Fac_Cholesky

Factor matrix a into the product of l and l.t using Cholesky Factorization a = l * l.t, where l.t is l's transpose. It uses the Cholesky–Banachiewicz algorithm.

Factor matrix a into the product of l and l.t using Cholesky Factorization a = l * l.t, where l.t is l's transpose. This is a more robust Cholesky Factorization algorithm. Adpated from Scala 2 code returned by GPT-3 on the query: "more robust Cholesky Factorization algorithm in Scala" Also #see math.stackexchange.com/questions/418945/cholesky-decomposition-in-positive-semi-definite-matrix

Factor matrix a into the product of l and l.t using Cholesky Factorization a = l * l.t, where l.t is l's transpose. It uses the Cholesky–Crout algorithm.

Return both the lower triangular matrix l and its transpose l.t.

Efficient calculation of inverse matrix a^-1 from existing factorization. a * a^-1 = I

Use the lower triangular matrix l from the Cholesky Factorization to solve a system of equations a * x = b. Return the solution x using forward and backward substitution.

Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the first matrix.

Factor a matrix into the product of two matrices, e.g., 'a = l * l.t' or a = q * r, returning both the first and second matrices.

Factor a matrix into the product of two matrices, e.g., 'a = l * l.t', returning only the second matrix.

Return whether the matrix has been factored has aleady been factored.

Reset by setting factored to false.

Flag indicating whether the matrix has been factored