{-| Module : Multilinear.Form Description : Linear functional constructors (finitely- or infinitely-dimensional) Copyright : (c) Artur M. Brodzki, 2018 License : BSD3 Maintainer : artur@brodzki.org Stability : experimental Portability : Windows/POSIX - This module provides convenient constructors that generates a linear functionals - Finitely-dimensional functionals provide much greater performance that infinitely-dimensional -} module Multilinear.Form ( -- * Generators -- ** Finite functionals Multilinear.Form.fromIndices, Multilinear.Form.const, Multilinear.Form.randomDouble, Multilinear.Form.randomDoubleSeed, Multilinear.Form.randomInt, Multilinear.Form.randomIntSeed, -- ** Infinite functionals Multilinear.Form.fromIndices', Multilinear.Form.const' ) where import Control.Monad.Primitive import Multilinear.Generic import Multilinear.Index.Infinite as Infinite import Multilinear.Tensor as Tensor import Statistics.Distribution invalidIndices :: String invalidIndices = "Indices and its sizes not compatible with structure of linear functional!" -- * Finite functional generators {-| Generate linear functional as function of indices -} {-# INLINE fromIndices #-} fromIndices :: ( Num a ) => String -- ^ Index name (one character) -> Int -- ^ Number of elements -> (Int -> a) -- ^ Generator function - returns a linear functional component at index @i@ -> Tensor a -- ^ Generated linear functional fromIndices [i] s f = Tensor.fromIndices ([],[]) ([i],[s]) \$ \[] [x] -> f x fromIndices _ _ _ = Err invalidIndices {-| Generate linear functional with all components equal to some @v@ -} {-# INLINE Multilinear.Form.const #-} const :: ( Num a ) => String -- ^ Index name (one character) -> Int -- ^ Number of elements -> a -- ^ Value of each element -> Tensor a -- ^ Generated linear functional const [i] s = Tensor.const ([],[]) ([i],[s]) const _ _ = \_ -> Err invalidIndices {-| Generate linear functional with random real components with given probability distribution. The functional 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" -} {-| - Normal : "Statistics.Distribution.Normal" -} {-| - StudentT : "Statistics.Distribution.StudentT" -} {-| - Uniform : "Statistics.Distribution.Uniform" -} {-| - F : "Statistics.Distribution.FDistribution" -} {-| - Laplace : "Statistics.Distribution.Laplace" -} {-# INLINE randomDouble #-} randomDouble :: ( ContGen d ) => String -- ^ Index name (one character) -> Int -- ^ Number of elements -> d -- ^ Continuous probability distribution (as from "Statistics.Distribution") -> IO (Tensor Double) -- ^ Generated linear functional randomDouble [i] s = Tensor.randomDouble ([],[]) ([i],[s]) randomDouble _ _ = \_ -> return \$ Err invalidIndices {-| Generate linear functional with random integer components with given probability distribution. The functional 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" -} {-# INLINE randomInt #-} randomInt :: ( DiscreteGen d ) => String -- ^ Index name (one character) -> Int -- ^ Number of elements -> d -- ^ Discrete probability distribution (as from "Statistics.Distribution") -> IO (Tensor Int) -- ^ Generated linear functional randomInt [i] s = Tensor.randomInt ([],[]) ([i],[s]) randomInt _ _ = \_ -> return \$ Err invalidIndices {-| Generate linear functional with random real components with given probability distribution and given seed. The functional 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" -} {-| - Normal : "Statistics.Distribution.Normal" -} {-| - StudentT : "Statistics.Distribution.StudentT" -} {-| - Uniform : "Statistics.Distribution.Uniform" -} {-| - F : "Statistics.Distribution.FDistribution" -} {-| - Laplace : "Statistics.Distribution.Laplace" -} {-# INLINE randomDoubleSeed #-} randomDoubleSeed :: ( 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 linear functional randomDoubleSeed [i] s = Tensor.randomDoubleSeed ([],[]) ([i],[s]) randomDoubleSeed _ _ = \_ _ -> return \$ Err invalidIndices {-| Generate linear functional with random integer components with given probability distribution and given seed. The functional is wrapped in a monad. -} {-| Available probability distributions: -} {-| - Binomial : "Statistics.Distribution.Binomial" -} {-| - Poisson : "Statistics.Distribution.Poisson" -} {-| - Geometric : "Statistics.Distribution.Geometric" -} {-| - Hypergeometric: "Statistics.Distribution.Hypergeometric" -} {-# INLINE randomIntSeed #-} randomIntSeed :: ( 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 linear functional randomIntSeed [i] s = Tensor.randomIntSeed ([],[]) ([i],[s]) randomIntSeed _ _ = \_ _ -> return \$ Err invalidIndices {-| Generate linear functional as function of indices -} {-# INLINE fromIndices' #-} fromIndices' :: ( Num a ) => String -- ^ Index name (one character) -> (Int -> a) -- ^ Generator function - returns a linear functional component at index @i@ -> Tensor a -- ^ Generated linear functional fromIndices' i = case i of [d] -> \f -> InfiniteTensor (Infinite.Covariant [d]) \$ (Scalar . f) <\$> [0..] _ -> \_ -> Err invalidIndices {-| Generate linear functional with all components equal to some @v@ -} {-# INLINE Multilinear.Form.const' #-} const' :: ( Num a ) => String -- ^ Index name (one character) -> a -- ^ Value of each element -> Tensor a -- ^ Generated linear functional const' i = case i of [d] -> \v -> InfiniteTensor (Infinite.Covariant [d]) \$ (\_ -> Scalar v) <\$> ([0..] :: [Int]) _ -> \_ -> Err invalidIndices