SmallMatrix_impl.h

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/*
 This file forms part of hpGEM. This package has been developed over a number of years by various people at the University of Twente and a full list of contributors can be found at
 http://hpgem.org/about-the-code/team
 
 This code is distributed using BSD 3-Clause License. A copy of which can found below.
 
 
 Copyright (c) 2014, University of Twente
 All rights reserved.
 
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 */
 
//Copyright (c) 2013-2023, The MercuryDPM Developers Team. All rights reserved.
//For the list of developers, see <http://www.MercuryDPM.org/Team>.
//
//Redistribution and use in source and binary forms, with or without
//modification, are permitted provided that the following conditions are met:
//  * Redistributions of source code must retain the above copyright
//    notice, this list of conditions and the following disclaimer.
//  * Redistributions in binary form must reproduce the above copyright
//    notice, this list of conditions and the following disclaimer in the
//    documentation and/or other materials provided with the distribution.
//  * Neither the name MercuryDPM nor the
//    names of its contributors may be used to endorse or promote products
//    derived from this software without specific prior written permission.
//
//THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
//ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
//WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
//DISCLAIMED. IN NO EVENT SHALL THE MERCURYDPM DEVELOPERS TEAM BE LIABLE FOR ANY
//DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
//(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
//LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
//ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
//(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
//SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
//Note: This code is copied and adapted from hpGEM (see license above), version 22th of January 2016. It has been
//integrated into MercuryDPM at 16th of March 2017.
 
 
#include "SmallMatrix.h"
 
 
extern "C"
{
 
void dgemv_(const char* trans, int* m, int* n, double* alpha, double* A, int* LDA, double* x, int* incx, double* beta,
            double* y, int* incy);
 
int
dgemm_(const char* transA, const char* transB, int* M, int* N, int* k, double* alpha, double* A, int* LDA, double* B,
       int* LDB, double* beta, double* C, int* LDC);
 
int daxpy_(int* N, double* DA, double* DX, int* INCX, double* DY, int* INCY);
 
void dgetrf_(int* M, int* N, double* A, int* lda, int* IPIV, int* INFO);
 
void dgetri_(int* N, double* A, int* lda, int* IPIV, double* WORK, int* lwork, int* INFO);
 
void dgesv_(int* N, int* NRHS, double* A, int* lda, int* IPIV, double* B, int* LDB, int* INFO);
}
 
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector<numberOfRows> SmallMatrix<numberOfRows, numberOfColumns>::operator*(SmallVector<numberOfColumns>& right)
{
    if (numberOfRows == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any rows.");
        return SmallVector<numberOfRows>();
    }
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
        return SmallVector<numberOfRows>();
    }
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int i_one = 1;
    double d_one = 1.0;
    double d_zero = 0.0;
    
    SmallVector<numberOfRows> result;
    
    logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, right.size());
    
    dgemv_("N", &nr, &nc, &d_one, this->data(), &nr, right.data(), &i_one, &d_zero, result.data(), &i_one);
    return result;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector<numberOfRows>
SmallMatrix<numberOfRows, numberOfColumns>::operator*(SmallVector<numberOfColumns>& right) const
{
    if (numberOfRows == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any rows.");
        return SmallVector<numberOfRows>();
    }
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
        return SmallVector<numberOfRows>();
    }
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int i_one = 1;
    double d_one = 1.0;
    double d_zero = 0.0;
    
    SmallVector<numberOfRows> result;
    
    logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, right.size());
    
    dgemv_("N", &nr, &nc, &d_one, (const_cast<double*>(this->data())), &nr, right.data(), &i_one, &d_zero,
           result.data(), &i_one);
    return result;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
template<unsigned int K>
SmallMatrix<numberOfRows, K>
SmallMatrix<numberOfRows, numberOfColumns>::operator*(const SmallMatrix<numberOfColumns, K>& other)
{
    int i = numberOfRows;
    int j = numberOfColumns;
    int k = K;
    
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a matrix with a matrix without any columns.");
        return SmallMatrix<numberOfRows, K>();
    }
    //The result of the matrix is left.numberOfRows, right.numberOfColumns()
    SmallMatrix<numberOfRows, K> C;
    
    double d_one = 1.0;
    double d_zero = 0.0;
    
    //Let the actual multiplication be done by Fortran
    dgemm_("N", "N", &i, &k, &j, &d_one, this->data(), &i, const_cast<double*>(other.data()), &j, &d_zero, C.data(),
           &i);
    
    return C;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
template<unsigned int K>
SmallMatrix<numberOfRows, K>
SmallMatrix<numberOfRows, numberOfColumns>::operator*(const SmallMatrix<numberOfColumns, K>& other) const
{
    int i = numberOfRows;
    int j = numberOfColumns;
    int k = K;
    
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a matrix with a matrix without any columns.");
        return SmallMatrix<numberOfRows, K>();
    }
    //The result of the matrix is left.Nrows, right.NCols()
    SmallMatrix<numberOfRows, K> C;
    
    double d_one = 1.0;
    double d_zero = 0.0;
    
    //Let the actual multiplication be done by Fortran
    dgemm_("N", "N", &i, &k, &j, &d_one, const_cast<double*>(this->data()), &i, const_cast<double*>(other.data()), &j,
           &d_zero, C.data(), &i);
    
    return C;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix<numberOfRows, numberOfColumns>&
SmallMatrix<numberOfRows, numberOfColumns>::operator*=(const SmallMatrix<numberOfColumns, numberOfColumns>& other)
{
    //blas does not support in-place multiply
    return (*this) = (*this) * other;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector<numberOfRows> SmallMatrix<numberOfRows, numberOfColumns>::computeWedgeStuffVector() const
{
    //copied from MiddleSizeMatrix to prevent constructing a temporary MiddleSizeMatrix
    logger.assert_debug(numberOfColumns == numberOfRows - 1,
                  "Matrix has wrong dimensions to construct the wedge stuff vector");
    SmallVector<numberOfRows> result;
    
    switch (numberOfRows)
    {
        case 2:
            result[0] = -(*this)(1, 0);
            result[1] = +(*this)(0, 0);
            break;
        case 3:
            result[0] = (*this)(1, 0) * (*this)(2, 1) - (*this)(2, 0) * (*this)(1, 1);
            result[1] = (*this)(0, 1) * (*this)(2, 0) - (*this)(0, 0) * (*this)(2, 1); // includes minus sign already!
            result[2] = (*this)(0, 0) * (*this)(1, 1) - (*this)(1, 0) * (*this)(0, 1);
            break;
        case 4:
            result[0] = (*this)(1, 0) * (-(*this)(2, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(2, 2)) +
                        (*this)(2, 0) * ((*this)(1, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(1, 2)) +
                        (*this)(3, 0) * (-(*this)(1, 1) * (*this)(2, 2) + (*this)(2, 1) * (*this)(1, 2));
            
            result[1] = (*this)(0, 0) * ((*this)(2, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(2, 2)) +
                        (*this)(2, 0) * (-(*this)(0, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(0, 2)) +
                        (*this)(3, 0) * ((*this)(0, 1) * (*this)(2, 2) - (*this)(2, 1) * (*this)(0, 2));
            result[2] = (*this)(0, 0) * (-(*this)(1, 1) * (*this)(3, 2) + (*this)(3, 1) * (*this)(1, 2)) +
                        (*this)(1, 0) * ((*this)(0, 1) * (*this)(3, 2) - (*this)(3, 1) * (*this)(0, 2)) +
                        (*this)(3, 0) * (-(*this)(0, 1) * (*this)(1, 2) + (*this)(1, 1) * (*this)(0, 2));
            result[3] = (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(2, 1) * (*this)(1, 2)) +
                        (*this)(1, 0) * (-(*this)(0, 1) * (*this)(2, 2) + (*this)(2, 1) * (*this)(0, 2)) +
                        (*this)(2, 0) * ((*this)(0, 1) * (*this)(1, 2) - (*this)(1, 1) * (*this)(0, 2));
            break;
        default:
            logger(ERROR, "Wedge product not implemented for this dimension");
    } //end switch
    
    return (result);
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix<numberOfRows, numberOfColumns> SmallMatrix<numberOfRows, numberOfColumns>::LUfactorisation() const
{
    int nr = numberOfRows;
    int nc = numberOfColumns;
    int nPivot = std::min(numberOfRows, numberOfColumns);
    int iPivot[nPivot];
    
    SmallMatrix result(*this);
    
    int info;
    
    dgetrf_(&nr, &nc, result.data(), &nr, iPivot, &info);
    
    return result;
}
 
//class template specialization for this one function is a waste of code duplication
//just let the compiler figure out which case it needs
template<unsigned int numberOfRows, unsigned int numberOfColumns>
Mdouble SmallMatrix<numberOfRows, numberOfColumns>::determinant() const
{
    logger.assert_debug(numberOfRows == numberOfColumns, "Matrix should be square to have a determinant!");
    
    switch (numberOfRows)
    {
        case 0:
            return 1;
        case 1:
            return (*this)(0, 0);
        case 2:
            return (*this)(0, 0) * (*this)(1, 1) - (*this)(0, 1) * (*this)(1, 0);
        
        case 3:
            return (*this)(0, 0) * ((*this)(1, 1) * (*this)(2, 2) - (*this)(1, 2) * (*this)(2, 1)) -
                   (*this)(0, 1) * ((*this)(1, 0) * (*this)(2, 2) - (*this)(2, 0) * (*this)(1, 2)) +
                   (*this)(0, 2) * ((*this)(1, 0) * (*this)(2, 1) - (*this)(2, 0) * (*this)(1, 1));
        
        case 4:
            return ((*this)(3, 0) * (*this)(2, 1) * (*this)(0, 3) - (*this)(2, 0) * (*this)(3, 1) * (*this)(0, 3)) *
                   (*this)(1, 2) +
                   (-(*this)(3, 0) * (*this)(0, 3) * (*this)(2, 2) + (*this)(2, 0) * (*this)(0, 3) * (*this)(3, 2)) *
                   (*this)(1, 1) +
                   ((*this)(3, 1) * (*this)(0, 3) * (*this)(2, 2) - (*this)(2, 1) * (*this)(0, 3) * (*this)(3, 2)) *
                   (*this)(1, 0) +
                   (-(*this)(3, 0) * (*this)(2, 1) * (*this)(1, 3) + (*this)(2, 0) * (*this)(3, 1) * (*this)(1, 3) +
                    (-(*this)(2, 0) * (*this)(3, 3) + (*this)(3, 0) * (*this)(2, 3)) * (*this)(1, 1) +
                    ((*this)(2, 1) * (*this)(3, 3) - (*this)(3, 1) * (*this)(2, 3)) * (*this)(1, 0)) * (*this)(0, 2) +
                   ((*this)(3, 0) * (*this)(1, 3) * (*this)(2, 2) - (*this)(2, 0) * (*this)(1, 3) * (*this)(3, 2) +
                    ((*this)(2, 0) * (*this)(3, 3) - (*this)(3, 0) * (*this)(2, 3)) * (*this)(1, 2) +
                    (-(*this)(2, 2) * (*this)(3, 3) + (*this)(2, 3) * (*this)(3, 2)) * (*this)(1, 0)) * (*this)(0, 1) +
                   (-(*this)(3, 1) * (*this)(1, 3) * (*this)(2, 2) + (*this)(2, 1) * (*this)(1, 3) * (*this)(3, 2) +
                    ((*this)(3, 1) * (*this)(2, 3) - (*this)(2, 1) * (*this)(3, 3)) * (*this)(1, 2) +
                    (*this)(1, 1) * ((*this)(2, 2) * (*this)(3, 3) - (*this)(2, 3) * (*this)(3, 2))) * (*this)(0, 0);
            // ... says Maple; this can possibly be done more efficiently,
            // maybe even with LU (with pivoting, though...)
        default:
            logger(ERROR, "Computing the Determinant for size % is not implemented", numberOfRows);
            break;
    }
    return 0;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallMatrix<numberOfRows, numberOfColumns> SmallMatrix<numberOfRows, numberOfColumns>::inverse() const
{
    logger.assert_debug(numberOfRows == numberOfColumns, "Cannot invert a non-square matrix");
    SmallMatrix<numberOfRows, numberOfColumns> result = (*this);
    
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int nPivot = numberOfRows;
    int iPivot[nPivot];
    
    int info = 0;
    
    dgetrf_(&nr, &nc, result.data(), &nr, iPivot, &info);
    
    int lwork = numberOfRows * numberOfColumns;
    SmallMatrix work;
    dgetri_(&nc, result.data(), &nc, iPivot, work.data(), &lwork, &info);
    
    return result;
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
template<unsigned int numberOfRightHandSideColumns>
void SmallMatrix<numberOfRows, numberOfColumns>::solve(SmallMatrix<numberOfRows, numberOfRightHandSideColumns>& B) const
{
    logger.assert_debug(numberOfRows == numberOfColumns, "can only solve for square matrixes");
    
    int n = numberOfRows;
    int nrhs = numberOfRightHandSideColumns;
    int info;
    
    int IPIV[numberOfRows];
    SmallMatrix<numberOfRows, numberOfColumns> matThis = *this;
    dgesv_(&n, &nrhs, matThis.data(), &n, IPIV, B.data(), &n, &info);
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
void SmallMatrix<numberOfRows, numberOfColumns>::solve(SmallVector<numberOfRows>& b) const
{
    logger.assert_debug(numberOfRows == numberOfColumns, "can only solve for square matrixes");
    
    int n = numberOfRows;
    int nrhs = 1;
    int info;
    
    int IPIV[numberOfRows];
    SmallMatrix matThis = *this;
    dgesv_(&n, &nrhs, matThis.data(), &n, IPIV, b.data(), &n, &info);
}
 
template<unsigned int numberOfRows, unsigned int numberOfColumns>
SmallVector<numberOfColumns> operator*(SmallVector<numberOfRows>& vec, SmallMatrix<numberOfRows, numberOfColumns>& mat)
{
    if (numberOfColumns == 0)
    {
        logger(WARN, "Trying to multiply a vector with a matrix without any columns.");
        return SmallVector<numberOfColumns>();
    }
    int nr = numberOfRows;
    int nc = numberOfColumns;
    
    int i_one = 1;
    double d_one = 1.0;
    double d_zero = 0.0;
    
    SmallVector<numberOfColumns> result;
    
    logger(DEBUG, "Matrix size: % x % \n Vector size: %", nr, nc, vec.size());
    
    dgemv_("T", &nr, &nc, &d_one, mat.data(), &nr, vec.data(), &i_one, &d_zero, result.data(), &i_one);
    return result;
}