Version 5.0 The LEDA User Manual

integer matrix inverse(const integer matrix& M, integer& D)
returns the inverse matrix of M. More precisely,
1/D times the matrix returned is the inverse of
M.
Precondition: determinant(M) ≠ 0.
bool
inverse(const integer matrix& M, integer matrix& inverse,
integer& D, integer vector& c)
determines whether M has an inverse. It also computes either
the inverse as (1/D) · inverse or a vector c such that c T · M = 0.
integer determinant(const integer matrix& M, integer matrix& L,
integer matrix& U, array& q, integer vector& c)
returns the determinant D of M and sufficient information to
verify that the value of the determinant is correct. If the determinant
is zero then c is a vector such that c T · M = 0. If
the determinant is non-zero then L and U are lower and upper
diagonal matrices respectively and q encodes a permutation matrix
Q with Q(i, j) = 1 iff i = q(j) such that L · M · Q = U,
L(0, 0) = 1, L(i, i) = U(i − 1, i − 1) for all i, 1 ≤ i < n, and
D = s · U(n − 1, n − 1) where s is the determinant of Q.
Precondition: M is quadratic.
bool verify determinant(const integer matrix& M, integer D,
integer matrix& L, integer matrix& U,
array q, integer vector& c)
verifies the conditions stated above.
integer determinant(const integer matrix& M)
returns the determinant of M.
Precondition: M is quadratic.
int sign of determinant(const integer matrix& M)
returns the sign of the determinant of M.
Precondition: M is quadratic.
bool linear solver(const integer matrix& M, const integer vector& b,
integer vector& x, integer& D,
integer matrix& spanning vectors, integer vector& c)
determines the complete solution space of the linear system M ·
x = b. If the system is unsolvable then c T ·M = 0 and c T ·b ≠ 0. If
the system is solvable then (1/D)x is a solution, and the columns
of spanning vectors are a maximal set of linearly independent
solutions to the corresponding homogeneous system.
Precondition: M.dim1() == b.dim().