mathsFunc Namespace Reference

Namespace for some extra maths function that are often needed. More...

Functions
Mdouble	gamma (Mdouble gamma_in)
	This is the gamma function returns the true value for the half integer value. More...
Mdouble	beta (Mdouble z, Mdouble w)
	This is the beta function, returns the approximation based on cmath's implementation of ln(gamma) More...
Mdouble	chi_squared (Mdouble x, unsigned int k)
	This is a chi_squared function return the value x and degrees of freedom k. More...
Mdouble	chi_squared_prob (Mdouble x, unsigned int k)
	This is the function which actually gives the probability back using a chi squared test. More...
Mdouble	goldenSectionSearch (Mdouble(*function)(const Mdouble), Mdouble min, Mdouble cur, Mdouble max, Mdouble endCondition, Mdouble curVal=std::numeric_limits< Mdouble >::quiet_NaN())
	This function performs a golden section search to find the location of the minimum of a function. More...
template<typename T >
int	sign (T val)
	This is a sign function, it returns -1 for negative numbers, 1 for positive numbers and 0 for 0. More...
template<typename T >
T	square (const T val)
	squares a number More...
template<typename T >
T	cubic (const T val)
	calculates the cube of a number More...
bool	isEqual (Mdouble v1, Mdouble v2, Mdouble absError)
	Compares the difference of two Mdouble with an absolute error, useful in UnitTests. More...
bool	isEqual (Vec3D v1, Vec3D v2, Mdouble absError)
	Compares the difference of two Vec3D with an absolute error, useful in UnitTests. More...
bool	isEqual (Matrix3D m1, Matrix3D m2, Mdouble absError)
	Compares the difference of two Vec3D with an absolute error, useful in UnitTests. More...
bool	isEqual (MatrixSymmetric3D m1, MatrixSymmetric3D m2, Mdouble absError)
bool	isEqual (Quaternion v1, Quaternion v2, double absError)
template<typename T >
constexpr T	factorial (const T t)
	factorial function More...
Mdouble	sin (Mdouble x)
Mdouble	cos (Mdouble x)
Mdouble	exp (Mdouble Exponent)
Mdouble	log (Mdouble Power)
template<typename T >
T	tan (T x)
Mdouble	chebyshev (Mdouble x, const Mdouble coef[], int N)
	Namespace for evaluating the zeroth modified Bessel function of the first kind, I0(x), required in StatisticsPoint.hcc. More...
Mdouble	I0_exp (Mdouble x)
Mdouble	I0 (Mdouble x)

Detailed Description

Namespace for some extra maths function that are often needed.

Function Documentation

Mdouble mathsFunc::beta	(	Mdouble	z,
		Mdouble	w
	)

This is the beta function, returns the approximation based on cmath's implementation of ln(gamma)

Computes the beta function for real numbers, based on cmath's approximation of the ln of the gamma function. See https://en.wikipedia.org/wiki/Beta_function for more details

Parameters

z	first Mdouble argument to compute the beta function of
w	second Mdouble argument to compute the beta function of

Returns

the value of beta(z,w) as an Mdouble

Definition at line 164 of file ExtendedMath.cc.

References exp().

Referenced by SuperQuadricParticle::computeMass(), Multipole::convertMultipoleToLocal(), InfiniteWall::getFurthestPointSuperQuadric(), SuperQuadricParticle::getVolume(), ParhamiMcMeekingSinterSpecies::set(), SuperQuadricParticle::setBoundingRadius(), SuperQuadricParticle::setInertia(), LocalExpansion::translateLocalExpansion(), and Multipole::TranslateMultipoleExpansionTo().

{
    return std::exp(std::lgamma(z) + std::lgamma(w) - std::lgamma(z + w));
}

Mdouble mathsFunc::chebyshev	(	Mdouble	x,
		const Mdouble	coef[],
		int	N
	)

Namespace for evaluating the zeroth modified Bessel function of the first kind, I0(x), required in StatisticsPoint.hcc.

Definition at line 293 of file ExtendedMath.cc.

References constants::i, and logger.

Referenced by I0_exp().

{
    const Mdouble* p = coef;
    Mdouble b0 = *p++;
    Mdouble b1 = 0, b2;
    int i = N - 1;
    
    logger.assert(i > 0, "i is greater than 0");
    do
    {
        b2 = b1;
        b1 = b0;
        b0 = x * b1 - b2 + *p++;
    } while (--i);
    
    return (0.5 * (b0 - b2));
}

Mdouble mathsFunc::chi_squared	(	Mdouble	x,
		unsigned int	k
	)

This is a chi_squared function return the value x and degrees of freedom k.

Definition at line 172 of file ExtendedMath.cc.

References exp(), and gamma().

Referenced by chi_squared_prob().

{
    
    Mdouble prefactor = pow(2, k / 2.0) * gamma(k / 2.0);
    Mdouble mainfactor = pow(x, k / 2.0 - 1) * exp(x / -2.0);
    
    return mainfactor / prefactor;
    
}

Mdouble mathsFunc::chi_squared_prob	(	Mdouble	x,
		unsigned int	k
	)

This is the function which actually gives the probability back using a chi squared test.

This calculates the probability based on a chi squared test First we calculated the cumulative chi_squared function.

This is the function which actually gives the probability back It is calculated by calling the normal chi_squared function and using the trapezoidal rule. The final results is 1-the cumulative chi_squared function

Definition at line 188 of file ExtendedMath.cc.

References chi_squared(), and constants::i.

Referenced by RNG::test().

{

//The current value was picked by tried were it stopped effect the 4 d.p.
    const int num_steps_per_unit = 100;
    Mdouble sum = 0;
    Mdouble x = 0;
    long int num_steps = static_cast<int>(num_steps_per_unit * x_max);
//Use trapezional rule, but ignoring the ends
    for (int i = 0; i < num_steps; i++)
    {
        x = x_max / num_steps * (i + 0.5);
        sum = sum + chi_squared(x, k);
    }
    return 1.0 - sum * x_max / num_steps;
    
}

Mdouble mathsFunc::cos

(

Mdouble

x

)

Definition at line 64 of file ExtendedMath.cc.

References constants::i, and constants::pi.

Referenced by ChuteWithHopper::addHopper(), LiquidBridgeWilletInteraction::computeAdhesionForce(), LiquidMigrationWilletInteraction::computeAdhesionForce(), BaseCluster::computeInternalStructure(), CircularPeriodicBoundary::createPeriodicParticle(), LevelSetWall::createVTKSphere(), VChute::getDistanceAndNormal(), SineWall::getDistanceAndNormal(), HorizontalScrew::getDistanceAndNormal(), HorizontalBaseScrew::getDistanceAndNormal(), Coil::getDistanceAndNormal(), InfiniteWallWithHole::getDistanceAndNormal(), Screw::getDistanceAndNormalLabCoordinates(), Vec3D::getFromCylindricalCoordinates(), RNG::getNormalVariate(), helpers::objectivenessTest(), BaseCluster::particleInsertionSuccessful(), HopperInsertionBoundary::placeParticle(), CircularPeriodicBoundary::rotateParticle(), Quaternion::setAngleZ(), Chute::setChuteAngleAndMagnitudeOfGravity(), Quaternion::setEuler(), sphericalHarmonics::sphericalHarmonics(), tan(), HorizontalBaseScrew::writeVTK(), HorizontalScrew::writeVTK(), Screw::writeVTK(), AxisymmetricIntersectionOfWalls::writeVTK(), and ScrewsymmetricIntersectionOfWalls::writeVTK().

{
    Mdouble N = floor(x / (2.0 * constants::pi) + 0.5);
    x -= N * 2.0 * constants::pi;
    Mdouble Sum = 1.0;
    Mdouble Power = 1;
    Mdouble Sign = 1;
    const Mdouble x2 = x * x;
    Mdouble Fact = 1.0;
    for (unsigned int i = 2; i < 25; i += 2)
    {
        Power *= x2;
        Fact *= i * (i - 1);
        Sign *= -1.0;
        Sum += Sign * Power / Fact;
    }
    return Sum;
}

template<typename T >

T mathsFunc::cubic

(

const T

val

)

calculates the cube of a number

Definition at line 113 of file ExtendedMath.h.

Referenced by Chute::addFlowParticlesCompactly(), CGCoordinates::XYZ::getGaussPrefactor(), PSD::getVolumetricMeanRadius(), CGCoordinates::XYZ::normalisePolynomialCoefficients(), and ChuteBottom::setupInitialConditions().

{
    return val * val * val;
}

Mdouble mathsFunc::exp

(

Mdouble

Exponent

)

Definition at line 84 of file ExtendedMath.cc.

References X.

Referenced by beta(), chi_squared(), CGCoordinates::Base_X_Y_Z::getGaussIntegralPrefactor(), CGCoordinates::Base_XY_XZ_YZ::getGaussIntegralPrefactor(), CGCoordinates::XYZ::getGaussIntegralPrefactor(), CGCoordinates::Base_XY_XZ_YZ::getGaussPrefactor(), CGCoordinates::XYZ::getGaussPrefactor(), helpers::getMaximumVelocity(), RNG::getPoissonVariate(), LinearPlasticViscoelasticNormalSpecies::getRestitutionCoefficient(), LinearViscoelasticNormalSpecies::getRestitutionCoefficient(), HGridOptimiser::histNumberParticlesPerCell(), I0(), log(), ParhamiMcMeekingSinterSpecies::set(), SinterNormalSpecies::setParhamiMcKeeping(), and sphericalHarmonics::sphericalHarmonics().

{
    Mdouble X, P, Frac, I, L;
    X = Exponent;
    Frac = X;
    P = (1.0 + X);
    I = 1.0;
    
    do
    {
        I++;
        Frac *= (X / I);
        L = P;
        P += Frac;
    } while (L != P);
    
    return P;
}

template<typename T >

constexpr T mathsFunc::factorial

(

const T

t

)

factorial function

Definition at line 153 of file ExtendedMath.h.

Referenced by sphericalHarmonics::computeSquaredFactorialValues(), HGridOptimiser::histNumberParticlesPerCell(), and sphericalHarmonics::sphericalHarmonics().

{
    return (t == 0) ? 1 : t * factorial(t - 1);
}

Mdouble mathsFunc::gamma

(

Mdouble

gamma_in

)

This is the gamma function returns the true value for the half integer value.

This is the gamma function, gives 'exact' answers for the half integer values This is done using the recussion relation and the known values for 1 and 0.5 Note, return NaN for non-half integer values.

Definition at line 137 of file ExtendedMath.cc.

References constants::sqrt_pi.

Referenced by chi_squared(), InfiniteWall::getFurthestPointSuperQuadric(), HopperInsertionBoundary::placeParticle(), and SuperQuadricParticle::setBoundingRadius().

{
    const Mdouble ep = 1e-5;
    
    if (gamma_in > 1.0 + ep)
    {
        return ((gamma_in - 1) * gamma(gamma_in - 1));
    }
    else
    {
        
        if ((gamma_in - ep < 1.0) && (gamma_in + ep > 1.0))
            return 1.0;
        else if ((gamma_in - ep < 0.5) && (gamma_in + ep > 0.5))
            return constants::sqrt_pi;
        else
            return std::numeric_limits<Mdouble>::quiet_NaN();
    }
} //end func gamma

Mdouble mathsFunc::goldenSectionSearch	(	Mdouble(*)(const Mdouble)	function,
		Mdouble	min,
		Mdouble	cur,
		Mdouble	max,
		Mdouble	endCondition,
		Mdouble	curVal = std::numeric_limits<Mdouble>::quiet_NaN()
	)

This function performs a golden section search to find the location of the minimum of a function.

Parameters

[in]	function	A function pointer to the function of which you want to calculate the location of its minimum.
[in]	min	The minimum location
[in]	cur	The current location
[in]	max	The maximum location
[in]	endCondition	The algorithm terminates when abs(max - min) < endCondition
[in]	curVal	The value of the function at the current location (on default this value is calculated internally)

Definition at line 206 of file ExtendedMath.cc.

{
    if (std::abs(max - min) < endCondition)
    {
        return 0.5 * (min + max);
    }
    std::cout << "Min=" << min << " Max=" << max << " diff=" << max - min << std::endl;
    Mdouble resphi = 2 - 0.5 * (1 + std::sqrt(5));
    Mdouble x;
    if (max - cur > cur - min)
    {
        x = cur + resphi * (max - cur);
    }
    else
    {
        x = cur - resphi * (cur - min);
    }
    if (std::isnan(curVal))
        curVal = function(cur);
    Mdouble xVal = function(x);
    if (xVal < curVal)
    {
        if (max - cur > cur - min)
        {
            return goldenSectionSearch(function, cur, x, max, endCondition, xVal);
        }
        else
        {
            return goldenSectionSearch(function, min, x, cur, endCondition, xVal);
        }
    }
    else
    {
        if (max - cur > cur - min)
        {
            return goldenSectionSearch(function, min, cur, x, endCondition, curVal);
        }
        else
        {
            return goldenSectionSearch(function, x, cur, max, endCondition, curVal);
        }
    }
}

Mdouble mathsFunc::I0

(

Mdouble

x

)

Definition at line 391 of file ExtendedMath.cc.

References exp(), and I0_exp().

{
    if (x < 0)
        x = -x;
    return exp(x) * I0_exp(x);
}

Mdouble mathsFunc::I0_exp

(

Mdouble

x

)

Definition at line 311 of file ExtendedMath.cc.

References A, and chebyshev().

Referenced by I0().

{
    // Coefficients for [0..8]
    const Mdouble A[] =
            {
                    -4.415341646479339379501E-18,
                    3.330794518822238097831E-17,
                    -2.431279846547954693591E-16,
                    1.715391285555133030611E-15,
                    -1.168533287799345168081E-14,
                    7.676185498604935616881E-14,
                    -4.856446783111929460901E-13,
                    2.955052663129639834611E-12,
                    -1.726826291441555707231E-11,
                    9.675809035373236912241E-11,
                    -5.189795601635262906661E-10,
                    2.659823724682386650351E-9,
                    -1.300025009986248042121E-8,
                    6.046995022541918949321E-8,
                    -2.670793853940611733911E-7,
                    1.117387539120103718151E-6,
                    -4.416738358458750563591E-6,
                    1.644844807072889708931E-5,
                    -5.754195010082103703981E-5,
                    1.885028850958416557291E-4,
                    -5.763755745385823658851E-4,
                    1.639475616941335798421E-3,
                    -4.324309995050575944301E-3,
                    1.054646039459499831831E-2,
                    -2.373741480589946881561E-2,
                    4.930528423967070848781E-2,
                    -9.490109704804764442101E-2,
                    1.716209015222087753491E-1,
                    -3.046826723431983986831E-1,
                    6.767952744094760849951E-1
            };
    
    // Coefficients for [8..infinity]
    const Mdouble B[] =
            {
                    -7.233180487874753954561E-18,
                    -4.830504485944182071261E-18,
                    4.465621420296759999011E-17,
                    3.461222867697461093101E-17,
                    -2.827623980516583484941E-16,
                    -3.425485619677219134621E-16,
                    1.772560133056526383601E-15,
                    3.811680669352622420751E-15,
                    -9.554846698828307648701E-15,
                    -4.150569347287222086631E-14,
                    1.540086217521409826911E-14,
                    3.852778382742142701141E-13,
                    7.180124451383666233671E-13,
                    -1.794178531506806117781E-12,
                    -1.321581184044771311881E-11,
                    -3.149916527963241364541E-11,
                    1.188914710784643834241E-11,
                    4.940602388224969589101E-10,
                    3.396232025708386345151E-9,
                    2.266668990498178064591E-8,
                    2.048918589469063741831E-7,
                    2.891370520834756482971E-6,
                    6.889758346916823984261E-5,
                    3.369116478255694089901E-3,
                    8.044904110141088316081E-1
            };
    
    if (x < 0)
        x = -x;
    
    if (x <= 8.0)
    {
        Mdouble y = (x / 2.0) - 2.0;
        return (chebyshev(y, A, 30));
    }
    
    return (chebyshev(32.0 / x - 2.0, B, 25) / sqrt(x));
    
}

bool mathsFunc::isEqual	(	Mdouble	v1,
		Mdouble	v2,
		Mdouble	absError
	)

Compares the difference of two Mdouble with an absolute error, useful in UnitTests.

Parameters

[in]	v1	The first Mdouble
[in]	v2	The second Mdouble
[in]	absError	The allowed maximum absolute error

Returns

True if the two Mdouble are equal

Definition at line 251 of file ExtendedMath.cc.

Referenced by checkTemplate(), isEqual(), ChuteInsertionBoundary::placeParticle(), SuperQuadricParticle::setBoundingRadius(), and MercuryBase::setHGridCellOverSizeRatio().

{
    return std::abs(v1 - v2) <= absError;
}

bool mathsFunc::isEqual	(	Vec3D	v1,
		Vec3D	v2,
		Mdouble	absError
	)

Compares the difference of two Vec3D with an absolute error, useful in UnitTests.

Parameters

[in]	v1	The first Vec3D
[in]	v2	The second Vec3D
[in]	absError	The allowed maximum absolute error

Returns

true if the two Vec3D are equal

Definition at line 257 of file ExtendedMath.cc.

References isEqual(), Vec3D::X, Vec3D::Y, and Vec3D::Z.

{
    return isEqual(v1.X, v2.X, absError) && isEqual(v1.Y, v2.Y, absError) && isEqual(v1.Z, v2.Z, absError);
}

bool mathsFunc::isEqual	(	Matrix3D	m1,
		Matrix3D	m2,
		Mdouble	absError
	)

Compares the difference of two Vec3D with an absolute error, useful in UnitTests.

Parameters

[in]	m1	The first Vec3D
[in]	m2	The second Vec3D
[in]	absError	The allowed maximum absolute error

Returns

true if the two Vec3D are equal

Definition at line 262 of file ExtendedMath.cc.

References isEqual(), Matrix3D::XX, Matrix3D::XY, Matrix3D::XZ, Matrix3D::YX, Matrix3D::YY, Matrix3D::YZ, Matrix3D::ZX, Matrix3D::ZY, and Matrix3D::ZZ.

{
    return (isEqual(m1.XX, m2.XX, absError)
            && isEqual(m1.XY, m2.XY, absError)
            && isEqual(m1.XZ, m2.XZ, absError)
            && isEqual(m1.YX, m2.YX, absError)
            && isEqual(m1.YY, m2.YY, absError)
            && isEqual(m1.YZ, m2.YZ, absError)
            && isEqual(m1.ZX, m2.ZX, absError)
            && isEqual(m1.ZY, m2.ZY, absError)
            && isEqual(m1.ZZ, m2.ZZ, absError));
}

bool mathsFunc::isEqual	(	MatrixSymmetric3D	m1,
		MatrixSymmetric3D	m2,
		Mdouble	absError
	)

Definition at line 275 of file ExtendedMath.cc.

References isEqual(), MatrixSymmetric3D::XX, MatrixSymmetric3D::XY, MatrixSymmetric3D::XZ, MatrixSymmetric3D::YY, MatrixSymmetric3D::YZ, and MatrixSymmetric3D::ZZ.

{
    return (isEqual(m1.XX, m2.XX, absError)
            && isEqual(m1.XY, m2.XY, absError)
            && isEqual(m1.XZ, m2.XZ, absError)
            && isEqual(m1.YY, m2.YY, absError)
            && isEqual(m1.YZ, m2.YZ, absError)
            && isEqual(m1.ZZ, m2.ZZ, absError));
}

bool mathsFunc::isEqual	(	Quaternion	v1,
		Quaternion	v2,
		double	absError
	)

Definition at line 285 of file ExtendedMath.cc.

References Quaternion::getComponent(), and isEqual().

{
    return isEqual(v1.getComponent(0), v2.getComponent(0), absError) &&
           isEqual(v1.getComponent(1), v2.getComponent(1), absError) &&
           isEqual(v1.getComponent(2), v2.getComponent(2), absError) &&
           isEqual(v1.getComponent(3), v2.getComponent(3), absError);
}

Mdouble mathsFunc::log

(

Mdouble

Power

)

Todo:

check if this function works

Definition at line 104 of file ExtendedMath.cc.

References A, exp(), and R.

Referenced by CircularPeriodicBoundary::checkBoundaryAfterParticleMoved(), helpers::computeDisptFromCollisionTimeAndRestitutionCoefficientAndTangentialRestitutionCoefficientAndEffectiveMass(), CircularPeriodicBoundary::createPeriodicParticle(), RNG::getNormalVariate(), SlidingFrictionSpecies::setCollisionTimeAndNormalAndTangentialRestitutionCoefficient(), LinearPlasticViscoelasticNormalSpecies::setCollisionTimeAndRestitutionCoefficient(), LinearViscoelasticNormalSpecies::setCollisionTimeAndRestitutionCoefficient(), HertzianViscoelasticNormalSpecies::setEffectiveElasticModulusAndRestitutionCoefficient(), LinearViscoelasticNormalSpecies::setRestitutionCoefficient(), LinearPlasticViscoelasticNormalSpecies::setRestitutionCoefficient(), and SinterNormalSpecies::setStiffnessAndRestitutionCoefficient().

{
    Mdouble N, P, L, R, A, E;
    E = 2.71828182845905;
    P = Power;
    N = 0.0;
    
    // This speeds up the convergence by calculating the integral
    while (P >= E)
    {
        P /= E;
        N++;
    }
    N += (P / E);
    P = Power;
    do
    {
        A = N;
        L = (P / (exp(N - 1.0)));
        R = ((N - 1.0) * E);
        N = ((L + R) / E);
    } while (N < A);
    //} while (N != A);
    
    return N;
}

template<typename T >

int mathsFunc::sign

(

T

val

)

This is a sign function, it returns -1 for negative numbers, 1 for positive numbers and 0 for 0.

Definition at line 95 of file ExtendedMath.h.

Referenced by PeriodicBoundaryHandler::checkIsReal(), SuperQuadricParticle::computeHessianLabFixed(), SuperQuadricParticle::computeShapeGradientLabFixed(), HorizontalScrew::getDistanceAndNormal(), Screw::getDistanceAndNormalLabCoordinates(), InfiniteWall::getFurthestPointSuperQuadric(), and PeriodicBoundaryHandler::updateParticles().

{
    return (T(0) < val) - (val < T(0));
}

Mdouble mathsFunc::sin

(

Mdouble

x

)

Definition at line 44 of file ExtendedMath.cc.

References constants::i, and constants::pi.

Referenced by ChuteWithHopper::addHopper(), BaseCluster::computeInternalStructure(), LevelSetWall::createVTKSphere(), VChute::getDistanceAndNormal(), SineWall::getDistanceAndNormal(), HorizontalScrew::getDistanceAndNormal(), HorizontalBaseScrew::getDistanceAndNormal(), Coil::getDistanceAndNormal(), InfiniteWallWithHole::getDistanceAndNormal(), Screw::getDistanceAndNormalLabCoordinates(), Vec3D::getFromCylindricalCoordinates(), ChuteWithHopper::getMaximumVelocityInducedByGravity(), RNG::getNormalVariate(), helpers::objectivenessTest(), BaseCluster::particleInsertionSuccessful(), HopperInsertionBoundary::placeParticle(), CircularPeriodicBoundary::rotateParticle(), Quaternion::setAngleZ(), Chute::setChuteAngleAndMagnitudeOfGravity(), Quaternion::setEuler(), tan(), HorizontalBaseScrew::writeVTK(), HorizontalScrew::writeVTK(), Screw::writeVTK(), AxisymmetricIntersectionOfWalls::writeVTK(), and ScrewsymmetricIntersectionOfWalls::writeVTK().

{
    Mdouble N = floor(x / (2.0 * constants::pi) + 0.5);
    x -= N * 2.0 * constants::pi;
    Mdouble Sum = 0;
    Mdouble Power = x;
    Mdouble Sign = 1;
    const Mdouble x2 = x * x;
    Mdouble Fact = 1.0;
    for (unsigned int i = 1; i < 25; i += 2)
    {
        Sum += Sign * Power / Fact;
        Power *= x2;
        Fact *= (i + 1) * (i + 2);
        Sign *= -1.0;
    }
    return Sum;
}

template<typename T >

T mathsFunc::square

(

const T

val

)

squares a number

Definition at line 104 of file ExtendedMath.h.

Referenced by DPMBase::checkParticleForInteractionLocal(), helpers::computeDisptFromCollisionTimeAndRestitutionCoefficientAndTangentialRestitutionCoefficientAndEffectiveMass(), SlidingFrictionInteraction::computeFrictionForce(), MindlinRollingTorsionInteraction::computeFrictionForce(), FrictionInteraction::computeFrictionForce(), BaseParticle::computeMass(), SinterInteraction::computeNormalForce(), HertzianSinterInteraction::computeSinterForce(), LinearPlasticViscoelasticNormalSpecies::computeTimeStep(), SinterNormalSpecies::computeTimeStep(), PSD::convertProbabilityDensityNumberDistributionToProbabilityDensityVolumeDistribution(), PSD::convertProbabilityDensityToProbabilityDensityNumberDistribution(), Matrix3D::deviator(), HertzianViscoelasticNormalSpecies::getCollisionTime(), LinearPlasticViscoelasticNormalSpecies::getCollisionTime(), SinterNormalSpecies::getCollisionTime(), LinearViscoelasticNormalSpecies::getCollisionTime(), StatisticsVector< T >::getCutoff2(), ParabolaChute::getDistanceAndNormal(), SineWall::getDistanceAndNormal(), HorizontalScrew::getDistanceAndNormal(), Coil::getDistanceAndNormal(), Screw::getDistanceAndNormalLabCoordinates(), CGCoordinates::XY::getDistanceSquared(), CGCoordinates::Y::getDistanceSquared(), CGCoordinates::YZ::getDistanceSquared(), CGCoordinates::Z::getDistanceSquared(), CGCoordinates::RZ::getDistanceSquared(), CGCoordinates::X::getDistanceSquared(), CGCoordinates::XZ::getDistanceSquared(), CGCoordinates::R::getDistanceSquared(), ChargedBondedInteraction::getElasticEnergy(), SinterInteraction::getElasticEnergy(), LinearViscoelasticInteraction::getElasticEnergy(), HertzianSinterInteraction::getElasticEnergy(), LinearPlasticViscoelasticInteraction::getElasticEnergy(), HertzianViscoelasticInteraction::getElasticEnergy(), IrreversibleAdhesiveInteraction::getElasticEnergy(), HertzianViscoelasticInteraction::getElasticEnergyAtEquilibrium(), CGCoordinates::Base_X_Y_Z::getGaussIntegralPrefactor(), CGCoordinates::Base_XY_XZ_YZ::getGaussIntegralPrefactor(), CGCoordinates::XYZ::getGaussIntegralPrefactor(), CGCoordinates::Base_XY_XZ_YZ::getGaussPrefactor(), CGCoordinates::XYZ::getGaussPrefactor(), helpers::getMaximumVelocity(), CGFields::GradVelocityField::getSquared(), CGFields::LiquidMigrationFields::getSquared(), CGFields::StandardFields::getSquared(), CGCoordinates::YZ::getTangentialSquared(), CGCoordinates::XY::getTangentialSquared(), CGCoordinates::RZ::getTangentialSquared(), CGCoordinates::XZ::getTangentialSquared(), CGCoordinates::XYZ::getTangentialSquared(), Mercury3D::hGridFindContactsWithTargetCell(), MercuryBase::hGridUpdateMove(), BaseParticle::isInContactWith(), CGCoordinates::Base_XY_XZ_YZ::normalisePolynomialCoefficients(), SuperQuadricParticle::setBoundingRadius(), StatisticsVector< T >::setCGWidth(), SlidingFrictionSpecies::setCollisionTimeAndNormalAndTangentialRestitutionCoefficient(), SlidingFrictionSpecies::setCollisionTimeAndNormalAndTangentialRestitutionCoefficientNoDispt(), LinearPlasticViscoelasticNormalSpecies::setCollisionTimeAndRestitutionCoefficient(), LinearViscoelasticNormalSpecies::setCollisionTimeAndRestitutionCoefficient(), LinearViscoelasticNormalSpecies::setRestitutionCoefficient(), LinearPlasticViscoelasticNormalSpecies::setRestitutionCoefficient(), SinterNormalSpecies::setStiffnessAndRestitutionCoefficient(), MatrixSymmetric3D::square(), and Matrix3D::square().

{
    return val * val;
}

template<typename T >

T mathsFunc::tan

(

T

x

)

Todo:

should be properly computed

Definition at line 176 of file ExtendedMath.h.

References cos(), and sin().

Referenced by ChuteWithHopper::addHopper(), VChute::getDistanceAndNormal(), and ChuteWithHopper::setHopper().

{
    return sin(x) / cos(x);
}