Documentation

Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Gauss

Gaussian Elimination algorithm #

The first step of Linarith.SimplexAlgorithm.findPositiveVector is finding initial feasible solution which is done by standard Gaussian Elimination algorithm implemented in this file.

source
@[reducible, inline]
abbrev Linarith.SimplexAlgorithm.Gauss.GaussM (n : Nat) (m : Nat) (matType : Nat → Nat → Type) (α : Type) :
Type

The monad for the Gaussian Elimination algorithm.

Equations
Instances For
    source
    def Linarith.SimplexAlgorithm.Gauss.findNonzeroRow {n : Nat} {m : Nat} {matType : Nat → Nat → Type} [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] (rowStart : Nat) (col : Nat) :
    Linarith.SimplexAlgorithm.Gauss.GaussM n m matType (Option Nat)

    Finds the first row starting from the rowStart with nonzero element in the column col.

    Equations
    • One or more equations did not get rendered due to their size.
    Instances For
      source
      def Linarith.SimplexAlgorithm.Gauss.getTableauImp {n : Nat} {m : Nat} {matType : Nat → Nat → Type} [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] :
      Linarith.SimplexAlgorithm.Gauss.GaussM n m matType (Linarith.SimplexAlgorithm.Tableau matType)

      Implementation of getTableau in GaussM monad.

      Equations
      • One or more equations did not get rendered due to their size.
      Instances For
        source
        def Linarith.SimplexAlgorithm.Gauss.getTableau {n : Nat} {m : Nat} {matType : Nat → Nat → Type} [Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm matType] (A : matType n m) :
        Lean.CoreM (Linarith.SimplexAlgorithm.Tableau matType)

        Given matrix A, solves the linear equation A x = 0 and returns the solution as a tableau where some variables are free and others (basic) variable are expressed as linear combinations of the free ones.

        Equations
        Instances For