Accessing Sparse Matrices

The following functions access basic properties of sparse matrices.

Elementary Properties

BaseRing(A): MtrxSprs -> Rng

CoefficientRing(A): MtrxSprs -> Rng

Given a sparse matrix \(A\) with entries lying in a ring \(R\), return \(R\).

NumberOfRows(A): MtrxSprs -> RngIntElt

Nrows(A): MtrxSprs -> RngIntElt

Given an \(m \times n\) sparse matrix \(A\), return \(m\), the number of rows of \(A\).

NumberOfColumns(A): MtrxSprs -> RngIntElt

Ncols(A): MtrxSprs -> RngIntElt

Given an \(m \times n\) sparse matrix \(A\), return \(n\), the number of columns of \(A\).

ElementToSequence(A): MtrxSprs -> [ <RngIntElt, RngIntElt, RngElt> ]

Eltseq(A): MtrxSprs -> [ <RngIntElt, RngIntElt, RngElt> ]

Given a sparse matrix \(A\) over the ring \(R\) having \(m\) rows and \(n\) columns, return the entries of \(A\) as a sequence of all tuples of the form <i, j, x> such that the \([i, j]\)-th entry of \(A\) equals \(x\) and \(x\) is non-zero. It is always true that SparseMatrix(Nrows(A), Ncols(A), Eltseq(A)) equals \(A\).

NumberOfNonZeroEntries(A): MtrxSprs -> RngIntElt

NNZEntries(A): MtrxSprs -> RngIntElt

Given a sparse matrix \(A\), return the number of non-zero entries in \(A\).

Density(A): MtrxSprs -> FldRe

Given a sparse matrix \(A\), return the density of \(A\) as a real number, which is the number of non-zero entries in \(A\) divided by the product of the number of rows of \(A\) and the number of columns of \(A\) (or zero if \(A\) has zero rows or columns).

Support(A, i): MtrxSprs, RngIntElt -> [RngIntElt]

Given a sparse matrix \(A\) having \(r\) rows, and an integer \(i\) such that \(1\leq i\leq r\), return the support of row \(i\) of \(A\); i.e., the column numbers of the non-zero entries of row \(i\) of \(A\).

Support(A): MtrxSprs -> [ <RngIntElt, RngIntElt, RngElt> ]

Given a sparse matrix \(A\), return the sequence of all pairs <i, j> such that the \([i, j]\)-th entry of \(A\) is non-zero.

Weights

RowWeight(A, i): MtrxSprs, RngIntElt -> RngIntElt

Given a sparse matrix \(A\) with \(m\) rows and an integer \(i\) such that \(1\leq i\leq m\), return the weight (number of non-zero entries) of the \(i\)-th row of \(A\).

RowWeights(A): MtrxSprs -> [RngIntElt]

Given a sparse matrix \(A\) with \(m\) rows, return the length \(m\) sequence of integers whose \(i\)-th entry is the weight of the \(i\)-th row of \(A\).

ColumnWeight(A, j): MtrxSprs, RngIntElt -> RngIntElt

Given a sparse matrix \(A\) with \(n\) columns and an integer \(j\) such that \(1\leq j\leq n\), return the weight (number of non-zero entries) of the \(j\)-th column of \(A\).

ColumnWeights(A): MtrxSprs -> [RngIntElt]

Given a sparse matrix \(A\) with \(n\) columns, return the length \(n\) sequence of integers whose \(j\)-th entry is the weight of the \(j\)-th column of \(A\).