Copyright | (c) Artur M. Brodzki 2018 |
---|---|

License | GLP-3 |

Maintainer | artur@brodzki.org |

Stability | experimental |

Portability | Windows/POSIX |

Safe Haskell | None |

Language | Haskell2010 |

- This module provides convenient constructors that generates n-forms (tensors with n lower indices with finite or infinite size).
- Finitely-dimensional n-forms provide much greater performance than infinitely-dimensional

## Synopsis

- fromIndices :: Num a => String -> [Int] -> ([Int] -> a) -> Tensor a
- const :: Num a => String -> [Int] -> a -> Tensor a
- randomDouble :: ContGen d => String -> [Int] -> d -> IO (Tensor Double)
- randomDoubleSeed :: (ContGen d, PrimMonad m) => String -> [Int] -> d -> Int -> m (Tensor Double)
- randomInt :: DiscreteGen d => String -> [Int] -> d -> IO (Tensor Int)
- randomIntSeed :: (DiscreteGen d, PrimMonad m) => String -> [Int] -> d -> Int -> m (Tensor Int)
- dot :: Num a => String -> Int -> Tensor a
- cross :: Num a => String -> Int -> Tensor a

# Generators

:: Num a | |

=> String | Indices names (one characted per index) |

-> [Int] | Indices sizes |

-> ([Int] -> a) | Generator function |

-> Tensor a | Generated N-form |

Generate N-form as function of its indices

:: Num a | |

=> String | Indices names (one characted per index) |

-> [Int] | Indices sizes |

-> a | N-form elements value |

-> Tensor a | Generated N-form |

Generate N-form with all components equal to `v`

:: ContGen d | |

=> String | Indices names (one character per index) |

-> [Int] | Indices sizes |

-> d | Continuous probability distribution (as from Statistics.Distribution) |

-> IO (Tensor Double) | Generated linear functional |

Generate n-vector with random real components with given probability distribution. The n-vector is wrapped in the IO monad.

Available probability distributions:

- Beta : Statistics.Distribution.BetaDistribution
- Cauchy : Statistics.Distribution.CauchyLorentz
- Chi-squared : Statistics.Distribution.ChiSquared
- Exponential : Statistics.Distribution.Exponential
- Gamma : Statistics.Distribution.Gamma
- Geometric : Statistics.Distribution.Geometric
- Normal : Statistics.Distribution.Normal
- StudentT : Statistics.Distribution.StudentT
- Uniform : Statistics.Distribution.Uniform
- F : Statistics.Distribution.FDistribution
- Laplace : Statistics.Distribution.Laplace

:: (ContGen d, PrimMonad m) | |

=> String | Index name (one character) |

-> [Int] | Number of elements |

-> d | Continuous probability distribution (as from Statistics.Distribution) |

-> Int | Randomness seed |

-> m (Tensor Double) | Generated n-vector |

Generate n-vector with random real components with given probability distribution and given seed. The form is wrapped in a monad.

Available probability distributions:

- Beta : Statistics.Distribution.BetaDistribution
- Cauchy : Statistics.Distribution.CauchyLorentz
- Chi-squared : Statistics.Distribution.ChiSquared
- Exponential : Statistics.Distribution.Exponential
- Gamma : Statistics.Distribution.Gamma
- Geometric : Statistics.Distribution.Geometric
- Normal : Statistics.Distribution.Normal
- StudentT : Statistics.Distribution.StudentT
- Uniform : Statistics.Distribution.Uniform
- F : Statistics.Distribution.FDistribution
- Laplace : Statistics.Distribution.Laplace

:: DiscreteGen d | |

=> String | Indices names (one character per index) |

-> [Int] | Indices sizes |

-> d | Discrete probability distribution (as from Statistics.Distribution) |

-> IO (Tensor Int) | Generated n-vector |

Generate n-vector with random integer components with given probability distribution. The n-vector is wrapped in the IO monad.

Available probability distributions:

- Binomial : Statistics.Distribution.Binomial
- Poisson : Statistics.Distribution.Poisson
- Geometric : Statistics.Distribution.Geometric
- Hypergeometric: Statistics.Distribution.Hypergeometric

:: (DiscreteGen d, PrimMonad m) | |

=> String | Index name (one character) |

-> [Int] | Number of elements |

-> d | Discrete probability distribution (as from Statistics.Distribution) |

-> Int | Randomness seed |

-> m (Tensor Int) | Generated n-vector |

Generate n-vector with random integer components with given probability distribution and given seed. The form is wrapped in a monad.

Available probability distributions:

- Binomial : Statistics.Distribution.Binomial
- Poisson : Statistics.Distribution.Poisson
- Geometric : Statistics.Distribution.Geometric
- Hypergeometric: Statistics.Distribution.Hypergeometric

# Common cases

:: Num a | |

=> String | Indices names (one characted per index) |

-> Int | Size of tensor (dot product is a square tensor) |

-> Tensor a | Generated dot product |

2-form representing a dot product

:: Num a | |

=> String | Indices names (one characted per index) |

-> Int | Size of tensor (dot product is a square tensor) |

-> Tensor a | Generated dot product |

Tensor representing a cross product (Levi - Civita symbol). It also allows to compute a determinant of square matrix - determinant of matrix `M`

is a equal to length of cross product of all columns of `M`