Hello,
Here is a snippet of LU decomposition code that illustrates the decomposition, solution, and then solution check via blas based routines for triangular matrix multiplication:
;; decompose (lu-decomposition mat per) ;; solve for x given b (lu-solve mat per b x) ;; check by multiplying mat by x. But mat is now a product of tridiagonal matrices L and U. ;; The LUx multiplication is done in two stages as L(Ux). For the upper multiplication we ;; specify the matrix-product-triangular using the Upper and :NonUnit diagonal. ;; For the lower, we specify :Lower and :Unit diagonal (matrix-product-triangular mat (matrix-product-triangular mat x 1 :Upper :NoTrans :NonUnit) 1 :Lower :NoTrans :Unit))
One can off course save the matrix mat before the decomposition and then use a direct matrix multiplication.
Mirko