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10 Sparse Chain complexes
 10.1  

10 Sparse Chain complexes

10.1  

10.1-1 SparseMat
‣ SparseMat( A )( function )

Inputs a matrix A and returns the matrix in sparse format.

Examples:

10.1-2 TransposeOfSparseMat
‣ TransposeOfSparseMat( A )( function )

Inputs a sparse matrix A and returns its transpose sparse format.

Examples:

10.1-3 ReverseSparseMat
‣ ReverseSparseMat( A )( function )

Inputs a sparse matrix A and modifies it by reversing the order of the columns. This function modifies A and returns no value.

Examples:

10.1-4 SparseRowMult
‣ SparseRowMult( A, i, k )( function )

Multiplies the i-th row of a sparse matrix A by k. The sparse matrix A is modified but nothing is returned.

Examples:

10.1-5 SparseRowInterchange
‣ SparseRowInterchange( A, i, k )( function )

Interchanges the i-th and j-th rows of a sparse matrix A by k. The sparse matrix A is modified but nothing is returned.

Examples:

10.1-6 SparseRowAdd
‣ SparseRowAdd( A, i, j, k )( function )

Adds k times the j-th row to the i-th row of a sparse matrix A. The sparse matrix A is modified but nothing is returned.

Examples:

10.1-7 SparseSemiEchelon
‣ SparseSemiEchelon( A )( function )

Converts a sparse matrix A to semi-echelon form (which means echelon form up to a permutation of rows). The sparse matrix A is modified but nothing is returned.

Examples:

10.1-8 RankMatDestructive
‣ RankMatDestructive( A )( function )

Returns the rank of a sparse matrix A. The sparse matrix A is modified during the calculation.

Examples:

10.1-9 RankMat
‣ RankMat( A )( function )

Returns the rank of a sparse matrix A.

Examples:

10.1-10 SparseChainComplex
‣ SparseChainComplex( Y )( function )

Inputs a regular CW-complex Y and returns a sparse chain complex which is chain homotopy equivalent to the cellular chain complex of Y. The function uses discrete vector fields to calculate a smallish chain complex.

Examples: 1 

10.1-11 SparseChainComplexOfRegularCWComplex
‣ SparseChainComplexOfRegularCWComplex( Y )( function )

Inputs a regular CW-complex Y and returns its cellular chain complex as a sparse chain complex. The function SparseChainComplex(Y) will usually return a smaller chain complex.

Examples:

10.1-12 SparseBoundaryMatrix
‣ SparseBoundaryMatrix( C, n )( function )

Inputs a sparse chain complex C and integer n. Returns the n-th boundary matrix of the chain complex in sparse format.

Examples:

10.1-13 Bettinumbers
‣ Bettinumbers( C, n )( function )

Inputs a sparse chain complex C and integer n. Returns the n-th Netti number of the chain complex.

Examples: 1 , 2 

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