#include <Core/Core.h>
#include <plugin/Eigen/Eigen.h>

 

using namespace Upp;

 

using namespace Eigen;

 

void NonLinearTests();

void FFTTests();

 

struct SerialTest {

    MatrixXd m;

    VectorXd v;

    SerialTest() : m(2, 2), v(3){}

    void Print() {

        Cout() << "\nHere is the matrix:\n" << m;

        Cout() << "\nHere is the vector:\n" << v;

    }

    void Serialize(Stream& stream) {

        ::Serialize(stream, m);

        ::Serialize(stream, v);

    }

    void Jsonize(JsonIO &jio) {

        jio("matrix", m)("vector", v);

    }

    void Xmlize(XmlIO &xml) {

        xml("matrix", m)("vector", v);

    }

};

        

CONSOLE_APP_MAIN

{

    StdLogSetup(LOG_COUT|LOG_FILE);

    

    UppLog() << "Eigen library demo";

    

    // https://eigen.tuxfamily.org/dox/group__TutorialMatrixClass.html

    UppLog() << "\n\nTutorial page 1 - The Matrix class";

    

    UppLog() << "\n\nCoefficient accessors";

    {

        MatrixXd m(2,2);

        m(0,0) = 3;

        m(1,0) = 2.5;

        m(0,1) = -1;

        m(1,1) = m(1,0) + m(0,1);

        UppLog() << "\nHere is the matrix m:\n" << m;

        

        VectorXd v(2);

        v(0) = 4;

        v(1) = v(0) - 1;

        UppLog() << "\nHere is the vector v:\n" << v;

    }

    UppLog() << "\n\nResizing";

    {

        MatrixXd m(2,5);

        m.resize(4,3);

        UppLog() << "\nThe matrix m is of size " << m.rows() << "x" << m.cols();

        UppLog() << "\nIt has " << m.size() << " coefficients";

 

        VectorXd v(2);

        v.resize(5);

        UppLog() << "\nThe vector v is of size " << v.size();

        UppLog() << "\nAs a matrix, v is of size " << v.rows() << "x" << v.cols();

    }

    UppLog() << "\n\nAssignment and resizing";

    {

        double _dat[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17};// Assignment from C vector

        VectorXd dat = Map<VectorXd>(_dat, sizeof(_dat)/sizeof(double));  

        UppLog() << "\nC array data is " << dat.transpose();

        

        const int dec = 5;

       VectorXd decimated = Map<VectorXd, 0, InnerStride<dec>>(dat.data(), 1+((dat.size()-1)/dec));

       UppLog() << "\nDecimated " << decimated.transpose();

        

        VectorXd even = Map<VectorXd, 0, InnerStride<2>>(dat.data(), (dat.size()+1)/2);

        UppLog() << "\nEven " << even.transpose();

        

        VectorXd odd = Map<VectorXd, 0, InnerStride<2>>(dat.data()+1, dat.size()/2);

        UppLog() << "\nOdd  " << odd.transpose();

    

        MatrixXf a(2,2);

        UppLog() << "\na is of size " << a.rows() << "x" << a.cols();

        MatrixXf b(3,3);

        a = b;

        UppLog() << "\na is now of size " << a.rows() << "x" << a.cols();

    }

    

    // https://eigen.tuxfamily.org/dox-devel/group__TutorialMatrixArithmetic.html

    UppLog() << "\n\nTutorial page 2 - Matrix and vector arithmetic";

    

    UppLog() << "\n\nAddition and subtraction";

    {

        Matrix2d a;

        a << 1, 2,

             3, 4;

        MatrixXd b(2,2);

        b << 2, 3,

             1, 4;

 

        UppLog() << "\na + b =\n" << a + b;

        UppLog() << "\na - b =\n" << a - b;

        UppLog() << "\nDoing a += b;";

        a += b;

        UppLog() << "\nNow a =\n" << a;

 

        Vector3d v(1,2,3);

        Vector3d w(1,0,0);

        UppLog() << "\n-v + w - v =\n" << -v + w - v;

    }

    UppLog() << "\n\nScalar multiplication and division";

    {

        Matrix2d a;

        a << 1, 2,

             3, 4;

        Vector3d v(1,2,3);

        UppLog() << "\na * 2.5 =\n" << a * 2.5;

        UppLog() << "\n0.1 * v =\n" << 0.1 * v;

        UppLog() << "\nDoing v *= 2;";

        v *= 2;

        UppLog() << "\nNow v =\n" << v;

    }

    UppLog() << "\n\nTransposition and conjugation";

    {

        MatrixXcf a = MatrixXcf::Random(2,2);

        UppLog() << "\nHere is the matrix a\n" << a;

        UppLog() << "\nHere is the matrix a^T\n" << a.transpose();

        UppLog() << "\nHere is the conjugate of a\n" << a.conjugate();

        UppLog() << "\nHere is the matrix a^*\n" << a.adjoint();

        

        VectorXd v(5);

        v << 1, 2, 3, 4, 5;

        UppLog() << "\n\nInitial vector  " << v.transpose();

        UppLog() <<   "\nReversed vector " << v.reverse().transpose();

    }

    UppLog() << "\n\nMatrix-matrix and matrix-vector multiplication";

    {

        Matrix2d mat;

        mat << 1, 2,

               3, 4;

        Vector2d u(-1,1), v(2,0);

        UppLog() << "\nHere is mat*mat:\n" << mat*mat;

        UppLog() << "\nHere is mat*u:\n" << mat*u;

        UppLog() << "\nHere is u^T*mat:\n" << u.transpose()*mat;

        UppLog() << "\nHere is u^T*v:\n" << u.transpose()*v;

        UppLog() << "\nHere is u*v^T:\n" << u*v.transpose();

        UppLog() << "\nLet's multiply mat by itself";

        mat *= mat;

        UppLog() << "\nNow mat is mat:\n" << mat;

    }

    UppLog() << "\n\nDot product and cross product";

    {

        Vector3d v(1,2,3);

          Vector3d w(0,1,2);

    

          UppLog() << "\nDot product: " << v.dot(w);

          double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar

          UppLog() << "\nDot product via a matrix product: " << dp;

          UppLog() << "\nCross product:\n" << v.cross(w);

    }

    UppLog() << "\n\nBasic arithmetic reduction operations";

    {

        Eigen::Matrix2d mat;

        mat << 1, 2,

               3, 4;

        UppLog() << "\nHere is mat.sum():       " << mat.sum();

        UppLog() << "\nHere is mat.prod():      " << mat.prod();

        UppLog() << "\nHere is mat.mean():      " << mat.mean();

        UppLog() << "\nHere is mat.minCoeff():  " << mat.minCoeff();

        UppLog() << "\nHere is mat.maxCoeff():  " << mat.maxCoeff();

        UppLog() << "\nHere is mat.trace():     " << mat.trace();

        

        Matrix3f m = Matrix3f::Random();

        ptrdiff_t i, j;

        float minOfM = m.minCoeff(&i, &j);

        UppLog() << "\nHere is the matrix m:\n" << m;

        UppLog() << "\nIts minimum coefficient (" << minOfM

               << ") is at position (" << i << "," << j << ")\n";

        

        RowVector4i v = RowVector4i::Random();

        ptrdiff_t maxOfV = v.maxCoeff(&i);

        UppLog() << "\nHere is the vector v: " << v;

        UppLog() << "\nIts maximum coefficient (" << maxOfV

               << ") is at position " << i;

    }

    

    // https://eigen.tuxfamily.org/dox/group__TutorialArrayClass.html

    UppLog() << "\n\nTutorial page 3 - The Array class and coefficient-wise operations ";

    

    UppLog() << "\n\nAccessing values inside an Array";

    {

        ArrayXXf  m(2,2);

        

        // assign some values coefficient by coefficient

        m(0,0) = 1.0; m(0,1) = 2.0;

        m(1,0) = 3.0; m(1,1) = m(0,1) + m(1,0);

        

        // print values to standard output

        UppLog() << "\n" << m;

        

        // using the comma-initializer is also allowed

        m << 1.0,2.0,

                3.0,4.0;

        

        // print values to standard output

        UppLog() << "\n" << m;

    }

    UppLog() << "\n\nAddition and subtraction";

    {

        ArrayXXf a(3,3);

        ArrayXXf b(3,3);

        a << 1,2,3,

                4,5,6,

                7,8,9;

        b << 1,2,3,

                1,2,3,

                1,2,3;

           

        // Adding two arrays

        UppLog() << "\na + b = " << "\n" << a + b;

        

        // Subtracting a scalar from an array

        UppLog() << "\na - 2 = " << "\n" << a - 2;

    }

    UppLog() << "\n\nArray multiplication";

    {

        ArrayXXf a(2,2);

        ArrayXXf b(2,2);

        a << 1,2,

                3,4;

        b << 5,6,

                7,8;

        UppLog() << "\na * b = " << "\n" << a * b;

    }

    UppLog() << "\n\nOther coefficient-wise operations";

    {

        ArrayXf a = ArrayXf::Random(5);

        a *= 2;

        UppLog() << "\na =" << "\n" << a;

        UppLog() << "\na.abs() =" << "\n" << a.abs();

        UppLog() << "\na.abs().sqrt() =" << "\n" << a.abs().sqrt();

        UppLog() << "\na.min(a.abs().sqrt()) =" << "\n" << a.min(a.abs().sqrt());

    }

    UppLog() << "\n\nConverting between array and matrix expressions";

    {

        MatrixXf m(2,2);

        MatrixXf n(2,2);

        m << 1,2,

                3,4;

        n << 5,6,

                7,8;

        

        UppLog() << "\n-- Matrix m*n: --" << "\n" << m * n;

        UppLog() << "\n-- Array m*n: --" << "\n" << m.array() * n.array();

        UppLog() << "\n-- With cwiseProduct: --" << "\n" << m.cwiseProduct(n);

        UppLog() << "\n-- Array m + 4: --" << "\n" << m.array() + 4;

    }

    {

        MatrixXf m(2,2);

        MatrixXf n(2,2);

        m << 1,2,

             3,4;

        n << 5,6,

             7,8;

        

        UppLog() << "\n-- Combination 1: --" << "\n" << (m.array() + 4).matrix() * m;

        UppLog() << "\n-- Combination 2: --" << "\n" << (m.array() * n.array()).matrix() * m;

    }

    

    // https://eigen.tuxfamily.org/dox/group__TutorialBlockOperations.html

    UppLog() << "\n\nTutorial page 4 - Block operations";

    

    UppLog() << "\n\nUsing block operations";

    {

        Eigen::MatrixXf m(4,4);

        m << 1, 2, 3, 4,

             5, 6, 7, 8,

             9,10,11,12,

                13,14,15,16;

        UppLog() << "\nBlock in the middle\n";

        UppLog() << m.block<2,2>(1,1);

        for (ptrdiff_t i = 1; i <= 3; ++i) {

            UppLog() << "\nBlock of size " << i << "x" << i << "\n";

            UppLog() << m.block(0, 0, i, i);

        }

    }

    {

        Array22d m;

        m << 1,2,

                3,4;

        Array44d a = Array44d::Constant(0.6);

        UppLog() << "\nHere is the array a:\n" << a;

        a.block<2,2>(1,1) = m;

        UppLog() << "\nHere is now a with m copied into its central 2x2 block:\n" << a;

        a.block(0,0,2,3) = a.block(2,1,2,3);

        UppLog() << "\nHere is now a with bottom-right 2x3 block copied into top-left 2x2 block:\n" << a;

    }

    UppLog() << "\n\nColumns and rows";

    {

        Eigen::MatrixXf m(3,3);

        m << 1,2,3,

             4,5,6,

                7,8,9;

        UppLog() << "\nHere is the matrix m:\n" << m;

        UppLog() << "\n2nd Row: " << m.row(1);

        m.col(2) += 3 * m.col(0);

        UppLog() << "\nAfter adding 3 times the first column into the third column, the matrix m is:\n";

        UppLog() << m;

    }

    UppLog() << "\n\nCorner-related operations";

    {

        Eigen::Matrix4f m;

        m << 1, 2, 3, 4,

                5, 6, 7, 8,

                9, 10,11,12,

                13,14,15,16;

        UppLog() << "\nm.leftCols(2) =\n" << m.leftCols(2);

        UppLog() << "\nm.bottomRows<2>() =\n" << m.bottomRows<2>();

        m.topLeftCorner(1,3) = m.bottomRightCorner(3,1).transpose();

        UppLog() << "\nAfter assignment, m = \n" << m;

    }

    UppLog() << "\n\nBlock operations for vectors";

    {

        Eigen::ArrayXf v(6);

        v << 1, 2, 3, 4, 5, 6;

        UppLog() << "\nv.head(3) =\n" << v.head(3);

        UppLog() << "\nv.tail<3>() = \n" << v.tail<3>();

        v.segment(1,4) *= 2;

        UppLog() << "\nafter 'v.segment(1,4) *= 2', v =\n" << v;

    }

    

    // https://eigen.tuxfamily.org/dox/group__TutorialAdvancedInitialization.html

    UppLog() << "\n\nTutorial page 5 - Advanced initialization";

 

    UppLog() << "\n\nThe comma initializer";

    {

        RowVectorXd vec1(3);

        vec1 << 1, 2, 3;

        UppLog() << "\nvec1 = " << vec1;

        

        RowVectorXd vec2(4);

        vec2 << 1, 4, 9, 16;

        UppLog() << "\nvec2 = " << vec2;

        

        RowVectorXd joined(7);

        joined << vec1, vec2;

        UppLog() << "\njoined = " << joined;

        

        MatrixXf matA(2, 2);

        matA << 1, 2, 3, 4;

        MatrixXf matB(4, 4);

        matB << matA, matA/10, matA/10, matA;

        UppLog() << matB;

        

        Matrix3f m;

        m.row(0) << 1, 2, 3;

        m.block(1,0,2,2) << 4, 5, 7, 8;

        m.col(2).tail(2) << 6, 9;                   

        UppLog() << m;

    }

    UppLog() << "\n\nSpecial matrices and arrays";

    {

        UppLog() << "\nA fixed-size array:\n";

        Array33f a1 = Array33f::Zero();

        UppLog() << a1 << "\n\n";

        

        UppLog() << "\nA one-dimensional dynamic-size array:\n";

        ArrayXf a2 = ArrayXf::Zero(3);

        UppLog() << a2 << "\n\n";

        

        UppLog() << "\nA two-dimensional dynamic-size array:\n";

        ArrayXXf a3 = ArrayXXf::Zero(3, 4);

        UppLog() << a3 << "\n";

        

        UppLog() << "\nA two-dimensional dynamic-size array set to 1.23:\n";

        MatrixXd a4 = MatrixXd::Constant(3, 4, 1.23);

        UppLog() << a4 << "\n";

        

        ArrayXXd table(10, 4);

        table.col(0) = ArrayXd::LinSpaced(10, 0, 90);

        table.col(1) = M_PI / 180 * table.col(0);

        table.col(2) = table.col(1).sin();

        table.col(3) = table.col(1).cos();

        UppLog() << "\n  Degrees   Radians      Sine    Cosine\n";

        UppLog() << table;

        

        const ptrdiff_t size = 6;

        MatrixXd mat1(size, size);

        mat1.topLeftCorner(size/2, size/2)     = MatrixXd::Zero(size/2, size/2);

        mat1.topRightCorner(size/2, size/2)    = MatrixXd::Identity(size/2, size/2);

        mat1.bottomLeftCorner(size/2, size/2)  = MatrixXd::Identity(size/2, size/2);

        mat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);

        UppLog() << "\n" << mat1;

        

        MatrixXd mat2(size, size);

        mat2.topLeftCorner(size/2, size/2).setZero();

        mat2.topRightCorner(size/2, size/2).setIdentity();

        mat2.bottomLeftCorner(size/2, size/2).setIdentity();

        mat2.bottomRightCorner(size/2, size/2).setZero();

        UppLog() << "\n" << mat2;

        

        MatrixXd mat3(size, size);

        mat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2),

                MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2);

        UppLog() << "\n" << mat3;

    }

    UppLog() << "\n\nUsage as temporary objects";

    {

        MatrixXd m = MatrixXd::Random(3,3);

        m = (m + MatrixXd::Constant(3,3,1.2)) * 50;

        UppLog() << "\nm =\n" << m;

        VectorXd v(3);

        v << 1, 2, 3;

        UppLog() << "\nm * v =\n" << m * v;

    }

    {

        MatrixXf mat = MatrixXf::Random(2, 3);

        UppLog() << mat;

        mat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat;

        UppLog() << mat;

    }

    

    // https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html

    UppLog() << "\n\nTutorial page 6 - Linear algebra and decompositions";

 

    UppLog() << "\n\nBasic linear solving    Ax = b";

    {

        Matrix3f A;

        Vector3f b;

        A << 1, 2, 3,  

             4, 5, 6,  

             7, 8,10;

        b << 3, 3, 4;

        UppLog() << "\nHere is the matrix A:\n" << A;

        UppLog() << "\nHere is the vector b:\n" << b;

        Vector3f x = A.colPivHouseholderQr().solve(b);

        UppLog() << "\nThe solution is:\n" << x;

    }

    {

        Matrix2f A, b;

        A << 2, -1, -1, 3;

        b << 1, 2, 3, 1;

        UppLog() << "\nHere is the matrix A:\n" << A;

        UppLog() << "\nHere is the right hand side b:\n" << b;

        Matrix2f x = A.ldlt().solve(b);

        UppLog() << "\nThe solution is:\n" << x;

    }

    UppLog() << "\n\nChecking if a solution really exists";

    {

        MatrixXd A = MatrixXd::Random(100,100);

        MatrixXd b = MatrixXd::Random(100,50);

        MatrixXd x = A.fullPivLu().solve(b);

        double relative_error = (A*x - b).norm() / b.norm(); // norm() is L2 norm

        UppLog() << "\nThe relative error is:\n" << relative_error;

    }

    UppLog() << "\n\nComputing eigenvalues and eigenvectors";

    {

        Matrix2f A;

        A << 1, 2, 2, 3;

        UppLog() << "\nHere is the matrix A:\n" << A;

        SelfAdjointEigenSolver<Matrix2f> eigensolver(A);

        UppLog() << "\nThe eigenvalues of A are:\n" << eigensolver.eigenvalues();

        UppLog() << "\nHere's a matrix whose columns are eigenvectors of A "

            << "corresponding to these eigenvalues:\n"

            << eigensolver.eigenvectors();

    }

    UppLog() << "\n\nComputing inverse and determinant";

    {

        Matrix3f A;

        A << 1, 2, 1,

             2, 1, 0,

            -1, 1, 2;

        UppLog() << "\nHere is the matrix A:\n" << A;

        UppLog() << "\nThe determinant of A is " << A.determinant();

        UppLog() << "\nThe inverse of A is:\n" << A.inverse();

    }

    UppLog() << "\n\nLeast squares solving";

    {

        MatrixXf A = MatrixXf::Random(5, 2);

        UppLog() << "\nHere is the matrix A:\n" << A;

        VectorXf b = VectorXf::Random(5);

        UppLog() << "\nHere is the right hand side b:\n" << b;

        UppLog() << "\nThe least-squares solution is:\n"

               << A.jacobiSvd(ComputeThinU | ComputeThinV).solve(b);

    }

    UppLog() << "\n\nSeparating the computation from the construction";

    {

        Matrix2f A, b;

        LLT<Matrix2f> llt;

        A << 2, -1, -1, 3;

        b << 1, 2, 3, 1;

        UppLog() << "\nHere is the matrix A:\n" << A;

        UppLog() << "\nHere is the right hand side b:\n" << b;

        UppLog() << "\nComputing LLT decomposition...";

        llt.compute(A);

        UppLog() << "\nThe solution is:\n" << llt.solve(b);

        A(1,1)++;

        UppLog() << "\nThe matrix A is now:\n" << A;

        UppLog() << "\nComputing LLT decomposition...";

        llt.compute(A);

        UppLog() << "\nThe solution is now:\n" << llt.solve(b);

    }

    UppLog() << "\n\nRank-revealing decompositions";

    {

        Matrix3f A;

        A << 1, 2, 5,

             2, 1, 4,

             3, 0, 3;

        UppLog() << "\nHere is the matrix A:\n" << A;

        FullPivLU<Matrix3f> lu_decomp(A);

        UppLog() << "\nThe rank of A is " << lu_decomp.rank();

        UppLog() << "\nHere is a matrix whose columns form a basis of the null-space of A:\n"

            << lu_decomp.kernel();

        UppLog() << "\nHere is a matrix whose columns form a basis of the column-space of A:\n"

            << lu_decomp.image(A); // yes, have to pass the original A

    }

    {

        Matrix2d A;

        A << 2, 1,

             2, 0.9999999999;

        FullPivLU<Matrix2d> lu(A);

        UppLog() << "\nBy default, the rank of A is found to be " << lu.rank();

        lu.setThreshold(1e-5);

        UppLog() << "\nWith threshold 1e-5, the rank of A is found to be " << lu.rank();

    }

    

    // https://eigen.tuxfamily.org/dox/group__TutorialReductionsVisitorsBroadcasting.html

    UppLog() << "\n\nTutorial page 7 - Reductions, visitors and broadcasting";

        

    UppLog() << "\n\nReductions";

    {

        Eigen::Matrix2d mat;

        mat << 1, 2,

               3, 4;

        UppLog() << "\nHere is mat.sum():       " << mat.sum();

        UppLog() << "\nHere is mat.prod():      " << mat.prod();

        UppLog() << "\nHere is mat.mean():      " << mat.mean();

        UppLog() << "\nHere is mat.minCoeff():  " << mat.minCoeff();

        UppLog() << "\nHere is mat.maxCoeff():  " << mat.maxCoeff();

        UppLog() << "\nHere is mat.trace():     " << mat.trace();

    }    

    UppLog() << "\n\nNorm computations";

    {

        VectorXf v(2);

        MatrixXf m(2,2), n(2,2);

        

        v << -1,

                 2;

        

        m << 1,-2,

            -3, 4;

        

        UppLog() << "\nv.squaredNorm() = " << v.squaredNorm();

        UppLog() << "\nv.norm() = " << v.norm();

        UppLog() << "\nv.lpNorm<1>() = " << v.lpNorm<1>();

        UppLog() << "\nv.lpNorm<Infinity>() = " << v.lpNorm<Infinity>();

        

        UppLog() << "\n";

        UppLog() << "\nm.squaredNorm() = " << m.squaredNorm();

        UppLog() << "\nm.norm() = " << m.norm();

        UppLog() << "\nm.lpNorm<1>() = " << m.lpNorm<1>();

        UppLog() << "\nm.lpNorm<Infinity>() = " << m.lpNorm<Infinity>();

    }

    UppLog() << "\n\nBoolean reductions";

    {

        ArrayXXf a(2,2);

        

        a << 1,2,

                3,4;

        

        UppLog() << "\n(a > 0).all()   = " << (a > 0).all();

        UppLog() << "\n(a > 0).any()   = " << (a > 0).any();

        UppLog() << "\n(a > 0).count() = " << (a > 0).count();

        UppLog() << "\n";

        UppLog() << "\n(a > 2).all()   = " << (a > 2).all();

        UppLog() << "\n(a > 2).any()   = " << (a > 2).any();

        UppLog() << "\n(a > 2).count() = " << (a > 2).count();

    }

    UppLog() << "\n\nVisitors";

    {

        Eigen::MatrixXf m(2,2);

        

        m << 1, 2,

                3, 4;

        

        //get location of maximum

        MatrixXf::Index maxRow, maxCol;

        float max = m.maxCoeff(&maxRow, &maxCol);

        

        //get location of minimum

        MatrixXf::Index minRow, minCol;

        float min = m.minCoeff(&minRow, &minCol);

        

        UppLog() << "\nMax: " << max <<  ", at: " << maxRow << "," << maxCol;

        UppLog() << "\nMin: " << min << ", at: " << minRow << "," << minCol;

    }

    UppLog() << "\n\nPartial reductions";

    {

        Eigen::MatrixXf mat(2,4);

        mat << 1, 2, 6, 9,

               3, 1, 7, 2;

        

        UppLog() << "\nColumn's maximum: \n" << mat.colwise().maxCoeff();

    }

    {

        Eigen::MatrixXf mat(2,4);

        mat << 1, 2, 6, 9,

               3, 1, 7, 2;

        

        UppLog() << "\nRow's maximum: \n" << mat.rowwise().maxCoeff();

    }

    UppLog() << "\n\nCombining partial reductions with other operations";

    {

        MatrixXf mat(2,4);

        mat << 1, 2, 6, 9,

               3, 1, 7, 2;

        

        MatrixXf::Index   maxIndex;

        float maxNorm = mat.colwise().sum().maxCoeff(&maxIndex);

        

        UppLog() << "\nMaximum sum at position " << maxIndex;

        

        UppLog() << "\nThe corresponding vector is: ";

        UppLog() << "\n" << mat.col( maxIndex );

        UppLog() << "\nAnd its sum is is: " << maxNorm;

    }

    UppLog() << "\n\nBroadcasting";

    {

        Eigen::MatrixXf mat(2,4);

        Eigen::VectorXf v(2);

        

        mat << 1, 2, 6, 9,

               3, 1, 7, 2;

             

        v << 0,

             1;

           

        //add v to each column of m

        mat.colwise() += v;

        

        UppLog() << "\nBroadcasting result: ";

        UppLog() << "\n" << mat;

    }

    {

        Eigen::MatrixXf mat(2,4);

        Eigen::VectorXf v(4);

        

        mat << 1, 2, 6, 9,

               3, 1, 7, 2;

             

        v << 0,1,2,3;

           

        //add v to each row of m

        mat.rowwise() += v.transpose();

        

        UppLog() << "\nBroadcasting result: ";

        UppLog() << "\n" << mat;

    }

    UppLog() << "\n\nCombining broadcasting with other operations";

    {

        Eigen::MatrixXf m(2,4);

        Eigen::VectorXf v(2);

        

        m << 1, 23, 6, 9,

                3, 11, 7, 2;

           

        v << 2,

             3;

        

        MatrixXf::Index index;

        // find nearest neighbour

        (m.colwise() - v).colwise().squaredNorm().minCoeff(&index);

        

        UppLog() << "\nNearest neighbour is column " << index << ":";

        UppLog() << "\n" << m.col(index);

    }

        

    UppLog() << "\n\nSerializing tests";

    {

        SerialTest serialTest, serialTest_j, serialTest_x, serialTest_s;

        serialTest.m << 1, 2,

                         4, 8;

        serialTest.v << 1, 2, 4;

 

        StoreAsJsonFile(serialTest, GetExeDirFile("Json.txt"));

        LoadFromJsonFile(serialTest_j, GetExeDirFile("Json.txt"));

        UppLog() << "\nJSON demo";

        serialTest_j.Print();

        

        StoreAsXMLFile(serialTest, "XMLdata", GetExeDirFile("Xml.txt"));

        LoadFromXMLFile(serialTest_x, GetExeDirFile("Xml.txt"));

        UppLog() << "\nXML demo";

        serialTest_x.Print();

        

        StoreToFile(serialTest, GetExeDirFile("Serial.dat"));

        LoadFromFile(serialTest_s, GetExeDirFile("Serial.dat"));

        UppLog() << "\nSerialization demo";

        serialTest_s.Print();

    }

    

    NonLinearTests();

    

    FFTTests();

    

    #ifdef flagDEBUG

    Cout() << "\nPress enter key to end";

    ReadStdIn();

    #endif   

}