piecewise_lin_cont.h

#include "basictools.h"
#include "fepc_easy.h"
#include "faltung.h"

class piecewise_constant
{
public:
    int n;
    double* grid; // array of size n + 1 // grid[0] = a, grid[n] = b
    double* value; // array of size n

    double integral();
};

class piecewise_linear
{
public:
    int n;
    double* grid; // array of size n + 1 // grid[0] = a, grid[n] = b
    double* start_value; // array of size n
    double* end_value; // array of size n

    double integral();
};

class piecewise_linear_continuous
{
public:
    piecewise_linear_continuous() {};

    int n;
    double* grid; // array of size n + 1 // grid[0] = a, grid[n] = b
    double* coeff; // array of size n + 1 // coefficiets of the basis functions (hat functions). The same as the values at gridpoints.

    double L1();
    double integral();
    double mass();

    piecewise_linear_continuous& operator = (const piecewise_linear_continuous& f);

    int multiplication_with_function (double* f, piecewise_constant& w);
    int multiplication_with_function (double* f, piecewise_linear& w);

    int ProjectToMassConservedExact();
    int ProjectToMassConservedShift();
    int ProjectToMassConservedPSD();

    int IsContinuousProjectionOf(piecewise_constant& f, double* diag, double* subdiag);
    int IsContinuousProjectionOf(piecewise_linear& f, double* diag, double* subdiag);

    piecewise_constant DiscontinuosRepresentation();
};

int fill_diagonal_part_of_Gramm_matrix(int n, double* grid, double* diag);
int fill_subdiagonal_part_of_Gramm_matrix(int n, double* grid, double* subdiag);