How do you code a LU factorization in Matlab?

[ L , U ] = lu( A ) factorizes the full or sparse matrix A into an upper triangular matrix U and a permuted lower triangular matrix L such that A = L*U . [ L , U , P ] = lu( A ) also returns a permutation matrix P such that A = P’*L*U . With this syntax, L is unit lower triangular and U is upper triangular.

How do you write an identity matrix in Matlab?

I = eye( n ) returns an n -by- n identity matrix with ones on the main diagonal and zeros elsewhere. I = eye( n , m ) returns an n -by- m matrix with ones on the main diagonal and zeros elsewhere. I = eye( sz ) returns an array with ones on the main diagonal and zeros elsewhere. The size vector, sz , defines size(I) .

How do you create a lower triangular matrix in Matlab?

L = tril( A ) returns the lower triangular portion of matrix A . L = tril( A , k ) returns the elements on and below the kth diagonal of A .

How do you find the LU value of a matrix in Matlab?

[L,U,p,q,R] = lu( A , ‘vector’ ) returns the permutation information in two row vectors p and q , such that R(:,p)\A(:,q) = L*U . lu( A ) returns the matrix that contains the strictly lower triangular matrix L (the matrix without its unit diagonal) and the upper triangular matrix U as submatrices.

What is LU factorization used for?

LU decomposition is a better way to implement Gauss elimination, especially for repeated solving a number of equations with the same left-hand side. That is, for solving the equation Ax = b with different values of b for the same A.

How do you find the determinant of a matrix in Matlab?

Description. d = det( A ) returns the determinant of square matrix A .

What does tril do in Matlab?

Description. tril( A ) returns a triangular matrix that retains the lower part of the matrix A . The upper triangle of the resulting matrix is padded with zeros. tril( A , k ) returns a matrix that retains the elements of A on and below the k -th diagonal.

How do you convert a matrix to upper triangular in Matlab?

U = triu( A ) returns the upper triangular portion of matrix A . U = triu( A , k ) returns the elements on and above the kth diagonal of A .