Solve linear equation system by given LU decomposition and vector of constants

Question

Given L and U LU decomposition and vector of constants b such that LU*x=b , is there any built in function which find the x ? Mean something like -

X = functionName(L,U,b) 

Note that in both L and U we are dealing with triangular matrices which can be solved directly by forward and backward substitution without using the Gaussian elimination process.

Edit :

Solving this linear equation system should be according to the following steps -

1. define y - s.t Ux=y
2. solve Ly=b by forward substitution
3. solve Ux=y by backward substitution
4. return y

Edit 2 :

I found linalg::matlinsolveLU but I didn't try it cause I have too old version (R2010a) . Is it working for anyone ?

Answer 1

If you have:

A = rand(3);
b = rand(3,1);

then the solution to the system can be simply computed as:

x = A\b

Or if you already have an LU decomposition of A, then:

[L,U] = lu(A);
xx = U\(L\b)

the mldivide function is smart enough to detect that the matrix is triangular and chose an algorithm accordingly (forward/backward substitution)