SPARSE MATRICES

DETAILS

 
Introduction

 
Creation of Sparse Matrices

      Construction of Initialized Sparse Matrices
            SparseMatrix(R, m, n, Q) : Rng, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] -> MtrxSprs
            SparseMatrix(R, m, n) : Rng, RngIntElt, RngIntElt -> MtrxSprs
            SparseMatrix(m, n) : RngIntElt, RngIntElt -> MtrxSprs

      Construction of Trivial Sparse Matrices
            SparseMatrix(R) : Rng -> MtrxSprs
            Example SMat_Create (H46E1)

 
Accessing Sparse Matrices

      Elementary Properties
            BaseRing(A) : MtrxSprs -> Rng
            NumberOfRows(A) : MtrxSprs -> RngIntElt
            NumberOfColumns(A) : MtrxSprs -> RngIntElt
            NumberOfNonZeroEntries(A) : MtrxSprs -> RngIntElt
            Density(A) : MtrxSprs -> FldRe
            Support(A, i) : MtrxSprs, RngIntElt -> [RngIntElt]

      Weights
            RowWeight(A, i) : MtrxSprs, RngIntElt -> RngIntElt
            RowWeights(A) : MtrxSprs -> [RngIntElt]
            ColumnWeight(A, j) : MtrxSprs, RngIntElt -> RngIntElt
            ColumnWeights(A) : MtrxSprs -> [RngIntElt]
            ColumnWeights(A) : MtrxSprs -> [RngIntElt]

      Predicates
            IsZero(A) : MtrxSprs -> BoolElt
            A eq B : MtrxSprs, MtrxSprs -> BoolElt

 
Accessing or Modifying Entries
      A[i, j] := x : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
      SetEntry(~A, i, j, x) : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
      Example SMat_Indexing (H46E2)

 
Conversion to and from Dense Matrices
      Matrix(A) : MtrxSprs -> Mtrx
      SparseMatrix(A) : Mtrx -> MtrxSprs

 
Changing Ring
      ChangeRing(A, R) : MtrxSprs, Ring -> MtrxSprs

 
Multiplying Vectors or Matrices by Sparse Matrices
      v * A : ModTupRng, MtrxSprs -> ModTupRng
      MultiplyByTranspose(v, A) : ModTupRng, MtrxSprs -> ModTupRng

 
Non-trivial Properties

      Nullspace
            Nullspace(A) : MtrxSprs -> ModTupRng
            NullspaceMatrix(A) : MtrxSprs -> Mtrx
            NullspaceOfTranspose(A) : MtrxSprs -> ModTupRng

      Rank
            Rank(A) : MtrxSprs -> RngIntElt

      Elementary Divisors (Smith Form)
            ElementaryDivisors(A) : MtrxSprs -> [RngElt]

      Verbosity
            SetVerbose("SparseMatrix", v) : MonStgElt, RngIntElt ->

 
Linear Systems (Structured Gaussian Elimination)
      ModularSolution(A, M) : MtrxSprs, RngIntElt -> ModTupRng

 
Bibliography