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num.cr
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Scientific computing in pure Crystal
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num.cr
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 [](https://gitter.im/crystal-data/bottle?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)  Num.cr is the core shard needed for scientific computing with Crystal - **Website:** https://crystal-data.github.io/num.cr - **API Documentation:** https://crystal-data.github.io/num.cr/ - **Source code:** https://github.com/crystal-data/num.cr - **Bug reports:** https://github.com/crystal-data/num.cr/issues It provides: - An n-dimensional `Tensor` data structure - Efficient `map`, `reduce` and `accumulate` routines - GPU accelerated routines backed by `OpenCL` - Linear algebra routines backed by `LAPACK` and `BLAS` ## Prerequisites `Num.cr` aims to be a scientific computing library written in pure Crystal. All standard operations and data structures are written in Crystal. Certain routines, primarily linear algebra routines, are instead provided by a `BLAS` or `LAPACK` implementation. Several implementations can be used, including `Cblas`, `Openblas`, and the `Accelerate` framework on Darwin systems. For GPU accelerated `BLAS` routines, the `ClBlast` library is required. `Num.cr` also supports `Tensor`s stored on a `GPU`. This is currently limited to `OpenCL`, and a valid `OpenCL` installation and device(s) are required. ## Installation Add this to your applications `shard.yml` ``` dependencies: num: github: crystal-data/num.cr ``` Several third-party libraries are required to use certain features of `Num.cr`. They are: - BLAS - LAPACK - OpenCL - ClBlast - NNPACK While not at all required, they provide additional functionality than is provided by the basic library. ## Just show me the code The core data structure implemented by `Num.cr` is the `Tensor`, an N-dimensional data structure. A `Tensor` supports slicing, mutation, permutation, reduction, and accumulation. A `Tensor` can be a view of another `Tensor`, and can support either C-style or Fortran-style storage. ### Creation There are many ways to initialize a `Tensor`. Most creation methods can allocate a `Tensor` backed by either `CPU` or `GPU` based storage. ```crystal [1, 2, 3].to_tensor Tensor.from_array [1, 2, 3] Tensor(UInt8, CPU(UInt8)).zeros([3, 3, 2]) Tensor.random(0.0...1.0, [2, 2, 2]) Tensor(Float32, OCL(Float32)).zeros([3, 2, 2]) Tensor(Float64, OCL(Float64)).full([3, 4, 5], 3.8) ``` ### Operations A `Tensor` supports a wide variety of numerical operations. Many of these operations are provided by `Num.cr`, but any operation can be mapped across one or more `Tensor`s using sophisticated broadcasted mapping routines. ```crystal a = [1, 2, 3, 4].to_tensor b = [[3, 4, 5, 6], [5, 6, 7, 8]].to_tensor puts a + b # a is broadcast to b's shape # [[ 4, 6, 8, 10], # [ 6, 8, 10, 12]] ``` When operating on more than two `Tensor`s, it is recommended to use `map` rather than builtin functions to avoid the allocation of intermediate results. All `map` operations support broadcasting. ```crystal a = [1, 2, 3, 4].to_tensor b = [[3, 4, 5, 6], [5, 6, 7, 8]].to_tensor c = [3, 5, 7, 9].to_tensor a.map(b, c) do |i, j, k| i + 2 / j + k * 3.5 end # [[12.1667, 20 , 27.9 , 35.8333], # [11.9 , 19.8333, 27.7857, 35.75 ]] ``` ### Mutation `Tensor`s support flexible slicing and mutation operations. Many of these operations return views, not copies, so any changes made to the results might also be reflected in the parent. ```crystal a = Tensor.new([3, 2, 2]) { |i| i } puts a.transpose # [[[ 0, 4, 8], # [ 2, 6, 10]], # # [[ 1, 5, 9], # [ 3, 7, 11]]] puts a.reshape(6, 2) # [[ 0, 1], # [ 2, 3], # [ 4, 5], # [ 6, 7], # [ 8, 9], # [10, 11]] puts a[..., 1] # [[ 2, 3], # [ 6, 7], # [10, 11]] puts a[1..., {..., -1}] # [[[ 6, 7], # [ 4, 5]], # # [[10, 11], # [ 8, 9]]] puts a[0, 1, 1].value # 3 ``` ### Linear Algebra `Tensor`s provide easy access to power Linear Algebra routines backed by LAPACK and BLAS implementations, and ClBlast for GPU backed `Tensor`s. ```crystal a = [[1, 2], [3, 4]].to_tensor.map &.to_f32 puts a.inv # [[-2 , 1 ], # [1.5 , -0.5]] puts a.eigvals # [-0.372281, 5.37228 ] puts a.matmul(a) # [[7 , 10], # [15, 22]] ``` ### Einstein Notation For representing certain complex contractions of `Tensor`s, Einstein notation can be used to simplify the operation. For example, the following matrix multiplication + summation operation: ```crystal a = Tensor.new([30, 40, 50]) { |i| i * 1_f32 } b = Tensor.new([40, 30, 20]) { |i| i * 1_f32 } result = Float32Tensor.zeros([50, 20]) ny, nx = result.shape b2 = b.swap_axes(0, 1) ny.times do |k| nx.times do |l| result[k, l] = (a[..., ..., k] * b2[..., ..., l]).sum end end ``` Can instead be represented in Einstein notiation as the following: ```crystal Num::Einsum.einsum("ijk,jil->kl", a, b) ``` This can lead to performance improvements due to optimized contractions on `Tensor`s. ``` einsum 2.22k (450.41µs) (± 0.86%) 350kB/op fastest manual 117.52 ( 8.51ms) (± 0.98%) 5.66MB/op 18.89× slower ``` ### Machine Learning `Num::Grad` provides a pure-crystal approach to find derivatives of mathematical functions. Use a `Num::Grad::Variable` with a `Num::Grad::Context` to easily compute these derivatives. ```crystal ctx = Num::Grad::Context(Tensor(Float64, CPU(Float64))).new x = ctx.variable([3.0].to_tensor) y = ctx.variable([2.0].to_tensor) # f(x) = x ** y f = x ** y puts f # => [9] f.backprop # df/dx = y * x = 6.0 puts x.grad # => [6.0] ``` `Num::NN` contains an extension to `Num::Grad` that provides an easy-to-use interface to assist in creating neural networks. Designing and creating a network is simple using Crystal's block syntax. ```crystal ctx = Num::Grad::Context(Tensor(Float64, CPU(Float64))).new x_train = [[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]].to_tensor y_train = [[0.0], [1.0], [1.0], [0.0]].to_tensor x = ctx.variable(x_train) net = Num::NN::Network.new(ctx) do input [2] # A basic network with a single hidden layer using # a ReLU activation function linear 3 relu linear 1 # SGD Optimizer sgd 0.7 # Sigmoid Cross Entropy to calculate loss sigmoid_cross_entropy_loss end 500.times do |epoch| y_pred = net.forward(x) loss = net.loss(y_pred, y_train) puts "Epoch: #{epoch} - Loss #{loss}" loss.backprop net.optimizer.update end # Clip results to make a prediction puts net.forward(x).value.map { |el| el > 0 ? 1 : 0} # [[0], # [1], # [1], # [0]] ``` Review the documentation for full implementation details, and if something is missing, open an issue to add it!
