An instance of this class remembers the result of its last decomposition. Usage pattern is as follows: Create an instance of this class, call a decompose method, then retrieve the decompositions, determinant, and/or solve as many equation problems as needed. Once another matrix needs to be LU-decomposed, you need not create a new instance of this class. Start again by calling a decompose method, then retrieve the decomposition and/or solve your equations, and so on. In case a LU matrix is already available, call method setLU instead of decompose and proceed with solving et al.
If a matrix shall not be overriden, use matrix.copy() and hand the the copy to methods.
For an m x n matrix A with m >= n, the LU decomposition is an m x n unit lower triangular matrix L, an n x n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U; If m < n, then L is m x m and U is m x n.
The LU decomposition with pivoting always exists, even if the matrix is singular, so the decompose methods will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. Attempting to solve such a system will throw an exception if isNonsingular() returns false.
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