Optimising matrices access and operations

Creating the K-diagonal matrix

1 files changed, 277 insertions, 0 deletions

diff --git a/include/mm/experiments/mmsubdiag.h b/include/mm/experiments/mmsubdiag.h
new file mode 100644
index 0000000..2f6c93c
--- /dev/null
+++ b/include/mm/experiments/mmsubdiag.h
@@ -0,0 +1,277 @@
+#pragma once
+
+#ifndef __TRIDIAG_H__
+#define __TRIDIAG_H__
+
+template<class T>
+class tridiag
+{
+    std::vector<T> diag, lower, upper;
+
+    struct row
+    {
+        std::size_t index;
+        tridiag& ref;
+
+        T shared_zero = 0;
+
+        row(std::size_t i, tridiag& _ref) : index(i), ref(_ref) {}
+
+        T& operator[](std::size_t j)
+        {
+            switch(static_cast<long int>(j) - index)
+            {
+            case -1:
+                return ref.lower[j];
+            case 0:
+                return ref.diag[j];
+            case 1:
+                return ref.upper[index];
+            default:
+                shared_zero = 0; // assure zero
+                return shared_zero;
+            }
+        }
+    };
+
+    struct const_row
+    {
+        std::size_t index;
+        const tridiag& ref;
+
+        const T shared_zero = 0;
+
+        const_row(std::size_t i, const tridiag& _ref) : index(i), ref(_ref) {}
+
+        const T& operator[](std::size_t j) const
+        {
+            switch(static_cast<long int>(j) - index)
+            {
+            case -1:
+                return ref.lower[j];
+            case 0:
+                return ref.diag[j];
+            case 1:
+                return ref.upper[index];
+            default:
+                return shared_zero;
+            }
+        }
+    };
+
+public:
+
+    tridiag(std::size_t N = 1) : diag(N), lower(N-1), upper(N-1)
+    {
+    } 
+
+    void resize(std::size_t N)
+    {
+        diag.reserve(N);
+        lower.reserve(N-1);
+        upper.reserve(N-1);
+    }
+
+    void zeros()
+    {
+        for (std::size_t i = 0; i < size()-1; ++i)
+                diag[i] = lower[i] = upper[i] = 0;
+
+        diag[size()-1] = 0;
+    }
+
+    // set diagonal to zero
+    void zeros_diag()
+    {
+        for (std::size_t i = 0; i < size(); ++i)
+            diag[i] = 0;
+    }
+
+    row operator[](std::size_t i)
+    {
+        return row(i, *this);
+    }
+
+    const const_row operator[](std::size_t i) const
+    {
+        return const_row(i, *this);
+    }
+
+    std::size_t size() const
+    {
+        return diag.size();
+    }
+
+    template<template <typename> class V>
+    V<T> solve(const V<T>& rhs)
+    {
+        V<T> solution(diag.size());
+        V<T> new_diag(diag);
+        V<T> new_rhs(rhs);
+
+        for(std::size_t i(1); i < size(); ++i)
+        {
+            T pivot = lower[i-1]/new_diag[i-1];
+            new_diag[i] -= pivot * upper[i-1];
+            new_rhs[i] -= pivot * new_rhs[i-1];
+        }
+
+        solution[size()-1] = new_rhs[size()-1] / new_diag[size()-1];
+
+        for(int i(static_cast<int>(size()-2)); i>=0; --i)
+            solution[i] = (new_rhs[i] - upper[i]*solution[i+1]) / new_diag[i];
+
+        return solution;
+    }
+
+    static constexpr tridiag id(size_t N)
+    {
+        tridiag<T> diag;
+
+        for (size_t k = 0; k < N; ++k)
+            diag[k][k] = 1;
+
+        return diag;
+    }
+
+    const std::vector<T>& d() const
+    {
+        return diag;
+    }
+
+    const std::vector<T>& down() const
+    {
+        return lower;
+    }
+
+    const std::vector<T>& up() const
+    {
+        return upper;
+    }
+};
+
+// multiplication operator overloading
+/*template<class T, template <class> class V>
+V<T> operator*(const tridiag<T>& M, const V<T>& v)
+{
+    const std::size_t N = v.size();
+
+    V<T> u(N);
+
+    u[0] = M[0][0] * v[0] + M[0][1] * v[1];
+
+    for (std::size_t k = 1; k < N-1; ++k)
+        u[k] = M[k][k-1] * v[k-1] + M[k][k] * v[k] + M[k][k+1] * v[k+1];
+
+    u[N-1] = M[N-1][N-2] * v[N-2] + M[N-1][N-1] * v[N-1];
+
+    return u;
+}*/
+
+template<class T, template <class> class V>
+V<T> operator*(const tridiag<T>& M, const V<T>& v)
+{
+    const std::size_t N = v.size();
+
+    V<T> u(N);
+
+    u[0] = M.d()[0] * v[0] + M.up()[0] * v[1];
+
+    for (std::size_t k = 1; k < N-1; ++k)
+        u[k] = M.down()[k] * v[k-1] + M.d()[k] * v[k] + M.up()[k] * v[k+1];
+
+    u[N-1] = M.down()[N-1] * v[N-2] + M.d()[N-1] * v[N-1];
+
+    return u;
+}
+
+template<class T>
+tridiag<T> operator+(tridiag<T> M, const tridiag<T>& A)
+{
+    if (M.size() != A.size())
+        return M;
+
+    const std::size_t N = M.size();
+
+    M[0][0] += A[0][0];
+    M[0][1] += A[0][1];
+
+    for (std::size_t k = 1; k < N-1; ++k)
+        for (std::size_t j = k-1; j <= k+1; ++j)
+            M[k][j] += A[k][j];
+
+    M[N-1][N-2] += A[N-1][N-2];
+    M[N-1][N-1] += A[N-1][N-1];
+
+    return M;
+}
+
+template<class T>
+tridiag<T> operator*(tridiag<T> M, const T& value)
+{
+    const std::size_t N = M.size();
+
+    M[0][0] *= value;
+    M[0][1] *= value;
+
+    for (std::size_t k = 1; k < N-1; ++k)
+        for (std::size_t j = k-1; j <= k+1; ++j)
+            M[k][j] *= value;
+
+    M[N-1][N-2] *= value;
+    M[N-1][N-1] *= value;
+
+    return M;
+}
+
+// add value * Id
+template<class T>
+tridiag<T> operator+(tridiag<T> M, const T& value)
+{
+    const std::size_t N = M.size();
+
+    for (std::size_t k = 0; k < N; ++k)
+        M[k][k] += value;
+
+    return M;
+}
+
+template<class T>
+tridiag<T> operator*(const T& value, const tridiag<T>& M)
+{
+    return M * value;
+}
+
+// add value * Id
+template<class T>
+tridiag<T> operator+(const T& value, const tridiag<T>& M)
+{    
+    return M + value;
+}
+
+#include <ostream>
+
+template<class T>
+std::ostream& operator<<(std::ostream& os, const tridiag<T>& M)
+{
+    const std::size_t N = M.size();
+
+
+    os << M[0][0] << " ";
+    os << M[0][1] << " ";
+    os << std::endl;
+
+    for (std::size_t k = 1; k < N-1; ++k) {
+        for (std::size_t j = k-1; j <= k+1; ++j)
+            os << M[k][j] << " ";
+        os << std::endl;
+    }
+
+
+    os << M[N-1][N-2] << " ";
+    os << M[N-1][N-1] << std::endl;
+
+    return os;
+}
+
+#endif