| Copyright | (c) Nils Alex 2020 |
|---|---|
| License | MIT |
| Maintainer | nils.alex@fau.de |
| Safe Haskell | None |
| Language | Haskell2010 |
Math.Tensor.LinearAlgebra.Equations
Description
Linear tensor equations.
Synopsis
- type Equation a = IntMap a
- tensorToEquations :: Integral a => T (Poly Rational) -> [Equation a]
- equationFromRational :: forall a. Integral a => Poly Rational -> Equation a
- equationsToSparseMat :: [Equation a] -> [((Int, Int), a)]
- equationsToMat :: Integral a => [Equation a] -> [[a]]
- tensorsToSparseMat :: Integral a => [T (Poly Rational)] -> [((Int, Int), a)]
- tensorsToMat :: Integral a => [T (Poly Rational)] -> [[a]]
- systemRank :: [T (Poly Rational)] -> Int
- type Solution = IntMap (Poly Rational)
- fromRref :: Matrix Z -> Solution
- fromRrefRev :: Matrix Z -> Solution
- fromRow :: forall a. Integral a => [a] -> Maybe (Int, Poly Rational)
- fromRowRev :: forall a. Integral a => [a] -> Maybe (Int, Poly Rational)
- applySolution :: Solution -> Poly Rational -> Poly Rational
- solveTensor :: Solution -> T (Poly Rational) -> T (Poly Rational)
- solveSystem :: [T (Poly Rational)] -> [T (Poly Rational)] -> [T (Poly Rational)]
- redefineIndets :: [T (Poly v)] -> [T (Poly v)]
Documentation
type Equation a = IntMap a Source #
A linear equation is a mapping from variable indices to coefficients
tensorToEquations :: Integral a => T (Poly Rational) -> [Equation a] Source #
Extract linear equations from tensor components. The equations are normalized, sorted, and made unique.
equationFromRational :: forall a. Integral a => Poly Rational -> Equation a Source #
Extract linear equation with integral coefficients from polynomial
tensor component with rational coefficients.
Made made integral by multiplying with the lcm of all denominators.
equationsToSparseMat :: [Equation a] -> [((Int, Int), a)] Source #
Convert list of equations to sparse matrix representation of the linear system.
equationsToMat :: Integral a => [Equation a] -> [[a]] Source #
Convert list of equations to dense matrix representation of the linear system.
tensorsToSparseMat :: Integral a => [T (Poly Rational)] -> [((Int, Int), a)] Source #
Extract sparse matrix representation for the linear system given by a list of existentially quantified tensors with polynomial values.
tensorsToMat :: Integral a => [T (Poly Rational)] -> [[a]] Source #
Extract dense matrix representation for the linear system given by a list of existentially quantified tensors with polynomial values.
systemRank :: [T (Poly Rational)] -> Int Source #
Rank of the linear system given by a list of existentially quantified tensors with polynomial values.
fromRref :: Matrix Z -> Solution Source #
Read substitution rules from reduced row echelon form of a linear system.
fromRow :: forall a. Integral a => [a] -> Maybe (Int, Poly Rational) Source #
Read single substitution rule from single row of reduced row echelon form.
applySolution :: Solution -> Poly Rational -> Poly Rational Source #
Apply substitution rules to tensor component.
solveTensor :: Solution -> T (Poly Rational) -> T (Poly Rational) Source #
Apply substitution rules to all components of a tensor.