A clarification about LsmBasisSystem

[andrea-110]

Hi,

I would like to understand something about LsmBasisSystem

In particular LsmBasisSystem::LsmBasisSystem(Size dim, Size order, PolynomType polynomType);

What is the relationship between the dimension (dim) and the size of the state returned by

Array EarlyExercisePathPricer<MultiPath>::state();

Do they need to be the same? It still works if they are different. What does it do?
(I haven't stepped through the code yet).


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[Klaus Spanderen-2]

Hi Andrea

On Friday 11 September 2009 22:39:53 Andrea wrote:

>
> In particular LsmBasisSystem::LsmBasisSystem(Size dim, Size order,
> PolynomType polynomType);
>
> What is the relationship between the dimension (dim) and the size of the
> state returned by
>
> Array EarlyExercisePathPricer<MultiPath>::state();
>

They should have the same size. if dim < size of state returned, the states
variables from dim to size-1 will be ignored within the regression. The
behaviour for dim > size is undefined. At least for this case one I'm going
to add a QL_REQUIRE to avoid it.  

best regards
 Klaus

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[andrea-110]

On 12/09/09 18:49, Klaus Spanderen wrote:

> They should have the same size. if dim<  size of state returned, the states
> variables from dim to size-1 will be ignored within the regression. The
> behaviour for dim>  size is undefined. At least for this case one I'm going
> to add a QL_REQUIRE to avoid it.
>

I've seen your change

         inline Real f_workaround(const Array& a, Size i) {
             QL_REQUIRE(i < a.size(),
                        "dimension of the basis system is too large");
             return a[i];
         }

but it still behaves the same.

As far as I understand, in this example

void foo()
{
     std::vector<boost::function1<Real, Array> > v = LsmBasisSystem::multiPathBasisSystem(2, 2,
LsmBasisSystem::Monomial);

     Array foo1(1);
     foo1[0] = 1.0;
     std::cout << v[0](foo1) << std::endl;

     Array foo2(2);
     foo2[0] = 1.0;
     foo2[1] = 1.0;
     std::cout << v[0](foo2) << std::endl;

     Array foo3(4);
     foo3[0] = 1.0;
     foo3[1] = 1.0;
     foo3[2] = 1.0;
     std::cout << v[0](foo3) << std::endl;
}

foo1 should trigger QL_REQUIRE
foo2 is OK,
foo3[2] is ignored.

But it prints
1
1
1

Just to be sure, I've tried to define QL_EXTRA_SAFETY_CHECKS at the very top of my source code. (no
exception is thrown).
Do I need also to recompile QL?

Or have I misunderstood the dimensions?
I have to admit I am completely lost with the boost binders used in the basis system.


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[Klaus Spanderen-2]

Hi Andrea

thanks for the example. The "problem" is that
 LsmBasisSystem::multiPathBasisSystem(2, 2, LsmBasisSystem::Monomial);
returns the following basis system
{ 1.0, x[0], x[1], x[0]^2, x[1]^2, x[0]*x[1] }.

Therefore v[0](foo1) and v[1](foo1) will pass whereas v[2](foo1) will cause
the error you've expected.

I agree this is not the expected behaviour. Therefore I've checked in another
version. Now v[...] will fail if x.size() != dim (hopefully;-).

Thanks for your advice.

best regards
 Klaus

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[andrea-110]

On 13/09/09 21:38, Klaus Spanderen wrote:
> Hi Andrea
>
> thanks for the example. The "problem" is that
>   LsmBasisSystem::multiPathBasisSystem(2, 2, LsmBasisSystem::Monomial);
> returns the following basis system
> { 1.0, x[0], x[1], x[0]^2, x[1]^2, x[0]*x[1] }.
>

Thanks for the explanation.
Using '[0]' was misleading, I should have tried all indices.

Will try again to be sure I understand.

> Therefore v[0](foo1) and v[1](foo1) will pass whereas v[2](foo1) will cause
> the error you've expected.
>
> I agree this is not the expected behaviour. Therefore I've checked in another
> version. Now v[...] will fail if x.size() != dim (hopefully;-).
>
> Thanks for your advice.
>
> best regards
>   Klaus

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