system_solvers_small.hpp

/*---------------------------------------------------------------------------*\
 *
 *  bitpit
 *
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 *
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// ========================================================================== //
//                         LINEAR ALGEBRA PACKAGE                             //
//                                                                            //
// Functions for basic linear algebra computations.                           //
// ========================================================================== //
// INFO                                                                       //
// ========================================================================== //
// Author            : Alessandro Alaia                                       //
// Data              : Sept 26, 2014                                          //
// Version           : v2.0                                                   //
//                                                                            //
// All rights reserved.                                                       //
// ========================================================================== //
# ifndef __BITPIT_SYSTEM_SOLVERS_SMALL_HPP__
# define __BITPIT_SYSTEM_SOLVERS_SMALL_HPP__
 
// ========================================================================== //
// INCLUDES                                                                   //
// ========================================================================== //
 
// Standard template library
# include <vector>
# include <cmath>
# include <array>
# include <iostream>
 
# include "bitpit_operators.hpp"
 
namespace bitpit{

namespace linearalgebra{
 
namespace constants{
 
extern const int ROW_MAJOR;
extern const int COL_MAJOR;
 
}
 
template <class T>
void cramer(                                                                  // Solve linear system using Cramer's rule
    std::vector< std::vector < T > >            &,                            // (input) coeff. matrix
    std::vector< T >                            &,                            // (input) source term
    std::vector< T >                            &                             // (input/output) solution
);
 
template <class T, size_t m, size_t n>
void cramer(                                                                  // Solve linear system using Cramer's rule
    std::array< std::array < T, n >, m >        &,                            // (input) coeff. matrix
    std::array< T, m >                          &,                            // (input) source term
    std::array< T, n >                          &                             // (input/output) solution
);
 
unsigned int factorizeLU(                                                              // LU decomposition of matrix
    std::vector<std::vector<double>>            &,                            // (input) Input matrix
    std::vector<std::vector<double>>            &,                            // (input/output) L factor
    std::vector<std::vector<double>>            &,                            // (input/output) U factor
    std::vector<std::vector<double>>            *                             // (input/optional) permutation matrix
);
 
template<size_t m>
unsigned int factorizeLU(                                                              // LU decomposition of matrix
    std::array<std::array<double, m>, m>        &,                            // (input) Input matrix
    std::array<std::array<double, m>, m>        &,                            // (input/output) L factor
    std::array<std::array<double, m>, m>        &,                            // (input/output) U factor
    std::array<std::array<double, m>, m>        *                             // (input/optional) permutation matrix
);
 
void backwardSubstitution(                                                           // Backward substitution algorithm
    std::vector<std::vector<double>>            &,                            // (input) Coeffs. matrix
    std::vector<double>                         &,                            // (input) Source term
    std::vector<double>                         &                             // (input/output) Solution
);
 
template<size_t m>
void backwardSubstitution(                                                           // Backward substitution algorithm
    std::array<std::array<double, m>, m>        &,                            // (input) Coeffs. matrix
    std::array<double, m>                       &,                            // (input) Source term
    std::array<double, m>                       &                             // (input/output) Solution
);
 
void forwardSubstitution(                                                            // Forward substitution algorithm
    std::vector<std::vector<double>>            &,                            // (input) Coeffs. matrix
    std::vector<double>                         &,                            // (input) Source term
    std::vector<double>                         &                             // (input/output) Solution
);
 
template<size_t m>
void forwardSubstitution(                                                            // Forward substitution algorithm
    std::array<std::array<double, m>, m>        &,                            // (input) Coeffs. matrix
    std::array<double, m>                       &,                            // (input) Source term
    std::array<double, m>                       &                             // (input/output) Solution
);
 
void solveLU(                                                                 // Solve linear system using LU factorization
    std::vector<std::vector<double>>            &,                            // (input) Input coeffs. matrix
    std::vector<double>                         &,                            // (input) Source term
    std::vector<double>                         &                             // (input/output) Solution
);
 
template<size_t m>
void solveLU(                                                                 // Solve linear system using LU factorization
    std::array<std::array<double, m>, m>        &,                            // (input) Input coeffs. matrix
    std::array<double, m>                       &,                            // (input) Source term
    std::array<double, m>                       &                             // (input/output) Solution
);
 
int solveLU(                                                                  // Solve linear system using Lapack DGESV
    int                                          ,                            // (input) Matrix layout
    std::vector<double>                         &,                            // (input) Input coeffs. matrix (linear)
    std::vector<double>                         &                             // (input/output) Source term / Solution
);
 
int solveLU(                                                                  // Solve linear system using Lapack DGESV
    int                                          ,                            // (input) Matrix layout
    int                                          ,                            // (input) Matrix order
    double                                      *,                            // (input) Pointer to input coeffs. matrix (linear)
    double                                      *,                            // (input/output) Pointer to source term / solution
    int                                         *                             // (output) Pivot indeces of the permutation matrix
);
 
}
 
}
 
// =================================================================================== //
// TEMPLATES                                                                           //
// =================================================================================== //
# include "system_solvers_small.tpp"
 
# endif