# [SciPy-user] solving Ax=b, known L: A = L L^T

Steve Schmerler elcorto@gmx....
Tue Aug 28 04:06:22 CDT 2007

```dmitrey wrote:
> Hi all,
> suppose I have a system Ax=b and I know (Cholesky) triangular L: A = L L^T
> what's the simplest way to obtain x now?
> (I meant python code)
> is it solve(L^T, solve(L,b))?
> or I should somehow inform solve() about L is triangular or, maybe, use
> other func?
> Documentation of numpy.linalg.solve doesn't say anything.
> Afaik MATLAB's '\' determ type of matrix automatically.
> Regards, D.
>

I don't do linalg much, but I know of linalg.cho_factor() and linalg.cho_solve().

In [42]: A
Out[42]:
array([[ 5.,  2.,  1.],
[ 2.,  5.,  2.],
[ 1.,  2.,  5.]])

In [43]: b
Out[43]: array([ 1.,  2.,  3.])

In [44]: linalg.solve(A,b, sym_pos=0)
Out[44]: array([ 0.02272727,  0.18181818,  0.52272727])

In [45]: linalg.solve(A,b, sym_pos=1)
Out[45]: array([ 0.02272727,  0.18181818,  0.52272727])

In [46]: linalg.cho_solve(linalg.cho_factor(A), b)
Out[46]: array([ 0.02272727,  0.18181818,  0.52272727])

--
cheers,
steve

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