Introduction to Sparse Matrices In Scilab - Projects

chfactchsolvespcholsparse Cholesky factorizationsparse Cholesky solversparse cholesky factorization with permutationsFigure 3 – Cholesky factorizations for sparse matrices.4 Cholesky factorizationsThe figure 3 presents the functions which allow to compute the Choleskydecomposition of sparse matrices.The chfact and chsolve functions can be combined in order to solvesparse linear systems of equations, if the matrix is symmetric positive definite.In the following example, we solve the equation Ax = b where A is a sparse5-by-5 symmetric definite positive matrix.Afull = [2 -1 0 0 0;-1 2 -1 0 0;0 -1 2 -1 0;0 0 -1 2 -1;0 0 0 -1 2];A = sparse ( Afull );h = chfact (A);b = [0 ; 0; 0; 0; 6];chsolve (h,b)The [R,P]=spchol(X) statement produces a sparse lower triangular matrixR and a sparse permutation matrix P such that P RR T P T = X. In thefollowing session, we use the spchol function to compute the sparse Choleskydecomposition of a symmetric definite positive matrix.--> Afull = [--> 2 -1 0 0 0;--> -1 2 -1 0 0;--> 0 -1 2 -1 0;--> 0 0 -1 2 -1;--> 0 0 0 -1 2-->];-->A = sparse ( Afull );-->[R,P]= spchol (A)P =( 5, 5) sparse matrix15