How to solve Ax=b , where A is a symmetry matrix .

[ztdepztdep]

Which function should i use.

[michael-lehn]

If A is positiv definite use the cholesky factorization (flens::lapack::potrf). Lapack documentation: http://www.netlib.org/lapack/explore-html/d1/d7a/group__double_p_ocomputational_ga2f55f604a6003d03b5cd4a0adcfb74d6.html

If A is not positive definite use the Bunch-Kaufman diagonal pivoting method (flens::sy::trf). Lapack documentation:
https://www.netlib.org/lapack/explore-html/d3/db6/group__double_s_ycomputational_gad91bde1212277b3e909eb6af7f64858a.html

[ztdepztdep]

If A is positiv definite use the cholesky factorization (flens::lapack::potrf). Lapack documentation: http://www.netlib.org/lapack/explore-html/d1/d7a/group__double_p_ocomputational_ga2f55f604a6003d03b5cd4a0adcfb74d6.html

If A is not positive definite use the Bunch-Kaufman diagonal pivoting method (flens::sy::trf). Lapack documentation: https://www.netlib.org/lapack/explore-html/d3/db6/group__double_s_ycomputational_gad91bde1212277b3e909eb6af7f64858a.html

Thank you very much. In my problem, I need to solve Ax=b repeatly where the matrix A doesn't change.
So how to seperate the solve process into two stages. first decomposet A, then solve it with different right hand side.

[michael-lehn]

It is already separated. flens::lapack::potrf and flens::sy::trf are computing the factorization. flens::lapack::potrs and flens::sy::trs solve the equation and require that the matrix was previously factorized.

Exactly how this is handled by LAPACK with 1) dgepotrf and dgepotrs or 2) dgesytrf and dgesytrs:

1. http://www.netlib.org/lapack/explore-html/d1/d7a/group__double_p_ocomputational_ga2f55f604a6003d03b5cd4a0adcfb74d6.html

and

http://www.netlib.org/lapack/explore-html/d1/d7a/group__double_p_ocomputational_ga167aa0166c4ce726385f65e4ab05e7c1.html

2. https://www.netlib.org/lapack/explore-html/d3/db6/group__double_s_ycomputational_gad91bde1212277b3e909eb6af7f64858a.html

and

https://www.netlib.org/lapack/explore-html/d3/db6/group__double_s_ycomputational_ga6a223e61effac7232e98b422f147f032.html

[ztdepztdep]

Thanks.
If I solve Ax=b with the "lapack::sv(A, piv, b)" , is the solution time slower than the " flens::sy::trf" and "flens::sy::trs". I am working on a spectral multidomain code, the speed is import for me to improve the efficiency.

[michael-lehn]

If I solve Ax=b with the "lapack::sv(A, piv, b)" , is the solution time slower than the " flens::sy::trf" and "flens::sy::trs".

Is this a question or an observation? What type does A have? GeMatrix or SyMatrix?

[ztdepztdep]

I tired to compile the "lapack-potrs.cc", the compiler feedback the following error:
`./flens/storage/array/arrayview.tcc:200:30: error: invalid use of member function ‘flens::ArrayView<T, I, A>::IndexType flens::ArrayView<T, I, A>::firstIndex() const [with T = double; I = flens::IndexOptions<>; A = std::allocator; flens::ArrayView<T, I, A>::IndexType = int]’ (did you forget the ‘()’ ?)
_data += _firstIndex - firstIndex;

/flens/storage/array/arrayview.tcc:202:17: error: cannot convert ‘flens::ArrayView<double, flens::IndexOptions<>, std::allocator >::firstIndex’ from type ‘flens::ArrayView<double, flens::IndexOptions<>, std::allocator >::IndexType (flens::ArrayView<double, flens::IndexOptions<>, std::allocator >::)() const {aka int (flens::ArrayView<double, flens::IndexOptions<>, std::allocator >::)() const}’ to type ‘flens::ArrayView<double, flens::IndexOptions<>, std::allocator >::IndexType {aka int}’
_firstIndex = firstIndex;`

Could you please help me out.

[michael-lehn]

There seemed to be an issue with gcc 11. After fixing an missing include I can compile lapack-potrs.cc in flens/examples as follows:

g++-11 -Wall -std=c++11 -I /Users/lehn/work/FLENS lapack-potrs.cc

This is not using an external LAPACK.

1. Can you first confirm that this compiles on you machine? If not: what compiler are you using
2. For using an external LAPACK: What LAPACK implementation are you using? MKL?

[ztdepztdep]

I compiled it in the KDevelop 4 with cmake, it gives me the above error. I still cann't make it work.

I tried to compile it in the terminal wth :
g++ -std=c++11 -O3 -I /home/ztdep/Downloads/FLENS-2012-10-01 main.cpp -o b it feeds back correct results.

[michael-lehn]

I am not familiar with KDevelop 4. But I compiling it on the terminal works it is just a matter of configuring the IDE. Most likely you just have to specify the correct compiler flags somewhere.

Is there a way to see how KDevelop 4 invokes the compiler?