01608 8.58189 27 | 6.15132 8.09649 28 | 6.16405 5.81923 29 | 3.07234 7.14281 30 | 4.10919 6.38804 31 | 2.9665 5.30797 32 | 4.09333 6.63553 33 | 5.62551 5.65647 34 | 4.90517 6.27995 35 | 4.8847 7.32103 36 | 5.58835 4.60537 37 | 8.09213 7.45106 38 | 4.37077 6.94562 39 | 3.71009 6.85742 40 | 4.20315 4.60728 41 | 4.72685 7.52036 42 | 6.34007 7.83467 43 | 4.07844 5.55581 44 | 2.32602 4.95526 45 | 5.66899 8.63053 46 | 7.29306 8.05774 47 | 5.68242 5.89045 48 | 4.5957 6.65504 49 | 4.83003 4.94802 50 | 5.08084 6.04463 51 | 4.04726 4.54704 52 | 4.20377 5.54231 53 | 2.51916 6.35499 54 | 6.20912 6.89301 55 | 3.27776 6.96892 56 | 1.32563 4.8233 57 | 3.40929 6.09756 58 | 6.87251 6.30003 59 | 3.83601 7.83547 60 | 5.13784 6.33883 61 | 4.88366 6.59026 62 | 5.71992 5.04449 63 | 5.67868 7.38863 64 | 3.66673 6.3691 65 | 5.11931 4.08177 66 | 4.83841 8.24535 67 | 5.30823 7.89441 68 | 6.59238 7.08117 69 | 6.50176 7.72884 70 | 2.4734 6.5848 71 | 4.89856 5.56919 72 | 6.03212 7.6736 73 | 3.36993 4.6803 74 | 6.88326 8.0949 75 | 5.6551 8.88415 76 | 6.22662 5.55753 77 | 7.24123 7.99841 78 | 5.91176 6.39267 79 | 4.73581 6.30805 80 | 3.43643 3.68549 81 | 7.89253 5.94836 82 | 5.54078 6.4136 83 | 5.71753 6.77294 84 | 3.4772 4.73904 85 | 4.63397 6.78753 86 | 6.76257 6.9776 87 | 4.60409 7.44333 88 | 3.89086 7.05717 89 | 4.23822 6.05349 90 | 5.53766 7.12207 91 | 6.51101 7.18789 92 | 3.17314 5.97846 93 | 3.45705 6.95076 94 | 6.37248 6.34209 95 | 5.7138 8.90435 96 | 5.69871 6.82426 97 | 3.5969 6.45118 98 | 7.95081 7.2952 99 | 4.96224 7.28647 100 | 6.27065 6.61742 101 | 5.91905 5.68828 102 | 6.60292 6.7778 103 | 3.4581 6.23861 104 | 5.15194 4.0876 105 | 6.37862 7.4056 106 | 4.4484 8.08953 107 | 5.34502 7.99043 108 | 5.02464 4.73026 109 | 3.14565 7.90735 110 | 4.08262 5.90371 111 | 6.74731 6.82575 112 | 4.4599 6.38457 113 | 7.18605 10.8665 114 | 5.17896 9.41558 115 | 6.40294 7.68106 116 | 3.00129 5.31708 117 | 5.29942 7.19457 118 | 8.22629 7.89854 119 | 3.74881 5.86598 120 | 4.38084 4.90158 121 | 7.72852 7.75288 122 | 2.99046 4.82481 123 | 7.36555 8.16846 124 | 4.03142 6.56927 125 | 5.39705 6.55261 126 | 2.64762 5.77129 127 | 6.30259 8.29711 128 | 2.88273 5.19736 129 | 6.45846 6.84525 130 | 5.55864 7.58292 131 | 3.7233 5.34288 132 | 4.14566 7.23268 133 | 6.73189 8.70435 134 | 6.28944 8.03451 135 | 3.70395 4.77436 136 | 3.36981 8.52264 137 | 5.03886 7.83391 138 | 3.37374 6.42048 139 | 4.38566 5.28952 140 | 7.77427 7.8868 141 | 6.41164 5.69855 142 | 5.36113 8.71171 143 | 4.59991 4.93205 144 | 6.35214 6.1348 145 | 5.35281 8.46326 146 | 6.07291 5.30571 147 | 5.14728 6.91676 148 | 6.42055 8.90867 149 | 6.63426 7.3938 150 | 4.6844 6.50485 151 | 4.73914 7.50951 152 | 3.73554 7.69706 153 | 4.83276 5.22763 154 | 4.79608 7.22376 155 | 4.38527 8.52666 156 | 5.04675 7.1933 157 | 6.94 8.69726 158 | 7.38372 6.95213 159 | 5.21512 6.43681 160 | 3.13331 5.76696 161 | 5.9184 6.85065 162 | 4.41348 4.01028 163 | 4.94589 5.71696 164 | 5.30295 4.27131 165 | 5.58847 7.54492 166 | 5.58194 6.51169 167 | 5.64032 5.79912 168 | 3.57368 4.3421 169 | 2.52102 6.12291 170 | 4.89453 6.67626 171 | 5.96083 9.14329 172 | 6.90014 6.76825 173 | 7.74593 6.38157 174 | 5.52606 5.82756 175 | 5.645 8.04593 176 | 4.15703 5.2269 177 | 5.6698 6.0843 178 | 5.16535 6.28985 179 | 4.65713 5.04234 180 | 6.97923 8.96958 181 | 4.46056 7.57686 182 | 4.07087 7.71989 183 | 6.29159 9.17017 184 | 4.43121 5.23774 185 | 4.11329 8.39212 186 | 3.97184 4.06871 187 | 3.75865 7.20994 188 | 7.06121 7.23449 189 | 6.26288 6.62298 190 | 4.63428 6.55644 191 | 4.96503 6.72958 192 | 5.24181 5.52654 193 | 3.61786 6.56779 194 | 6.32775 7.47512 195 | 3.53583 6.47336 196 | 5.92408 5.88287 197 | 5.61739 8.63334 198 | 3.70325 4.87852 199 | 3.13859 4.65313 200 | 7.1399 6.85088 201 | 6.04047 6.88692 202 | 5.68052 7.38279 203 | 3.23835 6.29804 204 | 3.53413 5.69802 205 | 5.11621 4.77933 206 | 4.57383 5.85161 207 | 5.36694 6.4514 208 | 6.50769 6.19715 209 | 4.37857 5.75527 210 | 5.75672 5.69329 211 | 5.52709 5.81469 212 | 4.05513 6.87586 213 | 4.01626 7.0885 214 | 4.78189 6.55538 215 | 6.90721 4.93882 216 | 4.25899 8.61299 217 | 5.10017 6.34343 218 | 6.68041 6.63903 219 | 3.53973 6.32604 220 | 6.21408 7.11405 221 | 6.25551 6.38346 222 | 6.04601 6.59376 223 | 3.24439 5.67678 224 | 3.81459 3.93809 225 | 4.68731 6.3571 226 | 5.68616 7.82584 227 | 2.21176 7.43547 228 | 5.53953 7.5688 229 | 2.5586 5.33472 230 | 5.1214 5.51168 231 | 4.03711 6.47803 232 | 4.41942 7.47413 233 | 2.87874 6.48688 234 | 3.70137 5.97489 235 | 7.37892 7.36492 236 | 4.42785 8.95149 237 | 3.41564 7.00624 238 | 5.5588 5.52772 239 | 4.69543 6.52668 240 | 2.27299 6.62142 241 | 8.03262 8.28276 242 | 5.67352 7.4779 243 | 3.91889 8.28631 244 | 4.88415 5.18361 245 | 6.51748 7.91132 246 | 7.64325 7.93591 247 | 3.80049 4.85236 248 | 5.33283 6.07272 249 | 6.11588 5.51164 250 | 5.34231 6.37583 251 | 5.26991 7.72534 252 | 4.31446 5.52464 253 | 4.00055 8.64281 254 | 4.42914 7.11663 255 | 5.39464 6.74853 256 | 4.57154 5.98584 257 | 3.91305 6.22797 258 | 3.73875 6.33655 259 | 5.89283 6.51971 260 | 4.2343 6.1432 261 | 5.54713 6.07414 262 | 4.14728 5.53819 263 | 4.26258 6.49447 264 | 6.32631 6.22247 265 | 7.00504 10.1798 266 | 3.12126 4.8532 267 | 8.22656 6.80128 268 | 4.29861 4.72904 269 | 5.80139 7.62202 270 | 3.80823 4.60003 271 | 8.47429 8.163 272 | 2.47723 5.19951 273 | 6.90959 5.90244 274 | 5.2993 7.22153 275 | 7.11205 7.987 276 | 7.17765 6.56876 277 | 6.28644 7.57325 278 | 5.40604 6.24184 279 | 5.43649 7.40379 280 | 4.11864 5.73557 281 | 3.38215 6.58195 282 | 2.97015 6.78643 283 | 5.73466 7.93254 284 | 6.21842 7.13359 285 | 4.63895 5.82154 286 | 6.36218 4.37643 287 | 5.42569 8.47021 288 | 6.76888 6.83964 289 | 6.23563 7.03758 290 | 3.3016 5.38605 291 | 5.64029 7.08 292 | 4.42566 4.67948 293 | 5.36316 8.43033 294 | 5.37276 7.949 295 | 5.08334 6.58973 296 | 4.76245 5.92213 297 | 5.43902 6.15782 298 | 7.68908 6.1291 299 | 3.40104 6.34071 300 | 3.62739 4.95691 301 | 6.39491 10.2357 302 | 3.54842 7.22819 303 | 7.15332 7.66832 304 | 4.43867 6.30916 305 | 3.619 5.87946 306 | 5.11541 8.09935 307 | 6.04625 6.50019 308 | 1.94485 6.56288 309 | 3.53688 4.88466 310 | 6.29483 7.03143 311 | 5.36992 7.00768 312 | 4.84663 6.97836 313 | 4.02368 6.14935 314 | 2.86033 6.0587 315 | 6.7612 6.20325 316 | 3.74545 4.28877 317 | 5.41681 7.71461 318 | 5.47317 5.48745 319 | 5.43545 7.56748 320 | 4.17893 4.48159 321 | 4.65143 6.07858 322 | 4.78807 6.02202 323 | 2.52384 6.40642 324 | 2.70734 3.98681 325 | 3.919 6.8943 326 | 3.25902 7.87718 327 | 5.47137 7.60947 328 | 6.38801 7.5854 329 | 4.16579 5.75494 330 | 5.68096 7.11635 331 | 4.55563 8.32136 332 | 6.33674 8.61941 333 | 6.14138 4.64598 334 | 5.5534 6.39466 335 | 3.90238 4.85324 336 | 3.59463 4.8075 337 | 4.78037 4.51867 338 | 2.41827 5.21087 339 | 7.06974 5.59429 340 | 5.88147 6.21732 341 | 4.33026 5.22808 342 | 4.92202 5.05208 343 | 4.06785 7.40473 344 | 3.30219 4.80442 345 | 4.46309 6.83449 346 | 5.58269 8.94313 347 | 4.24576 5.20813 348 | 4.01655 6.6161 349 | 5.38734 6.53307 350 | 4.70364 5.84135 351 | 6.6691 7.83884 352 | 4.87164 8.04567 353 | 5.23727 6.1653 354 | 7.08758 7.27917 355 | 5.95729 6.72063 356 | 4.46996 5.82397 357 | 4.78712 5.72477 358 | 7.36157 8.49838 359 | 4.15753 4.66365 360 | 5.46309 7.01733 361 | 3.64595 8.46409 362 | 4.67128 6.27121 363 | 4.36281 6.00558 364 | 6.20941 7.49494 365 | 5.27345 8.28249 366 | 5.45973 8.06057 367 | 4.47519 6.58326 368 | 5.6722 7.80491 369 | 5.73944 7.05948 370 | 5.82028 7.60252 371 | 2.73978 7.06907 372 | 4.21021 6.86491 373 | 4.8608 8.26846 374 | 4.88569 6.93182 375 | 4.70385 9.91589 376 | 3.90111 5.93661 377 | 7.14626 8.73065 378 | 4.20268 5.87822 379 | 2.81519 6.59044 380 | 4.86957 5.53183 381 | 5.35461 5.49635 382 | 5.60509 5.56324 383 | 5.77123 8.94594 384 | 7.0188 8.88566 385 | 5.24699 9.58424 386 | 5.84476 8.34625 387 | 5.38198 5.89272 388 | 6.47757 9.9809 389 | 5.35508 7.79276 390 | 3.45519 5.75672 391 | 5.6056 4.05302 392 | 5.19731 6.5758 393 | 4.47645 4.83 394 | 5.22606 5.97201 395 | 5.71905 7.99921 396 | 4.33238 7.11012 397 | 3.69629 6.99511 398 | 3.25543 4.59527 399 | 5.09756 7.14056 400 | 5.13373 6.11265 401 | 3.72409 5.83978 402 | 3.47529 4.15386 403 | 4.06862 6.2219 404 | 5.34769 8.24531 405 | 4.49332 6.91299 406 | 4.69658 7.9088 407 | 4.43389 6.88341 408 | 8.53222 11.0265 409 | 5.0168 8.86569 410 | 6.96761 9.61839 411 | 4.9375 6.29874 412 | 4.0649 6.09615 413 | 3.14637 5.85574 414 | 5.73645 8.15643 415 | 4.0423 7.16611 416 | 4.08154 7.12915 417 | 7.09272 6.57002 418 | 3.14543 4.12821 419 | 4.66455 4.73553 420 | 6.93144 7.30672 421 | 6.05616 6.71189 422 | 4.00284 6.57792 423 | 5.7291 6.466 424 | 5.59591 7.01232 425 | 5.75099 7.34586 426 | 3.24587 5.70792 427 | 4.42609 6.47035 428 | 1.03048 5.63466 429 | 1.83036 3.84772 430 | 3.15848 4.98251 431 | 6.07859 8.02596 432 | 8.11823 6.48337 433 | 5.89347 6.80993 434 | 4.19046 4.34262 435 | 3.41893 7.20542 436 | 6.44292 7.22399 437 | 7.53937 6.1544 438 | 5.58414 8.16731 439 | 5.23773 5.5312 440 | 4.90733 6.47999 441 | 3.2088 4.69374 442 | 5.70578 6.46068 443 | 5.74937 6.7908 444 | 5.43432 6.50659 445 | 6.39403 8.31745 446 | 3.42491 6.56008 447 | 7.28631 8.64031 448 | 4.70323 8.97252 449 | 6.6457 4.43444 450 | 6.92946 8.48017 451 | 6.3748 6.6897 452 | 7.06869 7.37824 453 | 6.62811 6.41003 454 | 6.20118 7.30667 455 | 5.23702 8.57667 456 | 4.88334 5.58192 457 | 5.78371 9.256 458 | 3.85459 5.8659 459 | 9.13837 7.30229 460 | 5.04906 8.49952 461 | 4.06597 6.54336 462 | 5.09979 5.47623 463 | 4.74473 7.24033 464 | 6.41037 5.27393 465 | 4.20968 6.00857 466 | 6.79385 5.52033 467 | 7.59645 9.22224 468 | 5.76845 6.11425 469 | 4.9381 5.96615 470 | 5.66736 8.05442 471 | 5.56172 6.93381 472 | 4.66946 6.19508 473 | 3.82189 4.98166 474 | 7.36514 6.27861 475 | 5.18654 6.542 476 | 4.79363 7.54806 477 | 5.74868 6.95819 478 | 3.79193 5.274 479 | 4.47697 5.99728 480 | 7.51772 9.22075 481 | 3.94009 7.13486 482 | 5.29267 5.51559 483 | 4.35174 7.85982 484 | 2.82329 5.19519 485 | 4.14759 6.88904 486 | 3.95549 7.13642 487 | 3.33184 7.23698 488 | 5.83022 7.70443 489 | 6.74495 6.88808 490 | 3.82471 7.18327 491 | 6.27184 6.92888 492 | 3.83353 6.39149 493 | 4.96382 7.62923 494 | 4.37913 6.64527 495 | 7.71284 6.96685 496 | 5.08203 7.31272 497 | 4.27408 6.60731 498 | 6.05368 7.711 499 | 6.07914 5.89194 500 | 3.82095 5.69468 501 | 5.30372 5.32938 502 | 5.14203 7.85254 503 | 2.60846 7.03435 504 | 7.37142 9.12851 505 | 5.53463 7.77673 506 | 6.22299 5.48791 507 | 4.89232 5.4278 508 | 4.66973 5.3135 509 | 5.23826 5.62808 510 | 4.2768 7.29915 511 | 7.05028 6.8177 512 | 5.52931 6.05362 513 | 4.69208 6.8289 514 | 6.30308 7.73105 515 | 5.61257 6.68497 516 | 6.02563 7.39214 517 | 5.56472 6.12067 518 | 3.85872 7.77631 519 | 6.80177 7.49544 520 | 5.06541 7.18284 521 | 6.54185 8.62147 522 | 3.75433 6.52159 523 | 3.6402 5.11863 524 | 3.82431 5.86452 525 | 2.91415 6.77738 526 | 5.75709 7.48834 527 | 4.66104 4.8349 528 | 3.13625 7.30454 529 | 5.47171 7.68667 530 | 5.54999 7.42974 531 | 5.32391 6.89768 532 | 8.92248 8.26913 533 | 8.58826 6.65608 534 | 5.30602 6.41974 535 | 4.10874 5.93125 536 | 3.82411 4.76122 537 | 4.80657 6.05776 538 | 7.79853 8.91319 539 | 5.96319 5.50253 540 | 7.47219 7.24042 541 | 6.18098 11.5047 542 | 4.92575 6.05863 543 | 8.65644 9.03281 544 | 6.21895 8.04918 545 | 5.12313 8.37573 546 | 5.3257 5.96507 547 | 2.08279 5.35143 548 | 5.70751 5.99677 549 | 5.72335 5.97932 550 | 2.74557 6.09755 551 | 3.99692 6.36763 552 | 6.37876 7.10975 553 | 6.4789 6.10108 554 | 3.59027 5.15626 555 | 5.56789 8.15146 556 | 7.4157 8.86453 557 | 5.68263 7.81274 558 | 4.17939 4.80023 559 | 4.28086 5.55185 560 | 6.89443 7.29844 561 | 5.56503 6.98389 562 | 4.92983 5.66378 563 | 3.95068 6.03683 564 | 1.33404 5.9585 565 | 5.01293 7.61127 566 | 5.00098 6.27567 567 | 5.03891 7.1321 568 | 3.91253 6.57006 569 | 3.25982 7.08788 570 | 4.98178 4.21718 571 | 8.65357 7.82609 572 | 3.37816 7.04846 573 | 5.08821 8.01765 574 | 4.29419 7.48057 575 | 3.42314 3.64219 576 | 2.81862 4.98426 577 | 6.85008 7.89563 578 | 4.57247 5.34044 579 | 5.81095 8.19552 580 | 5.12222 7.17983 581 | 6.53293 7.50208 582 | 4.45016 7.89315 583 | 6.27667 7.47161 584 | 5.70349 9.2214 585 | 4.503 7.10228 586 | 6.60479 7.75095 587 | 3.05904 5.71716 588 | 4.9414 7.01447 589 | 4.72037 6.67889 590 | 6.44277 9.27171 591 | 4.04834 8.36389 592 | 5.92391 7.83338 593 | 6.83873 7.55261 594 | 3.23201 6.33882 595 | 3.39235 4.05387 596 | 5.99535 6.01994 597 | 5.27745 6.29577 598 | 3.42849 7.07556 599 | 3.16775 6.84123 600 | 4.31136 8.65551 601 | 7.13453 5.71479 602 | 2.2317 7.74269 603 | 6.75376 6.60141 604 | 4.17294 5.71314 605 | 5.74899 6.28108 606 | 5.51284 8.37367 607 | 3.24162 5.83157 608 | 3.82078 6.21964 609 | 3.78531 4.69848 610 | 4.01556 5.55895 611 | 5.73716 6.32078 612 | 6.59875 7.05193 613 | 5.60109 7.13728 614 | 4.63702 7.06199 615 | 5.231 4.4507 616 | 5.62971 7.80997 617 | 5.63508 7.6339 618 | 4.60341 8.09215 619 | 5.46614 6.64327 620 | 4.52557 5.70982 621 | 5.84818 6.98696 622 | 3.63935 5.39566 623 | 7.05097 9.72355 624 | 6.34882 5.66682 625 | 6.46522 8.21166 626 | 3.28091 6.36498 627 | 2.57518 6.67533 628 | 4.82468 5.9774 629 | 7.51977 8.70065 630 | 5.65599 6.68908 631 | 2.8912 7.47363 632 | 7.76645 7.63114 633 | 5.36706 6.23732 634 | 6.20221 7.8906 635 | 6.25415 7.09321 636 | 4.14991 9.46635 637 | 4.39661 8.21474 638 | 4.68754 7.54009 639 | 3.45107 6.02375 640 | 5.67657 8.14193 641 | 2.58222 4.71175 642 | 6.98576 6.59407 643 | 4.58339 8.25412 644 | 7.45642 6.89184 645 | 5.30678 5.79025 646 | 6.89052 4.75068 647 | 3.87908 6.09283 648 | 6.04666 6.65264 649 | 4.37043 6.10196 650 | 7.31733 6.82783 651 | 6.78661 7.8023 652 | 6.87697 5.45149 653 | 4.72708 8.28906 654 | 5.14688 7.29918 655 | 4.00519 6.592 656 | 2.98618 5.24282 657 | 5.47223 7.67851 658 | 6.4225 6.68016 659 | 3.89658 5.24808 660 | 4.31694 7.18727 661 | 4.39173 5.84925 662 | 3.43673 6.34571 663 | 4.93148 7.4396 664 | 3.84133 4.5223 665 | 5.55397 8.00278 666 | 6.45181 8.66876 667 | 3.82812 4.71294 668 | 4.65469 6.02834 669 | 2.47012 4.12795 670 | 2.70354 4.928 671 | 5.56188 4.12987 672 | 5.51293 8.15635 673 | 5.01643 4.63026 674 | 4.44673 5.51361 675 | 5.48968 7.4698 676 | 5.55678 6.54205 677 | 7.18705 8.04393 678 | 4.66647 5.65045 679 | 4.65475 7.14432 680 | 4.85751 5.33583 681 | 4.37004 6.49639 682 | 3.80912 7.81752 683 | 6.36693 6.36996 684 | 3.79579 7.65684 685 | 6.70943 7.44998 686 | 4.79738 6.36386 687 | 4.9595 6.23179 688 | 4.98093 6.86274 689 | 4.67299 5.93298 690 | 4.6598 5.45426 691 | 4.76627 7.38181 692 | 5.89332 6.65955 693 | 5.65272 6.75484 694 | 3.54842 7.07835 695 | 3.80583 6.38194 696 | 4.34852 6.26525 697 | 5.99083 8.02936 698 | 5.99941 7.19213 699 | 5.60996 7.30261 700 | 4.06465 8.89328 701 | 3.73366 6.27102 702 | 4.46126 6.7963 703 | 5.01549 6.83778 704 | 8.32302 8.00272 705 | 5.47075 5.82236 706 | 2.91406 5.47656 707 | 5.6239 7.52718 708 | 1.47972 4.33915 709 | 4.79093 6.53638 710 | 4.396 5.49983 711 | 5.20691 7.46208 712 | 3.51736 5.62875 713 | 4.91835 7.17347 714 | 3.98106 5.79118 715 | 5.12517 6.03132 716 | 3.86484 5.88722 717 | 7.1524 8.10962 718 | 6.31607 5.88245 719 | 2.55292 7.24906 720 | 4.72707 9.04361 721 | 4.00638 4.00751 722 | 3.99857 6.09387 723 | 4.14407 6.2553 724 | 2.19182 6.05984 725 | 3.6771 6.61769 726 | 5.89362 6.77466 727 | 7.77723 6.20051 728 | 7.888 8.84844 729 | 2.8743 6.37668 730 | 4.54853 4.70019 731 | 5.5499 5.26532 732 | 1.12482 4.71491 733 | 3.8045 7.23118 734 | 4.41356 5.62142 735 | 4.43597 8.21463 736 | 3.47991 4.26434 737 | 4.49462 6.82138 738 | 6.58521 7.98257 739 | 5.2028 6.91507 740 | 4.44978 6.38714 741 | 4.1997 5.8766 742 | 7.52749 7.67011 743 | 7.65701 7.52054 744 | 5.88686 6.85729 745 | 4.91532 5.73886 746 | 4.03031 6.8856 747 | 4.66013 4.66227 748 | 4.40127 6.07626 749 | 1.66199 7.02743 750 | 3.53774 6.62016 751 | 4.72178 6.16666 752 | 6.29287 7.34404 753 | 5.10453 7.96306 754 | 6.87495 6.01145 755 | 5.22119 7.03142 756 | 1.78816 6.31916 757 | 4.47227 5.976 758 | 6.04612 9.23126 759 | 4.79991 5.80266 760 | 5.93324 7.46376 761 | 6.52456 7.26185 762 | 6.61517 5.95569 763 | 4.94916 8.37097 764 | 6.08583 8.45453 765 | 4.70026 6.52009 766 | 5.15651 7.96725 767 | 5.62686 5.4061 768 | 4.4616 5.35799 769 | 6.85888 7.0655 770 | 6.75517 8.80596 771 | 5.11239 4.55881 772 | 5.35278 8.27309 773 | 5.99861 7.4413 774 | 5.9582 7.35911 775 | 8.28373 6.93449 776 | 3.71403 6.25887 777 | 5.14412 6.34251 778 | 5.31924 5.21877 779 | 4.84491 8.46197 780 | 6.21255 6.91897 781 | 4.65483 8.28893 782 | 3.4523 6.59659 783 | 7.71233 8.51352 784 | 7.36536 4.15545 785 | 7.24313 8.09022 786 | 5.18743 5.95083 787 | 4.5109 7.4687 788 | 5.62067 7.06139 789 | 5.95865 7.38005 790 | 6.12442 8.35022 791 | 4.3019 8.17645 792 | 6.8784 9.84821 793 | 5.27063 6.34892 794 | 5.98798 7.96378 795 | 5.26391 5.11982 796 | 5.16842 6.22163 797 | 4.79539 4.81954 798 | 6.00828 7.64075 799 | 6.15599 8.26154 800 | 4.0456 6.23971 801 | 5.90724 6.62124 802 | 5.02199 7.31266 803 | 5.01594 6.97737 804 | 6.27403 6.49414 805 | 5.15028 4.07335 806 | 6.2214 7.10608 807 | 5.19888 7.53882 808 | 4.16368 6.50343 809 | 5.44269 6.3215 810 | 5.97767 6.94636 811 | 3.93498 3.95197 812 | 8.79532 8.28647 813 | 3.61172 6.10433 814 | 6.67157 6.18243 815 | 5.60735 4.87852 816 | 5.22764 7.06803 817 | 6.37565 7.40817 818 | 5.04457 4.10357 819 | 7.53011 7.40865 820 | 6.01825 5.72254 821 | 4.96598 6.37612 822 | 4.09563 4.86385 823 | 4.81064 6.93257 824 | 5.66866 7.09018 825 | 3.59149 4.94593 826 | 1.97988 3.45063 827 | 6.37965 8.13142 828 | 5.9823 6.29063 829 | 3.61996 3.26597 830 | 6.44753 5.70866 831 | 5.65691 7.38345 832 | 5.91831 5.02812 833 | 5.57017 5.12415 834 | 5.77652 6.96195 835 | 5.05204 5.12671 836 | 6.41712 8.86586 837 | 7.48633 7.71941 838 | 5.35287 9.01857 839 | 7.29935 7.98786 840 | 5.90848 7.79116 841 | 7.17955 8.31161 842 | 3.02874 5.86283 843 | 5.9017 8.43112 844 | 3.61428 6.2417 845 | 6.215 7.88429 846 | 4.31777 6.2102 847 | 3.58757 5.7472 848 | 5.36952 7.00454 849 | 4.34929 6.76848 850 | 4.50283 7.71705 851 | 3.98826 5.75071 852 | 7.19484 9.97457 853 | 4.95385 6.7108 854 | 5.5276 8.05509 855 | 5.8675 7.2123 856 | 7.75562 6.96498 857 | 6.81268 6.65108 858 | 4.44428 6.01544 859 | 6.79919 7.16351 860 | 4.98348 7.24341 861 | 8.03871 7.80992 862 | 5.08786 7.15425 863 | 4.8709 5.45642 864 | 5.36333 5.32424 865 | 4.93845 6.25861 866 | 6.24537 6.83518 867 | 5.02983 7.04746 868 | 6.17479 8.05751 869 | 5.20974 5.99394 870 | 6.88034 4.90612 871 | 3.77439 4.65649 872 | 6.96035 8.67182 873 | 3.77292 5.04985 874 | 5.99101 6.17519 875 | 6.37845 6.98779 876 | 4.57467 6.40543 877 | 4.41273 5.63981 878 | 5.92348 6.12036 879 | 7.19836 7.40732 880 | 5.25367 4.96457 881 | 7.27858 7.35896 882 | 5.84282 6.76103 883 | 3.48386 6.41121 884 | 5.26475 7.72568 885 | 3.46129 4.96228 886 | 2.4342 6.3127 887 | 3.02653 7.36143 888 | 4.5316 7.98053 889 | 3.19045 5.67573 890 | 4.76172 5.31511 891 | 3.87943 7.59487 892 | 7.79181 7.24781 893 | 4.51726 5.90547 894 | 7.01834 5.85426 895 | 6.24721 6.78717 896 | 5.07668 7.64201 897 | 4.69668 5.96439 898 | 10.3441 6.70913 899 | 6.35047 7.83514 900 | 6.78442 8.97522 901 | 5.53575 8.51801 902 | 5.11243 7.0465 903 | 6.73077 7.04516 904 | 5.56218 6.40059 905 | 2.944 6.02626 906 | 7.04411 8.94714 907 | 4.15884 5.91374 908 | 4.92684 7.47136 909 | 5.25642 5.55367 910 | 4.94056 5.44899 911 | 4.03227 7.00372 912 | 4.56073 3.5958 913 | 3.93113 8.43848 914 | 5.59818 8.27846 915 | 5.367 6.32979 916 | 7.04877 6.96914 917 | 5.88083 6.48932 918 | 4.06936 7.10301 919 | 5.97762 6.78054 920 | 5.80732 7.41936 921 | 3.56825 5.58237 922 | 6.9284 7.56614 923 | 2.56227 7.16082 924 | 5.2298 8.9573 925 | 5.38242 8.18763 926 | 4.1612 5.34141 927 | 3.87135 6.69716 928 | 6.236 5.40141 929 | 5.89447 6.84941 930 | 2.96883 7.28234 931 | 5.34425 8.29625 932 | 5.60218 8.43066 933 | 5.38202 5.14292 934 | 4.07462 3.98732 935 | 3.05924 6.18975 936 | 5.00423 6.21859 937 | 2.20921 5.24467 938 | 5.5394 7.61728 939 | 4.44378 7.22766 940 | 5.52138 7.37761 941 | 3.74783 5.88256 942 | 3.97796 8.2777 943 | 4.9262 7.98164 944 | 5.02064 6.33281 945 | 5.98306 7.22206 946 | 6.02076 8.39748 947 | 5.68883 7.69492 948 | 6.09242 6.70246 949 | 6.35874 5.94375 950 | 6.693 7.34012 951 | 4.91533 7.05798 952 | 4.59085 6.88705 953 | 7.06539 7.6557 954 | 6.85625 6.70528 955 | 5.47586 8.25144 956 | 6.58249 6.74796 957 | 6.26188 7.75079 958 | 6.94785 8.26643 959 | 5.86215 6.25001 960 | 3.34645 5.83139 961 | 5.5303 7.90899 962 | 6.81548 8.4345 963 | 5.74765 6.68186 964 | 3.5095 6.76506 965 | 7.41873 9.48488 966 | 5.28148 7.70298 967 | 4.42467 6.38118 968 | 3.06496 9.47572 969 | 9.07759 6.30613 970 | 3.8793 4.71314 971 | 3.71077 7.44204 972 | 5.17498 7.57531 973 | 4.5021 6.77292 974 | 7.49217 8.22032 975 | 5.68509 4.89606 976 | 6.44845 6.34962 977 | 4.78622 5.53932 978 | 7.89879 7.24436 979 | 5.97613 6.01523 980 | 4.4617 4.24669 981 | 5.24624 6.62411 982 | 3.45932 5.30284 983 | 7.27381 7.6906 984 | 4.71255 7.73696 985 | 4.95445 6.95174 986 | 6.02191 7.52777 987 | 4.05605 5.68996 988 | 5.4592 8.51887 989 | 4.371 6.82265 990 | 5.65784 6.99111 991 | 4.67507 7.54365 992 | 4.88228 7.47696 993 | 4.42045 7.24586 994 | 5.76159 7.52406 995 | 3.41984 6.82009 996 | 4.30782 8.22664 997 | 3.56917 6.72032 998 | 5.50851 4.72454 999 | 4.6257 6.49443 1000 | 6.0945 6.29769 1001 | 1002 | 1003 | 3.70287 2.79126 1004 | 2.08086 1.1504 1005 | -1.23658 2.08149 1006 | 4.67516 1.71848 1007 | 3.66963 3.39659 1008 | 3.44163 2.63195 1009 | 1.89865 2.21139 1010 | 4.55244 1.22496 1011 | 2.9667 1.06228 1012 | 2.23335 3.42714 1013 | 0.872817 0.809103 1014 | 2.24813 1.29536 1015 | 0.34511 2.36037 1016 | 4.20713 1.75097 1017 | 1.78089 1.91335 1018 | 4.01925 2.92304 1019 | 4.23919 2.68392 1020 | 2.32072 0.864505 1021 | 0.762817 1.92227 1022 | 2.79768 1.61902 1023 | 1.403 1.22472 1024 | -1.78987 2.09314 1025 | 5.36779 0.839805 1026 | 1.37261 2.49226 1027 | 2.49443 3.57598 1028 | 2.74606 1.85633 1029 | 2.09234 1.05433 1030 | 2.92229 1.95798 1031 | 3.15992 0.598176 1032 | 3.06825 3.09915 1033 | 0.566782 2.27778 1034 | 0.776733 1.20465 1035 | 1.37818 1.1029 1036 | 1.52191 0.754767 1037 | 2.13024 2.77073 1038 | 3.33013 2.80783 1039 | 1.54408 2.8774 1040 | 2.05531 1.93879 1041 | 0.962626 2.21118 1042 | 2.62664 2.83886 1043 | 2.33168 2.82949 1044 | 4.38842 1.99066 1045 | 0.75252 1.25332 1046 | 6.65782 1.23891 1047 | 0.997021 2.42301 1048 | 2.55725 1.21472 1049 | 0.425213 2.66462 1050 | -0.765278 1.37969 1051 | 1.3591 2.17327 1052 | 2.79076 3.85664 1053 | 2.0243 2.59965 1054 | 2.9425 1.92016 1055 | 3.94423 3.07709 1056 | 0.869093 1.39744 1057 | 0.330096 2.26889 1058 | 2.73709 2.85821 1059 | 2.18169 2.87298 1060 | 2.09561 2.98613 1061 | 0.930788 1.2893 1062 | 2.53395 1.11483 1063 | 1.64458 2.17554 1064 | 1.93171 2.14266 1065 | 6.03568 2.46783 1066 | 0.857424 1.33021 1067 | 2.4701 2.21038 1068 | 3.23715 1.30958 1069 | 4.40611 1.68339 1070 | 3.17157 1.5353 1071 | 4.20795 0.708054 1072 | 3.40152 1.47318 1073 | 3.10978 1.79239 1074 | 2.74658 1.17206 1075 | 5.47997 2.83241 1076 | 2.62271 1.84697 1077 | 1.26028 3.17388 1078 | 3.44735 1.2446 1079 | 1.31024 2.58012 1080 | 5.87538 3.9324 1081 | 1.47971 1.49437 1082 | 0.854999 0.0560544 1083 | 0.326572 1.53073 1084 | 5.06817 0.0648555 1085 | 0.95896 3.52445 1086 | 3.37037 2.38435 1087 | -1.50883 1.31936 1088 | -0.430117 2.00927 1089 | 1.51775 1.94153 1090 | 5.02134 2.96142 1091 | -0.49424 2.20768 1092 | 2.36642 1.83428 1093 | -2.69348 0.746999 1094 | -0.00973656 2.94825 1095 | 4.56178 1.4899 1096 | 2.33832 1.03877 1097 | 2.74808 1.31245 1098 | 0.0792328 2.60247 1099 | 2.77585 -0.355214 1100 | 1.04202 2.90096 1101 | 1.48194 1.88697 1102 | 5.79707 2.90698 1103 | 1.39245 1.71263 1104 | 0.933713 2.0805 1105 | 2.74397 1.70158 1106 | 2.08715 2.81145 1107 | 0.466525 0.934071 1108 | 3.89678 3.76161 1109 | 5.05428 2.93249 1110 | 4.92212 0.0653854 1111 | 3.76144 3.03516 1112 | 0.92264 1.82351 1113 | 6.20738 4.08428 1114 | 2.39976 3.83541 1115 | 2.6825 3.16514 1116 | 0.506673 1.224 1117 | 1.28861 1.55599 1118 | 1.18648 1.26123 1119 | 0.463462 2.02105 1120 | 6.96172 2.38456 1121 | 2.0727 1.75525 1122 | 0.425934 0.71329 1123 | 4.2352 2.43053 1124 | 2.84048 0.0679915 1125 | 6.39735 1.24437 1126 | 1.15396 3.58432 1127 | 0.428082 1.88032 1128 | 2.94758 0.85754 1129 | 1.52821 1.76547 1130 | 3.42709 1.5519 1131 | 2.0569 2.05089 1132 | 1.25992 1.34189 1133 | 3.44974 1.77442 1134 | 2.7203 2.18305 1135 | -0.328433 2.20129 1136 | 3.52731 2.57193 1137 | -0.869499 2.12354 1138 | 1.69453 1.22212 1139 | 1.96178 3.10079 1140 | 1.0345 2.57131 1141 | 2.06889 2.0372 1142 | 4.32691 2.30316 1143 | -1.0998 0.580853 1144 | 3.63868 1.7449 1145 | -0.532852 1.06252 1146 | 1.64158 -0.000263621 1147 | 3.77724 2.46788 1148 | 5.31222 2.74911 1149 | 4.01733 2.54671 1150 | 3.03295 0.834336 1151 | 2.79767 2.83192 1152 | 1.9924 2.73842 1153 | 0.232199 3.31621 1154 | 0.43277 0.67044 1155 | 3.84988 1.64282 1156 | 0.666032 0.825151 1157 | 1.83356 1.45198 1158 | -0.682524 0.567593 1159 | 2.95123 1.78752 1160 | 2.57169 1.94313 1161 | 2.1546 4.04833 1162 | 4.25988 2.3794 1163 | 4.56118 3.12789 1164 | 4.94031 3.1259 1165 | 0.811572 1.68606 1166 | 0.728236 0.739385 1167 | 0.471811 1.93344 1168 | -1.79622 1.51616 1169 | 1.50084 2.12984 1170 | 3.47874 1.95501 1171 | 3.4229 1.52304 1172 | -0.955065 2.35665 1173 | 0.924959 1.39863 1174 | 2.75688 1.75456 1175 | 3.3189 1.44815 1176 | 4.88946 1.6254 1177 | 2.37316 0.31409 1178 | -0.101108 0.422371 1179 | 2.46471 2.68754 1180 | 1.63152 1.09648 1181 | 1.12699 1.2888 1182 | -0.706205 2.44686 1183 | 1.95607 1.62058 1184 | 0.470095 3.01367 1185 | -0.475348 2.00877 1186 | 3.25139 2.42662 1187 | 3.11692 1.79866 1188 | 3.57882 2.49432 1189 | 2.27262 1.43998 1190 | 2.33894 1.69525 1191 | 2.6056 2.54821 1192 | 2.15349 2.05877 1193 | 6.36298 1.49306 1194 | 3.60254 0.599471 1195 | 1.72722 1.72405 1196 | 2.71276 1.949 1197 | 1.83319 1.33686 1198 | 5.42474 2.08904 1199 | 3.67107 0.322258 1200 | -1.85752 0.998852 1201 | 4.38982 2.22891 1202 | 4.75537 1.79426 1203 | -2.29498 1.40453 1204 | 2.9054 1.72913 1205 | 1.79555 1.62797 1206 | 1.39629 3.62731 1207 | 2.24714 3.19784 1208 | -0.950724 1.55831 1209 | 4.1144 1.3201 1210 | -0.133695 1.40967 1211 | 3.03799 2.43998 1212 | 2.50854 1.55464 1213 | 4.06356 2.49908 1214 | 3.31101 2.52803 1215 | 2.6801 2.88208 1216 | 1.69459 3.28573 1217 | 0.898475 4.3051 1218 | 0.489922 1.97688 1219 | -1.15364 2.42464 1220 | 3.23403 3.65002 1221 | -1.07996 1.38511 1222 | -0.98839 2.10188 1223 | 3.05115 2.15038 1224 | 0.705694 2.83582 1225 | 0.369912 1.72865 1226 | 2.97071 0.700372 1227 | 2.18797 3.39669 1228 | 2.86395 1.95778 1229 | 1.68858 1.05946 1230 | -1.74651 1.32307 1231 | 4.0774 2.77038 1232 | -0.0889176 0.783902 1233 | -0.858287 1.14445 1234 | 2.61197 0.747073 1235 | 3.39704 2.03166 1236 | 8.23546 -0.039051 1237 | 2.00956 2.39747 1238 | 2.71346 1.12442 1239 | 1.09581 1.54941 1240 | -1.70078 0.958339 1241 | -0.0925443 2.06311 1242 | 0.431957 2.77178 1243 | 1.7402 0.978389 1244 | -1.25972 2.05209 1245 | -1.536 0.913872 1246 | 3.74309 1.84522 1247 | 3.94223 2.661 1248 | 4.69395 2.53574 1249 | 0.349556 1.78562 1250 | 5.88537 2.16298 1251 | 0.653424 0.986013 1252 | -0.679746 1.32188 1253 | -2.63117 1.80837 1254 | 1.23235 1.64494 1255 | 2.33521 1.86237 1256 | 2.63379 0.0564138 1257 | -1.47183 1.80537 1258 | 3.04306 1.34503 1259 | 0.927698 0.834577 1260 | 3.89879 1.92081 1261 | 1.24667 3.14656 1262 | 1.5611 2.28903 1263 | 5.11455 4.29018 1264 | 1.04957 1.2958 1265 | 4.21314 3.37133 1266 | 0.680566 1.76972 1267 | 3.93265 1.13692 1268 | -0.137468 -0.637373 1269 | 5.48894 3.18558 1270 | 3.91274 0.164372 1271 | 0.906211 1.06223 1272 | 2.5606 3.53854 1273 | 5.10393 2.39897 1274 | 3.01352 2.30999 1275 | 2.90273 1.42475 1276 | 5.53402 1.57501 1277 | 2.63944 3.14504 1278 | 2.66736 1.67622 1279 | 1.41485 2.35698 1280 | 2.8656 2.44001 1281 | 2.4148 1.96226 1282 | 7.36181 2.6452 1283 | 3.52111 0.828298 1284 | -0.280059 2.83848 1285 | 2.80798 2.26086 1286 | 1.49362 1.93581 1287 | 0.95502 2.44209 1288 | -0.712927 2.3213 1289 | 2.81655 -0.0248835 1290 | 3.10555 2.33725 1291 | 5.82957 2.31074 1292 | 3.16784 0.526199 1293 | 3.60028 2.54996 1294 | 3.03932 1.69073 1295 | 0.377936 0.646614 1296 | -0.0686064 0.0443096 1297 | 0.698873 1.97329 1298 | 2.1507 1.22685 1299 | 2.2282 2.23867 1300 | 4.30984 1.17719 1301 | 1.3492 1.80011 1302 | 1.71948 2.12918 1303 | -1.67828 1.55014 1304 | 4.12566 2.98112 1305 | 2.96003 2.77556 1306 | 3.14781 1.46659 1307 | 3.90623 1.72746 1308 | 2.87353 2.00417 1309 | 1.35761 2.21957 1310 | 2.12799 1.33441 1311 | 7.10411 2.74267 1312 | 5.31213 2.6368 1313 | 4.01639 2.49891 1314 | 3.39404 2.08542 1315 | 2.09516 2.41732 1316 | -1.91258 1.0116 1317 | 4.1085 2.00275 1318 | 2.45701 1.48502 1319 | 4.46752 2.64359 1320 | 1.777 3.06585 1321 | 2.51395 2.51333 1322 | 1.77514 0.885414 1323 | 3.72168 1.66422 1324 | 3.56273 1.14298 1325 | 1.75117 2.2581 1326 | 1.44653 2.44359 1327 | 3.8777 2.37883 1328 | 2.74769 1.20224 1329 | 1.23279 0.878041 1330 | 1.24439 0.73197 1331 | 4.00483 2.59283 1332 | -0.706094 2.66752 1333 | 4.45358 3.34062 1334 | 1.33326 2.42312 1335 | 5.61402 3.09142 1336 | -0.428898 2.35684 1337 | -1.25514 1.95296 1338 | 4.30657 2.09369 1339 | 1.47555 2.04295 1340 | -0.0996077 1.96458 1341 | 0.231665 1.90797 1342 | 2.30645 2.27188 1343 | 2.14579 1.35245 1344 | 1.03252 2.01131 1345 | 3.47106 2.98996 1346 | 4.73547 1.00848 1347 | 2.91631 2.37509 1348 | -0.286002 2.0739 1349 | -0.0413328 1.5085 1350 | 2.67386 1.27125 1351 | -0.307496 1.26213 1352 | 1.83319 2.69705 1353 | 0.483737 -0.630201 1354 | 5.58034 3.07419 1355 | 1.26126 1.4768 1356 | -2.28928 3.26206 1357 | 5.01903 1.88234 1358 | 2.49834 1.42195 1359 | 3.01703 2.54707 1360 | 1.28699 1.68748 1361 | 4.91244 1.20187 1362 | 3.0803 3.63089 1363 | -0.576632 0.722909 1364 | 1.76778 3.14028 1365 | 4.11898 1.56223 1366 | 1.76743 2.60571 1367 | -0.533932 1.46622 1368 | 0.841687 2.6047 1369 | 4.37987 1.68969 1370 | -0.566783 0.944441 1371 | 2.77857 3.11788 1372 | 0.421264 1.04457 1373 | 0.325787 2.92814 1374 | 1.36232 0.476042 1375 | 1.03808 1.38907 1376 | 1.05502 3.35503 1377 | 3.7052 1.71128 1378 | 2.01383 2.49915 1379 | 0.709064 0.0704498 1380 | 4.95105 3.41103 1381 | 1.82748 1.722 1382 | 0.347962 1.28994 1383 | 2.77653 1.92708 1384 | 2.50723 3.57175 1385 | 4.55918 0.695216 1386 | 2.12278 2.19131 1387 | 2.99918 0.50217 1388 | 2.59138 2.54824 1389 | -0.580296 1.37554 1390 | 3.65085 1.63601 1391 | 5.46274 3.52874 1392 | 3.16885 2.51156 1393 | -0.832988 1.87607 1394 | 3.35069 2.15569 1395 | 2.27782 2.20245 1396 | 2.8058 1.8089 1397 | 2.53421 2.55641 1398 | 2.65762 1.46879 1399 | -0.073866 3.95582 1400 | 0.526844 0.987988 1401 | 0.500667 1.42098 1402 | 3.98872 0.934794 1403 | 3.54334 2.59574 1404 | 3.77679 1.8747 1405 | 4.77651 1.6794 1406 | 0.607604 1.95752 1407 | 3.91739 1.47083 1408 | 1.76399 1.51055 1409 | 3.83422 2.28752 1410 | -1.53941 0.338891 1411 | -0.822311 1.61154 1412 | 2.56545 2.19298 1413 | 0.32533 2.80357 1414 | 3.33251 0.949764 1415 | 6.48562 2.17903 1416 | 2.85073 1.79926 1417 | 3.08795 1.27916 1418 | 0.319415 2.19955 1419 | 3.32028 2.67449 1420 | 1.80316 1.22759 1421 | -1.98221 1.9939 1422 | 2.16955 1.34139 1423 | 0.288744 2.82967 1424 | 4.99544 1.53908 1425 | 1.43826 2.86056 1426 | 4.95645 2.75698 1427 | 2.86962 1.3697 1428 | 3.7321 2.1887 1429 | 0.927903 2.17483 1430 | 3.1273 4.29799 1431 | 2.42529 0.383433 1432 | -1.35566 0.387164 1433 | 2.81646 2.55867 1434 | 4.72048 1.17134 1435 | 1.24611 2.27351 1436 | 7.13035 2.45581 1437 | 1.44602 0.900707 1438 | 4.91586 0.995922 1439 | 0.908316 2.60037 1440 | 2.32911 2.20355 1441 | 2.32073 2.03413 1442 | 5.20898 2.28993 1443 | 2.23577 2.62619 1444 | 4.83791 2.17946 1445 | 5.47162 4.65111 1446 | 4.25332 1.71211 1447 | 0.162677 1.9759 1448 | 0.845059 2.72578 1449 | -0.717899 1.4134 1450 | 0.829316 1.41868 1451 | 0.64242 2.28095 1452 | -0.153864 2.25408 1453 | 0.895945 1.08119 1454 | 5.09858 1.20416 1455 | 3.02096 2.93649 1456 | 0.0296292 3.73308 1457 | -0.336276 2.00448 1458 | 5.45006 2.10091 1459 | 3.27579 1.00766 1460 | 4.65299 1.60082 1461 | 0.822091 -0.00866915 1462 | 0.627434 2.99514 1463 | 3.73864 3.48963 1464 | 0.729977 2.83078 1465 | 1.86079 1.30227 1466 | 3.09273 3.05906 1467 | -1.31152 2.43101 1468 | 1.14651 1.00881 1469 | 0.927722 2.00492 1470 | 4.07463 1.91829 1471 | 3.68267 1.35825 1472 | 1.0859 1.00252 1473 | 0.327868 1.13116 1474 | 3.26435 2.443 1475 | 2.64352 2.8987 1476 | -1.87607 0.99488 1477 | 3.82842 2.56345 1478 | 1.31557 1.10416 1479 | 1.19415 2.72455 1480 | 2.69143 2.62367 1481 | -2.84769 2.42513 1482 | 2.66216 1.86105 1483 | 3.92447 4.20867 1484 | 1.39058 1.24738 1485 | 1.1686 0.578938 1486 | 0.488955 1.70636 1487 | 5.52015 1.25426 1488 | 5.52486 -0.0827345 1489 | 3.34737 3.64642 1490 | 1.20731 2.17783 1491 | 2.3481 0.673143 1492 | 1.11494 1.84516 1493 | 3.07478 2.9467 1494 | 0.136392 0.534226 1495 | 8.44992 1.30796 1496 | 6.30529 2.45281 1497 | 2.80127 0.780872 1498 | 2.51637 1.89346 1499 | -0.925514 1.78725 1500 | 3.56176 1.633 1501 | 2.35347 1.98587 1502 | 2.83796 -0.0512254 1503 | 7.23807 2.81693 1504 | 5.44749 1.64381 1505 | 3.22821 1.48105 1506 | -0.242123 1.52864 1507 | 4.46834 1.91157 1508 | 3.01331 1.51067 1509 | 3.02248 3.09604 1510 | -0.68047 2.33721 1511 | 0.202713 1.97264 1512 | 0.549721 2.46757 1513 | -0.671165 3.718 1514 | -0.211002 1.54916 1515 | 2.97406 2.53775 1516 | 4.08833 4.10149 1517 | 5.03591 3.55662 1518 | 4.52166 3.33814 1519 | 4.97143 2.40781 1520 | 3.69352 0.76788 1521 | 6.57809 3.34609 1522 | -4.6426 1.23656 1523 | 2.66197 2.04853 1524 | 4.49602 1.61616 1525 | -0.195656 -0.0222669 1526 | 1.7073 3.45834 1527 | 3.54193 2.58711 1528 | 4.93739 2.55428 1529 | 4.91876 2.85263 1530 | 3.37204 -0.381803 1531 | 2.6528 1.14645 1532 | 7.90833 2.27929 1533 | 2.15531 1.68818 1534 | 4.5121 1.79992 1535 | 3.77693 1.82279 1536 | 3.27921 2.56141 1537 | 0.870685 2.4372 1538 | 3.20365 0.813649 1539 | 1.08144 2.14895 1540 | 3.51139 1.40904 1541 | 4.11454 3.96211 1542 | 0.364693 1.1213 1543 | -0.0478268 2.18325 1544 | -0.334217 2.56723 1545 | 4.59345 3.08526 1546 | 3.09127 2.53236 1547 | 1.36837 0.216368 1548 | 0.0865121 2.4772 1549 | 2.99899 4.16556 1550 | 1.36812 2.75498 1551 | 2.96412 3.7398 1552 | 3.92933 1.80381 1553 | 0.70227 1.35296 1554 | -1.20123 2.83255 1555 | 7.333 1.49297 1556 | 2.72037 1.50205 1557 | 5.99113 2.45766 1558 | 1.51285 2.60294 1559 | 7.72668 2.00723 1560 | 5.24005 0.344782 1561 | 0.63298 1.84953 1562 | 3.35489 2.20307 1563 | 5.73426 3.84997 1564 | 1.04444 1.52665 1565 | 0.0898066 2.07434 1566 | 1.77684 1.82155 1567 | 2.78169 1.69149 1568 | 6.03644 3.01002 1569 | -0.0437386 2.85617 1570 | 1.24749 1.60241 1571 | 2.39737 2.46606 1572 | 2.49952 1.57949 1573 | 2.66475 1.12129 1574 | -0.474279 1.93479 1575 | 1.56673 1.65556 1576 | 3.83008 0.236043 1577 | 4.00811 2.48337 1578 | -2.95101 0.834473 1579 | 3.07282 0.89647 1580 | 3.46909 3.60683 1581 | 6.4098 4.02368 1582 | 1.30865 2.49943 1583 | 1.44866 1.43416 1584 | 1.99554 1.94269 1585 | 3.82217 2.51134 1586 | 5.76644 1.3382 1587 | 4.53324 0.731904 1588 | 3.18286 2.44156 1589 | -3.26077 1.97137 1590 | 0.648282 2.16121 1591 | 0.0121047 1.51001 1592 | 3.63134 1.44676 1593 | 2.90491 -0.58225 1594 | 0.702816 1.77482 1595 | 5.19432 2.90984 1596 | 5.33584 2.9041 1597 | 1.78571 1.25116 1598 | 4.10259 1.75488 1599 | 6.72778 1.39007 1600 | 4.57121 2.76288 1601 | 4.05341 1.47814 1602 | 3.36643 2.36227 1603 | 1.74629 2.60784 1604 | 2.11633 2.77902 1605 | 1.70515 1.47845 1606 | 2.38373 4.59413 1607 | 4.43128 2.37561 1608 | 2.00098 2.2592 1609 | 3.99561 2.53124 1610 | 5.55636 3.32981 1611 | 0.639966 1.54171 1612 | 0.1113 2.29269 1613 | 3.01382 1.79832 1614 | 2.84262 2.86003 1615 | 1.39534 0.637871 1616 | 5.4771 2.57149 1617 | 4.32274 1.84043 1618 | 1.75107 1.16877 1619 | -0.605764 2.29395 1620 | 7.07375 1.65134 1621 | -0.363287 1.08075 1622 | 2.42233 1.72178 1623 | 2.43908 1.64546 1624 | 2.88058 1.12751 1625 | 4.82702 2.44548 1626 | 0.396493 2.15983 1627 | 3.16958 1.78651 1628 | -2.77446 2.00299 1629 | 1.97296 2.34644 1630 | 1.98887 2.24823 1631 | 4.03608 3.57916 1632 | 2.48738 0.97327 1633 | 1.2647 1.38995 1634 | 1.28491 1.54878 1635 | 2.94061 3.39442 1636 | 1.23654 1.24964 1637 | -1.41566 0.582644 1638 | 2.17732 1.87115 1639 | -0.430276 2.47707 1640 | 3.48916 1.5045 1641 | 2.01969 2.479 1642 | 3.62809 1.37121 1643 | 2.74119 2.5682 1644 | 1.439 3.69056 1645 | 2.37757 1.49667 1646 | 1.64235 2.69586 1647 | 2.12842 1.19556 1648 | 2.90916 1.2037 1649 | 4.86679 0.483688 1650 | 5.05946 2.36604 1651 | 3.49222 2.72934 1652 | 5.44887 1.06064 1653 | 2.13481 1.89938 1654 | 1.36857 1.23426 1655 | 1.04911 2.54164 1656 | 1.21278 2.68314 1657 | 5.81054 0.827739 1658 | 3.23461 3.01656 1659 | 0.837902 1.12759 1660 | 3.3107 3.06912 1661 | 3.47323 0.717212 1662 | 1.40509 1.21008 1663 | 0.266732 2.14019 1664 | 2.57575 0.433658 1665 | 1.36522 1.57302 1666 | 0.332217 0.713992 1667 | 5.87801 3.15811 1668 | 2.71465 3.2032 1669 | -0.322911 1.70915 1670 | -1.27324 1.10886 1671 | -0.60608 2.31073 1672 | 2.86565 2.7612 1673 | 1.86906 2.11027 1674 | 2.11508 3.35035 1675 | 0.492824 1.85037 1676 | -0.427327 1.21944 1677 | 2.95691 3.19985 1678 | 1.51148 3.08678 1679 | 0.749241 2.87804 1680 | 7.00303 2.29494 1681 | 4.37084 1.89917 1682 | 2.14915 2.71987 1683 | -0.568341 3.16569 1684 | 1.63008 1.72932 1685 | 4.52231 3.14077 1686 | -0.660633 1.23195 1687 | 2.84397 0.669961 1688 | 0.601276 1.98003 1689 | 3.26063 0.888815 1690 | 4.53584 2.80722 1691 | 2.65847 1.89646 1692 | 3.24068 1.04275 1693 | 3.7235 2.44731 1694 | -0.212875 2.35903 1695 | 5.47841 2.9507 1696 | 1.73109 2.52854 1697 | 0.0380728 1.30629 1698 | 2.42248 2.18708 1699 | -0.38103 2.61777 1700 | 4.89075 2.32596 1701 | 1.38165 0.352219 1702 | 3.39283 2.26959 1703 | -0.914985 2.26657 1704 | 4.27261 2.00316 1705 | 1.52776 1.36604 1706 | 4.14395 1.84748 1707 | 3.91747 2.81138 1708 | 2.66036 1.79398 1709 | 0.480363 2.10137 1710 | 4.03513 2.37231 1711 | -2.05862 1.33603 1712 | 1.26526 0.0255168 1713 | 2.98452 2.97213 1714 | 4.84086 2.02915 1715 | 3.45732 0.931362 1716 | 5.1095 2.20567 1717 | 2.47332 1.22749 1718 | 3.11334 2.51324 1719 | 4.5079 2.10702 1720 | 5.73397 2.20903 1721 | 2.60339 1.05951 1722 | 3.58851 3.10678 1723 | 0.96558 2.45168 1724 | -0.601448 1.29976 1725 | 2.424 1.63351 1726 | 5.13825 1.39217 1727 | 1.51904 0.489319 1728 | 3.07757 1.31227 1729 | 4.55664 3.50617 1730 | 3.02229 1.54738 1731 | 2.71552 3.66853 1732 | -0.0925946 0.0889657 1733 | 0.49272 1.11203 1734 | 3.54343 2.89552 1735 | 4.46965 2.14482 1736 | 3.30551 1.84733 1737 | 2.42957 1.58515 1738 | 4.70261 3.26584 1739 | 4.64805 2.40162 1740 | 0.172022 1.69594 1741 | 2.41407 2.01327 1742 | 2.41687 1.58337 1743 | 4.92418 0.867796 1744 | 4.24804 3.54864 1745 | 2.3714 2.74364 1746 | -1.68655 1.07413 1747 | 2.18954 1.40857 1748 | 0.640967 1.04911 1749 | 2.00822 2.43401 1750 | -4.04861 0.755786 1751 | 2.27837 1.19646 1752 | 3.67554 3.56396 1753 | -0.692943 0.0677744 1754 | 2.40111 0.739728 1755 | -0.445121 4.2114 1756 | 2.37573 2.77911 1757 | -0.155025 2.8286 1758 | 3.99734 2.78583 1759 | 2.25473 1.20705 1760 | 4.88237 3.76176 1761 | 2.49207 1.72561 1762 | 1.40758 2.43782 1763 | 2.83653 2.36367 1764 | 6.06144 2.44784 1765 | 1.36019 1.53963 1766 | -3.36753 0.468981 1767 | 5.30994 2.44231 1768 | 1.9585 1.39444 1769 | 1.35863 3.3928 1770 | 2.90924 1.58289 1771 | 3.13111 1.61013 1772 | 1.46205 2.88757 1773 | 5.72814 3.0099 1774 | -0.335738 -0.0697402 1775 | 1.37473 2.30354 1776 | 3.41531 0.849781 1777 | 3.33359 2.46935 1778 | 4.87531 2.50409 1779 | 0.752074 2.19705 1780 | 1.43599 2.96597 1781 | 1.10334 1.53263 1782 | 2.82717 2.83064 1783 | 8.4505 2.72071 1784 | 2.45611 2.76754 1785 | 2.18985 1.90816 1786 | 4.81681 4.62685 1787 | 1.50281 1.59521 1788 | 1.6896 1.0429 1789 | 1.69778 1.98133 1790 | 3.75086 2.99725 1791 | 4.50136 3.66068 1792 | 2.61416 2.97759 1793 | 0.275738 2.35971 1794 | 1.1594 3.29303 1795 | 0.741869 2.38897 1796 | 0.394594 0.83294 1797 | 3.42166 2.70704 1798 | 1.13056 2.39407 1799 | 6.23129 2.1573 1800 | 0.441213 1.64783 1801 | 4.15699 1.98632 1802 | 1.92693 3.01716 1803 | 2.91001 3.62087 1804 | 2.2506 1.71774 1805 | 2.42825 2.86187 1806 | 2.94417 1.31888 1807 | 2.81449 2.05784 1808 | 3.0102 2.13261 1809 | 4.95368 3.04207 1810 | 1.66326 1.86135 1811 | 5.09456 2.16509 1812 | 5.53905 1.65675 1813 | 3.93909 0.579044 1814 | 7.29634 2.32576 1815 | 2.06456 0.818894 1816 | 2.54748 1.56357 1817 | 0.983288 0.452984 1818 | 1.45295 1.26858 1819 | 3.81907 1.81427 1820 | 1.23735 2.35717 1821 | 2.53851 2.82708 1822 | 3.44823 0.59987 1823 | 2.16266 3.20051 1824 | 0.669778 3.10859 1825 | 0.844067 1.45419 1826 | 1.91048 0.787995 1827 | 2.79874 3.08319 1828 | 0.793862 0.146647 1829 | 1.5777 2.25313 1830 | 3.33653 3.22763 1831 | 2.10251 0.294822 1832 | 0.640446 1.39395 1833 | 2.47063 1.70246 1834 | 4.87008 1.91478 1835 | 2.28299 1.12278 1836 | 3.3463 1.01883 1837 | 3.30643 1.82397 1838 | 2.28121 2.18399 1839 | 3.75541 1.66331 1840 | 2.31661 2.82944 1841 | 5.2468 2.15583 1842 | 2.50994 3.04978 1843 | -0.0982234 2.15726 1844 | 5.39776 1.2116 1845 | 0.845123 1.18948 1846 | 1.66768 2.85506 1847 | 2.08479 2.38391 1848 | -0.092328 1.34018 1849 | 3.92341 1.38384 1850 | 2.82547 0.391025 1851 | 0.914588 2.01975 1852 | 4.05675 1.63785 1853 | 0.642898 -0.389946 1854 | 5.90428 2.61938 1855 | 0.909129 1.5967 1856 | 1.33617 1.95265 1857 | 2.22401 1.5512 1858 | 1.09653 3.71921 1859 | 1.54138 -0.142108 1860 | 6.56999 0.16839 1861 | 2.78702 3.43962 1862 | 2.98214 2.57647 1863 | 5.86979 0.825116 1864 | 2.47132 2.42819 1865 | 0.787812 2.1145 1866 | 1.56837 1.50207 1867 | 1.60456 2.68694 1868 | 3.22299 2.51003 1869 | -0.557637 1.04583 1870 | 3.08919 3.19007 1871 | 1.14911 2.21057 1872 | 2.76256 2.106 1873 | 2.76243 0.67263 1874 | 4.71277 2.41474 1875 | 3.01912 0.945432 1876 | 1.4566 2.86121 1877 | 2.34184 0.49387 1878 | 1.67186 1.66838 1879 | 1.59052 1.52993 1880 | 3.44472 1.68544 1881 | 4.14336 2.31839 1882 | 4.75823 2.05506 1883 | 2.36966 3.28112 1884 | 2.18335 2.20515 1885 | 1.59984 3.72065 1886 | 2.07503 2.17889 1887 | -0.247773 -0.267323 1888 | 4.89897 1.33912 1889 | 2.85387 1.24807 1890 | 4.51968 2.54703 1891 | 2.41589 2.45229 1892 | 1.74538 1.82216 1893 | 0.540253 -0.375884 1894 | 3.78783 3.09108 1895 | 0.214959 2.12247 1896 | 3.24439 0.272564 1897 | 4.80358 1.2433 1898 | 1.62117 1.44201 1899 | 2.5875 0.381671 1900 | 3.17606 2.86244 1901 | 4.69924 1.62393 1902 | 1.71719 0.238346 1903 | 1.03096 1.06262 1904 | -0.316772 0.60062 1905 | 0.249819 3.54339 1906 | 5.51938 2.14505 1907 | 0.664685 0.949899 1908 | 1.88236 0.0547926 1909 | -0.453601 3.1893 1910 | 2.3809 2.20479 1911 | 5.07104 2.62693 1912 | 5.02187 3.23632 1913 | 1.82568 1.12158 1914 | 0.89364 3.53458 1915 | 1.84679 1.47948 1916 | 4.15599 2.9876 1917 | 3.69796 1.59755 1918 | 4.60376 1.60961 1919 | 2.98951 1.35037 1920 | 0.0899245 1.67058 1921 | 3.71796 1.47521 1922 | 2.3636 0.952642 1923 | 1.80972 1.82365 1924 | -3.14878 1.86095 1925 | 2.90513 2.90725 1926 | 1.08357 0.192489 1927 | 1.31236 2.84319 1928 | 5.23099 1.83398 1929 | 1.66448 1.86448 1930 | 0.737214 1.10394 1931 | -1.81196 1.02203 1932 | -0.640967 2.60805 1933 | 4.89775 2.73371 1934 | -1.462 1.98601 1935 | 2.93878 1.87994 1936 | 1.47954 2.09552 1937 | 1.53976 2.66167 1938 | -0.402025 0.819182 1939 | 4.7377 2.37292 1940 | 0.642571 0.953856 1941 | 0.762856 2.44125 1942 | -2.04824 0.930713 1943 | 2.21223 1.36769 1944 | 0.397345 1.58786 1945 | 4.20853 2.06325 1946 | 4.45877 2.0655 1947 | 3.47358 2.30167 1948 | 4.94209 1.82031 1949 | 2.2032 2.85351 1950 | 3.36937 0.445313 1951 | 4.2679 2.22769 1952 | -1.18711 2.15756 1953 | 2.93336 1.24944 1954 | 0.062092 0.295985 1955 | 4.41356 2.56558 1956 | 0.536829 2.38045 1957 | 1.10022 2.14035 1958 | 3.43 4.21547 1959 | 1.97871 2.16054 1960 | 4.57 0.90866 1961 | -0.89966 0.534549 1962 | 3.5259 1.76584 1963 | 1.12148 2.20006 1964 | 3.86739 1.36668 1965 | 0.27318 0.0588512 1966 | 2.05855 2.98984 1967 | 0.9776 -0.385405 1968 | 4.7055 0.568066 1969 | 4.90433 1.72278 1970 | -1.58103 1.194 1971 | -0.59132 1.56148 1972 | 0.564568 1.23745 1973 | 4.60769 1.88525 1974 | 6.06677 2.91232 1975 | 4.63781 0.301828 1976 | 2.32598 0.239851 1977 | 7.62153 3.11829 1978 | 4.40073 2.09372 1979 | 2.97263 0.677611 1980 | 1.52076 1.36239 1981 | 5.83578 2.53845 1982 | 2.79217 1.26547 1983 | 5.07183 4.388 1984 | 1.64587 0.0711668 1985 | 3.49751 3.57979 1986 | 0.0302592 1.68528 1987 | 2.80617 0.509407 1988 | -0.38187 -0.36432 1989 | 7.34424 3.4279 1990 | 0.618613 1.63949 1991 | 5.77641 1.62675 1992 | 2.93404 1.40461 1993 | 2.61991 2.61175 1994 | 2.0631 3.02274 1995 | 4.02591 2.96055 1996 | 1.06214 1.20781 1997 | 3.50137 2.68129 1998 | 1.42734 2.13079 1999 | 2.62895 1.4283 2000 | 1.8446 3.2435 2001 | 2.49434 2.64785 2002 | 1.84947 1.62372 2003 | 2004 | 2005 | -6.5652 5.58045 2006 | -1.7931 8.47715 2007 | -7.26475 6.10444 2008 | -1.48867 2.20874 2009 | -7.94137 4.00289 2010 | -6.97711 6.73683 2011 | -5.08871 7.30454 2012 | -7.35315 5.86926 2013 | -4.211 8.26276 2014 | -4.44116 8.31014 2015 | -2.8489 3.96345 2016 | -6.47126 4.80879 2017 | -8.08872 10.2059 2018 | -5.9625 3.95722 2019 | -3.58957 5.09386 2020 | -4.36757 8.12184 2021 | -6.28169 5.46652 2022 | -4.35804 4.91981 2023 | -4.32418 8.83673 2024 | -4.24562 7.20754 2025 | -2.25401 7.06443 2026 | -3.63242 4.27097 2027 | -7.17698 6.882 2028 | -4.19224 10.0805 2029 | -4.96213 5.72987 2030 | -6.07793 9.29566 2031 | -6.98173 3.9317 2032 | -7.34416 8.74152 2033 | -7.45102 6.99411 2034 | -4.06175 5.77915 2035 | -6.41329 6.15893 2036 | -6.85824 7.74334 2037 | -5.69957 5.99699 2038 | -4.78411 8.24192 2039 | -3.79375 9.59602 2040 | -3.02152 0.357205 2041 | -1.30739 5.05971 2042 | -5.12787 8.68351 2043 | -5.02429 8.45752 2044 | -6.07492 4.1253 2045 | -4.65642 7.98424 2046 | -5.87645 9.38039 2047 | -6.39008 4.87932 2048 | -2.91272 7.57442 2049 | -5.0502 5.23882 2050 | -2.47659 7.20973 2051 | -6.52966 3.87169 2052 | -4.56176 1.93531 2053 | -5.91259 7.02011 2054 | -5.86827 6.99707 2055 | -5.5668 3.85732 2056 | -5.6336 5.75989 2057 | -6.24657 5.67624 2058 | -5.85726 3.17309 2059 | -4.95404 5.19369 2060 | -5.3717 8.52156 2061 | -0.0775356 8.06218 2062 | -5.98528 5.78117 2063 | -8.8166 3.34543 2064 | -4.90948 5.57457 2065 | -4.50559 4.83204 2066 | -5.37784 4.10328 2067 | -7.58941 4.18144 2068 | -3.71311 9.41328 2069 | -4.00496 4.36261 2070 | -4.50453 4.85324 2071 | -3.25534 5.41579 2072 | -4.1864 8.61234 2073 | -4.34329 1.21886 2074 | -4.42368 8.0659 2075 | -8.28671 7.73342 2076 | -1.32955 5.17938 2077 | -2.426 6.50514 2078 | -3.99333 6.35284 2079 | -5.80595 3.24989 2080 | -8.77127 9.53982 2081 | -6.02928 7.00469 2082 | -5.01176 4.10971 2083 | -3.48847 4.26275 2084 | -6.05916 6.53387 2085 | -3.43531 6.15468 2086 | -2.41532 4.83185 2087 | -3.12426 6.94651 2088 | -5.95887 6.03562 2089 | -5.03984 0.511769 2090 | -6.14771 10.4869 2091 | -6.34347 5.36564 2092 | -3.22397 6.61566 2093 | -4.30361 7.01862 2094 | -6.94212 2.59516 2095 | -5.33929 7.14983 2096 | -5.6264 5.50768 2097 | -8.71241 5.22456 2098 | -6.93794 6.87658 2099 | -5.06569 5.09149 2100 | -5.82636 7.66522 2101 | -3.81416 2.83972 2102 | -4.79608 6.81741 2103 | -4.44831 9.25882 2104 | -1.09733 10.1507 2105 | -6.92863 5.28938 2106 | -5.41113 9.70944 2107 | -2.57761 5.49724 2108 | -7.5664 7.30101 2109 | -6.80497 5.59258 2110 | -6.11282 8.40219 2111 | -3.75766 5.31675 2112 | -4.44621 7.72444 2113 | -5.0747 4.36839 2114 | -3.70546 4.24936 2115 | -3.25625 1.90278 2116 | -2.05517 4.73909 2117 | -3.33198 2.55459 2118 | -4.73629 7.62003 2119 | -5.98307 5.45549 2120 | -1.49729 8.77729 2121 | -6.48899 2.97366 2122 | -6.8312 5.19139 2123 | 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-------------------------------------------------------------------------------- /k-means/kmeans.ml: -------------------------------------------------------------------------------- 1 | (** kmeans.ml --- K-means clustering 2 | 3 | [MIT License] Copyright (C) 2015 Akinori ABE 4 | *) 5 | 6 | open Format 7 | 8 | module Array = struct 9 | include Array 10 | 11 | let iter2 f x y = iteri (fun i xi -> f xi y.(i)) x 12 | 13 | let foldi f init x = 14 | snd (fold_left (fun (i, acc) xi -> (i+1, f i acc xi)) (0, init) x) 15 | 16 | let min f x = 17 | foldi 18 | (fun i (i0, v0) xi -> let v = f xi in if v0 > v then (i, v) else (i0, v0)) 19 | (-1, max_float) x 20 | 21 | let fold_left2 f init x y = foldi (fun i acc xi -> f acc xi y.(i)) init x 22 | 23 | let map2_sum f = fold_left2 (fun acc xi yi -> acc +. f xi yi) 0.0 24 | end 25 | 26 | (** [distance x y] returns the square of the L2 norm of the distance between 27 | vectors [x] and [y], i.e., [||x - y||^2]. *) 28 | let distance = Array.map2_sum (fun xi yi -> let diff = xi -. yi in diff *. diff) 29 | 30 | (** [kmeans k xs] performs [k]-means clustering algorithm for data set [xs]. 31 | @return [(means, cs)] where [means] is an array of mean vectors, and [cs] is 32 | an array such that the [i]-th element is the class number of [xs.(i)]. *) 33 | let kmeans k xs = 34 | let d = Array.length xs.(0) in (* the dimension of a sample *) 35 | let calc_means cs = (* Compute the mean of each class *) 36 | let z = Array.init k (fun _ -> (ref 0, Array.make d 0.0)) in 37 | let sum_up ci xi = 38 | let (n, sum) = z.(ci) in 39 | Array.iteri (fun j xij -> sum.(j) <- sum.(j) +. xij) xi; (* sum += xi *) 40 | incr n 41 | in 42 | let normalize (n, sum) = 43 | let c = 1.0 /. float !n in 44 | Array.map (( *. ) c) sum 45 | in 46 | Array.iter2 sum_up cs xs; 47 | Array.map normalize z 48 | in 49 | let update means cs = (* Update class assignment *) 50 | Array.foldi (fun i updated xi -> 51 | let ci', _ = Array.min (distance xi) means in 52 | if cs.(i) <> ci' then (cs.(i) <- ci' ; true) else updated) 53 | false xs 54 | in 55 | let m = Array.length xs in (* the number of samples *) 56 | let cs = Array.init m (fun i -> i mod k) in (* class assignment *) 57 | let rec loop () = 58 | let means = calc_means cs in 59 | if update means cs then loop () else (means, cs) 60 | in 61 | loop () (* loop until convergence *) 62 | 63 | let show_result k xs cs = 64 | let ys = Array.map snd Dataset.samples in (* answers *) 65 | let tbl = Array.make_matrix k k 0 in 66 | Array.iter2 (fun ci yi -> tbl.(ci).(yi) <- succ tbl.(ci).(yi)) cs ys; 67 | for prd = 0 to k - 1 do 68 | for ans = 0 to k - 1 do 69 | printf "Prediction = %d, Answer = %d: %d points@\n" 70 | prd ans tbl.(prd).(ans) 71 | done 72 | done 73 | 74 | let () = 75 | let k = Dataset.n_classes in 76 | let xs = Array.map fst Dataset.samples in 77 | let (means, cs) = kmeans k xs in 78 | printf "mean vectors:@\n"; 79 | Array.iteri (fun i mi -> 80 | printf "[%d]" i; 81 | Array.iter (printf " %.2f") mi; 82 | print_newline ()) 83 | means; 84 | show_result k xs cs 85 | -------------------------------------------------------------------------------- /levinson-durbin/levinson.ml: -------------------------------------------------------------------------------- 1 | (** levinson.ml --- an implementation of Levinson-Durbin recursion 2 | 3 | [MIT Lisence] Copyright (C) 2015 Akinori ABE 4 | *) 5 | 6 | open Format 7 | 8 | module Array = struct 9 | include Array 10 | 11 | (** [mapi_sum f [|x1; x2; ...; xn|]] is [f x1 +. f x2 +. ... +. f xn]. *) 12 | let mapi_sum f x = 13 | let acc = ref 0.0 in 14 | for i = 0 to length x - 1 do acc := !acc +. f i x.(i) done; 15 | !acc 16 | end 17 | 18 | (** [autocorr x tau] computes autocorrelation [[|r(0); r(1); ...; [r(tau)]|]]. 19 | *) 20 | let autocorr x tau = 21 | let n = Array.length x in 22 | let r = Array.make (tau + 1) 0.0 in 23 | for i = 0 to tau do 24 | for t = 0 to n-i-1 do r.(i) <- r.(i) +. x.(t) *. x.(t + i) done 25 | done; 26 | r 27 | 28 | (** [levinson r] computes AR coefficients by Levinson-Durbin recursion where 29 | [r = [|r(0); r(1); ...; r(n)|]] is autocorrelation. 30 | @return [([ar(1); ar(2); ...; ar(n)], sigma2)] where [ar(i)] is the [i]-th 31 | coefficient of AR([n]) and [sigma2] is variance of errors. 32 | *) 33 | let levinson r = 34 | let n = Array.length r in 35 | if n = 0 then failwith "empty autocorrelation"; 36 | let rec aux m ar sigma2 = 37 | let m' = m + 1 in 38 | if m' = n then (ar, sigma2) 39 | else begin 40 | let ar' = Array.make (m+1) 0.0 in 41 | ar'.(m) <- (r.(m+1) -. Array.mapi_sum (fun i ai -> ai *. r.(m-i)) ar) 42 | /. sigma2; 43 | for i = 0 to m-1 do ar'.(i) <- ar.(i) -. ar'.(m) *. ar.(m-1-i) done; 44 | let sigma2' = sigma2 *. (1.0 -. ar'.(m) *. ar'.(m)) in 45 | aux (m+1) ar' sigma2' 46 | end 47 | in 48 | aux 0 [||] r.(0) 49 | 50 | let print_ar_coeffs label data order = 51 | let r = autocorr data (order + 1) in 52 | let (ar, sigma2) = levinson r in 53 | let ar_str = Array.to_list ar 54 | |> List.map (sprintf "%g") 55 | |> String.concat "; " in 56 | printf "%s:@\n @[AR = [|%s|]@\nsigma^2 = %g@]@." label ar_str sigma2 57 | 58 | let main () = 59 | let order = 20 in (* AR order *) 60 | print_ar_coeffs "Sound /a/" Dataset.a order; 61 | print_ar_coeffs "Sound /i/" Dataset.i order; 62 | print_ar_coeffs "Sound /u/" Dataset.u order; 63 | print_ar_coeffs "Sound /e/" Dataset.e order; 64 | print_ar_coeffs "Sound /o/" Dataset.o order 65 | 66 | let () = main () 67 | -------------------------------------------------------------------------------- /lu-decomposition/lu.ml: -------------------------------------------------------------------------------- 1 | (** lu.ml --- LU decompisition by Crout's method 2 | 3 | [MIT License] Copyright (C) 2015 Akinori ABE 4 | *) 5 | 6 | open Format 7 | 8 | module Array = struct 9 | include Array 10 | 11 | let init_matrix m n f = init m (fun i -> init n (f i)) 12 | 13 | let matrix_size a = 14 | let m = length a in 15 | let n = if m = 0 then 0 else length a.(0) in 16 | (m, n) 17 | 18 | (** [swap x i j] swaps [x.(i)] and [x.(j)]. *) 19 | let swap x i j = 20 | let tmp = x.(i) in 21 | x.(i) <- x.(j); 22 | x.(j) <- tmp 23 | end 24 | 25 | (** [foldi f init i j] is [f (... (f (f init i) (i+1)) ...) j]. *) 26 | let foldi f init i j = 27 | let acc = ref init in 28 | for k = i to j do acc := f !acc k done; 29 | !acc 30 | 31 | (** [sumi f i j] is [f i +. f (i+1) +. ... +. f j] *) 32 | let sumi f i j = foldi (fun acc k -> acc +. f k) 0.0 i j 33 | 34 | (** [maxi f i j] computes the index of the maximum in [f i, f (i+1), ..., f j]. 35 | *) 36 | let maxi f i j = 37 | foldi 38 | (fun (k0, v0) k -> let v = f k in if v0 < v then (k, v) else (k0, v0)) 39 | (-1, ~-. max_float) i j 40 | |> fst 41 | 42 | (** [lup a] computes LUP decomposition of square matrix [a] by Crout's method. 43 | @return [(p, lu)] where [p] is an array of permutation indices and [lu] is 44 | a matrix containing lower and upper triangular matrices. 45 | *) 46 | let lup a0 = 47 | let a = Array.copy a0 in 48 | let m, n = Array.matrix_size a in 49 | let r = min m n in 50 | let p = Array.init m (fun i -> i) in (* permutation indices *) 51 | let lu = Array.make_matrix m n 0.0 in 52 | let aux i j q = a.(i).(j) -. sumi (fun k -> lu.(i).(k) *. lu.(k).(j)) 0 q in 53 | let get_pivot j = maxi (fun i -> abs_float a.(i).(j)) j (m-1) in 54 | for j = 0 to r - 1 do 55 | (* pivot selection (swapping rows) *) 56 | let j' = get_pivot j in 57 | if j <> j' then Array.(swap p j j' ; swap a j j' ; swap lu j j'); 58 | (* Compute LU decomposition *) 59 | for i = 0 to j do lu.(i).(j) <- aux i j (i-1) done; 60 | if abs_float lu.(j).(j) > 1e-6 (* Avoid divsion by zero *) 61 | then for i = j+1 to m-1 do lu.(i).(j) <- aux i j (j-1) /. lu.(j).(j) done 62 | done; 63 | (* Compute the right block in the upper trapezoidal matrix *) 64 | for j = r to n-1 do 65 | for i = 0 to r-1 do lu.(i).(j) <- aux i j (i-1) done 66 | done; 67 | (p, lu) 68 | 69 | (** Matrix multiplication *) 70 | let gemm x y = 71 | let m, k = Array.matrix_size x in 72 | let k', n = Array.matrix_size y in 73 | assert(k = k'); 74 | Array.init_matrix m n 75 | (fun i j -> sumi (fun l -> x.(i).(l) *. y.(l).(j)) 0 (k - 1)) 76 | 77 | let print_mat label x = 78 | printf "%s =@\n" label; 79 | Array.iter (fun xi -> 80 | Array.iter (printf " %10g") xi; 81 | print_newline ()) x 82 | 83 | let () = 84 | let a = 85 | [| 86 | [| 0.; 2.; 3.; 0.; 9.; 0.; 2.; 3.; 0.|]; 87 | [|-1.; 1.; 4.; 2.; 3.; -1.; 1.; 4.; 2.|]; 88 | [| 6.; 0.;-9.; 1.; 0.; 6.; 0.;-9.; 1.|]; 89 | [| 3.; 5.; 0.; 0.; 1.; 3.; 5.; 0.; 0.|]; 90 | [|-8.; 3.; 1.;-5.; 2.; -8.; 3.; 1.;-5.|]; 91 | [|-2.;-1.;-1.; 4.; 6.; -2.;-1.;-1.; 4.|]; 92 | [| 0.; 2.; 3.; 0.; 9.; 0.; 2.; 3.; 0.|]; 93 | [|-1.; 1.; 4.; 2.; 3.; -1.; 1.; 4.; 2.|]; 94 | [| 6.; 0.;-9.; 1.; 0.; 6.; 0.;-9.; 1.|]; 95 | |] in 96 | let p, lu = lup a in 97 | let m, n = Array.matrix_size lu in 98 | let r = min m n in 99 | let l = (* a lower trapezoidal matrix *) 100 | Array.init_matrix m r 101 | (fun i j -> if i > j then lu.(i).(j) else if i = j then 1.0 else 0.0) in 102 | let u = (* an upper trapezoidal matrix *) 103 | Array.init_matrix r n 104 | (fun i j -> if i <= j then lu.(i).(j) else 0.0) in 105 | let p = (* a permutation matrix *) 106 | Array.init_matrix m m (fun i j -> if i = p.(j) then 1.0 else 0.0) in 107 | let a' = gemm p (gemm l u) in (* ['a] is equal to [a]. *) 108 | print_mat "matrix A" a; 109 | print_mat "matrix L" l; 110 | print_mat "matrix U" u; 111 | print_mat "matrix P" p; 112 | print_mat "matrix P * L * U" a' 113 | -------------------------------------------------------------------------------- /neural-network/naive-multilayer/neuralNetwork.ml: -------------------------------------------------------------------------------- 1 | (** neuralNetwork.ml --- multilayer neural network for binary classification 2 | 3 | [MIT Lisence] Copyright (C) 2015 Akinori ABE 4 | *) 5 | 6 | open Format 7 | 8 | (* ================================================================= * 9 | * Utility functions for array 10 | * ================================================================= *) 11 | 12 | module Array = struct 13 | include Array 14 | 15 | let init_matrix m n f = init m (fun i -> init n (f i)) 16 | 17 | let matrix_size a = 18 | let m = length a in 19 | let n = if m = 0 then 0 else length a.(0) in 20 | (m, n) 21 | 22 | let map2 f x y = mapi (fun i xi -> f xi y.(i)) x 23 | 24 | let iter2 f x y = iteri (fun i xi -> f xi y.(i)) x 25 | let iteri2 f x y = iteri (fun i xi -> f i xi y.(i)) x 26 | 27 | let fold_left2 f init x y = 28 | let acc = ref init in 29 | for i = 0 to length x - 1 do acc := f !acc x.(i) y.(i) done; 30 | !acc 31 | 32 | let map_sum f = fold_left (fun acc xi -> acc +. f xi) 0.0 33 | let map2_sum f = fold_left2 (fun acc xi yi -> acc +. f xi yi) 0.0 34 | end 35 | 36 | (* ================================================================= * 37 | * BLAS-like functions for linear algebraic operations 38 | * ================================================================= *) 39 | 40 | (** Dot product of two vectors *) 41 | let dot = Array.map2_sum ( *. ) 42 | 43 | (** Execute [y := alpha * x + y] where [alpha] is a scalar, [x] and [y] are 44 | vectors. *) 45 | let axpy ~alpha x y = 46 | let n = Array.length x in 47 | for i = 0 to n - 1 do y.(i) <- alpha *. x.(i) +. y.(i) done 48 | 49 | (** [gemv a x y] computes [a * x + y] where [a] is a matrix, and [x] and [y] are 50 | vectors. *) 51 | let gemv a x y = Array.map2 (fun ai yi -> dot ai x +. yi) a y 52 | 53 | (** [gemv_t a x] computes [a^T * x] where [a] is a matrix and [x] is a vector. 54 | *) 55 | let gemv_t a x = 56 | let (_, n) = Array.matrix_size a in 57 | let y = Array.make n 0.0 in 58 | Array.iter2 (fun ai xi -> axpy ~alpha:xi ai y) a x; 59 | y 60 | 61 | (** [ger x y] computes outer product [x y^T] of vectors [x] and [y]. *) 62 | let ger x y = Array.map (fun xi -> Array.map (( *. ) xi) y) x 63 | 64 | (* ================================================================= * 65 | * Multilayer neural network 66 | * ================================================================= *) 67 | 68 | (** A layer in a multilayer neural network *) 69 | type layer = 70 | { 71 | actv_f : float array -> float array; (** an activation function *) 72 | actv_f' : float array -> float array array; (** the derivative of [actv_f]*) 73 | weight : float array array; (** a weight matrix *) 74 | bias : float array; (** a bias vector *) 75 | } 76 | 77 | (** Forward propagation *) 78 | let forwardprop lyrs x0 = 79 | List.fold_left 80 | (fun xi lyr -> lyr.actv_f (gemv lyr.weight xi lyr.bias)) 81 | x0 lyrs 82 | 83 | (** An error function (cross-entropy) *) 84 | let error y t = ~-. (Array.map2_sum (fun ti yi -> ti *. log yi) t y) 85 | 86 | (** The derivative of an error function *) 87 | let error' = Array.map2 (fun yi ti -> ~-. ti /. yi) 88 | 89 | (** Error backpropagation *) 90 | let backprop lyrs x0 t = 91 | let rec calc_delta x = function 92 | | [] -> failwith "empty neural network" 93 | | [lyr] -> (* output layer *) 94 | let y = lyr.actv_f (gemv lyr.weight x lyr.bias) in 95 | let delta = gemv_t (lyr.actv_f' y) (error' y t) in 96 | (delta, []) 97 | | lyr :: ((uplyr :: _) as lyrs') -> (* hidden layer *) 98 | let y = lyr.actv_f (gemv lyr.weight x lyr.bias) in 99 | let (updelta, tl) = calc_delta y lyrs' in 100 | let delta = gemv_t (lyr.actv_f' y) (gemv_t uplyr.weight updelta) in 101 | (delta, (y, updelta) :: tl) 102 | in 103 | let (delta0, tl) = calc_delta x0 lyrs in 104 | (x0, delta0) :: tl 105 | 106 | (** Update parameters in the given neural network according to the given input 107 | and target (stochastic gradient descent). *) 108 | let train ~eta lyrs x0 t = 109 | let alpha = ~-. eta in 110 | let res = backprop lyrs x0 t in 111 | List.iter2 112 | (fun (x, delta) lyr -> 113 | let dw = ger delta x in 114 | let db = delta in 115 | Array.iter2 (axpy ~alpha) dw lyr.weight; 116 | axpy ~alpha db lyr.bias) 117 | res lyrs 118 | 119 | (* ================================================================= * 120 | * Gradient checking 121 | * 122 | * Gradient checking is a approach to verify whether implementation of 123 | * error backpropagation algorithm is correct, or not. See 124 | * http://ufldl.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization 125 | * for details. 126 | * ================================================================= *) 127 | 128 | (** Compute the gradient of error function by naive numerical differentiation *) 129 | let approx_gradient ?(epsilon = 1e-4) lyrs x0 t = 130 | let (lyr0, lyrs') = match lyrs with 131 | | [] -> failwith "empty neural network" 132 | | hd :: tl -> (hd, tl) in 133 | let lyr0_bias_eps i eps = 134 | let bias = Array.mapi (fun j bj -> if i=j then bj+.eps else bj) lyr0.bias in 135 | { lyr0 with bias } 136 | in 137 | let lyr0_weight_eps i j eps = 138 | let aux k l wkl = if i = k && j = l then wkl +. eps else wkl in 139 | let weight = Array.mapi (fun k -> Array.mapi (aux k)) lyr0.weight in 140 | { lyr0 with weight } 141 | in 142 | let calc_grad lyr0_eps = 143 | let calc_error lyr0' = error (forwardprop (lyr0' :: lyrs') x0) t in 144 | let e_p = calc_error (lyr0_eps (~+. epsilon)) in 145 | let e_n = calc_error (lyr0_eps (~-. epsilon)) in 146 | (e_p -. e_n) /. (2.0 *. epsilon) 147 | in 148 | let (m, n) = Array.matrix_size lyr0.weight in 149 | let db = Array.init m (fun i -> calc_grad (lyr0_bias_eps i)) in 150 | let dw = Array.init_matrix m n (fun i j -> calc_grad (lyr0_weight_eps i j)) in 151 | (db, dw) 152 | 153 | let eq_significant_digits ?(epsilon = 1e-9) ?(digits = 1e-3) x y = 154 | let check_float z = match classify_float z with 155 | | FP_infinite -> false 156 | | FP_nan -> false 157 | | _ -> true 158 | in 159 | if not (check_float x && check_float y) then failwith "divergence"; 160 | let abs_x = abs_float x in 161 | if abs_x < epsilon 162 | then abs_float y < epsilon (* true if both x and y are nealy zero *) 163 | else begin (* check significant digits *) 164 | let d = (x -. y) *. (0.1 ** (floor (log10 abs_x) +. 1.0)) in 165 | abs_float d < digits 166 | end 167 | 168 | let check_gradient lyrs x0 t = 169 | let warn s x y = 170 | if not (eq_significant_digits x y) 171 | then eprintf "** %s is %.16g, but should be %.16g@." s x y 172 | in 173 | let (x, delta) = List.hd (backprop lyrs x0 t) in 174 | let dw = ger delta x in 175 | let db = delta in 176 | let (db', dw') = approx_gradient lyrs x0 t in 177 | Array.iteri2 (fun i -> warn (sprintf "dE/db[%d]" i)) db db'; 178 | Array.iteri2 (fun i -> 179 | Array.iteri2 (fun j -> 180 | warn (sprintf "dE/dw[%d,%d]" i j))) dw dw' 181 | 182 | (* ================================================================= * 183 | * Activation functions 184 | * ================================================================= *) 185 | 186 | (** The hyperbolic tangent *) 187 | let actv_tanh = Array.map tanh 188 | 189 | (** The derivative of the hyperbolic tangent *) 190 | let actv_tanh' z = 191 | let n = Array.length z in 192 | Array.init_matrix n n (fun i j -> if i=j then 1.0 -. z.(i) *. z.(i) else 0.0) 193 | 194 | (** The softmax function (used at the output layer for classification) *) 195 | let actv_softmax x = 196 | let y = Array.map exp x in 197 | let c = 1.0 /. Array.map_sum (fun yi -> yi) y in 198 | Array.map (( *. ) c) y 199 | 200 | (** The derivative of the softmax function *) 201 | let actv_softmax' z = 202 | let n = Array.length z in 203 | Array.init_matrix n n 204 | (fun i j -> if i = j then (1.0 -. z.(i)) *. z.(i) else ~-. (z.(i) *. z.(j))) 205 | 206 | (** A linear function (used at the output layer for regression) *) 207 | let actv_linear x = x 208 | 209 | (** The derivative of a linear function *) 210 | let actv_linear z = 211 | let n = Array.length z in 212 | Array.init_matrix n n (fun i j -> if i = j then 1.0 else 0.0) 213 | 214 | (* ================================================================= * 215 | * Main routine 216 | * ================================================================= *) 217 | 218 | (** Return a layer of a neural network. *) 219 | let make_layer actv_f actv_f' dim1 dim2 = 220 | let rand () = Random.float 2.0 -. 1.0 in 221 | { actv_f; actv_f'; 222 | weight = Array.init_matrix dim2 dim1 (fun _ _ -> rand ()); 223 | bias = Array.init dim2 (fun _ -> rand ()); } 224 | 225 | (** Evaluate an error *) 226 | let evaluate lyrs samples = 227 | Array.map_sum (fun (x, t) -> error (forwardprop lyrs x) t) samples 228 | 229 | let main samples = 230 | let (input_dim, output_dim) = 231 | let (x, t) = samples.(0) in 232 | (Array.length x, Array.length t) 233 | in 234 | let hidden1_dim = 10 in 235 | let hidden2_dim = 5 in 236 | let nnet = [ 237 | make_layer actv_tanh actv_tanh' input_dim hidden1_dim; 238 | make_layer actv_tanh actv_tanh' hidden1_dim hidden2_dim; 239 | make_layer actv_softmax actv_softmax' hidden2_dim output_dim; ] in 240 | for i = 1 to 1000 do 241 | Array.iter (fun (x, t) -> 242 | (* check_gradient nnet x t; *) 243 | train ~eta:0.01 nnet x t) samples; 244 | if i mod 100 = 0 245 | then printf "Loop #%d: Error = %g@." i (evaluate nnet samples) 246 | done 247 | 248 | let () = main Dataset.samples 249 | -------------------------------------------------------------------------------- /qr-decomposition/qr.ml: -------------------------------------------------------------------------------- 1 | (** qr.ml --- QR decompisition by Householder transformation 2 | 3 | [MIT License] Copyright (C) 2015 Akinori ABE *) 4 | 5 | open Format 6 | 7 | module Array = struct 8 | include Array 9 | 10 | let init_matrix m n f = init m (fun i -> init n (f i)) 11 | 12 | let matrix_size a = 13 | let m = length a in 14 | let n = if m = 0 then 0 else length a.(0) in 15 | (m, n) 16 | 17 | let map2 f x y = mapi (fun i xi -> f xi y.(i)) x 18 | let iter2 f x y = iteri (fun i xi -> f xi y.(i)) x 19 | 20 | let fold_left2 f init x y = 21 | let acc = ref init in 22 | for i = 0 to length x - 1 do acc := f !acc x.(i) y.(i) done; 23 | !acc 24 | end 25 | 26 | (* ================================================================= * 27 | * BLAS-like functions for linear algebraic operations 28 | * ================================================================= *) 29 | 30 | (** Dot product of two vectors *) 31 | let dot = Array.fold_left2 (fun acc xi yi -> acc +. xi *. yi) 0.0 32 | 33 | (** Execute [y := alpha * x + y] where [alpha] is a scalar, [x] and [y] are 34 | vectors. *) 35 | let axpy ~alpha x y = 36 | let n = Array.length x in 37 | for i = 0 to n - 1 do y.(i) <- alpha *. x.(i) +. y.(i) done 38 | 39 | (** [gemv_t a x] computes [a^T * x] where [a] is a matrix and [x] is a vector. 40 | *) 41 | let gemv_t a x = 42 | let (_, n) = Array.matrix_size a in 43 | let y = Array.make n 0.0 in 44 | Array.iter2 (fun ai xi -> axpy ~alpha:xi ai y) a x; 45 | y 46 | 47 | (** [gemm x y] computes [x * y] where [x] and [y] are (rectangular) matrices. *) 48 | let gemm x y = 49 | let m, k = Array.matrix_size x in 50 | let k', n = Array.matrix_size y in 51 | assert(k = k'); 52 | Array.map (gemv_t y) x 53 | 54 | (** Transpose a given matrix. *) 55 | let trans a = 56 | let m, n = Array.matrix_size a in 57 | Array.init_matrix n m (fun i j -> a.(j).(i)) 58 | 59 | (* ================================================================= * 60 | * QR decomposition via Householder transformation 61 | * ================================================================= *) 62 | 63 | (** [householder x y] returns householder transformation matrix [h] (such that 64 | [h * x] = [y] and [h * y] = [x]). *) 65 | let householder x y = 66 | let z = Array.map2 ( -. ) x y in 67 | let c = 2. /. dot z z in 68 | let h i zi j zj = (if i = j then 1. else 0.) -. c *. zi *. zj in 69 | Array.mapi (fun i zi -> Array.mapi (h i zi) z) z 70 | 71 | (** [gemm_householder k x h] multiplies matrix [x] and householder matrix [h] 72 | (of the [k]-th iteration). *) 73 | let gemm_householder k x h = 74 | let t = Array.length h in 75 | let update_row xi = 76 | let xi' = Array.sub xi k t in 77 | Array.iteri (fun j hj -> xi.(j+k) <- dot xi' hj) h 78 | in 79 | Array.iter update_row x 80 | 81 | (** [qr a] computes QR-decomposition of (rectangular) matrix [a] via Householder 82 | transformation. 83 | @return [(q, r)] where [q] is an orthogonal matrix and [r] is a right 84 | trapezoidal matrix. *) 85 | let qr a = 86 | let w = trans a in (* a working memory *) 87 | let (m, n) = Array.matrix_size w in 88 | let q = Array.make n [||] in (* orthogonal matrix *) 89 | for k = 0 to min m n - 1 do 90 | (* Compute householder transformation matrix [h]. *) 91 | let x = Array.sub w.(k) k (n - k) in 92 | let y = Array.make (Array.length x) 0. in 93 | y.(0) <- copysign (sqrt (dot x x)) (~-. (x.(0))); 94 | let h = householder x y in 95 | (* Update orthogonal matrix [q] *) 96 | if k = 0 then Array.blit h 0 q 0 n else gemm_householder k q h; 97 | (* Update working memory [w] *) 98 | w.(k).(k) <- y.(0); 99 | gemm_householder k (Array.sub w (k + 1) (m - k - 1)) h 100 | done; 101 | let r = Array.init_matrix n m (fun i j -> if i <= j then w.(j).(i) else 0.) in 102 | (q, r) 103 | 104 | (* ================================================================= * 105 | * Main routine 106 | * ================================================================= *) 107 | 108 | let print_mat label x = 109 | printf "%s =@\n" label; 110 | Array.iter (fun xi -> 111 | Array.iter (printf " %8.4f") xi; 112 | print_newline ()) x 113 | 114 | let _ = 115 | let a = 116 | [| 117 | [| 0.; 2.; 3.; 0.; 9.|]; 118 | [|-1.; 1.; 4.; 2.; 3.|]; 119 | [| 6.; 0.;-9.; 1.; 0.|]; 120 | [| 3.; 5.; 0.; 0.; 1.|]; 121 | [|-8.; 3.; 1.;-5.; 2.|]; 122 | [|-2.;-1.;-1.; 4.; 6.|] 123 | |] in 124 | let q, r = qr a in 125 | print_mat "Q" q; 126 | print_mat "R" r; 127 | print_mat "Q * R" (gemm q r) 128 | -------------------------------------------------------------------------------- /wav/wav.ml: -------------------------------------------------------------------------------- 1 | (** wav.mli, wav.ml --- A lightweight WAV reader/writer 2 | 3 | [MIT License] Copyright (C) 2015 Akinori ABE *) 4 | 5 | open Format 6 | 7 | (* WAVE (linear PCM) data format 8 | 9 | +-----+-------+---------------------------------------------+ 10 | | pos | bytes | Meaning | 11 | +-----+-------+---------------------------------------------+ 12 | | 0 | 4 | RIFF header "RIFF" | 13 | | 4 | 4 | #bytes of file - 8 | 14 | | 8 | 4 | WAVE header "WAVE" | 15 | | 12 | 4 | FMT chunk "fmt " | 16 | | 16 | 4 | #bytes of FMT chunk (16 in linear PCM) | 17 | | 20 | 2 | Format ID (1 in linear PCM) | 18 | | 22 | 2 | #channels (monoral = 1, stereo = 2) | 19 | | 24 | 4 | Sampling rate [Hz] | 20 | | 28 | 4 | Data speed [Byte/sec] | 21 | | 32 | 2 | Block size [Byte/(sample * #channels)] | 22 | | 34 | 2 | #bits per one sample [bit/sample] (8 or 16) | 23 | | 36 | 4 | DATA chunk "data" | 24 | | 40 | 4 | #bytes of DATA chunk | 25 | | 44 | ? | Data | 26 | +-----+-------+---------------------------------------------+ *) 27 | 28 | type wav_data = 29 | | MONORAL of float array 30 | | STEREO of (float * float) array 31 | 32 | (** Output little-endian unsigned 16-bit integer. *) 33 | let output_le_u16 oc n = 34 | output_byte oc (n land 0xff); 35 | output_byte oc ((n land 0xff00) lsr 8) 36 | 37 | (** Output little-endian unsigned 31-bit integer. *) 38 | let output_le_u31 oc n = 39 | output_le_u16 oc (n land 0xffff); 40 | output_le_u16 oc ((n land 0x7fff0000) lsr 16) 41 | 42 | let output_le_s8 oc n = output_byte oc (if n >= 0 then n else n + 0x100) 43 | let output_le_s16 oc n = output_le_u16 oc (if n >= 0 then n else n + 0x10000) 44 | let output_le_s8f oc x = output_le_s8 oc (int_of_float (x *. 128.)) 45 | let output_le_s16f oc x = output_le_s16 oc (int_of_float (x *. 32768.)) 46 | 47 | let save ?(sampling_bits = 16) ~sampling_rate filename x = 48 | let channels, n = match x with 49 | | MONORAL x -> 1, Array.length x 50 | | STEREO x -> 2, Array.length x in 51 | let output_pt = match sampling_bits with 52 | | 8 -> output_le_s8f 53 | | 16 -> output_le_s16f 54 | | _ -> invalid_arg "Invalid sampling bits (8 or 16 is supported)" in 55 | let block_size = channels * (sampling_bits / 8) in 56 | let data_bytes = n * block_size in 57 | let oc = open_out_bin filename in 58 | output_string oc "RIFF"; 59 | output_le_u31 oc (36 + data_bytes); (* #bytes of DATA chunk *) 60 | output_string oc "WAVEfmt "; 61 | output_le_u31 oc 16; (* #bytes of FMT chunk *) 62 | output_le_u16 oc 1; (* format ID (linear PCM) *) 63 | output_le_u16 oc channels; (* #channels *) 64 | output_le_u31 oc sampling_rate; (* sampling rate *) 65 | output_le_u31 oc (block_size * sampling_rate); (* data speed *) 66 | output_le_u16 oc block_size; (* block size *) 67 | output_le_u16 oc sampling_bits; (* #bits per one sample *) 68 | output_string oc "data"; (* DATA chunk *) 69 | output_le_u31 oc data_bytes; (* #bytes of DATA chunk *) 70 | begin match x with 71 | | MONORAL x -> Array.iter (output_pt oc) x 72 | | STEREO x -> Array.iter (fun (l, r) -> output_pt oc l ; output_pt oc r) x 73 | end; 74 | close_out oc 75 | 76 | (** Input little-endian unsigned 16-bit integer. *) 77 | let input_le_u16 ic = 78 | let n1 = input_byte ic in 79 | let n2 = input_byte ic in 80 | n1 lor (n2 lsl 8) 81 | 82 | (** Input little-endian unsigned 31-bit integer. *) 83 | let input_le_u31 ic = 84 | let n1 = input_le_u16 ic in 85 | let n2 = input_le_u16 ic in 86 | n1 lor (n2 lsl 16) 87 | 88 | let signed_of_unsigned m n = if n < m then n else n - m * 2 89 | 90 | let input_le_s8 ic = signed_of_unsigned 0x80 (input_byte ic) 91 | let input_le_s16 ic = signed_of_unsigned 0x8000 (input_le_u16 ic) 92 | let input_le_s8f ic = float (input_le_s8 ic) *. (1. /. 128.) 93 | let input_le_s16f ic = float (input_le_s16 ic) *. (1. /. 32768.) 94 | 95 | let check_format ic = 96 | if really_input_string ic 4 <> "RIFF" then failwith "Not RIFF format"; 97 | seek_in ic 8; 98 | if really_input_string ic 8 <> "WAVEfmt " then failwith "Not WAVE format"; 99 | let fmt_bytes = input_le_u31 ic in 100 | let fmt_id = input_le_u16 ic in 101 | if fmt_bytes <> 16 || fmt_id <> 1 then failwith "Not linear PCM format"; 102 | seek_in ic 36; 103 | if really_input_string ic 4 <> "data" then failwith "No DATA chunk" 104 | 105 | let load_points ~data_bytes ~sampling_bits ~channels ic = 106 | let n = data_bytes / (channels * sampling_bits / 8) in 107 | let input_pt = if sampling_bits = 8 then input_le_s8f else input_le_s16f in 108 | let input_pt2 ic = 109 | let x = input_pt ic in 110 | let y = input_pt ic in 111 | (x, y) 112 | in 113 | match channels with 114 | | 1 -> MONORAL (Array.init n (fun _ -> input_pt ic)) 115 | | 2 -> STEREO (Array.init n (fun _ -> input_pt2 ic)) 116 | | _ -> failwith "Unexpected #channels" 117 | 118 | let load filename = 119 | let ic = open_in_bin filename in 120 | check_format ic; 121 | seek_in ic 22; 122 | let channels = input_le_u16 ic in 123 | let sampling_rate = input_le_u31 ic in 124 | seek_in ic 34; 125 | let sampling_bits = input_le_u16 ic in 126 | seek_in ic 40; 127 | let data_bytes = input_le_u31 ic in 128 | let x = load_points ~data_bytes ~sampling_bits ~channels ic in 129 | close_in ic; 130 | (sampling_rate, x) 131 | -------------------------------------------------------------------------------- /wav/wav.mli: -------------------------------------------------------------------------------- 1 | (** wav.mli, wav.ml --- A lightweight WAV reader/writer 2 | 3 | [MIT License] Copyright (C) 2015 Akinori ABE *) 4 | 5 | type wav_data = 6 | | MONORAL of float array 7 | | STEREO of (float * float) array 8 | 9 | (** [load filename] loads a wav file of path [filename]. 10 | @return [(fs, x)] where [fs] is the sampling rate and [x] is wav data. *) 11 | val load : string -> int * wav_data 12 | 13 | (** [save ?sampling_bits ~sampling_rate filename x] saves data [x] into a wav 14 | file of path [filename]. 15 | @param sampling_bits quantization bits ([8] or [16]). 16 | @param sampling_rate the sampling rate of [data] (Hz). *) 17 | val save : ?sampling_bits:int -> sampling_rate:int -> string -> wav_data -> unit 18 | --------------------------------------------------------------------------------