int main()
{
printf("\n Dla równania f(x) = 0, gdzie f(x) = 3x + 2 - e^x, wczytać a, b należące");
printf("\n do zbioru liczb rzeczywistych takie, by a < b oraz f(a) * f(b) < 0. Następnie,");
printf("\n dopóki \"użytownik się nie znudzi\", wczytywać wartości 0 < E < 1 i metodą");
printf("\n połowienia na [a, b] przybliżyc z dokładnością E rozwiązanie tego równania.");
printf("\n Rozwiązanie to przybliżyc również metodą Newtona z x_0 = a, przy czym, x_k");
printf("\n będzie dobrym przybliżeniem, gdy |x_k - x_(k - 1)| <= E. Porównać ilość");
printf("\n kroków wykonanych metodą połowienia i metodą Newtona.\n");
double a, b;
printf("\n Podaj a należące do zbioru liczb rzeczywistych:\n a = ");
scanf("%lf", &a);
b = a;
while(a >= b || equation(a) * equation(b) >= 0)
{
printf("\n Podaj b należące do zbioru liczb rzeczywistych,\n takie by b > a oraz f(b) * f(a) < 0\n b = ");
scanf("%lf", &b);
}
double epsilon, rB, rN;
int choice;
while (1)
{
printf("\n 1 - Przybliż rozwiązanie równania z dokładnością E metodą połowienia i Newtona");
printf("\n 2 - Zakoncz program");
printf("\n Twoj wybor: ");
scanf("%i", &choice);
switch (choice)
{
case 1:
epsilon = 0;
while (epsilon <= 0 || epsilon >= 1)
{
printf("\n Podaj E, takie by 0 < E < 1:\n E = ");
scanf("%lf", &epsilon);
}
rB = bisection(a, b, epsilon);
rN = newton(a, epsilon);
printf("\n Metoda połowienia:\n %lf - przybliżone rozwiązanie\n %i - ilość kroków\n", rB, iB);
printf("\n Metoda Newtona:\n %lf - przybliżone rozwiązanie\n %i - ilość kroków\n", rN, iN);
iB = iN = 0;
break;
case 2:
printf("\n");
return 0;
}
}
}
void MorrisLecar::rungekutta(){
V0=V;
n0=n;
double CouplePlusNoise=Network::sm_gCouple[No]/C+Network::sm_gNoise[No];
equation();
DV1=(DV+CouplePlusNoise)*Network::sm_dt;
Dn1=Dn*Network::sm_dt;
V=V0+DV1/2.0;
n=n0+Dn1/2.0;
equation();
DV2=(DV+CouplePlusNoise)*Network::sm_dt;
Dn2=Dn*Network::sm_dt;
V=V0+DV2/2.0;
n=n0+Dn2/2.0;
equation();
DV3=(DV+CouplePlusNoise)*Network::sm_dt;
Dn3=Dn*Network::sm_dt;
V=V0+DV3;
n=n0+Dn3;
equation();
DV4=(DV+CouplePlusNoise)*Network::sm_dt;
Dn4=Dn*Network::sm_dt;
V=V0+(DV1+2.0*DV2+2.0*DV3+DV4)/6.0;
n=n0+(Dn1+2.0*Dn2+2.0*Dn3+Dn4)/6.0;
}
void DRBPointLightData::updateRange(const glm::mat4 &transformation)
{
float errorRate = 0.01f;
glm::vec3 lightRange;
glm::vec3 equation(_range.z, _range.y, _range.x);
// if the value of equation.z + equation.y * dist + equation.x * dist * dist == 256
// then the pixels are not lighted anymore (pxlColor = final_color / attenuation)
equation.z -= 256;
if (equation.x == 0) // first degree
{
// infinite range if there is no distance attenuation
AGE_ASSERT(equation.y != 0);
lightRange = glm::vec3(-equation.z / equation.y);
}
else // second degree
{
float d = Mathematic::secondDegreeDiscriminant(equation);
glm::vec2 res = Mathematic::resolveSecondDegree(equation, d);
lightRange = glm::vec3(glm::max(res.x, res.y));
}
AGE_ASSERT(lightRange.x > 0);
_sphereTransform = glm::scale(transformation, lightRange + lightRange * errorRate);
_positionLightProperty->autoSet(glm::vec3(_sphereTransform[3]));
setTransformation(_sphereTransform);
}
bool Mod2_System::add (I begin, I end, unsigned int rhs)
{
if (not consistent())
return false; // an already inconsistent system remains so
bitmap::BitMap lhs(size(),begin,end); // convert iterators to bitmap
// now new equation is given by |lhs| and |rhs|; reduce it w.r.t. old ones:
for (unsigned int i=0; i<eqn.size(); ++i)
if (lhs.isMember(eqn[i].lhs[0]))
rhs += eliminate(i,lhs);
if (lhs.empty() and rhs%2==0)
return true; // we've ended up with a trivial equation, don't add it!
unsigned long our_index = eqn.size(); // the number of the new equation
eqn.push_back(equation(rhs)); // push equation with for now empty LHS
equation& eq = eqn.back();
if (eq.lhs.empty())
return false; // we're done, and have just added an inconsistent equation
eq.lhs.assign(lhs.begin(),lhs.end()); // else fill in LHS from the |BitMap|
pivot_index[eq.lhs[0]] = our_index; // we are the pivot for column |lhs[0]|
return true;
}
void CEquSystem::releaseVariables()
{
for (auto i = equNumb(); i--;)
equation(i)->releaseEquation();
resetEquNumb();
}
bool CEquSystem::isSolved() const
{
for (auto i = equNumb(); i--;)
if (!equation(i)->solved())
return false;
return true;
}
double bisection(double left, double right, double epsilon)
{
double point = (left + right) / 2;
while(fabs(left - right) > epsilon)
{
iB++;
point = (left + right) / 2;
if (equation(point) == 0) break;
else if (equation(point) * equation(left) < 0) right = point;
else left = point;
}
return point;
}
std::string
Polynomial::toString() const
{
std::ostringstream stream;
stream << "[Polynomial][" << name() << "][" << equation() << "][" <<
parameterCount() << " parameters]";
return stream.str();
}
void SplineFitting::CalcSpline(double *Xi, double *Yi, int n, int boundType, double b1, double b2)
{
assert((boundType == 1) || (boundType == 2));
double *matrixA = new double[n * n];
if(matrixA == NULL)
{
return;
}
double *d = new double[n];
if(d == NULL)
{
delete[] matrixA;
return;
}
m_valN = n;
m_valXi.assign(Xi, Xi + m_valN);
m_valYi.assign(Yi, Yi + m_valN);
m_valMi.resize(m_valN);
memset(matrixA, 0, sizeof(double) * n * n);
matrixA[ARR_INDEX(0, 0, m_valN)] = 2.0;
matrixA[ARR_INDEX(m_valN - 1, m_valN - 1, m_valN)] = 2.0;
if(boundType == 1) /*第一类边界条件*/
{
matrixA[ARR_INDEX(0, 1, m_valN)] = 1.0; //v0
matrixA[ARR_INDEX(m_valN - 1, m_valN - 2, m_valN)] = 1.0; //un
double h0 = Xi[1] - Xi[0];
d[0] = 6 * ((Yi[1] - Yi[0]) / h0 - b1) / h0; //d0
double hn_1 = Xi[m_valN - 1] - Xi[m_valN - 2];
d[m_valN - 1] = 6 * (b2 - (Yi[m_valN - 1] - Yi[m_valN - 2]) / hn_1) / hn_1; //dn
}
else /*第二类边界条件*/
{
matrixA[ARR_INDEX(0, 1, m_valN)] = 0.0; //v0
matrixA[ARR_INDEX(m_valN - 1, m_valN - 2, m_valN)] = 0.0; //un
d[0] = 2 * b1; //d0
d[m_valN - 1] = 2 * b2; //dn
}
/*计算ui,vi,di，i = 2,3,...,n-1*/
for(int i = 1; i < (m_valN - 1); i++)
{
double hi_1 = Xi[i] - Xi[i - 1];
double hi = Xi[i + 1] - Xi[i];
matrixA[ARR_INDEX(i, i - 1, m_valN)] = hi_1 / (hi_1 + hi); //ui
matrixA[ARR_INDEX(i, i, m_valN)] = 2.0;
matrixA[ARR_INDEX(i, i + 1, m_valN)] = 1 - matrixA[ARR_INDEX(i, i - 1, m_valN)]; //vi = 1 - ui
d[i] = 6 * ((Yi[i + 1] - Yi[i]) / hi - (Yi[i] - Yi[i - 1]) / hi_1) / (hi_1 + hi); //di
}
ThomasEquation equation(m_valN, matrixA, d);
equation.Resolve(m_valMi);
m_bCalcCompleted = true;
delete[] matrixA;
delete[] d;
}
TEST_F(SquareEquationTest, deltaIsNonNegative)
{
std::vector<double> polynom{-2,1,1};
SquareEquation equation(polynom);
std::vector<double> result;
result.push_back(1.);
result.push_back(-2.);
EXPECT_EQ(equation.solveEquation(), result);
}
void MarchingCubes::insideOutsideTest(float (*equation) (int, int, int), float isoValue) {
for (int x = 0; x < size.x + 1; x++) {
for (int y = 0; y < size.y + 1; y++) {
for (int z = 0; z < size.z + 1; z++) {
points[index(x, y, z)] = equation(x - size.x/2, y - size.y/2,
z - size.z/2) < isoValue;
}
}
}
}
void render(image *im) {
// set number of threads
omp_set_num_threads(num_threads);
int i, j;
// division is used for scaling the picture to 100 logical pixels
int division = Logic < resolution ? resolution/Logic : Logic/resolution;
if(resolution > Logic){
#pragma omp parallel for private(j)
for(i = 0; i < resolution; i++)
for(j = 0; j < resolution; j++)
// calculate distance from each pixel and color it
im -> map[i][j][0] = equation(i / division, j / division);
}
else {
#pragma omp parallel for private(j)
for(i = 0; i < resolution; i++)
for(j = 0; j < resolution; j++)
// calculate distance from each pixel and color it
im -> map[i][j][0] = equation(i * division, j * division);
}
}
void abstractor_provert::pred_abstract_block(
goto_programt::const_targett target,
const predicatest &predicates,
abstract_transition_relationt &
abstract_transition_relation)
{
#if 0
symex_target_equationt equation(ns);
std::vector<exprt> curr_predicates,
next_predicates,
predicates_wp;
std::list<exprt> constraints;
build_equation(
ns,
predicates,
concrete_model,
target,
constraints,
equation,
curr_predicates,
next_predicates,
predicates_wp);
#if 0
std::cout << equation;
#endif
// make them all non-deterministic for now
for(unsigned i=0; i<predicates.size(); i++)
abstract_transition_relation.values[i].make_nil();
// predicate image
#ifdef HAVE_PROVER
predicate_image_prover(
message_handler,
curr_predicates,
next_predicates,
predicates_wp,
constraints,
equation,
ns,
abstract_transition_relation);
#else
throw "no support for prover linked in";
#endif
#endif
}
CEquSystem::~CEquSystem()
{
delete[] varPntr();
delete[] varDefinedPtr();
delete[] getDefEquationPntr();
releaseVariables();
for (auto i = equNumbMax(); i--;)
delete equation(i);
delete[] equPntr();
delete[] equIndx();
delete equArray();
}
vector<double> equation(const T &f){
vector<double> res;
if(f.degree() == 1){
if(sign(f.coef[1]))res.push_back(-f.coef[0] / f.coef[1]);
return res;
}
vector<double> droot = equation(f.derivative());
droot.insert(droot.begin(), -INF);
droot.push_back(INF);
for(int i=0;i<(int)droot.size()-1;i++){
double tmp = find(f, droot[i], droot[i + 1]);
if(tmp < INF) res.push_back(tmp);
}
return res;
}
void MorrisLecar::rungekutta_s(){
V0=V;
n0=n;
equation();
DV1=DV*single_dt;
Dn1=Dn*single_dt;
V=V0+DV1/2.0;
n=n0+Dn1/2.0;
equation();
DV2=DV*single_dt;
Dn2=Dn*single_dt;
V=V0+DV2/2.0;
n=n0+Dn2/2.0;
equation();
DV3=DV*single_dt;
Dn3=Dn*single_dt;
V=V0+DV3;
n=n0+Dn3;
equation();
DV4=DV*single_dt;
Dn4=Dn*single_dt;
V=V0+(DV1+2.0*DV2+2.0*DV3+DV4)/6.0;
n=n0+(Dn1+2.0*Dn2+2.0*Dn3+Dn4)/6.0;
}
double newton(double left, double epsilon)
{
double pointPlus, point = left;
while (1)
{
iN++;
pointPlus = point - equation(point) / equationDerivative(point);
if (fabs(point - pointPlus) <= epsilon) break;
else point = pointPlus;
}
return pointPlus;
}
bool LeastSquare(const std::vector<double>& x_value, const std::vector<double>& y_value,
int M, std::vector<double>& a_value)
{
assert(x_value.size() == y_value.size());
assert(a_value.size() == M);
double *matrix = new double[M * M];
double *b= new double[M];
std::vector<double> x_m(x_value.size(), 1.0);
std::vector<double> y_i(y_value.size(), 0.0);
for(int i = 0; i < M; i++)
{
matrix[ARR_INDEX(0, i, M)] = std::accumulate(x_m.begin(), x_m.end(), 0.0);
for(int j = 0; j < static_cast<int>(y_value.size()); j++)
{
y_i[j] = x_m[j] * y_value[j];
}
b[i] = std::accumulate(y_i.begin(), y_i.end(), 0.0);
for(int k = 0; k < static_cast<int>(x_m.size()); k++)
{
x_m[k] *= x_value[k];
}
}
for(int row = 1; row < M; row++)
{
for(int i = 0; i < M - 1; i++)
{
matrix[ARR_INDEX(row, i, M)] = matrix[ARR_INDEX(row - 1, i + 1, M)];
}
matrix[ARR_INDEX(row, M - 1, M)] = std::accumulate(x_m.begin(), x_m.end(), 0.0);
for(int k = 0; k < static_cast<int>(x_m.size()); k++)
{
x_m[k] *= x_value[k];
}
}
GuassEquation equation(M, matrix, b);
delete[] matrix;
delete[] b;
return equation.Resolve(a_value);
}
float PointLightComponent::computePointLightRange(float minValue, glm::vec3 const &attenuation)
{
glm::vec3 equation(attenuation.z, attenuation.y, attenuation.x - minValue);
float discriminant = Mathematic::secondDegreeDiscriminant(equation);
if (discriminant == 0)
{
return (Mathematic::resolveSecondDegree(equation));
}
else if (discriminant > 0)
{
glm::vec2 results = Mathematic::resolveSecondDegree(equation, discriminant);
return (glm::max(results.x, results.y));
}
else
{
assert(!"The impossible has happenned :/");
return (0);
}
}
int main()
{
int a, b, c, d;
printf("(ax+b)(cx+d)\n");
printf("a = ");
scanf("%d", &a);
printf("b = ");
scanf("%d", &b);
printf("c = ");
scanf("%d", &c);
printf("d = ");
scanf("%d", &d);
equation(a, b, c, d);
return 0;
}
int main()
{
double a, b, c, x1, x2;
printf("Input coefficient of x^2: ");
scanf("%lf", &a);
printf("Input coefficient of x: ");
scanf("%lf", &b);
printf("Input free member: ");
scanf("%lf", &c);
double x = equation(a, b, c, &x1, &x2);
if (x == NO_ROOTS) {
printf("Equation hasn't roots.");
return 0;
}
if (x == SAME_ROOT) {
printf("Equation has one root: x = %lf.\n", x1);
return 0;
}
printf("x1 = %lf, x2 = %lf\n", x1, x2);
return 0;
}
void srs_ui_but::CButProjection::cameraInfoCB(const sensor_msgs::CameraInfo::ConstPtr &cam_info)
{
// std::cerr << "Camera callback. Frame id: " << cam_info->header.frame_id << std::endl;
boost::mutex::scoped_lock( m_cameraInfoLock );
// Get camera info
ROS_DEBUG("OctMapPlugin: Set camera info: %d x %d\n", cam_info->height, cam_info->width);
if( !m_camera_model.fromCameraInfo(*cam_info) )
return;
m_camera_size = m_camera_model.fullResolution();
Ogre::Vector3 position;
Ogre::Quaternion orientation;
vis_manager_->getFrameManager()->getTransform(cam_info->header, position, orientation);
// const cv::Mat_<double> pm( m_camera_model.projectionMatrix() );
// convert vision (Z-forward) frame to ogre frame (Z-out)
orientation = orientation * Ogre::Quaternion(Ogre::Degree(180), Ogre::Vector3::UNIT_X);
// Get z-axis
Ogre::Vector3 normal( orientation.zAxis() );
normal.normalise();
// Compute camera plane equation
Ogre::Vector4 equation( normal.x, normal.y, normal.z, -normal.dotProduct( position) );
float width = cam_info->width;
float height = cam_info->height;
// Possibly malformed camera info...
if( width == 0.0 || height == 0.0 )
return;
double fx = cam_info->P[0];
double fy = cam_info->P[5];
/*
Ogre::Radian fovy( 2.0*atan(height / (2.0 * fy)) );
if( fovy != fovy)
return; // NAN
double aspect_ratio = width / height;
if( aspect_ratio != aspect_ratio )
return; //NaN
*/
// Add the camera's translation relative to the left camera (from P[3]);
// Tx = -1*(P[3] / P[0])
double tx = -1.0 * (cam_info->P[3] / fx);
Ogre::Vector3 right = orientation * Ogre::Vector3::UNIT_X;
position = position + (right * tx);
// std::cerr << right * tx << std::endl;
double ty = -1 * (cam_info->P[7] / fy);
Ogre::Vector3 down = orientation * Ogre::Vector3::UNIT_Y;
position = position + (down * ty);
if( !rviz::validateFloats( position ))
{
return;
}
if( m_projectionData != 0 )
{
m_projectionData->setProjectorPosition( position );
m_projectionData->setProjectorOrientation( orientation );
// f.setFOVy( fovX );
// m_projectionData->setFOVy( fovy );
// m_projectionData->setAspectRatio( aspect_ratio );
m_projectionData->setCameraModel( *cam_info );
m_projectionData->setProjectorEquation( equation );
m_projectionData->updateMatrices();
}
}
QString KstEquation::propertyString() const {
return equation();
}
void Leaf::initData()
{
if (pData)
{
delete[] pData;
delete[] pIndices;
}
//example equation: y=+-sqrt(1 - x*x/100) (also is symmetric around x)
unsigned int nInternalQuaterSteps = 5;
//number of points
dataCount = 3*(nInternalQuaterSteps*2+1) + 2;
//number of triangles
unsigned int nTriangles = 2*4*nInternalQuaterSteps+4;
//number of indices
indicesCount = 3*nTriangles;
pData = new VertexData [dataCount];
pIndices = new unsigned int [indicesCount];
//fill in pData array
//right up
unsigned int startIndex = 0;
for (unsigned int i=0; i<nInternalQuaterSteps+1; i++)
{
float xPos = (1.0f +i)/(nInternalQuaterSteps+2);
float yPos = equation(xPos);
pData[startIndex+i].pos = glm::vec3(xPos/2, (yPos+1)/2,0);
pData[startIndex+i].nor = glm::vec3(0,0,-1);
pData[startIndex+i].tex = glm::vec2((xPos+1)/2, (yPos+1)/2);
}
//right down
startIndex += nInternalQuaterSteps+1;
for (unsigned int i=0; i<nInternalQuaterSteps; i++)
{
float xPos = (1.0f + nInternalQuaterSteps-i)/(nInternalQuaterSteps+2);
float yPos = -equation(xPos);
pData[startIndex+i].pos = glm::vec3(xPos/2, (yPos+1)/2,0);
pData[startIndex+i].nor = glm::vec3(0,0,-1);
pData[startIndex+i].tex = glm::vec2((xPos+1)/2, (yPos+1)/2);
}
startIndex += nInternalQuaterSteps;
//left up
for (unsigned int i=0; i<nInternalQuaterSteps+1; i++)
{
float xPos = -(1.0f+i)/(nInternalQuaterSteps+2);
float yPos = equation(xPos);
pData[startIndex+i].pos = glm::vec3(xPos/2, (yPos+1)/2,0);
pData[startIndex+i].nor = glm::vec3(0,0,-1);
pData[startIndex+i].tex = glm::vec2((xPos+1)/2, (yPos+1)/2);
}
//left down
startIndex += nInternalQuaterSteps+1;
for (unsigned int i=0; i<nInternalQuaterSteps; i++)
{
float xPos = -(1.0f + nInternalQuaterSteps-i)/(nInternalQuaterSteps+2);
float yPos = -equation(xPos);
pData[startIndex+i].pos = glm::vec3(xPos/2, (yPos+1)/2,0);
pData[startIndex+i].nor = glm::vec3(0,0,-1);
pData[startIndex+i].tex = glm::vec2((xPos+1)/2, (yPos+1)/2);
}
startIndex += nInternalQuaterSteps;
//center up
for (unsigned int i=0; i<nInternalQuaterSteps+1; i++)
{
float xPos = (1.0f + i)/(nInternalQuaterSteps+2);
float yPos = equation(xPos);
pData[startIndex+i].pos = glm::vec3(0, (yPos+1)/2,0);
pData[startIndex+i].nor = glm::vec3(0,0,-1);
pData[startIndex+i].tex = glm::vec2(0.5f,0.5f);
}
//center down
startIndex += nInternalQuaterSteps+1;
for (unsigned int i=0; i<nInternalQuaterSteps; i++)
{
float xPos = (1.0f + nInternalQuaterSteps-i)/(nInternalQuaterSteps+2);
float yPos = -equation(xPos);
pData[startIndex+i].pos = glm::vec3(0, (yPos+1)/2,0);
pData[startIndex+i].nor = glm::vec3(0,0,-1);
pData[startIndex+i].tex = glm::vec2(0.5f,0.5f);
}
startIndex += nInternalQuaterSteps;
//generate north pole
pData[startIndex].pos = glm::vec3(0,1,0);
pData[startIndex].nor = glm::vec3(0,0,-1);
pData[startIndex].tex = glm::vec2(0.5f, 1.0f);
//generate south pole
pData[startIndex+1].pos = glm::vec3(0,0,0);
pData[startIndex+1].nor = glm::vec3(0,0,-1);
pData[startIndex+1].tex = glm::vec2(0.5f, 0.0f);
//fill in pIndices array
//fill in side triangles (first 6*radialStep*(heightStep-1))
//fill in pData array
startIndex = 0;
//center and right
unsigned int startIndex1 = 0;//right
unsigned int startIndex2 = 2*(2*nInternalQuaterSteps+1);//center
for (unsigned int i=0; i<2*nInternalQuaterSteps; i++)
{
pIndices[startIndex+6*i+0] = startIndex2+i;
pIndices[startIndex+6*i+1] = startIndex1+i;
pIndices[startIndex+6*i+2] = startIndex1+i+1;
pIndices[startIndex+6*i+3] = startIndex2+i;
pIndices[startIndex+6*i+4] = startIndex1+i+1;
pIndices[startIndex+6*i+5] = startIndex2+i+1;
}
startIndex += 3*4*nInternalQuaterSteps;
//left and center
startIndex1 = 2*(2*nInternalQuaterSteps+1);//center
startIndex2 = 1*(2*nInternalQuaterSteps+1);//left
for (unsigned int i=0; i<2*nInternalQuaterSteps; i++)
{
pIndices[startIndex+6*i+0] = startIndex2+i;
pIndices[startIndex+6*i+1] = startIndex1+i;
pIndices[startIndex+6*i+2] = startIndex1+i+1;
pIndices[startIndex+6*i+3] = startIndex2+i;
pIndices[startIndex+6*i+4] = startIndex1+i+1;
pIndices[startIndex+6*i+5] = startIndex2+i+1;
}
startIndex += 3*4*nInternalQuaterSteps;
//connect north pole
unsigned int northPoleIndex = 3*(2*nInternalQuaterSteps+1);
pIndices[startIndex+0] = 2*nInternalQuaterSteps+1;//left top
pIndices[startIndex+1] = 2*(2*nInternalQuaterSteps+1);//center top
pIndices[startIndex+2] = northPoleIndex;
pIndices[startIndex+3] = 2*(2*nInternalQuaterSteps+1);//center top
pIndices[startIndex+4] = 0;//right top
pIndices[startIndex+5] = northPoleIndex;
startIndex += 3*2;
//connect south pole
unsigned int southPoleIndex = 3*(2*nInternalQuaterSteps+1)+1;
pIndices[startIndex+0] = 2*nInternalQuaterSteps+1+2*nInternalQuaterSteps;//left bottom
pIndices[startIndex+1] = southPoleIndex;
pIndices[startIndex+2] = 2*(2*nInternalQuaterSteps+1)+2*nInternalQuaterSteps;//center bottom
pIndices[startIndex+3] = 2*(2*nInternalQuaterSteps+1)+2*nInternalQuaterSteps;//center bottom
pIndices[startIndex+4] = southPoleIndex;
pIndices[startIndex+5] = 2*nInternalQuaterSteps;//right bottom
startIndex += 3*2;
}
bool simulator_loop_detectiont::check_prefix(
const predicatest &predicates,
const abstract_modelt &abstract_model,
abstract_counterexamplet &abstract_counterexample,
concrete_counterexamplet &concrete_counterexample,
fail_infot &fail_info)
{
assert(abstract_counterexample.steps.size()!=0);
// no loop? Do normal stuff.
if(!abstract_counterexample.has_loops())
return simulator_symext::check_prefix(
predicates,
abstract_model,
abstract_counterexample,
concrete_counterexample,
fail_info);
// clean up
concrete_counterexample.clear();
loop_infos.clear();
// phase 1: build parameterized equation
status("Loop Simulation Phase I");
concrete_counterexamplet phase_I_counterexample;
{
// build equation
symex_target_equationt equation(concrete_model.ns);
goto_symex_statet state;
prefixt::step_mapt step_map;
build_parameterized_equation(abstract_counterexample,
equation, state,
fail_info, step_map);
// now we have all recurrence predicates in refinement_infos
#ifdef DEBUG
std::list<fail_infot::induction_infot>::const_iterator it;
for (it = fail_info.induction_infos.begin();
it != fail_info.induction_infos.end(); it++)
{
const std::list<exprt> &predicates = it->predicates;
std::cout << "Induction predicate(s): ";
for (std::list<exprt>::const_iterator p_it = predicates.begin ();
p_it != predicates.end (); p_it++)
{
const exprt &pred = *p_it;
std::cout << from_expr(ns, "", pred);
std::list<exprt>::const_iterator next = p_it; next++;
if (next != predicates.end ())
std::cout << ", ";
}
std::cout << std::endl;
}
std::cout << "LOOP_INFO size: " << loop_infos.size () << std::endl;
#endif
// run decision procedure
if(check_phase_I_equation(equation, state,
abstract_counterexample,
phase_I_counterexample,
step_map, fail_info))
{
fail_info.use_invariants = true;
return true; // spurious
}
// it could still be spurious
fail_info.use_invariants = false;
}
// phase 2: unwind counterexample
status("Loop Simulation Phase II");
#ifdef DEBUG
std::cout << abstract_counterexample;
#endif
{
abstract_counterexamplet unwound_counterexample;
unwind_counterexample(
abstract_counterexample,
phase_I_counterexample,
unwound_counterexample);
unwound_counterexample.swap(abstract_counterexample);
return simulator_symext::check_prefix(
predicates,
abstract_model,
abstract_counterexample,
concrete_counterexample,
fail_info);
}
}
int main(int argc, char const *argv[])
{
printf("Golden-Section Search v1\n");
printf("Created by Ozan Yildiz\n\n");
// Variables
double xLow = 0, xHigh = 2; // Max and min variables
double x1 = 0, x2 = 0, xOpt = 0, d = 0, epsilon = 0; // Function unknows variables
double fLow, f1, f2, fHigh; // Function
// Golden Ratio
double R = (sqrt(5) - 1) / 2;
printf("Golden ratio is %.4lf\n\n", R);
printf("x(low)\tf(flow)\tx2\tf2\tx1\tf1\tx(high)\tf(high)\td\tepsil\n");
{ // Variables calculation
d = dCalc(R, xHigh, xLow);
x1 = x1Calc(xLow, d);
x2 = x2Calc(xHigh, d);
}
{ // Functions calculation
fLow = equation(xLow);
f2 = equation(x2);
f1 = equation(x1);
fHigh = equation(xHigh);
}
for (int i = 0; i < ITERATION; i++)
{
printf("%.4lf\t%.4lf\t%.4lf\t%.4lf\t%.4lf\t%.4lf\t%.4lf\t%.4lf\t%.4lf\t%.2lf\n", xLow,fLow, x2, f2, x1, f1, xHigh, fHigh, d, epsilon);
if (f2 > f1)
{
// New x High value and calculate
xHigh = x1;
fHigh = f1;
// New x1 value and f1 function
x1 = x2;
f1 = f2;
// Optimum x and Epsilon calc
xOpt = x2;
epsilon = epsilonCalc(R, xHigh, xLow, xOpt);
// New d, x2, and f2 calculate
{
d = dCalc(R, xHigh, xLow);
x2 = x2Calc(xHigh, d);
f2 = equation(x2);
}
}
else if(f2 < f1)
{
// New x Low value and calculate
xLow = x2;
fLow = f2;
// x2 value and f2 function
x2 = x1;
f2 = f1;
// Optimum x and Epsilon calc
xOpt = x1;
epsilon = epsilonCalc(R, xHigh, xLow, xOpt);
// New d, x1 and f1 calculate
{
d = dCalc(R, xHigh, xLow);
x1 = x1Calc(xLow, d);
f1 = equation(x1);
}
}
}
system("PAUSE");
return 0;
}
void MorrisLecar::euler_s(){
equation();
V+=DV*single_dt;
n+=Dn*single_dt;
}
void MorrisLecar::euler(){
equation();
V+=(DV+Network::sm_gCouple[No]/C+Network::sm_gNoise[No])*Network::sm_dt;
n+=Dn*Network::sm_dt;
}
bool termination_baset::bmc(
concrete_modelt &model,
fine_timet &modelchecker_time,
fine_timet &unsafe_time,
fine_timet &safe_time)
{
bool res=false;
#if 0
std::ofstream out("model");
model.goto_functions.output(ns, out);
out.close();
#endif
fine_timet before=current_time();
symex_target_equationt equation(ns);
custom_symext symex(ns, shadow_context, equation);
satcheckt satcheck;
bv_pointerst bv_pointers(ns, satcheck);
symex.options.set_option("assertions", true);
satcheck.set_verbosity(2);
satcheck.set_message_handler(get_message_handler());
bv_pointers.set_verbosity(2);
bv_pointers.set_message_handler(get_message_handler());
try
{
symex(model.goto_functions);
bv_pointerst::resultt satres;
if(!symex.has_remaining_claims())
satres=bv_pointerst::D_UNSATISFIABLE;
else
{
equation.convert(bv_pointers);
satres=bv_pointers.dec_solve();
}
modelchecker_time+=current_time()-before;
switch(satres)
{
case bv_pointerst::D_TAUTOLOGY:
case bv_pointerst::D_SATISFIABLE:
unsafe_time+=current_time()-before;
res=false;
break;
case bv_pointerst::D_UNSATISFIABLE:
safe_time+=current_time()-before;
res=true;
break;
default:
throw("SAT Solver error.");
break;
}
}
catch (const std::bad_alloc &s)
{
status(std::string("BMC Exception: Memory exhausted"));
}
catch (const std::string &s)
{
status(std::string("BMC Exception: ") + s);
}
catch (const char *s)
{
status(std::string("BMC Exception: ") + s);
}
catch (unsigned u)
{
status(std::string("BMC Exception: ") + i2string(u));
}
return res;
}
void abstractor_satqet::pred_abstract_block(
goto_programt::const_targett target,
const predicatest &predicates,
abstract_transition_relationt &
abstract_transition_relation)
{
#if 0
symex_target_equationt equation(ns);
std::vector<exprt> curr_predicates,
next_predicates,
predicates_wp;
std::list<exprt> constraints;
build_equation(
ns,
predicates,
concrete_model,
target,
constraints,
equation,
curr_predicates,
next_predicates,
predicates_wp);
#if 0
std::cout << equation;
#endif
// find unchanged predicates
// find predicates with value
for(unsigned i=0; i<predicates.size(); i++)
{
if(predicates_wp[i]==predicates[i])
{
abstract_transition_relation.values.erase(i);
//std::cout << "UNCHANGED: P" << i << std::endl;
}
else
{
#if 0
std::cout << "DIFFERENT: P" << i << std::endl;
std::cout << "WP: " << from_expr(ns, "", predicates_wp[i]) << std::endl;
std::cout << "P: " << from_expr(ns, "", predicates[i]) << std::endl;
#endif
abstract_transition_relation.values[i]=
get_value(i, predicates, predicates_wp[i]);
// if it changes, it's output
abstract_transition_relation.to_predicates.insert(i);
}
}
// if there is no nondeterministic predicate, we are done
if(!abstract_transition_relation.has_nondeterminism())
return;
#ifdef HAVE_SATQE
predicate_image_satqe(
get_message_handler(),
curr_predicates,
next_predicates,
constraints,
equation,
ns,
abstract_transition_relation);
#else
throw "no support for satqe linked in";
#endif
#endif
}