LU decomposition

lu-decompose and lu-solve are provided to solve simultaneous linear equations. First, lu-decompose decomposes a matrix into a lower triangle matrix and an upper triable matrix. If the given matrix is singular, LU-decompose returns NIL, otherwise it returns the permutation vector which should be supplied to LU-solve. Lu-solve computes the solution for a LU matrix with a given constant vector. This method is efficient if solutions for many combinations of different constant vectors and the same factor matrix are required. Simultaneous-equation would be more handy when you wish to get only one solution. Lu-determinant computes a determinant of a lu-decomposed matrix. Inverse-matrix function computes an inverse matrix using lu-decompose once, and lu-solve n times. Computation time for a 3*3 matrix is estimated to be 4 milli-sec.

lu-decompose matrix &optional result [function]

performs lu-decomposition of matrix.

lu-solve lu-mat perm-vector bvector [result] [function]

solves a linear simultaneous equations which has already been lu-decomposed. perm-vector should be the result returned by lu-decompose.

lu-determinant lu-mat perm-vector [function]

computes the determinant value for a matrix which has already been lu-decomposed.

simultaneous-equation mat vec [function]

solves a linear simultaneous equations whose coefficients are described in mat and constant values in vec.

inverse-matrix mat [function]

makes the inverse matrix of the square matrix, mat.

pseudo-inverse mat [function]

computes the pseudo inverse matrix using the singular value decomposition.