Eigen demo
Eigen package demo
eigen_demo.cpp
#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
}
fft.cpp
#include <Core/Core.h>
#include <plugin/Eigen/Eigen.h>
using namespace Upp;
#ifdef USE_FFTW
#include <fftw3.h>
#endif
using namespace Eigen;
void FFTTests()
{
UppLog() << "\nFFT sample\nGets the FFT of equation"
"\n f(t) = 2*sin(2*PI*t/50 - PI/3) + 5*sin(2*PI*t/30 - PI/2) + 30*sin(2*PI*t/10 - PI/5)"
"\nsampled with a frequency of 14 samples/second";
int numData = 8000;
double samplingFrecuency = 14;
// Filling the data series
VectorXd timebuf(numData);
{
double t = 0;
for (int i = 0; i < numData; ++i, t = i/samplingFrecuency)
timebuf[i] = 2*sin(2*M_PI*t/50 - M_PI/3) + 5*sin(2*M_PI*t/30 - M_PI/2) + 30*sin(2*M_PI*t/10 - M_PI/5);
}
// FFT
VectorXcd freqbuf;
FFT<double> fft;
fft.SetFlag(fft.HalfSpectrum);
fft.fwd(freqbuf, timebuf);
// Filter the FFT. Frequencies between 1/25 and 1/35 Hz are removed
// Original FFT is not changed for saving it later
VectorXcd freqbuf2(freqbuf.size());
{
for (int i = 0; i < freqbuf.size(); ++i) {
double freq = i*samplingFrecuency/numData;
double T = 1/freq;
if (T > 25 && T < 35)
freqbuf2[i] = 0;
else
freqbuf2[i] = freqbuf[i];
}
}
// Inverse filtered FFT to get filtered series
VectorXd timebuf2(numData);
fft.inv(timebuf2, freqbuf2);
String csvSep = ";";
// Saving original and filtered FFT
{
String str;
str << "Frec" << csvSep << "T" << csvSep << "fft" << csvSep << "Filtered fft";
for (int i = 0; i < freqbuf.size(); ++i) {
double freq = i*samplingFrecuency/numData;
double T = 1/freq;
str << "\n" << freq << csvSep << (freq > 0 ? FormatDouble(T) : "") << csvSep
<< 2*std::abs(freqbuf[i])/numData << csvSep
<< 2*std::abs(freqbuf2[i])/numData;
}
String fftFileName = GetExeDirFile("fft.csv");
UppLog() << "\nFFT saved in '" << fftFileName << "'";
VERIFY(SaveFile(fftFileName, str));
}
// Saving original and filtered series
{
String str;
str << "Time" << csvSep << "Data" << csvSep << "Filtered data";
double t = 0;
for (int i = 0; i < numData; ++i, t = i*1/samplingFrecuency)
str << "\n" << t << csvSep << timebuf[i] << csvSep << timebuf2[i];;
String dataFileName = GetExeDirFile("data.csv");
UppLog() << "\nSource data saved in '" << dataFileName << "'";
VERIFY(SaveFile(dataFileName, str));
}
}
non-linear.cpp
#include <Core/Core.h>
#include <plugin/Eigen/Eigen.h>
using namespace Upp;
using namespace Eigen;
#define VerifyIsApprox(a, b) (fabs(a-(b)) < 0.0001)
struct Eckerle4_functor : NonLinearOptimizationFunctor<double> {
Eckerle4_functor() : NonLinearOptimizationFunctor(3, 35) {}
static const double x[35];
static const double y[35];
int operator()(const VectorXd &b, VectorXd &fvec) const {
ASSERT(b.size() == unknowns);
ASSERT(fvec.size() == datasetLen);
for(int i = 0; i < 35; i++)
fvec[i] = b[0]/b[1] * exp(-0.5*(x[i]-b[2])*(x[i]-b[2])/(b[1]*b[1])) - y[i];
return 0;
}
};
const double Eckerle4_functor::x[35] = {400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};
const double Eckerle4_functor::y[35] = {0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710 };
struct Thurber_functor : NonLinearOptimizationFunctor<double> {
static VectorXd _x, _y;
Thurber_functor() : NonLinearOptimizationFunctor() {
double x[] = {-3.067, -2.981, -2.921, -2.912, -2.840, -2.797, -2.702, -2.699, -2.633, -2.481, -2.363, -2.322, -1.501, -1.460, -1.274, -1.212, -1.100, -1.046, -0.915, -0.714, -0.566, -0.545, -0.400, -0.309, -0.109, -0.103, 0.010, 0.119, 0.377, 0.790, 0.963, 1.006, 1.115, 1.572, 1.841, 2.047, 2.200};
double y[] = {80.574, 84.248, 87.264, 87.195, 89.076, 89.608, 89.868, 90.101, 92.405, 95.854, 100.696, 101.060, 401.672, 390.724, 567.534, 635.316, 733.054, 759.087, 894.206, 990.785, 1090.109, 1080.914, 1122.643, 1178.351, 1260.531, 1273.514, 1288.339, 1327.543, 1353.863, 1414.509, 1425.208, 1421.384, 1442.962, 1464.350, 1468.705, 1447.894, 1457.628};
_x = Map<VectorXd>(x, sizeof(x)/sizeof(double));
_y = Map<VectorXd>(y, sizeof(y)/sizeof(double));
unknowns = 7;
datasetLen = _x.size();
}
int operator()(const VectorXd &b, VectorXd &fvec) const {
ASSERT(b.size() == unknowns);
ASSERT(fvec.size() == datasetLen);
for(int i = 0; i < datasetLen; i++) {
double x = _x[i], xx = x*x, xxx = xx*x;
fvec[i] = (b[0] + b[1]*x + b[2]*xx + b[3]*xxx)/(1. + b[4]*x + b[5]*xx + b[6]*xxx) - _y[i];
}
return 0;
}
};
VectorXd Thurber_functor::_x, Thurber_functor::_y;
void NonLinearOptimization() {
UppLog() << "\n\nNon linear equations optimization using Levenberg Marquardt based on Minpack\n"
"(Given a set of non linear equations and a set of data longer than the equations, "
"the program finds the equation coefficients that better fit with the equations)";
{
UppLog() << "\n\nEckerle4 equation\nSee: http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml";
VectorXd x(3);
x << 1., 10., 500.; // Initial values
Eckerle4_functor functor;
NumericalDiff<Eckerle4_functor> numDiff(functor);
LevenbergMarquardt<NumericalDiff<Eckerle4_functor> > lm(numDiff);
int ret = lm.minimize(x);
if (ret == LevenbergMarquardtSpace::ImproperInputParameters ||
ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation)
UppLog() << "\nNo convergence!: " << ret;
else {
if (VerifyIsApprox(lm.fvec.squaredNorm(), 1.4635887487E-03))
UppLog() << "\nNorm^2 is right";
else
UppLog() << "\nNorm^2 is NOT right";
if (VerifyIsApprox(x[0], 1.5543827178) &&
VerifyIsApprox(x[1], 4.0888321754) &&
VerifyIsApprox(x[2], 4.5154121844E+02))
UppLog() << "\nNon-linear function optimization is right!";
else
UppLog() << "\nNon-linear function optimization is NOT right!";
}
}
{
UppLog() << "\n\nThis is a simpler way, using NonLinearOptimization()";
double x[] = {400.0, 405.0, 410.0, 415.0, 420.0, 425.0, 430.0, 435.0, 436.5, 438.0, 439.5, 441.0, 442.5, 444.0, 445.5, 447.0, 448.5, 450.0, 451.5, 453.0, 454.5, 456.0, 457.5, 459.0, 460.5, 462.0, 463.5, 465.0, 470.0, 475.0, 480.0, 485.0, 490.0, 495.0, 500.0};
double f[] = {0.0001575, 0.0001699, 0.0002350, 0.0003102, 0.0004917, 0.0008710, 0.0017418, 0.0046400, 0.0065895, 0.0097302, 0.0149002, 0.0237310, 0.0401683, 0.0712559, 0.1264458, 0.2073413, 0.2902366, 0.3445623, 0.3698049, 0.3668534, 0.3106727, 0.2078154, 0.1164354, 0.0616764, 0.0337200, 0.0194023, 0.0117831, 0.0074357, 0.0022732, 0.0008800, 0.0004579, 0.0002345, 0.0001586, 0.0001143, 0.0000710};
int num = sizeof(x)/sizeof(double);
VectorXd y(3);
y << 1., 10., 500.;
VERIFY(NonLinearOptimization(y, num, [&](const VectorXd &y, VectorXd &residual)->int {
for(int i = 0; i < num; i++)
residual[i] = y[0]/y[1] * exp(-0.5*(x[i]-y[2])*(x[i]-y[2])/(y[1]*y[1])) - f[i];
return 0;
}));
VERIFY(VerifyIsApprox(y[0], 1.5543827178) &&
VerifyIsApprox(y[1], 4.0888321754) &&
VerifyIsApprox(y[2], 4.5154121844E+02));
}
{
UppLog() << "\n\nThurber equation\nSee: http://www.itl.nist.gov/div898/strd/nls/data/thurber.shtml\n";
VectorXd x(7);
x << 1000, 1000, 400, 40, 0.7, 0.3, 0.0; // Initial values
Thurber_functor functor; // Vars and equations known at run time
NumericalDiff<Thurber_functor> numDiff(functor);
LevenbergMarquardt<NumericalDiff<Thurber_functor> > lm(numDiff);
lm.parameters.ftol = 1.E4*NumTraits<double>::epsilon();
lm.parameters.xtol = 1.E4*NumTraits<double>::epsilon();
int ret = lm.minimize(x);
VERIFY(!(ret == LevenbergMarquardtSpace::ImproperInputParameters ||
ret == LevenbergMarquardtSpace::TooManyFunctionEvaluation));
VERIFY(VerifyIsApprox(lm.fvec.squaredNorm(), 5.64270823E+03));
VERIFY(VerifyIsApprox(x[0], 1.2881396E+03) &&
VerifyIsApprox(x[1], 1.4910792E+03) &&
VerifyIsApprox(x[2], 5.8323836E+02) &&
VerifyIsApprox(x[3], 7.5416644E+01) &&
VerifyIsApprox(x[4], 9.6629502E-01) &&
VerifyIsApprox(x[5], 3.9797285E-01) &&
VerifyIsApprox(x[6], 4.9727297E-02));
}
}
struct Hybrd_functor : NonLinearOptimizationFunctor<double>
{
Hybrd_functor() : NonLinearOptimizationFunctor<double>(9, 9) {}
int operator()(const VectorXd &x, VectorXd &fvec) const {
double temp, temp1, temp2;
const ptrdiff_t n = x.size();
ASSERT(fvec.size() == n);
for (ptrdiff_t k = 0; k < n; k++) {
temp = (3. - 2.*x[k])*x[k];
temp1 = 0.;
if (k)
temp1 = x[k-1];
temp2 = 0.;
if (k != n-1)
temp2 = x[k+1];
fvec[k] = temp - temp1 - 2.*temp2 + 1.;
}
return 0;
}
};
void NonLinearSolving() {
UppLog() << "\n\nNon linear equation solving using the Powell hybrid method (\"dogleg\") based on Minpack. "
<< "(Finds a zero of a system of n nonlinear equations in n variables)";
const int n = 9;
VectorXd x;
x.setConstant(n, -1.); // Initial values
Hybrd_functor functor;
HybridNonLinearSolver<Hybrd_functor> solver(functor);
int ret = solver.solveNumericalDiff(x);
VERIFY(!(ret == HybridNonLinearSolverSpace::ImproperInputParameters ||
ret == HybridNonLinearSolverSpace::TooManyFunctionEvaluation ||
ret == HybridNonLinearSolverSpace::NotMakingProgressJacobian ||
ret == HybridNonLinearSolverSpace::NotMakingProgressIterations));
VERIFY(VerifyIsApprox(solver.fvec.blueNorm(), 1.192636e-08));
VERIFY(VerifyIsApprox(x[0], -0.5706545) &&
VerifyIsApprox(x[1], -0.6816283) &&
VerifyIsApprox(x[2], -0.7017325) &&
VerifyIsApprox(x[3], -0.7042129) &&
VerifyIsApprox(x[4], -0.701369) &&
VerifyIsApprox(x[5], -0.6918656) &&
VerifyIsApprox(x[6], -0.665792) &&
VerifyIsApprox(x[7], -0.5960342) &&
VerifyIsApprox(x[8], -0.4164121));
UppLog() << "\n\nThis is a simpler way, using SolveNonLinearEquations()";
x.setConstant(n, -1.); // Initial values
VERIFY(SolveNonLinearEquations(x, [&](const VectorXd &x, VectorXd &residual)->int {
const ptrdiff_t n = x.size();
ASSERT(residual.size() == n);
for (ptrdiff_t k = 0; k < n; k++) {
double temp1 = 0.;
if (k)
temp1 = x[k-1];
double temp2 = 0.;
if (k != n-1)
temp2 = x[k+1];
residual[k] = (3. - 2.*x[k])*x[k] - temp1 - 2.*temp2 + 1.;
}
return 0;
})); // No convergence!
VERIFY(VerifyIsApprox(x[0], -0.5706545) &&
VerifyIsApprox(x[1], -0.6816283) &&
VerifyIsApprox(x[2], -0.7017325) &&
VerifyIsApprox(x[3], -0.7042129) &&
VerifyIsApprox(x[4], -0.701369) &&
VerifyIsApprox(x[5], -0.6918656) &&
VerifyIsApprox(x[6], -0.665792) &&
VerifyIsApprox(x[7], -0.5960342) &&
VerifyIsApprox(x[8], -0.4164121));
}
void NonLinearTests() {
NonLinearSolving();
NonLinearOptimization();
}
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