int main()
{
float integral(float(*p)(float),float a,float b,int n);
float fsin(float x);
float fcos(float x);
float fexp(float x);
float a1,b1,a2,b2,a3,b3,c,(*p)(float);
int n;
printf("Input the num:");
scanf("%d",&n);
printf("input a1,b1:");
scanf("%f,%f",&a1,&b1);
printf("input a2,b2:");
scanf("%f,%f",&a2,&b2);
printf("input a3,b3:");
scanf("%f,%f",&a3,&b3);
p = fsin;
c = integral(p,a1,b1,n);//求出sin（n）的定积分
printf("The integral of sin(n) is :%f\n",c);
p = fcos;
c = integral(p,a2,b2,n);//求出cos（n）的定积分
printf("The integral of cos(n) is :%f\n",c);
p = fexp;
c = integral(p,a3,b3,n);//求出exp（n）的定积分
printf("The integral of exp(n) is :%f\n",c);
return 0;
}
void dumpMoment(const Everything& e, const char* filename, int moment, vector3<> origin)
{ const GridInfo& g = e.gInfo;
FILE* fp = fopen(filename, "w");
if(!fp) die("Error opening %s for writing.\n", filename);
// Calculates the electronic moment about origin
ScalarField r0, r1, r2;
nullToZero(r0, g); nullToZero(r1, g); nullToZero(r2, g);
applyFunc_r(g, rn_pow_x, 0, g.R, moment, origin, r0->data());
applyFunc_r(g, rn_pow_x, 1, g.R, moment, origin, r1->data());
applyFunc_r(g, rn_pow_x, 2, g.R, moment, origin, r2->data());
vector3<> elecMoment;
elecMoment[0] = integral(e.eVars.n[0]*r0);
elecMoment[1] = integral(e.eVars.n[0]*r1);
elecMoment[2] = integral(e.eVars.n[0]*r2);
fprintf(fp, "Electron moment of order %i: %f\t%f\t%f", moment, elecMoment[0], elecMoment[1], elecMoment[2]);
// Calculates the ionic moment about the origin
vector3<> ionMoment(0., 0., 0.);
for(auto sp: e.iInfo.species)
for(unsigned n=0; n < sp->atpos.size(); n++)
{ vector3<> cartesianCoord = g.R * map_to_interval(sp->atpos[n]);
for(int j=0; j<3; j++)
ionMoment[j] += -sp->Z * pow(cartesianCoord[j], moment);
}
fprintf(fp, "\nIon moment of order %i: %f\t%f\t%f", moment, ionMoment[0], ionMoment[1], ionMoment[2]);
// Calculates the total (elec+ion) dipole moment
fprintf(fp, "\nTotal moment of order %i: %f\t%f\t%f", moment, ionMoment[0]+elecMoment[0], ionMoment[1]+elecMoment[1], ionMoment[2]+elecMoment[2]);
}
float filteredpulsetrain (float edge,float period,float x,float dx)
{
/* First, normalize so period == 1 and our domain of interest is > 0 */
float w = dx/period;
float x0 = x/period - w/2.0f;
float x1 = x0+w;
float nedge = edge / period;
float result;
if( x0 == x1 )
{
/* Trap the unfiltered case so it doesn't return 0 (when dx << x). */
result = (x0 - floor(x0) < nedge) ? 0.0f : 1.0f;
}
else
{
result = (integral(x1, nedge) - integral(x0, nedge)) / w;
/*
The above integral is subject to its own aliasing as we go beyond
where the pattern should be extinct. We try to avoid that by
switching to a constant value.
*/
float extinct = smoothstep( 0.4f, 0.5f, w );
result = result + extinct * (1.0f - nedge - result);
}
return result;
}
int main()
{
double r0 = integral( &sqr, -1, 1 );
printf( "> %lf\n", r0 );
double r1 = integral( &cub, -1, 2 );
printf( "> %lf\n", r1 );
return 0;
}
int main(int argc, char *argv[]) {
double result;
int rank;
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
result = integral(0, pi, .0000000001, f1);
if (rank == 0) { printf("%4.20lf\n", result); }
result = integral(0, pi, .0000000001, f2);
if (rank == 0) { printf("%4.20lf\n", result); }
MPI_Finalize();
return 0;
}
int main() {
float N, result;
N = 100;
result = integral(N);
printf("%f\n",result);
for(N = 1E3; N < 10E3; N += 1E3) {
result = integral(N);
printf("%f\n",result);
}
return 0;
}
int _tmain(int argc, _TCHAR* argv[])
{
try
{
ProviderInfo provInfo;
provInfo.Name( VPN_DEF_PROV );
provInfo.Type( VPN_PROV_TYPE );
provInfo.SessionKeyAlgId( CPCSP_ENCRYPT_ID );
CmdLineInput cmd( argc, argv );
Settings settings( cmd, provInfo );
IntegralTest integral( settings );
//integral.AddTest( new KeyGeneration );
//integral.AddTest( new Encryption );
//integral.AddTest( new Exportation );
integral.AddTest( new Hash );
integral.AddTest( new Signing );
//integral.AddTest( new DiffieHellman );
//integral.AddTest( new EncryptMessage );
//integral.AddTest( new SignMessage );
//integral.AddTest( new Multithread );
//integral.AddTest( new Stress );
//integral.AddTest( new ContainerOnTheDevice );
integral.Run();
}
catch( std::exception& e )
{
std::cerr <<"\n" <<e.what() <<"\n";
}
return 0;
}
/***********************************************************************//**
* @brief Radial profile
*
* @param[in] theta Angular distance from DMBurkert centre (radians).
* @return Profile value.
***************************************************************************/
double GModelSpatialRadialProfileDMBurkert::profile_value(const double& theta) const
{
// Update precompuation cache
update();
// Initialize integral value
double value = 0.0;
// Set up integration limits
double los_min = m_halo_distance.value() - m_mass_radius;
double los_max = m_halo_distance.value() + m_mass_radius;
// Handle case where observer is within halo mass radius
if (los_min < 0.0) {
los_min = 0.0;
}
// Set up integral
halo_kernel_los integrand(m_scale_radius.value(),
m_halo_distance.value(),
theta,
m_core_radius.value());
GIntegral integral(&integrand);
// Compute value
value = integral.romberg(los_min, los_max) * m_scale_density_squared;
// Return value
return value;
}
inline void rotatedIntegralImage(double descriptor_dir,
const cv::KeyPoint& kpt,
const cv::Mat& img,
const int& patch_size,
cv::Mat& win_integral_image)
{
//* Nearest neighbour version (faster) */
descriptor_dir *= (float)(CV_PI/180);
float sin_dir = sin(descriptor_dir);
float cos_dir = cos(descriptor_dir);
float win_offset = (int)(patch_size/2);
cv::Mat win(patch_size, patch_size, CV_8U);
//******************************************************//
// faster version: xin yang @ 2012-07-05 11:22am
//******************************************************//
float start_x = kpt.pt.x - win_offset*cos_dir + win_offset*sin_dir;
float start_y = kpt.pt.y - win_offset*sin_dir - win_offset*cos_dir;
for(int i = 0; i < patch_size; i++, start_x -= sin_dir, start_y += cos_dir){
float pixel_x = start_x;
float pixel_y = start_y;
for(int j = 0; j < patch_size; j++, pixel_x += cos_dir, pixel_y += sin_dir){
int x = (int)(pixel_x + 0.5);
int y = (int)(pixel_y + 0.5);
win.at<unsigned char>(i, j) = img.at<unsigned char>(y, x);
}
}
integral(win, win_integral_image, CV_32S);
}
/***********************************************************************//**
* @brief Integrate function
*
* This code illustrates the integration of a function.
***************************************************************************/
int main(void) {
// Create instance of function
function fct(3.0);
// Create an integral object based on the function
GIntegral integral(&fct);
// Set relative integration precision
integral.eps(1.0e-8);
// Integrate over the interval [-10,10]
double result = integral.romberg(-15.0, +15.0);
// Print result (should be basically 1)
std::cout << "Integral: " << result << std::endl;
// Create a derivative object based on the function
GDerivative derivative(&fct);
// Print derivatives
std::cout << "Derivative(0): " << derivative.value(0.0) << std::endl;
std::cout << "Derivative(3): " << derivative.value(3.0) << std::endl;
std::cout << "Derivative(-3): " << derivative.value(-3.0) << std::endl;
// Exit
return 0;
}
std::unique_ptr<typename ElementaryPotentialOperator<
BasisFunctionType, KernelType, ResultType>::LocalAssembler>
ElementaryPotentialOperator<BasisFunctionType, KernelType, ResultType>::
makeAssembler(const Space<BasisFunctionType> &space,
const arma::Mat<CoordinateType> &evaluationPoints,
const QuadratureStrategy &quadStrategy,
const EvaluationOptions &options) const {
// Collect the standard set of data necessary for construction of
// assemblers
typedef Fiber::RawGridGeometry<CoordinateType> RawGridGeometry;
typedef std::vector<const Fiber::Shapeset<BasisFunctionType> *>
ShapesetPtrVector;
typedef std::vector<std::vector<ResultType>> CoefficientsVector;
typedef LocalAssemblerConstructionHelper Helper;
shared_ptr<RawGridGeometry> rawGeometry;
shared_ptr<GeometryFactory> geometryFactory;
shared_ptr<Fiber::OpenClHandler> openClHandler;
shared_ptr<ShapesetPtrVector> shapesets;
shared_ptr<const Grid> grid = space.grid();
Helper::collectGridData(space, rawGeometry, geometryFactory);
Helper::makeOpenClHandler(options.parallelizationOptions().openClOptions(),
rawGeometry, openClHandler);
Helper::collectShapesets(space, shapesets);
// Now create the assembler
return quadStrategy.makeAssemblerForPotentialOperators(
evaluationPoints, geometryFactory, rawGeometry, shapesets,
make_shared_from_ref(kernels()),
make_shared_from_ref(trialTransformations()),
make_shared_from_ref(integral()), openClHandler,
options.parallelizationOptions(), options.verbosityLevel());
}
/***********************************************************************//**
* @brief Returns model energy flux between [emin, emax] (units: erg/cm2/s)
*
* @param[in] emin Minimum photon energy.
* @param[in] emax Maximum photon energy.
* @return Energy flux (erg/cm2/s).
*
* Computes
*
* \f[
* \int_{\tt emin}^{\tt emax} S_{\rm E}(E | t) E \, dE
* \f]
*
* where
* - [@p emin, @p emax] is an energy interval, and
* - \f$S_{\rm E}(E | t)\f$ is the spectral model (ph/cm2/s/MeV).
* The integration is done numerically.
***************************************************************************/
double GModelSpectralExpPlaw::eflux(const GEnergy& emin,
const GEnergy& emax) const
{
// Initialise flux
double eflux = 0.0;
// Compute only if integration range is valid
if (emin < emax) {
// Setup integration kernel
eflux_kernel integrand(m_norm.value(), m_index.value(),
m_pivot.value(), m_ecut.value());
GIntegral integral(&integrand);
// Get integration boundaries in MeV
double e_min = emin.MeV();
double e_max = emax.MeV();
// Perform integration
eflux = integral.romberg(e_min, e_max);
// Convert from MeV/cm2/s to erg/cm2/s
eflux *= gammalib::MeV2erg;
} // endif: integration range was valid
// Return
return eflux;
}
/***********************************************************************//**
* @brief Kernel for offset angle integration of background model
*
* @param[in] theta Offset angle from ROI centre (radians).
*
* Computes
*
* \f[
* K(\rho | E, t) = \sin \theta \times
* \int_{0}^{2\pi}
* B(\theta,\phi | E, t) d\phi
* \f]
*
* where \f$B(\theta,\phi | E, t)\f$ is the background model for a specific
* observed energy \f$E\f$ and time \f$t\f$.
***************************************************************************/
double GCTAModelIrfBackground::npred_roi_kern_theta::eval(const double& theta)
{
// Initialise value
double value = 0.0;
// Continue only if offset angle is positive
if (theta > 0.0) {
// Setup phi integration kernel
GCTAModelIrfBackground::npred_roi_kern_phi integrand(m_bgd,
m_logE,
theta);
// Integrate over phi
GIntegral integral(&integrand);
integral.eps(g_cta_inst_background_npred_phi_eps);
value = integral.romberg(0.0, gammalib::twopi) * std::sin(theta);
// Debug: Check for NaN
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(value) || gammalib::is_infinite(value)) {
std::string origin = "GCTAModelIrfBackground::npred_roi_kern_theta::eval"
"(" + gammalib::str(theta) + ")";
std::string message = " NaN/Inf encountered (value=" +
gammalib::str(value) + ")";
gammalib::warning(origin, message);
}
#endif
} // endif: offset angle was positive
// Return value
return value;
}
/***********************************************************************//**
* @brief Evaluate function
*
* @param[in] srcEng True photon energy.
* @param[in] srcTime True photon arrival time.
* @return Model value (ph/cm2/s/MeV).
*
* Computes
*
* \f[
* S_{\rm E}(E | t) = {\tt m\_integral}
* \frac{{\tt m\_index}+1}
* {{\tt e\_max}^{{\tt m\_index}+1} -
* {\tt e\_min}^{{\tt m\_index}+1}}
* E^{\tt m\_index}
* \f]
*
* for \f${\tt m\_index} \ne -1\f$ and
*
* \f[
* S_{\rm E}(E | t) =
* \frac{{\tt m\_integral}}
* {\log {\tt e\_max} - \log {\tt e\_min}}
* E^{\tt m\_index}
* \f]
*
* for \f${\tt m\_index} = -1\f$, where
* - \f${\tt e\_min}\f$ is the minimum energy of an interval,
* - \f${\tt e\_max}\f$ is the maximum energy of an interval,
* - \f${\tt m\_integral}\f$ is the integral flux between
* \f${\tt e\_min}\f$ and \f${\tt e\_max}\f$, and
* - \f${\tt m\_index}\f$ is the spectral index.
***************************************************************************/
double GModelSpectralPlaw2::eval(const GEnergy& srcEng,
const GTime& srcTime) const
{
// Update precomputed values
update(srcEng);
// Compute function value
double value = m_integral.value() * m_norm * m_power;
// Compile option: Check for NaN/Inf
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(value) || gammalib::is_infinite(value)) {
std::cout << "*** ERROR: GModelSpectralPlaw2::eval";
std::cout << "(srcEng=" << srcEng;
std::cout << ", srcTime=" << srcTime << "):";
std::cout << " NaN/Inf encountered";
std::cout << " (value=" << value;
std::cout << ", integral=" << integral();
std::cout << ", m_norm=" << m_norm;
std::cout << ", m_power=" << m_power;
std::cout << ")" << std::endl;
}
#endif
// Return
return value;
}
std::unique_ptr<typename ElementaryLocalOperator<BasisFunctionType,
ResultType>::LocalAssembler>
ElementaryLocalOperator<BasisFunctionType, ResultType>::makeAssembler(
const QuadratureStrategy &quadStrategy,
const AssemblyOptions &options) const {
typedef Fiber::RawGridGeometry<CoordinateType> RawGridGeometry;
typedef std::vector<const Fiber::Shapeset<BasisFunctionType> *>
ShapesetPtrVector;
shared_ptr<RawGridGeometry> testRawGeometry, trialRawGeometry;
shared_ptr<GeometryFactory> testGeometryFactory, trialGeometryFactory;
shared_ptr<Fiber::OpenClHandler> openClHandler;
shared_ptr<ShapesetPtrVector> testShapesets, trialShapesets;
bool cacheSingularIntegrals;
this->collectDataForAssemblerConstruction(
options, testRawGeometry, trialRawGeometry, testGeometryFactory,
trialGeometryFactory, testShapesets, trialShapesets, openClHandler,
cacheSingularIntegrals);
assert(testRawGeometry == trialRawGeometry);
assert(testGeometryFactory == trialGeometryFactory);
return quadStrategy.makeAssemblerForLocalOperators(
testGeometryFactory, testRawGeometry, testShapesets, trialShapesets,
make_shared_from_ref(testTransformations()),
make_shared_from_ref(trialTransformations()),
make_shared_from_ref(integral()), openClHandler);
}
/***********************************************************************//**
* @brief Returns model energy flux between [emin, emax] (units: erg/cm2/s)
*
* @param[in] emin Minimum photon energy.
* @param[in] emax Maximum photon energy.
* @return Energy flux (erg/cm2/s).
*
* Computes
*
* \f[
* \int_{\tt emin}^{\tt emax} S_{\rm E}(E | t) E \, dE
* \f]
*
* where
* - [@p emin, @p emax] is an energy interval, and
* - \f$S_{\rm E}(E | t)\f$ is the spectral model (ph/cm2/s/MeV).
* The integration is done numerically.
***************************************************************************/
double GModelSpectralSmoothBrokenPlaw::eflux(const GEnergy& emin,
const GEnergy& emax) const
{
// Initialise flux
double eflux = 0.0;
// Compute only if integration range is valid
if (emin < emax) {
// Initialise function to integrate
eflux_kern kernel(prefactor(), index1(), pivot(),
index2(), breakenergy(), beta());
// Initialise integral class with function
GIntegral integral(&kernel);
// Set integration precision
integral.eps(1.0e-8);
// Calculate integral between emin and emax
eflux = integral.romberg(emin.MeV(), emax.MeV());
// Convert from MeV/cm2/s to erg/cm2/s
eflux *= gammalib::MeV2erg;
} // endif: integration range was valid
// Return flux
return eflux;
}
/***********************************************************************//**
* @brief Temporally integrates spatially and spectrally integrated Npred
* kernel
*
* @param[in] model Gamma-ray source model.
*
* @exception GException::gti_invalid
* Good Time Interval is invalid.
*
* Computes
* \f[N_{\rm pred} = \int_{\rm GTI} \int_{E_{\rm bounds}} \int_{\rm ROI}
* S(\vec{p}, E, t) PSF(\vec{p'}, E', t' | \vec{d}, \vec{p}, E, t) \,
* {\rm d}\vec{p'} {\rm d}E' {\rm d}t'\f]
* where
* \f$S(\vec{p}, E, t)\f$ is the source model,
* \f$PSF(\vec{p'}, E', t' | \vec{d}, \vec{p}, E, t)\f$ is the point
* spread function,
* \f$\vec{p'}\f$ is the measured photon direction,
* \f$E'\f$ is the measured photon energy,
* \f$t'\f$ is the measured photon arrival time,
* \f$\vec{p}\f$ is the true photon arrival direction,
* \f$E\f$ is the true photon energy,
* \f$t\f$ is the true photon arrival time, and
* \f$d\f$ is the instrument pointing.
*
* \f${\rm GTI}\f$ are the Good Time Intervals that are stored in the
* GObservation::m_gti member.
* Note that MET is used for the time integration interval. This, however,
* is no specialisation since npred_grad_kern_spec::eval() converts the
* argument back in a GTime object by assuming that the argument is in MET,
* hence the correct time system will be used at the end by the method.
***************************************************************************/
double GObservation::npred_temp(const GModel& model) const
{
// Initialise result
double result = 0.0;
// Loop over GTIs
for (int i = 0; i < events()->gti().size(); ++i) {
// Set integration interval in seconds
double tstart = events()->gti().tstart(i).secs();
double tstop = events()->gti().tstop(i).secs();
// Throw exception if time interval is not valid
if (tstop <= tstart) {
throw GException::gti_invalid(G_NPRED_TEMP, events()->gti().tstart(i),
events()->gti().tstop(i));
}
// Setup integration function
GObservation::npred_temp_kern integrand(this, &model);
GIntegral integral(&integrand);
// Do Romberg integration
result += integral.romb(tstart, tstop);
} // endfor: looped over GTIs
// Return result
return result;
}
/**
* Integrate down the centre of this unknown
* This will not take into account changes
* in the jacobian across the extent of the basis
* function
*/
static
typename UnknownT::NumberT
integrate(
const UnknownT& unknown,
const CoordinatesInterface<DIM,
typename UnknownT::NumberT>& geom,
const int direction)
{
GaussLegendre<UnknownT::ORDER, NumberT> quad;
ValueT integral(0.0);
for (auto interval1D :
unknown.linearIntervals1D(direction)) {
NumberT intervalMin = interval1D.minimum(0);
NumberT intervalMax = interval1D.maximum(0);
auto nodes = quad.nodes(intervalMin, intervalMax);
auto weights = quad.weights(intervalMin, intervalMax);
auto location = unknown.centres();
for (std::size_t j = 0; j < nodes.size(); ++j) {
location[direction] = nodes[j];
integral += weights[j] *
unknown.value(direction, nodes[j]) *
geom.jacobian(direction, nodes[j]);
}
}
return integral;
}
static bool matchTemplate_CCOEFF(InputArray _image, InputArray _templ, OutputArray _result)
{
matchTemplate(_image, _templ, _result, CV_TM_CCORR);
UMat image_sums, temp;
integral(_image, image_sums, CV_32F);
int type = image_sums.type(), depth = CV_MAT_DEPTH(type), cn = CV_MAT_CN(type);
ocl::Kernel k("matchTemplate_Prepared_CCOEFF", ocl::imgproc::match_template_oclsrc,
format("-D CCOEFF -D T=%s -D T1=%s -D cn=%d", ocl::typeToStr(type), ocl::typeToStr(depth), cn));
if (k.empty())
return false;
UMat templ = _templ.getUMat();
UMat result = _result.getUMat();
if (cn==1)
{
Scalar templMean = mean(templ);
float templ_sum = (float)templMean[0];
k.args(ocl::KernelArg::ReadOnlyNoSize(image_sums), ocl::KernelArg::ReadWrite(result), templ.rows, templ.cols, templ_sum);
}
else
{
Vec4f templ_sum = Vec4f::all(0);
templ_sum = (Vec4f)mean(templ);
k.args(ocl::KernelArg::ReadOnlyNoSize(image_sums), ocl::KernelArg::ReadWrite(result), templ.rows, templ.cols, templ_sum); }
size_t globalsize[2] = { result.cols, result.rows };
return k.run(2, globalsize, NULL, false);
}
/***********************************************************************//**
* @brief Kernel for zenith angle Npred integration of background model
*
* @param[in] theta Offset angle from ROI centre (radians).
*
* Computes
*
* \f[
* K(\rho | E, t) = \sin \theta \times
* \int_{\phi_{\rm min}}^{\phi_{\rm max}}
* S_{\rm p}(\theta,\phi | E, t) \,
* N_{\rm pred}(\theta,\phi) d\phi
* \f]
*
* The azimuth angle integration range
* \f$[\phi_{\rm min}, \phi_{\rm max}\f$
* is limited to an arc around the vector connecting the model centre to
* the ROI centre. This limitation assures proper converges properly.
***************************************************************************/
double GCTAModelBackground::npred_roi_kern_theta::eval(const double& theta)
{
// Initialise value
double value = 0.0;
// Continue only if offset angle is positive
if (theta > 0.0) {
// Compute sine of offset angle
double sin_theta = std::sin(theta);
#if defined(G_NPRED_AROUND_ROI)
double dphi = gammalib::pi;
#else
double dphi = 0.5 * gammalib::cta_roi_arclength(theta,
m_dist,
m_cosdist,
m_sindist,
m_roi,
m_cosroi);
#endif
// Continue only if arc length is positive
if (dphi > 0.0) {
// Compute phi integration range
double phi_min = m_omega0 - dphi;
double phi_max = m_omega0 + dphi;
// Setup phi integration kernel
GCTAModelBackground::npred_roi_kern_phi integrand(m_model,
m_obsEng,
m_obsTime,
m_rot,
theta,
sin_theta);
// Integrate over phi
GIntegral integral(&integrand);
integral.eps(1e-3);
value = integral.romb(phi_min, phi_max) * sin_theta;
// Debug: Check for NaN
#if defined(G_NAN_CHECK)
if (gammalib::is_notanumber(value) || gammalib::is_infinite(value)) {
std::cout << "*** ERROR: GCTAModelBackground::npred_roi_kern_theta::eval";
std::cout << "(theta=" << theta << "):";
std::cout << " NaN/Inf encountered";
std::cout << " (value=" << value;
std::cout << ", sin_theta=" << sin_theta;
std::cout << ")" << std::endl;
}
#endif
} // endif: arc length was positive
} // endif: offset angle was positive
// Return value
return value;
}
double Fex_H2O_FittedCorrelations::compute(const ScalarFieldTilde* Ntilde, ScalarFieldTilde* Phi_Ntilde) const
{ double PhiEx = 0.0;
//Quadratic part:
ScalarFieldTilde V_O = double(gInfo.nr)*(COO*Ntilde[0] + COH*Ntilde[1]); Phi_Ntilde[0] += V_O;
ScalarFieldTilde V_H = double(gInfo.nr)*(COH*Ntilde[0] + CHH*Ntilde[1]); Phi_Ntilde[1] += V_H;
PhiEx += 0.5*gInfo.dV*(dot(V_O,Ntilde[0]) + dot(V_H,Ntilde[1]));
//Compute gaussian weighted densities:
ScalarField NObar = I(fex_gauss*Ntilde[0]), Phi_NObar; nullToZero(Phi_NObar, gInfo);
ScalarField NHbar = I(fex_gauss*Ntilde[1]), Phi_NHbar; nullToZero(Phi_NHbar, gInfo);
//Evaluated weighted density functional:
#ifdef GPU_ENABLED
ScalarField fex(ScalarFieldData::alloc(gInfo,isGpuEnabled()));
Fex_H20_FittedCorrelations_gpu(gInfo.nr, NObar->dataGpu(), NHbar->dataGpu(),
fex->dataGpu(), Phi_NObar->dataGpu(), Phi_NHbar->dataGpu());
PhiEx += integral(fex);
#else
PhiEx += gInfo.dV*threadedAccumulate(Fex_H2O_FittedCorrelations_calc, gInfo.nr,
NObar->data(), NHbar->data(), Phi_NObar->data(), Phi_NHbar->data());
#endif
//Convert gradients:
Phi_Ntilde[0] += fex_gauss*Idag(Phi_NObar);
Phi_Ntilde[1] += fex_gauss*Idag(Phi_NHbar);
return PhiEx;
}
static bool matchTemplate_SQDIFF_NORMED(InputArray _image, InputArray _templ, OutputArray _result)
{
matchTemplate(_image, _templ, _result, CV_TM_CCORR);
int type = _image.type(), cn = CV_MAT_CN(type);
ocl::Kernel k("matchTemplate_SQDIFF_NORMED", ocl::imgproc::match_template_oclsrc,
format("-D SQDIFF_NORMED -D T=%s -D cn=%d", ocl::typeToStr(type), cn));
if (k.empty())
return false;
UMat image = _image.getUMat(), templ = _templ.getUMat();
_result.create(image.rows - templ.rows + 1, image.cols - templ.cols + 1, CV_32F);
UMat result = _result.getUMat();
UMat image_sums, image_sqsums;
integral(image.reshape(1), image_sums, image_sqsums, CV_32F, CV_32F);
UMat templ_sqsum;
if (!sumTemplate(_templ, templ_sqsum))
return false;
k.args(ocl::KernelArg::ReadOnlyNoSize(image_sqsums), ocl::KernelArg::ReadWrite(result),
templ.rows, templ.cols, ocl::KernelArg::PtrReadOnly(templ_sqsum));
size_t globalsize[2] = { result.cols, result.rows };
return k.run(2, globalsize, NULL, false);
}
Mat CScale::get(const Mat &img, SqNeighbourhood nbhd)
{
int width = img.cols;
int height = img.rows;
int nChannels = img.channels();
Mat res(img.size(), img.type());
vec_mat_t vChannels;
split(img, vChannels);
Mat integralImg;
for (byte c = 0; c < nChannels; c++) {
integral(vChannels[c], integralImg);
for (int y = 0; y < height; y++) {
int y0 = MAX(0, y - nbhd.upperGap);
int y1 = MIN(y + nbhd.lowerGap, height - 1);
byte *pRes = res.ptr<byte>(y);
int *pI0 = integralImg.ptr<int>(y0);
int *pI1 = integralImg.ptr<int>(y1 + 1);
for (int x = 0; x < width; x++) {
int x0 = MAX(0, x - nbhd.leftGap);
int x1 = MIN(x + nbhd.rightGap, width - 1);
int S = (x1 - x0 + 1) * (y1 - y0 + 1);
float med = static_cast<float>(pI1[x1 + 1] - pI1[x0] - pI0[x1 + 1] + pI0[x0]) / S;
pRes[nChannels * x + c] = static_cast<byte>(med + 0.5f);
} // x
} // y
} // c
return res;
}
double integral_g_dx_dy(double xi, double xf, int n, double yi, double yf, int m){
Param *p = (Param*) malloc(sizeof(Param));
p->xi=xi;
p->xf=xf;
p->n=n;
return integral(integral_g_dx_aux, p, yi, yf, m);
}
void Predator::selectObject(Mat& img, BoundingBox& bb)
{
this->nnClassifier->release();
this->ffClassifier->release();
this->detector->objW = bb.w;
this->detector->objH = bb.h;
this->ffClassifier->init(this->params->n_ferns, this->params->n_features, this->params->min_scale, this->params->max_scale);
this->detector->init();
this->currBB = bb;
this->currBB.conf = 1.0f;
this->currBB.valid = true;
this->detectedBB = BoundingBox();
cvtColor( img, this->currImg, CV_RGB2GRAY );
integral( this->currImg, this->integralImg,this->integralImgSqr, CV_64F);
this->initialLearning();
this->initialized = true;
}
void CvLBPEvaluator::setImage( const Mat &img, uchar clsLabel, int idx )
{
CV_DbgAssert( !sum.empty() );
CvFeatureEvaluator::setImage( img, clsLabel, idx );
Mat innSum( winSize.height + 1, winSize.width + 1, sum.type(), sum.ptr<int>( (int) idx ) );
integral( img, innSum );
}
void Dump::dumpRsol(ScalarField nbound, string fname)
{
//Compute normalization factor for the partition:
int nAtomsTot = 0; for(const auto& sp: e->iInfo.species) nAtomsTot += sp->atpos.size();
const double nFloor = 1e-5/nAtomsTot; //lower cap on densities to prevent Nyquist noise in low density regions
ScalarField nAtomicTot;
for(const auto& sp: e->iInfo.species)
{ RadialFunctionG nRadial;
logSuspend(); sp->getAtom_nRadial(0,0, nRadial, true); logResume();
for(unsigned atom=0; atom<sp->atpos.size(); atom++)
{ ScalarField nAtomic = radialFunction(e->gInfo, nRadial, sp->atpos[atom]);
double nMin, nMax; callPref(eblas_capMinMax)(e->gInfo.nr, nAtomic->dataPref(), nMin, nMax, nFloor);
nAtomicTot += nAtomic;
}
}
ScalarField nboundByAtomic = (nbound*nbound) * inv(nAtomicTot);
ScalarField rInv0(ScalarFieldData::alloc(e->gInfo));
{ logSuspend(); WignerSeitz ws(e->gInfo.R); logResume();
threadLaunch(set_rInv, e->gInfo.nr, e->gInfo.S, e->gInfo.RTR, &ws, rInv0->data());
}
//Compute bound charge 1/r and 1/r^2 expectation values weighted by atom-density partition:
FILE* fp = fopen(fname.c_str(), "w");
fprintf(fp, "#Species rMean +/- rSigma [bohrs] (rMean +/- rSigma [Angstrom]) sqrt(Int|nbound^2|) in partition\n");
for(const auto& sp: e->iInfo.species)
{ RadialFunctionG nRadial;
logSuspend(); sp->getAtom_nRadial(0,0, nRadial, true); logResume();
for(unsigned atom=0; atom<sp->atpos.size(); atom++)
{ ScalarField w = radialFunction(e->gInfo, nRadial, sp->atpos[atom]) * nboundByAtomic;
//Get r centered at current atom:
ScalarFieldTilde trans; nullToZero(trans, e->gInfo); initTranslation(trans, e->gInfo.R*sp->atpos[atom]);
ScalarField rInv = I(trans * J(rInv0), true);
//Compute moments:
double wNorm = integral(w);
double rInvMean = integral(w * rInv) / wNorm;
double rInvSqMean = integral(w * rInv * rInv) / wNorm;
double rInvSigma = sqrt(rInvSqMean - rInvMean*rInvMean);
double rMean = 1./rInvMean;
double rSigma = rInvSigma / (rInvMean*rInvMean);
//Print stats:
fprintf(fp, "Rsol %s %.2lf +/- %.2lf ( %.2lf +/- %.2lf A ) Qrms: %.1le\n", sp->name.c_str(),
rMean, rSigma, rMean/Angstrom, rSigma/Angstrom, sqrt(wNorm));
}
}
fclose(fp);
}
void PCM::propagateCavityGradients(const ScalarField& A_shape, ScalarField& A_nCavity, ScalarFieldTilde& A_rhoExplicitTilde, bool electricOnly) const
{ if(fsp.pcmVariant == PCM_SGA13)
{ //Propagate gradient w.r.t expanded cavities to nCavity:
((PCM*)this)->A_nc = 0;
const ScalarField* A_shapeEx[2] = { &A_shape, &Acavity_shapeVdw };
for(int i=0; i<2; i++)
{ //First compute derivative w.r.t expanded electron density:
ScalarField A_nCavityEx;
ShapeFunction::propagateGradient(nCavityEx[i], *(A_shapeEx[i]), A_nCavityEx, fsp.nc, fsp.sigma);
((PCM*)this)->A_nc += (-1./fsp.nc) * integral(A_nCavityEx*nCavityEx[i]);
//then propagate to original electron density:
ScalarField nCavityExUnused; //unused return value below
ShapeFunction::expandDensity(wExpand[i], Rex[i], nCavity, nCavityExUnused, &A_nCavityEx, &A_nCavity);
}
}
else if(fsp.pcmVariant == PCM_CANDLE)
{ ScalarField A_nCavityEx;
ScalarFieldTilde A_phiExt;
double A_pCavity=0.;
ShapeFunction::propagateGradient(nCavityEx[0], coulomb(Sf[0]*rhoExplicitTilde), I(wExpand[0]*J(A_shape)) + Acavity_shapeVdw,
A_nCavityEx, A_phiExt, A_pCavity, fsp.nc, fsp.sigma, fsp.pCavity);
A_nCavity += fsp.Ztot * I(Sf[0] * J(A_nCavityEx));
if(!electricOnly) A_rhoExplicitTilde += coulomb(Sf[0]*A_phiExt);
((PCM*)this)->A_nc = (-1./fsp.nc) * integral(A_nCavityEx*nCavityEx[0]);
((PCM*)this)->A_eta_wDiel = integral(A_shape * I(wExpand[1]*J(shapeVdw)));
((PCM*)this)->A_pCavity = A_pCavity;
}
else if(isPCM_SCCS(fsp.pcmVariant))
{ //Electrostatic and volumetric combinations via shape:
ShapeFunctionSCCS::propagateGradient(nCavity, A_shape - fsp.cavityPressure, A_nCavity, fsp.rhoMin, fsp.rhoMax, epsBulk);
//Add surface contributions:
ScalarField shapePlus, shapeMinus;
ShapeFunctionSCCS::compute(nCavity+(0.5*fsp.rhoDelta), shapePlus, fsp.rhoMin, fsp.rhoMax, epsBulk);
ShapeFunctionSCCS::compute(nCavity-(0.5*fsp.rhoDelta), shapeMinus, fsp.rhoMin, fsp.rhoMax, epsBulk);
VectorField Dn = gradient(nCavity);
ScalarField DnLength = sqrt(lengthSquared(Dn));
ScalarField A_shapeMinus = (fsp.cavityTension/fsp.rhoDelta) * DnLength;
ScalarField A_DnLength = (fsp.cavityTension/fsp.rhoDelta) * (shapeMinus - shapePlus);
A_nCavity -= divergence(Dn * (inv(DnLength) * A_DnLength));
ShapeFunctionSCCS::propagateGradient(nCavity+(0.5*fsp.rhoDelta), -A_shapeMinus, A_nCavity, fsp.rhoMin, fsp.rhoMax, epsBulk);
ShapeFunctionSCCS::propagateGradient(nCavity-(0.5*fsp.rhoDelta), A_shapeMinus, A_nCavity, fsp.rhoMin, fsp.rhoMax, epsBulk);
}
else //All gradients are w.r.t the same shape function - propagate them to nCavity (which is defined as a density product for SaLSA)
{ ShapeFunction::propagateGradient(nCavity, A_shape + Acavity_shape, A_nCavity, fsp.nc, fsp.sigma);
((PCM*)this)->A_nc = (-1./fsp.nc) * integral(A_nCavity*nCavity);
}
}
/***********************************************************************//**
* @brief Remove thetacut
*
* @param[in] rsp CTA response.
*
* Removes thetacut from Aeff values read from a FITS file. Note that this
* method should only be called once directly after loading all response
* components.
***************************************************************************/
void GCTAAeffArf::remove_thetacut(const GCTAResponse& rsp)
{
// Continue only if thetacut value has been set
if (m_thetacut > 0.0) {
// Get maximum integration radius
double rmax = m_thetacut * gammalib::deg2rad;
// Loop over Aeff array
for (int i = 0; i < m_aeff.size(); ++i) {
// Setup integration kernel for on-axis PSF
cta_npsf_kern_rad_azsym integrand(rsp,
rmax,
0.0,
m_logE[i],
0.0,
0.0,
0.0,
0.0);
// Setup integration
GIntegral integral(&integrand);
integral.eps(rsp.eps());
// Perform integration
double fraction = integral.romb(0.0, rmax);
// Set scale factor
double scale = 1.0;
if (fraction > 0.0) {
scale /= fraction;
#if defined(G_DEBUG_APPLY_THETACUT)
std::cout << "GCTAAeffArf::apply_thetacut:";
std::cout << " logE=" << m_logE[i];
std::cout << " scale=" << scale;
std::cout << " fraction=" << fraction;
std::cout << std::endl;
#endif
}
else {
std::cout << "WARNING: GCTAAeffArf::apply_thetacut:";
std::cout << " Non-positive integral occured in";
std::cout << " PSF integration.";
std::cout << std::endl;
}
// Apply scaling factor
if (scale != 1.0) {
m_aeff[i] *= scale;
}
} // endfor: looped over Aeff array
} // endif: thetacut value was set
// Return
return;
}
int main(int argc, char** argv) {
float twopi = 2 * 3.14;
float integral_of_f = integral(0.0, 1.0, square, 1e3);
/*float integral_of_sin = integral(0.0, twopi, sin, 10);*/
printf("Całka z funkjci f (0.0 - 1.0) = %g\n", integral_of_f);
/*printf("Całka z sinus (0 - 2pi) = %g\n", integral_of_sin);*/
return 0;
}