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89 lines
2.7 KiB
ReStructuredText
89 lines
2.7 KiB
ReStructuredText
.. highlight:: c
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Linear algebra
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===============================================
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Several standard linear algebra operations are provided for the matrix and vector.
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Note however that matrix and vector are not the main purpose of this library,
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hence the linear algebra support is less extended than other purely matrix library,
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like e.g. Eigen.
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The computation are done when possible by calling lapack and blas.
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In some important cases (like matrix product), a slow but generic version is also
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provided for type that lapack do not treat (e.g. matrix of int, matrix of custom objects)
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but be aware that these are not optimized for performance and should be used only in
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non critical part of the codes.
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matrix product
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--------------------
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The * operator map the matrix x matrix and matrix x vector product.
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Example : matrix * matrix and * vector ...
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.. compileblock::
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#include <triqs/arrays.hpp>
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using triqs::arrays::matrix; using triqs::clef::placeholder;
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int main() {
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// declare an init 2 matrices
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placeholder<0> i_; placeholder<1> j_;
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matrix<double> A (2,2), B(2,2), C;
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A(i_,j_) << i_ + j_ ; B(i_,j_) << 2*i_ + j_ ;
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// Making the product
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C= A*B;
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// Note that the * returns a lazy object
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// that has ImmutableArray concept, and defines a specialized version assignment.
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// compiler rewrites this as something like matmul_with_lapack (A,B,C);
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// There are no temporary here.
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std::cout<< " C = " << C<< std::endl;
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std::cout<< " A*B = " << A*B << std::endl; // NB A*B does not return a matrix, but
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// a lazy expression which is not evaluated until needed.
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}
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For types that lapack do not use, a generic version of the matrix product is provided.
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(same syntax, the dispatch is made at compile time depending of the type of the matrices).
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NB :
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* The **generic** version of the product will be used if
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both matrices do not have the same type.
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**Is this reasonnable ??**.
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* Is the matrix's slowest index is not contiguous, blas/lapack can not be called directly.
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So a temporary copy will be made to reorganize the matrix before calling blas/lapack.
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Code is therefore (normally !) always correct, but this can produce a serious performance hit.
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Matrix inversion
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----------------------
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The inverse function return a lazy inverse of any object which has ImmutableMatrix concept
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and can therefore be mixed with any other matrix expression.
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Example : TO BE WRITTEN
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LU decomposition
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----------------------
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Done. doc to be written
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Diagonalization
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-------------------
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Done. doc to be written
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SVD decomposition
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-------------------
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To be done
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Interface with Eigen
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------------------------
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To be implemented. Only possible for when order is known at compile time.
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