matrix.h

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#ifndef GEOGRAM_BASIC_MATRIX
#define GEOGRAM_BASIC_MATRIX
 
#include <geogram/basic/common.h>
#include <geogram/basic/vecg.h>
#include <initializer_list>
 
namespace GEO {
 
    /************************************************************************/
 
 
    template <index_t DIM, class FT>
    class Matrix {
    public:
        typedef Matrix<DIM, FT> matrix_type;
 
        typedef FT value_type;
 
        static constexpr index_t dim = DIM;
 
        inline Matrix() {
            load_identity();
        }
 
        explicit Matrix(const FT* vals) {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] = *vals;
                    ++vals;
                }
            }
        }
 
        Matrix(const std::initializer_list< std::initializer_list<FT> >& Mi) {
            index_t i = 0;
            for(auto& it: Mi) {
                index_t j = 0;
                for(auto& jt: it) {
                    geo_debug_assert(i < DIM);
                    geo_debug_assert(j < DIM);
                    coeff_[i][j] = jt;
                    ++j;
                }
                ++i;
            }
        }
 
 
        inline index_t dimension() const {
            return DIM;
        }
 
        inline void load_zero() {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] = FT(0);
                }
            }
        }
 
        inline void load_identity() {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] = (i == j) ? FT(1) : FT(0);
                }
            }
        }
 
        inline bool is_identity() const {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    FT rhs = ((i == j) ? FT(1) : FT(0));
                    if(coeff_[i][j] != rhs) {
                        return false;
                    }
                }
            }
            return true;
        }
 
        inline FT& operator() (index_t i, index_t j) {
            geo_debug_assert(i < DIM);
            geo_debug_assert(j < DIM);
            return coeff_[i][j];
        }
 
        inline const FT& operator() (index_t i, index_t j) const {
            geo_debug_assert(i < DIM);
            geo_debug_assert(j < DIM);
            return coeff_[i][j];
        }
 
        inline matrix_type& operator+= (const matrix_type& m) {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] += m.coeff_[i][j];
                }
            }
            return *this;
        }
 
        inline matrix_type& operator-= (const matrix_type& m) {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] -= m.coeff_[i][j];
                }
            }
            return *this;
        }
 
        inline matrix_type& operator*= (FT val) {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] *= val;
                }
            }
            return *this;
        }
 
        inline matrix_type& operator/= (FT val) {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    coeff_[i][j] /= val;
                }
            }
            return *this;
        }
 
        inline matrix_type operator+ (const matrix_type& m) const {
            matrix_type result = *this;
            result += m;
            return result;
        }
 
        inline matrix_type operator- (const matrix_type& m) const {
            matrix_type result = *this;
            result -= m;
            return result;
        }
 
        inline matrix_type operator* (FT val) const {
            matrix_type result = *this;
            result *= val;
            return result;
        }
 
        inline matrix_type operator/ (FT val) const {
            matrix_type result = *this;
            result /= val;
            return result;
        }
 
        matrix_type operator* (const matrix_type& m) const {
            matrix_type result;
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    result.coeff_[i][j] = FT(0);
                    for(index_t k = 0; k < DIM; k++) {
                        result.coeff_[i][j] += coeff_[i][k] * m.coeff_[k][j];
                    }
                }
            }
            return result;
        }
 
        matrix_type inverse() const {
            matrix_type result;
            bool invertible = compute_inverse(result);
            geo_assert(invertible);
            return result;
        }
 
 
        bool compute_inverse(matrix_type& result) const {
            FT val=FT(0.0), val2=FT(0.0);
            matrix_type tmp = (*this);
 
            result.load_identity();
 
            for(index_t i = 0; i != DIM; i++) {
                val = tmp(i, i);                     /* find pivot */
                index_t ind = i;
                for(index_t j = i + 1; j != DIM; j++) {
                    if(fabs(tmp(j, i)) > fabs(val)) {
                        ind = j;
                        val = tmp(j, i);
                    }
                }
 
                if(ind != i) {
                    for(index_t j = 0; j != DIM; j++) {
                        val2 = result(i, j);
                        result(i, j) = result(ind, j);
                        result(ind, j) = val2;           /* swap columns */
                        val2 = tmp(i, j);
                        tmp(i, j) = tmp(ind, j);
                        tmp(ind, j) = val2;
                    }
                }
 
                if(val == 0.0) {
                    return false;
                }
 
                for(index_t j = 0; j != DIM; j++) {
                    tmp(i, j) /= val;
                    result(i, j) /= val;
                }
 
                for(index_t j = 0; j != DIM; j++) {
                    if(j == i) {
                        continue;                       /* eliminate column */
                    }
                    val = tmp(j, i);
                    for(index_t k = 0; k != DIM; k++) {
                        tmp(j, k) -= tmp(i, k) * val;
                        result(j, k) -= result(i, k) * val;
                    }
                }
            }
 
            return true;
        }
 
        matrix_type transpose() const {
            matrix_type result;
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j < DIM; j++) {
                    result(i, j) = (* this)(j, i);
                }
            }
            return result;
        }
 
        inline const FT* data() const {
            return &(coeff_[0][0]);
        }
 
        inline FT* data() {
            return &(coeff_[0][0]);
        }
 
        void get_lower_triangle(FT* store) const {
            for(index_t i = 0; i < DIM; i++) {
                for(index_t j = 0; j <= i; j++) {
                    *store++ = coeff_[i][j];
                }
            }
        }
 
    private:
        FT coeff_[DIM][DIM];
    };
 
    /************************************************************************/
 
    template <index_t DIM, class FT>
    inline std::ostream& operator<< (
        std::ostream& output, const Matrix<DIM, FT>& m
    ) {
        const char* sep = "";
        for(index_t i = 0; i < DIM; i++) {
            for(index_t j = 0; j < DIM; j++) {
                output << sep << m(i, j);
                sep = " ";
            }
        }
        return output;
    }
 
    template <index_t DIM, class FT>
    inline std::istream& operator>> (
        std::istream& input, Matrix<DIM, FT>& m
    ) {
        for(index_t i = 0; i < DIM; i++) {
            for(index_t j = 0; j < DIM; j++) {
                input >> m(i, j);
            }
        }
        return input;
    }
 
    /************************************************************************/
 
    template <index_t DIM, class FT> inline
    void mult(const Matrix<DIM, FT>& M, const FT* x, FT* y) {
        for(index_t i = 0; i < DIM; i++) {
            y[i] = 0;
            for(index_t j = 0; j < DIM; j++) {
                y[i] += M(i, j) * x[j];
            }
        }
    }
 
    /************************************************************************/
 
    template <index_t DIM, class FT> inline
    vecng<DIM,FT> operator*(
        const Matrix<DIM, FT>& M, const vecng<DIM,FT>& x
    ) {
        vecng<DIM,FT> y;
        for(index_t i = 0; i < DIM; i++) {
            y[i] = 0;
            for(index_t j = 0; j < DIM; j++) {
                y[i] += M(i, j) * x[j];
            }
        }
        return y;
    }
 
    template <index_t DIM, class FT> inline
    vecng<DIM,FT> mult(
        const Matrix<DIM, FT>& M, const vecng<DIM,FT>& x
    ) {
        vecng<DIM,FT> y;
        for(index_t i = 0; i < DIM; i++) {
            y[i] = 0;
            for(index_t j = 0; j < DIM; j++) {
                y[i] += M(i, j) * x[j];
            }
        }
        return y;
    }
 
    /************************************************************************/
 
}
 
#endif