LUDecomposition.hpp

/*--------------------------------------------------------------------------------------------
Copyright (c) 2019, NDEVR LLC
tyler.parke@ndevr.org
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Subject to the terms of the Enterprise+ Agreement, NDEVR hereby grants 
Licensee a limited, non-exclusive, non-transferable, royalty-free license 
(without the right to sublicense) to use the API solely for the purpose of 
Licensee's internal development efforts to develop applications for which 
the API was provided.
 
The above copyright notice and this permission notice shall be included in all 
copies or substantial portions of the Software.
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR
PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE
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DEALINGS IN THE SOFTWARE.
 
Library: Base
File: LUDecomposition
Included in API: True
Author(s): Tyler Parke
 *-----------------------------------------------------------------------------------------**/
#pragma once
#include <NDEVR/Matrix.h>
namespace NDEVR
{
    template<class t_type, uint01 t_m, uint01 t_n>
    class LUDecomposition
    {
    public:
        LUDecomposition(const Matrix<t_type, t_m, t_n>& A)
            : LU(A)
        {
 
            // Use a "left-looking", dot-product, Crout/Doolittle algorithm.
 
            for (uint01 i = 0; i < t_m; i++)
            {
                piv[i] = i;
            }
            pivsign = 1;
            Vector<t_m, t_type> LUrowi(0.0);
            Vector<t_m, t_type> LUcolj(0.0);
 
            // Outer loop.
 
            for (uint01 j = 0; j < t_n; j++) 
            {
 
                // Make a copy of the j-th column to localize references.
                for (uint01 i = 0; i < t_m; i++) 
                    LUcolj[i] = LU[i][j];
 
                // Apply previous transformations.
 
                for (uint01 i = 0; i < t_m; i++) 
                {
                    LUrowi = LU[i];
 
                    // Most of the time is spent in the following dot product.
 
                    uint01 kmax = getMin(i, j);
                    t_type s(0);
                    for (uint01 k = 0; k < kmax; k++)
                        s += LUrowi[k] * LUcolj[k];
 
                    LUrowi[j] = LUcolj[i] -= s;
                }
 
                // Find pivot and exchange if necessary.
 
                uint01 p = j;
                for (uint01 i = j + 1; i < t_m; i++) 
                {
                    if (abs(LUcolj[i]) > abs(LUcolj[p]))
                        p = i;
                }
                if (p != j) 
                {
                    for (uint01 k = 0; k < t_n; k++) 
                    {
                        std::swap(LU[p][k], LU[j][k]);
                    }
                    std::swap(piv[p], piv[j]);
                    pivsign = -pivsign;
                }
 
                // Compute multipliers.
 
                if (j < t_m && LU[j][j] != 0.0) 
                {
                    for (uint01 i = j + 1; i < t_m; i++) {
                        LU[i][j] /= LU[j][j];
                    }
                }
            }
        }
 
         /* ------------------------
            Public Methods
          * ------------------------ */

 
        bool isNonsingular() const 
        {
            for (uint01 j = 0; j < t_n; j++) 
            {
                if (LU[j][j] == 0)
                    return false;
            }
            return true;
        }

 
        Matrix<t_type, t_m, t_n> getL() const
        {
            Matrix<t_type, t_m, t_n> mat(0.0);
            for (uint01 i = 0; i < t_m; i++) 
            {
                for (uint01 j = 0; j < t_n; j++) 
                {
                    if (i > j)
                        mat[i][j] = LU[i][j];
                    else if (i == j)
                        mat[i][j] = t_type(1);
                    else
                        mat[i][j] = t_type(0);
                }
            }
            return mat;
        }

 
        Matrix<t_type, t_m, t_n> getU() const
        {
            Matrix<t_type, t_n, t_n> mat(0.0);
            for (uint01 i = 0; i < t_n; i++)
            {
                for (uint01 j = 0; j < t_n; j++)
                {
                    if (i <= j)
                        mat[i][j] = LU[i][j];
                    else
                        mat[i][j] = t_type(0);
                }
            }
            return mat;
        }

        template<class t_pivot_type = sint04>
        Vector<t_m, t_pivot_type> getPivot() const
        {
            return piv.template as<t_m, t_pivot_type>();
        }

 
        t_type det() const
        {
            static_assert(t_m == t_n, "Matrix must be square.");
            t_type d = cast<t_type>(pivsign);
            for (uint01 j = 0; j < t_n; j++)
                d *= LU[j][j];
            return d;
        }

        template<uint01 t_nx>
        Matrix<t_type, t_m, t_nx> solve(const Matrix<t_type, t_m, t_nx>& B)
        {
            lib_assert(isNonsingular(), "Matrix cannot be singular.");
 
            // Copy right hand side with pivoting
            Matrix<t_type, t_m, t_nx> mat = B.template subMatrix<0, t_nx - 1>(piv);
 
            // Solve L*Y = B(piv,:)
            for (uint01 k = 0; k < t_n; k++) 
            {
                for (uint01 i = k + 1; i < t_n; i++) 
                {
                    for (uint01 j = 0; j < t_nx; j++) 
                    {
                        mat[i][j] -= mat[k][j] * LU[i][k];
                    }
                }
            }
            // Solve U*X = Y;
            for (uint01 k = t_n - 1; IsValid(k); k--)
            {
                for (uint01 j = 0; j < t_nx; j++)
                    mat[k][j] /= LU[k][k];
                for (uint01 i = 0; i < k; i++) 
                {
                    for (uint01 j = 0; j < t_nx; j++)
                        mat[i][j] -= mat[k][j] * LU[i][k];
                }
            }
            return mat;
        }
 
        private:
            Matrix<t_type, t_m, t_n> LU;

            sint04 pivsign;

            Vector<t_m, uint01> piv;
    };
}