bool_mat_get_entry mat i j

Returns the entry of matrix mat at row i and column j. foreign import ccall "bool_mat.h bool_mat_get_entry"

bool_mat_set_entry mat i j x

Sets the entry of matrix mat at row i and column j to x.

bool_mat_init mat r c

Initializes the matrix, setting it to the zero matrix with r rows and c columns.

bool_mat_clear mat

Clears the matrix, deallocating all entries.

bool_mat_is_empty mat

Returns nonzero iff the number of rows or the number of columns in mat is zero. Note that this does not depend on the entry values of mat.

bool_mat_is_square mat

Returns nonzero iff the number of rows is equal to the number of columns in mat.

bool_mat_set dest src

Sets dest to src. The operands must have identical dimensions.

bool_mat_print mat

Prints each entry in the matrix.

bool_mat_fprint file mat

Prints each entry in the matrix to the stream file.

bool_mat_equal mat1 mat2

Returns nonzero iff the matrices have the same dimensions and identical entries.

bool_mat_any mat

Returns nonzero iff mat has a nonzero entry.

bool_mat_all mat

Returns nonzero iff all entries of mat are nonzero.

bool_mat_is_diagonal A

Returns nonzero iff \(i \ne j \implies \bar{A_{ij}}\).

bool_mat_is_lower_triangular A

Returns nonzero iff \(i < j \implies \bar{A_{ij}}\).

bool_mat_is_transitive mat

Returns nonzero iff \(A_{ij} \wedge A_{jk} \implies A_{ik}\).

bool_mat_is_nilpotent A

Returns nonzero iff some positive matrix power of \(A\) is zero.

bool_mat_randtest mat state

Sets mat to a random matrix.

bool_mat_randtest_diagonal mat state

Sets mat to a random diagonal matrix.

bool_mat_randtest_nilpotent mat state

Sets mat to a random nilpotent matrix.

bool_mat_zero mat

Sets all entries in mat to zero.

bool_mat_one mat

Sets the entries on the main diagonal to ones, and all other entries to zero.

bool_mat_directed_path A

Sets \(A_{ij}\) to \(j = i + 1\). Requires that \(A\) is a square matrix.

bool_mat_directed_cycle A

Sets \(A_{ij}\) to \(j = (i + 1) \mod n\) where \(n\) is the order of the square matrix \(A\).

bool_mat_transpose dest src

Sets dest to the transpose of src. The operands must have compatible dimensions. Aliasing is allowed.

bool_mat_complement B A

Sets B to the logical complement of A. That is \(B_{ij}\) is set to \(\bar{A_{ij}}\). The operands must have the same dimensions.

bool_mat_add res mat1 mat2

Sets res to the sum of mat1 and mat2. The operands must have the same dimensions.

bool_mat_mul res mat1 mat2

Sets res to the matrix product of mat1 and mat2. The operands must have compatible dimensions for matrix multiplication.

bool_mat_mul_entrywise res mat1 mat2

Sets res to the entrywise product of mat1 and mat2. The operands must have the same dimensions.

bool_mat_sqr B A

Sets B to the matrix square of A. The operands must both be square with the same dimensions.

bool_mat_pow_ui B A exp

Sets B to A raised to the power exp. Requires that A is a square matrix.

bool_mat_trace mat

Returns the trace of the matrix, i.e. the sum of entries on the main diagonal of mat. The matrix is required to be square. The sum is in the boolean semiring, so this function returns nonzero iff any entry on the diagonal of mat is nonzero.

bool_mat_nilpotency_degree A

Returns the nilpotency degree of the \(n \times n\) matrix A. It returns the smallest positive \(k\) such that \(A^k = 0\). If no such \(k\) exists then the function returns \(-1\) if \(n\) is positive, and otherwise it returns \(0\).

bool_mat_transitive_closure B A

Sets B to the transitive closure \(\sum_{k=1}^\infty A^k\). The matrix A is required to be square.

bool_mat_get_strongly_connected_components p A

Partitions the \(n\) row and column indices of the \(n \times n\) matrix A according to the strongly connected components (SCC) of the graph for which A is the adjacency matrix. If the graph has \(k\) SCCs then the function returns \(k\), and for each vertex \(i \in [0, n-1]\), \(p_i\) is set to the index of the SCC to which the vertex belongs. The SCCs themselves can be considered as nodes in a directed acyclic graph (DAG), and the SCCs are indexed in postorder with respect to that DAG.

bool_mat_all_pairs_longest_walk B A

Sets \(B_{ij}\) to the length of the longest walk with endpoint vertices \(i\) and \(j\) in the graph whose adjacency matrix is A. The matrix A must be square. Empty walks with zero length which begin and end at the same vertex are allowed. If \(j\) is not reachable from \(i\) then no walk from \(i\) to \(j\) exists and \(B_{ij}\) is set to the special value \(-1\). If arbitrarily long walks from \(i\) to \(j\) exist then \(B_{ij}\) is set to the special value \(-2\).

The function returns \(-2\) if any entry of \(B_{ij}\) is \(-2\), and otherwise it returns the maximum entry in \(B\), except if \(A\) is empty in which case \(-1\) is returned. Note that the returned value is one less than that of nilpotency_degree.

This function can help quantify entrywise errors in a truncated evaluation of a matrix power series. If A is an indicator matrix with the same sparsity pattern as a matrix \(M\) over the real or complex numbers, and if \(B_{ij}\) does not take the special value \(-2\), then the tail \(\left[ \sum_{k=N}^\infty a_k M^k \right]_{ij}\) vanishes when \(N > B_{ij}\).