void Camera::lockShader(gdl::AShader& shader, bool setColor, glm::vec4 const& color) const
{
if (setColor)
shader.setUniform(SHADER_CURRENT_COLOR, color);
shader.setUniform(SHADER_TRANSFORMATION_MATRIX, getTransformationMatrix());
shader.setUniform(SHADER_PROJECTION_MATRIX, getProjectionMatrix());
}
Mat RANSAC::compute(std::vector<Mat>& X, std::vector<Mat>& Y){
static int num_points = 5;
Mat T = Mat::eye(4, 4, CV_32FC1);
Mat best_T = Mat::eye(4, 4, CV_32FC1);
int max_inliers = 0;
std::srand(unsigned(std::time(0)));
std::vector<int> indices;
for (int i = 0; i < X.size(); ++i) indices.push_back(i);
for (int i = 0; i < m_max_iterations; i++){
//get random points
std::random_shuffle(indices.begin(), indices.end(), myrandom);
std::vector<Mat> new_X;
std::vector<Mat> new_Y;
for (int j = 0; j < num_points; ++j){
new_X.push_back(X[indices[j]]);
new_Y.push_back(Y[indices[j]]);
}
//compute T
T = getTransformationMatrix(new_X, new_Y);
int inliers = countInliers(T, X, Y, m_margin);
if (inliers > max_inliers){
best_T = T;
max_inliers = inliers;
}
}
static float percentage_outliers = 0;
percentage_outliers = (percentage_outliers + (X.size() - max_inliers)* 100.f / X.size()) / 2;
printf("Ouliers(Accumulated): %.2f%% Inliers: %i \n", percentage_outliers, max_inliers);
return best_T;
}
void Image::render() {
if(visible) {
if(texture) {
if(parent)
{
texture->render(this->parent->rec*getTransformationMatrix());
} else {
texture->render(getTransformationMatrix());
}
}
}
}
void Map::draw(){
GLuint obj_transform = gl::GetUniformLocation(_shader_program, "obj_transform");
glm::mat4 obj_transform_matrix = getTransformationMatrix();
gl::UseProgram(_shader_program);
gl::UniformMatrix4fv(obj_transform, 1, gl::FALSE_, &obj_transform_matrix[0][0]);
_cached_mesh->Render("all");
gl::UseProgram(0);
}
/*
* Compute power basis coefficients from B-spline basis coefficients
*/
DenseMatrix getPowerBasisCoefficients(DenseVector c, std::vector<unsigned int> degrees, std::vector<double> lb, std::vector<double> ub)
{
// Calculate tensor product transformation matrix T*lambda = c
DenseMatrix T = getTransformationMatrix(degrees, lb, ub);
// Compute power basis coefficients from B-spline basis coefficients
DenseMatrix L = T.colPivHouseholderQr().solve(c);
return L;
}
std::vector<double> Transformation::transformToNormal(double kalAngleX, double kalAngleY, double kalAngleZ, double gyroXrate, double gyroYrate, double gyroZrate, double dt) {
getTransformationMatrix(gyroXrate, gyroYrate, gyroZrate, dt);
std::vector<double> absoluteAcceleration(3);
for (int i = 0; i < 3; i++) {
absoluteAcceleration[i] = kalAngleX * matrix[0][i]
+ kalAngleY * matrix[1][i]
+ kalAngleZ * matrix[2][i];
}
cancelGravity(absoluteAcceleration);
return absoluteAcceleration;
}
Mat Transformation::getTransformationMatrix(vector<Point2f> corners, Size outputImageSize)
{
// Corners of the destination image
vector<Point2f> quad_pts;
quad_pts.push_back(Point2f(0, 0));
quad_pts.push_back(Point2f(outputImageSize.width, 0));
quad_pts.push_back(Point2f(outputImageSize.width, outputImageSize.height));
quad_pts.push_back(Point2f(0, outputImageSize.height));
return getTransformationMatrix(corners, quad_pts);
}
/*
* Calculate coefficients of B-spline representing a multivariate polynomial
*
* The polynomial f(x), with x in R^n, has m terms on the form
* f(x) = c(0)*x(0)^E(0,0)*x(1)^E(0,1)*...*x(n-1)^E(0,n-1)
* +c(1)*x(0)^E(1,0)*x(1)^E(1,1)*...*x(n-1)^E(1,n-1)
* +...
* +c(m-1)*x(0)^E(m-1,0)*x(1)^E(m-1,1)*...*x(n-1)^E(m-1,n-1)
* where c in R^m is a vector with coefficients for each of the m terms,
* and E in N^(mxn) is a matrix with the exponents of each variable in each of the m terms,
* e.g. the first row of E defines the first term with variable exponents E(0,0) to E(0,n-1).
*
* Note: E must be a matrix of nonnegative integers
*/
DenseMatrix getBSplineBasisCoefficients(DenseVector c, DenseMatrix E, std::vector<double> lb, std::vector<double> ub)
{
unsigned int dim = E.cols();
unsigned int terms = E.rows();
assert(dim >= 1); // At least one variable
assert(terms >= 1); // At least one term (assumes that c is a column vector)
assert(terms == c.rows());
assert(dim == lb.size());
assert(dim == ub.size());
// Get highest power of each variable
DenseVector powers = E.colwise().maxCoeff();
// Store in std vector
std::vector<unsigned int> powers2;
for (unsigned int i = 0; i < powers.size(); ++i)
powers2.push_back(powers(i));
// Calculate tensor product transformation matrix T
DenseMatrix T = getTransformationMatrix(powers2, lb, ub);
// Compute power basis coefficients (lambda vector)
SparseMatrix L(T.cols(),1);
L.setZero();
for (unsigned int i = 0; i < terms; i++)
{
SparseMatrix Li(1,1);
Li.insert(0,0) = 1;
for (unsigned int j = 0; j < dim; j++)
{
int e = E(i,j);
SparseVector li(powers(j)+1);
li.reserve(1);
li.insert(e) = 1;
SparseMatrix temp = Li;
Li = kroneckerProduct(temp, li);
}
L += c(i)*Li;
}
// Compute B-spline coefficients
DenseMatrix C = T*L;
return C;
}
int ParticleSystem::render()
{
Matrix4f modelMat; // final model matrix
//passing in the material information
if (materialUsed){
material.render(shader);
}
//passing the texture sample information
if (textureUsed){
texture.bindToTextureUnit();
texture.setTextureSampler(shader, "texture");
}
glDepthMask(GL_FALSE);
glEnable(GL_BLEND);
glBlendFunc(GL_ONE_MINUS_SRC_ALPHA, GL_ONE);
//glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
modelMat = getTransformationMatrix();
// move matrix to shader
shader.useProgram(1);
shader.copyMatrixToShader(modelMat, "model");
// bind the vao
glBindVertexArray(vao);
// draw using indices
glDrawArrays(GL_POINTS, 0, numIndices);
// unbind the vao
glBindVertexArray(0);
renderChildren(modelMat);
glDisable(GL_BLEND);
glDepthMask(GL_TRUE);
return 0;
}
void POP03::runProblem()
{
// Problem 3 (Nataraj)
// cout << "\n\nSolving problem P03..." << endl;
int dim = 4;
// x1,x2,l1,l2
std::vector<double> costs = {1, 0, 0, 0};
std::vector<double> lb = {-10,-10,0,-1000};
std::vector<double> ub = {10,10,100,1000};
std::vector<double> z0(dim,0);
std::vector<VariablePtr> vars;
for (int i = 0; i < dim; i++)
{
auto var = std::make_shared<Variable>(costs.at(i), lb.at(i), ub.at(i));
vars.push_back(var);
}
ConstraintSetPtr cs = std::make_shared<ConstraintSet>();
{ // x1^2 = l1
VariablePtr var = vars.at(0);
std::vector<double> thislb = {var->getLowerBound()};
std::vector<double> thisub = {var->getUpperBound()};
std::vector<unsigned int> deg = {2};
DenseVector c(3);
c.setZero();
c(0) = 0;
c(1) = 0;
c(2) = 1;
DenseMatrix T = getTransformationMatrix(deg, thislb, thisub);
DenseMatrix coeffs = T*c;
std::vector< std::vector<double> > knots = getRegularKnotVectors(deg, thislb, thisub);
BSpline bs(coeffs.transpose(), knots, deg);
std::vector<VariablePtr> cvars = {var, vars.at(2)};
ConstraintPtr cbs = std::make_shared<ConstraintBSpline>(cvars, bs, true);
cs->add(cbs);
}
{ // x1^3 = l1
VariablePtr var = vars.at(0);
std::vector<double> thislb = {var->getLowerBound()};
std::vector<double> thisub = {var->getUpperBound()};
std::vector<unsigned int> deg = {3};
DenseVector c(4); c.setZero();
c(0) = 0;
c(1) = 0;
c(2) = 0;
c(3) = 1;
DenseMatrix T = getTransformationMatrix(deg, thislb, thisub);
DenseMatrix coeffs = T*c;
std::vector< std::vector<double> > knots = getRegularKnotVectors(deg, thislb, thisub);
BSpline bs(coeffs.transpose(), knots, deg);
std::vector<VariablePtr> cvars = {var, vars.at(3)};
ConstraintPtr cbs = std::make_shared<ConstraintBSpline>(cvars, bs, true);
cs->add(cbs);
}
{ // x2 - l1 <= 0, x2 - l2 <= 0
DenseMatrix A(2,3);
A.setZero();
A(0,0) = -1; A(0,1) = 1;
A(1,0) = 1; A(1,1) = 2; A(1,2) = -1;
DenseVector b; b.setZero(2); b(1) = -1e-5;
std::vector<VariablePtr> cvars = {
vars.at(1),
vars.at(2),
vars.at(3)
};
ConstraintPtr lincon = std::make_shared<ConstraintLinear>(cvars, A, b, false);
cs->add(lincon);
}
BB::BranchAndBound bnb(cs);
Timer timer;
timer.start();
SolverResult res = bnb.optimize();
timer.stop();
cout << "Time: " << timer.getMilliSeconds() << " (ms)" << endl;
if (res.status == SolverStatus::OPTIMAL)
fopt_found = res.objectiveValue;
}
int main () {
//start logger system
assert(restart_gl_log());
hardware = {}; //must initialize window before starting gl stuff
//create our main window
assert(start_gl());
cursor = {};
cursor.vertexData = new GLfloat[36 + (3 * 6)];
setCursorCoordinates(cursor.vertexData, &cursor);
GLfloat*cursorColourData = new GLfloat[36 + (3 * 6)];
{
for (int i = 0; i < 12; ++i) {
cursorColourData[i * 3] = 0.5f;
cursorColourData[i * 3 + 1] = 0.0f;
cursorColourData[i * 3 + 2] = 0.5f;
};
for (int j = 12; j < 17; ++j) {
cursorColourData[j * 3] = 0.5f;
cursorColourData[j * 3 + 1] = 0.5f;
cursorColourData[j * 3 + 2] = 0.5f;
}
}
grid = {};
grid.numberOfLines = 100;
grid.heightValue = 0.0f;
GLfloat *gridColourData = new GLfloat[100 * 2 * 3];
{
int totalVerteces = 100 * 2;
for (int i = 0; i < totalVerteces; ++i) {
gridColourData[i * 3 ] = 0.5f;
gridColourData[i * 3 + 1] = 0.0f;
gridColourData[i * 3 + 2] = 0.5f;
}
}
//Create our gridPoints coordinates
GLfloat *gridVertexData = new GLfloat[grid.numberOfLines * 6];
{
for (int i = 0; i < grid.numberOfLines; ++i) {
//draw the lines parallel to the x axis
if (i < 50) {
gridVertexData[i * 6] = i - 25; //
gridVertexData[i * 6 + 1] = grid.heightValue;
gridVertexData[i * 6 + 2] = -100.f;
gridVertexData[i * 6 + 3] = i - 25; //
gridVertexData[i * 6 + 4] = grid.heightValue;
gridVertexData[i * 6 + 5] = 100.0f;
}
//draw the lines parallel to the z axis;
if (i >= 50) {
gridVertexData[i * 6] = -100.0f; //
gridVertexData[i * 6 + 1] = grid.heightValue;
gridVertexData[i * 6 + 2] = i - 50 - 25.0f;
gridVertexData[i * 6 + 3] = 100.0f; //
gridVertexData[i * 6 + 4] = grid.heightValue;
gridVertexData[i * 6 + 5] = i - 50 - 25.0f;
}
}
}
//create our wall items //2 triangles , 3 points each, 3 coordinate
Wall wall = {};
wall.scale = vec3(1.0f, 0, 1.0f);
wall.position = vec3(1.0f, 1.0f, 1.0f);
GLfloat *wallVertexData = new GLfloat[2 * 3 * 3];
{
wallVertexData[0] = wall.scale.v[0] * 0.5f;
wallVertexData[1] = 0.0f;
wallVertexData[2] = - wall.scale.v[2] * 0.5f;
wallVertexData[3] = -wall.scale.v[0] * 0.5f;
wallVertexData[4] = 0.0f;
wallVertexData[5] = + wall.scale.v[2] * 0.5f;
wallVertexData[6] = - wall.scale.v[0] * 0.5f;
wallVertexData[7] = 0.0f;
wallVertexData[8] = - wall.scale.v[2] * 0.5f;
wallVertexData[9] = + wall.scale.v[0] * 0.5f;
wallVertexData[10] = 0.0f;
wallVertexData[11] = - wall.scale.v[2] * 0.5f;
wallVertexData[12] = + wall.scale.v[0] * 0.5f;
wallVertexData[13] = 0.0f;
wallVertexData[14] = + wall.scale.v[2] * 0.5f;
wallVertexData[15] = - wall.scale.v[0] * 0.5f;
wallVertexData[16] = 0.0f;
wallVertexData[17] = + wall.scale.v[2] * 0.5f;
}
GLfloat *wallColourData = new GLfloat[2 * 3 * 3];
{
for (int i = 0; i < 6; ++i) {
wallColourData[i * 3 + 0] = 0.8f;
wallColourData[i * 3 + 1] = 0.8f;
wallColourData[i * 3 + 2] = 0.8f;
}
}
glfwSetCursorPosCallback(hardware.window,cursor_position_callback);
glfwSetInputMode(hardware.window, GLFW_CURSOR, GLFW_CURSOR_DISABLED);
glfwSetKeyCallback(hardware.window, key_callback);
glfwSetInputMode(hardware.window,GLFW_STICKY_KEYS, 1);
GLuint shader_program = create_programme_from_files(VERTEX_SHADER, FRAGMENT_SHADER);
/* get version info */
glEnable (GL_DEPTH_TEST); /* enable depth-testing */
glDepthFunc (GL_LESS);
createVertexBufferObject(&wallColourVbo, 3 * 3 * 2 * sizeof(GLfloat), wallColourData);
createVertexBufferObject(&wallVertexVbo, 3 * 3 * 2 * sizeof(GLfloat), wallVertexData);
createVertexBufferObject(&grid.vertexVbo, grid.numberOfLines * 6 * sizeof(GLfloat), gridVertexData);
createVertexBufferObject(&grid.colourVbo, grid.numberOfLines * 6 * sizeof(GLfloat), gridColourData);
createVertexBufferObject(&cursor.vertexVbo, (36 + (3 * 6)) * sizeof(GLfloat), cursor.vertexData);
createVertexBufferObject(&cursor.colourVbo, (36 + (3 * 6)) * sizeof(GLfloat), cursorColourData);
createVertexArrayObjet(&wallVao, &wallVertexVbo, 3);
createVertexArrayObjet(&grid.vao, &grid.vertexVbo, 3);
createVertexArrayObjet(&cursor.vao, &cursor.vertexVbo, 3);
cursor.colourAttributeIndex = 1;
grid.colourAttributeIndex = 1;
wallColourAttributeIndex = 1;
setColourMesh(&cursor.vao, &cursor.colourVbo, 3, &cursor.colourAttributeIndex);
setColourMesh(&grid.vao, &grid.colourVbo, 3, &grid.colourAttributeIndex);
setColourMesh(&wallVao, &wallColourVbo, 3, &wallColourAttributeIndex);
free(cursor.vertexData);
free(cursorColourData);
free(wallVertexData);
free(wallColourData);
// camera stuff
#define PI 3.14159265359
#define DEG_TO_RAD (2.0 * PI) / 360.0
float near = 0.1f;
float far = 100.0f;
double fov = 67.0f * DEG_TO_RAD;
float aspect = (float)hardware.vmode->width /(float)hardware.vmode->height;
// matrix components
double range = tan (fov * 0.5f) * near;
double Sx = (2.0f * near) / (range * aspect + range * aspect);
double Sy = near / range;
float Sz = -(far + near) / (far - near);
float Pz = -(2.0f * far * near) / (far - near);
GLfloat proj_mat[] = {
Sx, 0.0f, 0.0f, 0.0f,
0.0f, Sy, 0.0f, 0.0f,
0.0f, 0.0f, Sz, -1.0f,
0.0f, 0.0f, Pz, 0.0f
};
camera = {};
//create view matrix
camera.pos[0] = 0.0f; // don't start at zero, or we will be too close
camera.pos[1] = 0.0f; // don't start at zero, or we will be too close
camera.pos[2] = 0.5f; // don't start at zero, or we will be too close
camera.T = translate (identity_mat4 (), vec3 (-camera.pos[0], -camera.pos[1], -camera.pos[2]));
camera.Rpitch = rotate_y_deg (identity_mat4 (), -camera.yaw);
camera.Ryaw = rotate_y_deg (identity_mat4 (), -camera.yaw);
camera.viewMatrix = camera.Rpitch * camera.T;
cursor.yaw = cursor.roll = cursor.pitch += 0.0f;
calculateCursorRotations(&cursor);
//create the viewmatrix of the wall
wall.T= translate (identity_mat4 (), vec3 (2.0f, 2.0f, 2.0f));
glUseProgram(shader_program);
camera.view_mat_location = glGetUniformLocation(shader_program, "view");
camera.proj_mat_location = glGetUniformLocation(shader_program, "proj");
glUniformMatrix4fv(camera.view_mat_location, 1, GL_FALSE, camera.viewMatrix.m);
glUniformMatrix4fv(camera.proj_mat_location, 1, GL_FALSE, proj_mat);
glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
glEnable(GL_CULL_FACE);
glCullFace(GL_FRONT);
walls.push_back(wall);
while (!glfwWindowShouldClose (hardware.window)) {
updateMovement(&camera);
calculateViewMatrices(&camera, &cursor);
//set the new view matrix @ the shader level
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glViewport(0, 0, hardware.vmode->width, hardware.vmode->height);
glUseProgram(shader_program);
//draw the cursor
glUniformMatrix4fv(camera.view_mat_location, 1, GL_FALSE, cursor.viewMatrix.m);
glBindVertexArray(cursor.vao);
glDrawArrays(GL_TRIANGLES, 0, 18);
//draw the walls in place
//for each wall, draw it.
//get view matrix
for ( std::vector<Wall>::iterator it = walls.begin(); it != walls.end(); ++it) {
Wall tempWall = *it;
getTransformationMatrix(&tempWall);
glUniformMatrix4fv(camera.view_mat_location, 1, GL_FALSE, tempWall.transformationMatrix.m);
glBindVertexArray(wallVao);
glDrawArrays(GL_TRIANGLES, 0, 6);
}
//draw the grid
glUniformMatrix4fv(camera.view_mat_location, 1, GL_FALSE, camera.viewMatrix.m);
glBindVertexArray(grid.vao);
glDrawArrays(GL_LINES, 0, grid.numberOfLines* 2);
glfwPollEvents();
if (GLFW_PRESS == glfwGetKey(hardware.window, GLFW_KEY_ESCAPE)) {
glfwSetWindowShouldClose(hardware.window, 1);
}
glfwSwapBuffers(hardware.window);
}
/* close GL context and any other GLFW resources */
glfwTerminate();
return 0;
}
CVecR3 Local::convertToGlobal(const CVecR3& local) const {
MatR33 transformation = getTransformationMatrix();
CVecR3 global = transformation * local + origin_;
return global;
}
MatR33 Local::convertToGlobal(const MatR33& local) const {
MatR33 transformation = getTransformationMatrix();
MatR33 transformationTransposed = getTransformationMatrix().transpose();
MatR33 global = transformation * local * transformationTransposed;
return global;
}
void POP10::runProblem()
{
// Problem 10 (Nataraj), QP
// Five 1-D B-splines
cout << "\n\nSolving problem P10..." << endl;
int dim = 6+5; // x1,..,x5,y,l1,...,l5
// x1,x2,x3,x4,l1,l2,l3
std::vector<double> costs = {0,0,0,0,0,-10,1,1,1,1,1};
std::vector<double> lb = {0,0,0,0,0,0,-INF,-INF,-INF,-INF,-INF};
std::vector<double> ub = {1,1,1,1,1,INF,INF,INF,INF,INF,INF};
std::vector<double> z0(dim,0);
std::vector<VariablePtr> vars;
for (int i = 0; i < dim; i++)
{
auto var = std::make_shared<Variable>(costs.at(i), lb.at(i), ub.at(i));
vars.push_back(var);
}
ConstraintSetPtr cs = std::make_shared<ConstraintSet>();
std::vector<double> a = {-10.5,-7.5,-3.5,-2.5,-1.5};
// Add one B-spline for each variable
for (int i = 0; i < 5; i++)
{
std::vector<VariablePtr> cvars = {
vars.at(i),
vars.at(i+6)
};
std::vector<double> thislb = {cvars.at(0)->getLowerBound()};
std::vector<double> thisub = {cvars.at(0)->getUpperBound()};
std::vector<unsigned int> deg = {2};
// Poly coeffs
DenseVector c(3);
c.setZero();
c(0) = 0;
c(1) = a.at(i);
c(2) = -0.5; // -50 or -0.5 (Floudas' problem has -50)
DenseMatrix T = getTransformationMatrix(deg, thislb, thisub);
DenseMatrix coeffs = T*c;
std::vector< std::vector<double> > knots = getRegularKnotVectors(deg, thislb, thisub);
BSpline bs(coeffs.transpose(), knots, deg);
ConstraintPtr cbs = std::make_shared<ConstraintBSpline>(cvars, bs, true);
cs->add(cbs);
}
{ // Linear constraints
std::vector<VariablePtr> cvars = {
vars.at(0),
vars.at(1),
vars.at(2),
vars.at(3),
vars.at(4),
vars.at(5)
};
DenseMatrix A = DenseMatrix::Zero(2,6);
A(0,0) = 6; A(0,1) = 3; A(0,2) = 3; A(0,3) = 2; A(0,4) = 1;
A(1,0) = 10; A(1,2) = 10; A(1,5) = 1;
DenseVector b;
b.setZero(2);
b(0) = 6.5;
b(1) = 20;
ConstraintPtr lincon = std::make_shared<ConstraintLinear>(cvars, A, b, false);
cs->add(lincon);
}
BB::BranchAndBound bnb(cs);
Timer timer;
timer.start();
SolverResult res = bnb.optimize();
timer.stop();
cout << "Time: " << timer.getMilliSeconds() << " (ms)" << endl;
cout << "Time: " << timer.getMicroSeconds() << " (us)" << endl;
if (res.status == SolverStatus::OPTIMAL)
fopt_found = res.objectiveValue;
}
void POP01::runProblem()
{
// Problem 1 (Nataraj)
// cout << "\n\nSolving problem P01..." << endl;
int dim = 4;
// x1,x2,l1,l2
std::vector<double> costs = {-1, -1, 0, 0};
std::vector<double> lb = {0,0,-INF,-INF};
std::vector<double> ub = {3,4,INF,INF};
//std::vector<double> z0(dim,0);
std::vector<VariablePtr> vars;
for (int i = 0; i < dim; i++)
{
auto var = std::make_shared<Variable>(costs.at(i), lb.at(i), ub.at(i));
vars.push_back(var);
}
ConstraintSetPtr cs = std::make_shared<ConstraintSet>();
{ // 2*x1^4 - 8*x1^3 + 8*x1^2 + 2
std::vector<VariablePtr> cvars = {vars.at(0), vars.at(2)};
std::vector<double> thislb = {cvars.at(0)->getLowerBound()};
std::vector<double> thisub = {cvars.at(0)->getUpperBound()};
std::vector<unsigned int> deg = {4};
DenseVector c(5);
c.setZero();
c(0) = 2;
c(1) = 0;
c(2) = 8;
c(3) = -8;
c(4) = 2;
DenseMatrix T = getTransformationMatrix(deg, thislb, thisub);
DenseMatrix coeffs = T*c;
std::vector< std::vector<double> > knots = getRegularKnotVectors(deg, thislb, thisub);
BSpline bs(coeffs, knots, deg);
ConstraintPtr cbs = std::make_shared<ConstraintBSpline>(cvars, bs, true);
cs->add(cbs);
}
{ // 4*x1^4 - 32*x1^3 + 88*x1^2 - 96*x1 + 36
std::vector<VariablePtr> cvars = {vars.at(0), vars.at(3)};
std::vector<double> thislb = {cvars.at(0)->getLowerBound()};
std::vector<double> thisub = {cvars.at(0)->getUpperBound()};
std::vector<unsigned int> deg = {4};
DenseVector c(5); c.setZero();
c(0) = 36;
c(1) = -96;
c(2) = 88;
c(3) = -32;
c(4) = 4;
DenseMatrix T = getTransformationMatrix(deg, thislb, thisub);
DenseMatrix coeffs = T*c;
std::vector< std::vector<double> > knots = getRegularKnotVectors(deg, thislb, thisub);
BSpline bs(coeffs, knots, deg);
ConstraintPtr cbs = std::make_shared<ConstraintBSpline>(cvars, bs, true);
cs->add(cbs);
}
{ // x2 - l1 <= 0, x2 - l2 <= 0
std::vector<VariablePtr> cvars = {
vars.at(1),
vars.at(2),
vars.at(3)
};
DenseMatrix A(2,3);
A.setZero();
A(0,0) = 1; A(0,1) = -1;
A(1,0) = 1; A(1,2) = -1;
DenseVector b; b.setZero(2);
ConstraintPtr lincon = std::make_shared<ConstraintLinear>(cvars, A, b, false);
cs->add(lincon);
}
BB::BranchAndBound solver(cs);
Timer timer;
timer.start();
SolverResult res = solver.optimize();
timer.stop();
cout << res << endl;
cout << res.primalVariables << endl;
cout << "Time: " << timer.getMilliSeconds() << " (ms)" << endl;
if (res.status == SolverStatus::OPTIMAL)
fopt_found = res.objectiveValue;
}