FDMLinearSystem2.h

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/*************************************************************************
> File Name: FDMLinearSystem2.h
> Project Name: CubbyFlow
> Author: Chan-Ho Chris Ohk
> Purpose: Linear system (Ax=b) for 2-D finite differencing.
> Created Time: 2017/08/12
> Copyright (c) 2018, Chan-Ho Chris Ohk
*************************************************************************/
#ifndef CUBBYFLOW_FDM_LINEAR_SYSTEM2_H
#define CUBBYFLOW_FDM_LINEAR_SYSTEM2_H

#include <Core/Array/Array2.h>
#include <Core/Matrix/MatrixCSR.h>
#include <Core/Size/Size2.h>
#include <Core/Vector/VectorN.h>

namespace CubbyFlow
{
    struct FDMMatrixRow2
    {
        double center = 0.0;

        double right = 0.0;

        double up = 0.0;
    };

    using FDMVector2 = Array2<double>;

    using FDMMatrix2 = Array2<FDMMatrixRow2>;

    struct FDMLinearSystem2
    {
        FDMMatrix2 A;

        FDMVector2 x;
        
        FDMVector2 b;

        void Clear();

        void Resize(const Size2& size);
    };

    struct FDMCompressedLinearSystem2
    {
        MatrixCSRD A;

        VectorND x;

        VectorND b;

        void Clear();
    };

    struct FDMBLAS2
    {
        using ScalarType = double;
        using VectorType = FDMVector2;
        using MatrixType = FDMMatrix2;

        static void Set(ScalarType s, VectorType* result);

        static void Set(const VectorType& v, VectorType* result);

        static void Set(ScalarType s, MatrixType* result);

        static void Set(const MatrixType& m, MatrixType* result);

        static double Dot(const VectorType& a, const VectorType& b);

        static void AXPlusY(double a, const VectorType& x, const VectorType& y, VectorType* result);

        static void MVM(const MatrixType& m, const VectorType& v, VectorType* result);

        static void Residual(const MatrixType& a, const VectorType& x, const VectorType& b, VectorType* result);

        static ScalarType L2Norm(const VectorType& v);

        static ScalarType LInfNorm(const VectorType& v);
    };

    struct FDMCompressedBLAS2
    {
        using ScalarType = double;
        using VectorType = VectorND;
        using MatrixType = MatrixCSRD;

        static void Set(ScalarType s, VectorType* result);

        static void Set(const VectorType& v, VectorType* result);

        static void Set(ScalarType s, MatrixType* result);

        static void Set(const MatrixType& m, MatrixType* result);

        static double Dot(const VectorType& a, const VectorType& b);

        static void AXPlusY(double a, const VectorType& x, const VectorType& y, VectorType* result);

        static void MVM(const MatrixType& m, const VectorType& v, VectorType* result);

        static void Residual(const MatrixType& a, const VectorType& x, const VectorType& b, VectorType* result);

        static ScalarType L2Norm(const VectorType& v);

        static ScalarType LInfNorm(const VectorType& v);
    };
}

#endif