A complete framework for numerical computing based on LuaJIT which combines the **ease of use** of scripting languages (MATLAB, R, ...) with the **high performance** of compiled languages (C/C++, Fortran, ...).

**Lua** is a dynamic language characterized by a small number of simple but powerful concepts that allow to easily implement complex algorithms. Lua is fast to learn thanks to its high-level nature, to the concise syntax and to the precise documentation. Lua is a proven robust language that offers both object-oriented and functional programming features.

**LuaJIT** is an extremely optimized Just In Time compiler for Lua. Start-up and warm-up times are negligible, compile times are in the microsecond to millisecond range and the typical performance of compiled LuaJIT programs is close to the one of C/C++. LuaJIT includes the FFI library which allows to call C function directly.

The figure above compares the running time required (lower is better) to run the Julia benchmark suite. Timings are relative to the C implementation.

The details: Linux x64 / gcc 5.2.1 / Julia 0.4.1 / SciLua 1.0 latest, implementation: perf-v1.2.sci.lua.

The easiest way to install SciLua is via the ULua distribution.

Having installed (i.e. unzipped) ULua, execute:

```
ulua/bin/upkg add sci # Install the sci package (SciLua).
ulua/bin/upkg add sci-lang # Install the sci-lang package (SciLua syntax extensions).
```

This is the suggested way as all dependencies are handled by the package manager and SciLua can be kept up to date using `upkg update`

.

Alternatively, it is possible to install SciLua manually. Download and unzip sci~latest.zip and sci-lang~latest.zip into folders named respectively `sci`

and `sci-lang`

and make sure that such modules can be found by LuaJIT (check `package.path`

documentation). Notice that SciLua requires xsys and OpenBLAS to be installed as well.

The `sci`

package contains a general purpose scientific computing library composed of the following modules:

Sub-Module | Description |
---|---|

sci.alg | vector and matrix algebra |

sci.diff | automatic differentiation |

sci.dist | statistical distributions |

sci.fmin | function minimization algorithms |

sci.fmax | function maximization algorithms |

sci.math | special mathematical functions |

sci.mcmc | MCMC algorithms |

sci.prng | pseudo random number generators |

sci.qrng | quasi random number generators |

sci.quad | quadrature algorithms |

sci.root | root-finding algorithms |

sci.stat | statistical functions |

Each sub-module has to be loaded separately (`require 'sci'`

is not allowed):

```
-- No global key is set:
local alg = require "sci.alg" -- Load sci.alg module.
local dist = require "sci.dist" -- Load sci.dist module.
```

Based on the LuaJIT Language Toolkit, the `sci-lang`

package contains the `scilua`

executable which extends the syntax of LuaJIT for easier linear algebra operations:

- algebra expressions constructed via empty bracket
`[]`

indexing - element-wise operations via plain Lua operators
`+-*/^%`

- matrix multiplication via
`**`

- matrix exponentiation via
`^^`

- transposition via
```

- efficient implementation minimizes required allocations and loops
- support for assignments

For example, the `rand_mat_stat`

benchmark shown above is implemented as:

```
local function randmatstat(t)
local n = 5
local v, w = alg.vec(t), alg.vec(t)
for i=1,t do
local a, b, c, d = randn(n, n), randn(n, n), randn(n, n), randn(n, n)
local P = alg.join(a..b..c..d)
local Q = alg.join(a..b, c..d)
v[i] = alg.trace((P[]`**P[])^^4) -- Matrix transpose, product and power.
w[i] = alg.trace((Q[]`**Q[])^^4) -- Matrix transpose, product and power.
end
return sqrt(stat.var(v))/stat.mean(v), sqrt(stat.var(w))/stat.mean(w)
end
```