LUdecomp

[pauljsymonds]

can you take a look at the LUdecomp.py for the Doolittle algorithm.

If you take the matrix:

a = np.array([[2, -1, 0],
[-1, 2, -1],
[0, -1, 2]],float)

b = np.array([7,3,2], float)

x = array([7.2500, 7.5000, 4.7500])

Which you can get by simply running LUSolve(a,b)

When reading the book, it mentions that the following steps are required:

LUsolve(LUdecomp(a), b)

but this gives:

array([7.6667, 8.3333, 5.6667])

I think this example may be incorrect?

I have checked this with ColeskiSol

choleskiSol(choleski(A),b)

array([7.2500, 7.5000, 4.7500])

Is my assumption correct?

[nickcafferry]

Yes. you're right. This example is wrong. You can also check it on sympy online shell .

In addition to the solvers in the solver.py file, we can solve the system Ax=b by passing the b vector to the matrix A’s LUsolve function. Here we’ll cheat a little choose A and x then multiply to get b. Then we can solve for x and check that it’s correct:
`

a = Matrix([ [2, -1, 0], [-1, 2, -1], [0, -1, 2] ])
b = Matrix(3,1,[7,3,2])
x = a.LUsolve(b)
x
`
Which will return a fraction version of the solution.