mirror of
https://github.com/triqs/dft_tools
synced 2024-11-01 11:43:47 +01:00
74 lines
1.9 KiB
ReStructuredText
74 lines
1.9 KiB
ReStructuredText
.. highlight:: c
|
|
|
|
Linear algebra
|
|
===============================================
|
|
|
|
.. warning::
|
|
|
|
Doc still largely to be written and updated....
|
|
|
|
Several standard linear algebra operations are provided for the matrix and vector.
|
|
Note however that matrix and vector are not the main purpose of this library,
|
|
hence the linear algebra support is less extended than other purely matrix library,
|
|
like e.g. Eigen.
|
|
|
|
The computation are done when possible by calling lapack and blas.
|
|
In some important cases (like matrix product), a slow but generic version is also
|
|
provided for type that lapack do not treat (e.g. matrix of int, matrix of custom objects)
|
|
but be aware that these are not optimized for performance and should be used only in
|
|
non critical part of the codes.
|
|
|
|
matrix product
|
|
--------------------
|
|
|
|
The * operator map the matrix x matrix and matrix x vector product.
|
|
|
|
Example : matrix * matrix and * vector ...
|
|
|
|
..
|
|
compileblock::
|
|
#include <triqs/arrays.hpp>
|
|
using triqs::arrays::matrix; using triqs::clef::placeholder;
|
|
int main() {
|
|
// declare an init 2 matrices
|
|
placeholder<0> i_; placeholder<1> j_;
|
|
matrix<double> A (2,2), B(2,2), C;
|
|
A(i_,j_) << i_ + j_ ; B(i_,j_) << 2*i_ + j_ ;
|
|
C= A*B;
|
|
std::cout<< " C = " << C<< std::endl;
|
|
}
|
|
|
|
For types that lapack do not use, a generic version of the matrix product is provided.
|
|
(same syntax, the dispatch is made at compile time depending of the type of the matrices).
|
|
|
|
|
|
Matrix inversion
|
|
----------------------
|
|
|
|
The inverse function return a lazy inverse of any object which has ImmutableMatrix concept
|
|
and can therefore be mixed with any other matrix expression.
|
|
|
|
Example : TO BE WRITTEN
|
|
|
|
|
|
LU decomposition
|
|
----------------------
|
|
|
|
Done. doc to be written
|
|
|
|
Diagonalization
|
|
-------------------
|
|
Done. doc to be written
|
|
|
|
SVD decomposition
|
|
-------------------
|
|
|
|
To be done
|
|
|
|
Interface with Eigen
|
|
------------------------
|
|
|
|
To be implemented. Only possible for when order is known at compile time.
|
|
|
|
|