void dry_revolute_joint_3D::doForce(kte_pass_flag aFlag, const shared_ptr<frame_storage>& aStorage) {
if((!mEnd) || (!mBase))
return;
using std::fabs;
if(!mAngle) {
mBase->Force += mEnd->Force;
mBase->Torque += mEnd->Torque;
} else {
rot_mat_3D<double> R(axis_angle<double>(mAngle->q,mAxis).getRotMat());
vect<double,3> tmp_f = R * mEnd->Force;
mBase->Force += tmp_f;
double tmp_t = mEnd->Torque * mAxis;
if(fabs(mAngle->q_dot) > mSlipVelocity)
mAngle->f += tmp_t - mAngle->q_dot / fabs(mAngle->q_dot) * mSlipCoef * norm_2(tmp_f);
else {
mAngle->f += tmp_t - mAngle->q_dot / mSlipVelocity * mStictionCoef * norm_2(tmp_f);
};
mBase->Torque += R * ( mEnd->Torque - tmp_t * mAxis );
};
if((aFlag == store_dynamics) && (aStorage)) {
if(aStorage->frame_3D_mapping[mEnd]) {
aStorage->frame_3D_mapping[mEnd]->Force = mEnd->Force;
aStorage->frame_3D_mapping[mEnd]->Torque = mEnd->Torque;
};
};
};
//Does the actual calling of Runge Kutta: default precision is TOLERANCE defined in
//def.h
//Returns >0 if there's a problem with the running
int RGE::callRK(double x1, double x2, DoubleVector & v,
DoubleVector (*derivs)(double, const DoubleVector &),
double eps) {
using std::fabs;
using std::log;
double tol;
if (eps < 0.0) tol = TOLERANCE;
else if (eps < EPSTOL) tol = EPSTOL;
else tol = eps;
// x1 == x2 with high precision
if (close(fabs(x1), fabs(x2), EPSTOL)) return 0;
// RGE in terms of natural log of renormalisation scale
double from = log(fabs(x1));
double to = log(fabs(x2));
double guess = (from - to) * 0.1; //first step size
double hmin = (from - to) * tol * 1.0e-5;
int err =
integrateOdes(v, from, to, tol, guess, hmin, derivs, odeStepper);
setMu(x2);
return err;
}
T hypot_imp(T x, T y, const Policy& pol)
{
//
// Normalize x and y, so that both are positive and x >= y:
//
using std::fabs; using std::sqrt; // ADL of std names
x = fabs(x);
y = fabs(y);
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable: 4127)
#endif
// special case, see C99 Annex F:
if(std::numeric_limits<T>::has_infinity
&& ((x == std::numeric_limits<T>::infinity())
|| (y == std::numeric_limits<T>::infinity())))
return policies::raise_overflow_error<T>("boost::math::hypot<%1%>(%1%,%1%)", 0, pol);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
if(y > x)
(std::swap)(x, y);
if(x * tools::epsilon<T>() >= y)
return x;
T rat = y / x;
return x * sqrt(1 + rat*rat);
} // template <class T> T hypot(T x, T y)
TEST(AgradFwdFabs,FvarFvarDouble) {
using stan::agrad::fvar;
using std::fabs;
fvar<fvar<double> > x;
x.val_.val_ = 1.5;
x.val_.d_ = 2.0;
fvar<fvar<double> > a = fabs(x);
EXPECT_FLOAT_EQ(fabs(1.5), a.val_.val_);
EXPECT_FLOAT_EQ(2.0, a.val_.d_);
EXPECT_FLOAT_EQ(0, a.d_.val_);
EXPECT_FLOAT_EQ(0, a.d_.d_);
fvar<fvar<double> > y;
y.val_.val_ = 1.5;
y.d_.val_ = 2.0;
a = fabs(y);
EXPECT_FLOAT_EQ(fabs(1.5), a.val_.val_);
EXPECT_FLOAT_EQ(0, a.val_.d_);
EXPECT_FLOAT_EQ(2.0, a.d_.val_);
EXPECT_FLOAT_EQ(0, a.d_.d_);
}
int closestValue(TreeNode* root, double target) {
stack<TreeNode *> st;
TreeNode *p = root;
int res = root->val;
int val;
while (true) {
while (p != NULL) {
st.push(p);
p = p->left;
}
if (st.empty()) {
break;
}
p = st.top()->right;
val = st.top()->val;
st.pop();
if (fabs(val - target) < fabs(res - target)) {
res = val;
}
if (val >= target) {
break;
}
}
while (!st.empty()) {
st.pop();
}
return res;
}
void dry_revolute_joint_2D::doForce(kte_pass_flag aFlag, const shared_ptr<frame_storage>& aStorage) {
if((!mEnd) || (!mBase))
return;
using std::fabs;
if(!mAngle) {
mBase->Force += mEnd->Force;
mBase->Torque += mEnd->Torque;
} else {
vect<double,2> tmp_f = rot_mat_2D<double>(mAngle->q) * mEnd->Force;
mBase->Force += tmp_f;
if(fabs(mAngle->q_dot) > mSlipVelocity)
mAngle->f += mEnd->Torque - mAngle->q_dot / fabs(mAngle->q_dot) * mSlipCoef * norm_2(tmp_f);
else {
mAngle->f += mEnd->Torque - mAngle->q_dot / mSlipVelocity * mStictionCoef * norm_2(tmp_f);
};
};
if((aFlag == store_dynamics) && (aStorage)) {
if(aStorage->frame_2D_mapping[mEnd]) {
aStorage->frame_2D_mapping[mEnd]->Force = mEnd->Force;
aStorage->frame_2D_mapping[mEnd]->Torque = mEnd->Torque;
};
};
};
bool ViewInfo::isOblique() {
int i;
double d = 0.0;
for (i=0; i<3; i++) {
d += (fabs(m2p[0][i]*m2p[1][i]) + fabs(m2p[0][i]*m2p[2][i]) + fabs(m2p[1][i]*m2p[2][i]));
}
if(fabs(d) < 1.0e-4) return false;
else return true;
}
// If the destination is within one delta step away, the object has arrived.
// Set the location to the destination, stop, and return true.
// Otherwise, add the delta to the location, and return false.
bool Moving_object::update_location()
{
Cartesian_vector diff = destination - location;
if ((fabs(diff.delta_x) <= fabs(delta.delta_x)) && (fabs(diff.delta_y) <= fabs(delta.delta_y))) {
location = destination;
stop_moving();
return true;
}
location = location + delta;
return false;
}
//member function to find maximum absolute value in a given column and range within that column and return the corresponding row indice
int squareMatrix::FindMaxInCol(const int &c, const int &start, const int &end)const{
double maxVal = 0.0;
int maxRow = 0;
for( int ii = start; ii < end+1; ii++ ){
if( fabs((*this).Data(ii,c)) > maxVal ){
maxVal = fabs((*this).Data(ii,c));
maxRow = ii;
}
}
return maxRow;
}
void test_grad(const F& fun,
const std::vector<double>& args) {
using std::fabs;
std::vector<double> diffs_finite = finite_diffs(fun,args);
std::vector<double> diffs_var = grad(fun,args);
EXPECT_EQ(diffs_finite.size(), diffs_var.size());
for (size_t i = 0; i < args.size(); ++i) {
double tolerance = 1e-6 * fmax(fabs(diffs_finite[i]), fabs(diffs_var[i])) + 1e-14;
EXPECT_NEAR(diffs_finite[i], diffs_var[i], tolerance);
}
}
// get consistent clipping on different platforms by making line
// edges meet clipping box if close
void _Clipper::fixPt(QPointF& pt) const
{
if( fabs(pt.x() - clip.left()) < 1e-4 )
pt.setX(clip.left());
if( fabs(pt.x() - clip.right()) < 1e-4 )
pt.setX(clip.right());
if( fabs(pt.y() - clip.top()) < 1e-4 )
pt.setY(clip.top());
if( fabs(pt.y() - clip.bottom()) < 1e-4 )
pt.setY(clip.bottom());
}
void CPISwapTest::zciisconsistency() {
CommonVars common;
ZeroCouponInflationSwap::Type ztype = ZeroCouponInflationSwap::Payer;
Real nominal = 1000000.0;
Date startDate(common.evaluationDate);
Date endDate(25, November, 2059);
Calendar cal = UnitedKingdom();
BusinessDayConvention paymentConvention = ModifiedFollowing;
DayCounter dummyDC, dc = ActualActual();
Period observationLag(2,Months);
Rate quote = 0.03714;
ZeroCouponInflationSwap zciis(ztype, nominal, startDate, endDate, cal,
paymentConvention, dc, quote, common.ii,
observationLag);
// simple structure so simple pricing engine - most work done by index
ext::shared_ptr<DiscountingSwapEngine>
dse(new DiscountingSwapEngine(common.nominalTS));
zciis.setPricingEngine(dse);
QL_REQUIRE(fabs(zciis.NPV())<1e-3,"zciis does not reprice to zero");
std::vector<Date> oneDate;
oneDate.push_back(endDate);
Schedule schOneDate(oneDate, cal, paymentConvention);
CPISwap::Type stype = CPISwap::Payer;
Real inflationNominal = nominal;
Real floatNominal = inflationNominal * std::pow(1.0+quote,50);
bool subtractInflationNominal = true;
Real dummySpread=0.0, dummyFixedRate=0.0;
Natural fixingDays = 0;
Date baseDate = startDate - observationLag;
Real baseCPI = common.ii->fixing(baseDate);
ext::shared_ptr<IborIndex> dummyFloatIndex;
CPISwap cS(stype, floatNominal, subtractInflationNominal, dummySpread, dummyDC, schOneDate,
paymentConvention, fixingDays, dummyFloatIndex,
dummyFixedRate, baseCPI, dummyDC, schOneDate, paymentConvention, observationLag,
common.ii, CPI::AsIndex, inflationNominal);
cS.setPricingEngine(dse);
QL_REQUIRE(fabs(cS.NPV())<1e-3,"CPISwap as ZCIIS does not reprice to zero");
for (Size i=0; i<2; i++) {
QL_REQUIRE(fabs(cS.legNPV(i)-zciis.legNPV(i))<1e-3,"zciis leg does not equal CPISwap leg");
}
// remove circular refernce
common.hcpi.linkTo(ext::shared_ptr<ZeroInflationTermStructure>());
}
inline
fvar<T>
fabs(const fvar<T>& x) {
using std::fabs;
using stan::math::NOT_A_NUMBER;
if(x.val_ > 0.0)
return fvar<T>(fabs(x.val_), x.d_);
else if(x.val_ == 0.0)
return fvar<T>(fabs(x.val_), NOT_A_NUMBER);
else
return fvar<T>(fabs(x.val_), -x.d_);
}
bool TesterDouble::testEquals( double actualValue, double expectedValue,
const char * lineText, int lineNumber ) const
{
if( fabs(actualValue - expectedValue) < epsilon )
return true;
printf( "%s\nat line %i - "
"Actual: %le - Expected: %le\n"
"The value is within %le of expected. Epsilon is %le\n\n",
lineText, lineNumber,
actualValue, expectedValue,
fabs(actualValue - expectedValue), epsilon);
return false;
}
void test_grad_multi_student_t(const F& fun,
const std::vector<T_y> & vec_y,
const std::vector<T_mu> & vec_mu,
const std::vector<T_sigma> & vec_sigma,
const T_nu & nu) {
using std::fabs;
std::vector<double> diffs_finite = finite_diffs_multi_normal(fun,vec_y,vec_mu,vec_sigma,nu);
std::vector<double> diffs_var = grad_multi_normal(fun,vec_y,vec_mu,vec_sigma,nu);
EXPECT_EQ(diffs_finite.size(), diffs_var.size());
for (size_t i = 0; i < diffs_finite.size(); ++i) {
double tolerance = 1e-6 * fmax(fabs(diffs_finite[i]), fabs(diffs_var[i])) + 1e-14;
EXPECT_NEAR(diffs_finite[i], diffs_var[i], tolerance);
}
}
void broyden_good_method(const Vector& x_prev, Vector& x0, RootedFunction f, const T& tol = std::numeric_limits<T>::epsilon(), std::size_t max_iter = 50)
{
using std::fabs;
typedef typename vect_traits<Vector>::value_type ValueType;
typedef typename vect_traits<Vector>::size_type SizeType;
Vector dx = x0 - x_prev;
Vector y0 = f(x0);
Vector dy = y0 - f(x_prev);
std::size_t iter = 0;
mat<ValueType, mat_structure::square> J_inv = mat<ValueType, mat_structure::identity>(dx.size());
Vector Jdy = dy;
ValueType denom = dx * dy;
if( fabs(denom) < tol )
throw singularity_error("Broyden's good method failed due to a stationary point!");
Vector dxJ = dx;
for(SizeType i = 0; i < dx.size(); ++i)
for(SizeType j = 0; j < dx.size(); ++j)
J_inv(i,j) += (dx[i] - dy[i]) * dx[j] / denom;
while(true) {
dx = -J_inv * y0;
x0 += dx;
if(norm_2(dx) < tol)
return;
if( ++iter > max_iter )
throw maximum_iteration("Broyden's good method diverged, as detected by reaching the maximum iteration limit!");
dy = f(x0) - y0;
y0 += dy;
Jdy = J_inv * dy;
denom = dx * Jdy;
if( fabs(denom) < tol )
throw singularity_error("Broyden's good method failed due to a stationary point!");
dxJ = dx * J_inv;
for(SizeType i = 0; i < dx.size(); ++i)
for(SizeType j = 0; j < dx.size(); ++j)
J_inv(i,j) += (dx[i] - Jdy[i]) * dxJ[j] / denom;
};
return x0;
};
typename boost::enable_if_c< is_readable_matrix<Matrix>::value,
bool >::type is_diagonal(const Matrix& A, typename mat_traits<Matrix>::value_type NumTol = typename mat_traits<Matrix>::value_type(1E-8) ) {
if(A.get_row_count() != A.get_col_count())
return false;
typedef typename mat_traits< Matrix >::size_type SizeType;
using std::fabs;
for(SizeType i=0;i<A.get_row_count();i++)
for(SizeType j=0;j<i;j++)
if((fabs(A(j,i)) > NumTol) || (fabs(A(i,j)) > NumTol))
return false;
return true;
};
int AxisInfo::mapIndex(spViewInfo_t view, int i) {
if(i<0 || i>2) return i;
if(view == nullView) return i;
double d=0.0;
int ind=i;
for(int j=0;j<3;j++) {
if(fabs(view->p2m[j][i]) > d) {
d=fabs(view->p2m[j][i]);
ind = j;
}
}
return ind;
}
TEST(prob_transform,cov_matrix_jacobian) {
using stan::math::var;
using stan::math::determinant;
using std::log;
using std::fabs;
int K = 4;
//unsigned int K = 4;
unsigned int K_choose_2 = 6;
Matrix<var,Dynamic,1> X(K_choose_2 + K);
X << 1.0, 2.0, -3.0, 1.7, 9.8,
-12.2, 0.4, 0.2, 1.2, 2.7;
std::vector<var> x;
for (int i = 0; i < X.size(); ++i)
x.push_back(X(i));
var lp = 0.0;
Matrix<var,Dynamic,Dynamic> Sigma = stan::math::cov_matrix_constrain(X,K,lp);
std::vector<var> y;
for (int m = 0; m < K; ++m)
for (int n = 0; n <= m; ++n)
y.push_back(Sigma(m,n));
std::vector<std::vector<double> > j;
stan::math::jacobian(y,x,j);
Matrix<double,Dynamic,Dynamic> J(10,10);
for (int m = 0; m < 10; ++m)
for (int n = 0; n < 10; ++n)
J(m,n) = j[m][n];
double log_abs_jacobian_det = log(fabs(determinant(J)));
EXPECT_FLOAT_EQ(log_abs_jacobian_det,lp.val());
}
int
compute_residual(const int n, const double * const v1, const double * const v2,
double * const residual)
{
double local_residual = 0.0;
PERFLOG(compute_residual,IN(n));
for (int i = 0; i < n; i++)
{
double diff = fabs(v1[i] - v2[i]);
if (diff > local_residual)
local_residual = diff;
}
#ifdef USING_SSTMAC
// a little compute modeling
SSTMAC_compute_loop(0, n, 2/3.0/1.5);
#endif
PERFSTOP(compute_residual,IN(n));
// Use MPI's reduce function to collect all partial sums
double global_residual = 0;
MPI_Allreduce(&local_residual, &global_residual, 1, MPI_DOUBLE, MPI_SUM,
MPI_COMM_WORLD);
*residual = global_residual;
return (0);
}
inline
fvar<T>
gamma_q(const fvar<T>& x1, const double x2){
using stan::math::gamma_q;
using std::log;
using std::exp;
using std::pow;
using std::fabs;
using boost::math::tgamma;
using boost::math::digamma;
T u = gamma_q(x1.val_, x2);
T S = 0;
double s = 1;
double l = log(x2);
T g = tgamma(x1.val_);
T dig = digamma(x1.val_);
int k = 0;
T delta = s / (x1.val_ * x1.val_);
while (fabs(delta) > 1e-6) {
S += delta;
++k;
s *= -x2 / k;
delta = s / ((k + x1.val_) * (k + x1.val_));
}
T der1 = (1.0 - u) * ( dig - l ) + exp( x1.val_ * l ) * S / g;
return fvar<T>(u, x1.d_ * der1);
}
void bisection_method(T& low, T& hi, RootedFunction f, const T& tol = std::numeric_limits<T>::epsilon())
{
using std::fabs;
T low_value = f(low);
T hi_value = f(hi);
if( low_value * hi_value > 0.0 )
return;
while(fabs(hi - low) > tol) {
T mid = 0.5 * (hi + low);
T mid_value = f(mid);
if(mid_value * hi_value > 0.0) {
hi = mid;
hi_value = mid_value;
} else {
low = mid;
low_value = mid_value;
};
};
};
int test_error_vec (const DualVector& random_vec,
const Vector& error_vec)
{
using std::max;
using std::fabs;
typedef typename ValueType<Vector>::type Scalar;
static const Scalar tol = std::numeric_limits<Scalar>::epsilon() * 10;
Scalar max_abs_error = 0;
for (unsigned int i=0; i != error_vec.size(); ++i)
{
max_abs_error = max(max_abs_error, fabs(error_vec.raw_at(i)));
// Handle NaNs properly. Testing max_abs_error for NaN is
// impossible because IEEE sucks:
// https://en.wikipedia.org/wiki/IEEE_754_revision#min_and_max
if (max_abs_error > tol || error_vec[i] != error_vec[i])
{
std::cerr << "Value " << random_vec.raw_at(i) <<
"\nError " << error_vec.raw_at(i) <<
"\nTol " << tol << std::endl;
return 1;
}
}
return 0;
}
int test_error_vec (const DualVector& random_vec,
const Vector& error_vec)
{
using std::max;
using std::fabs;
typedef typename ValueType<Vector>::type Scalar;
static const Scalar tol = std::numeric_limits<Scalar>::epsilon() * 10;
Scalar max_abs_error = 0;
for (unsigned int i=0; i != error_vec.size(); ++i)
{
max_abs_error = max(max_abs_error, fabs(error_vec.raw_at(i)));
if (max_abs_error > tol)
{
std::cerr << "Value " << random_vec.raw_at(i) <<
"\nError " << error_vec.raw_at(i) <<
"\nTol " << tol << std::endl;
return 1;
}
}
return 0;
}
void grad_2F1(T& gradA, T& gradC, T a, T b, T c, T z, T precision = 1e-6) {
using std::fabs;
gradA = 0;
gradC = 0;
T gradAold = 0;
T gradCold = 0;
int k = 0;
T tDak = 1.0 / (a - 1);
while (fabs(tDak * (a + (k - 1)) ) > precision || k == 0) {
const T r = ( (a + k) / (c + k) ) * ( (b + k) / (T)(k + 1) ) * z;
tDak = r * tDak * (a + (k - 1)) / (a + k);
if (r == 0) break;
gradAold = r * gradAold + tDak;
gradCold = r * gradCold - tDak * ((a + k) / (c + k));
gradA += gradAold;
gradC += gradCold;
++k;
if (k > 200) break;
}
}
static
double get_proper_distance(const BaseTopology& b_space, const rt_metric_type& rt_dist, const point_type& a, const point_type& b) {
using std::fabs;
svp_reach_time_metric< base_time_topo, true > p_rt_dist(rt_dist);
double reach_time = p_rt_dist(a.pt, b.pt, b_space.get_space_topology());
return fabs(b.time - a.time) + reach_time;
};
// TODO Check for reference passing or const reference passing
double canberra_location(long nl, long ne, std::vector<std::vector<long> >& lists, long k, std::vector<long>& i1, std::vector<long>& i2, std::vector<double>& dist)
{
long i, idx1, idx2, l1, l2, count;
double distance, indicator;
indicator = 0.0;
count = 0;
for (idx1 = 1; idx1 <= nl - 1; idx1++)
for (idx2 = idx1 + 1; idx2 <= nl; idx2++)
{
distance = 0.0;
for (i = 1; i <= ne; i++)
{
l1 = lists[idx1 - 1][i - 1] + 1 <= k + 1 ? lists[idx1 - 1][i - 1] + 1 : k + 1;
l2 = lists[idx2 - 1][i - 1] + 1 <= k + 1 ? lists[idx2 - 1][i - 1] + 1 : k + 1;
distance += fabs(l1 - l2) / (l1 + l2);
}
i1[count] = idx1 - 1;
i2[count] = idx2 - 1;
dist[count] = distance;
count++;
indicator += 2.0 * distance / (nl * (nl - 1));
}
return (indicator);
}
inline
fvar<typename stan::return_type<T,double>::type>
gamma_p(const fvar<T>& x1, double x2){
using stan::math::gamma_p;
using std::log;
using std::exp;
using std::pow;
using std::fabs;
using boost::math::tgamma;
using boost::math::digamma;
typename stan::return_type<T,double>::type u = gamma_p(x1.val_, x2);
T S = 0.0;
double s = 1.0;
double l = log(x2);
T g = tgamma(x1.val_);
T dig = digamma(x1.val_);
int k = 0;
T delta = s / (x1.val_ * x1.val_);
while (fabs(delta) > 1e-6) {
S += delta;
++k;
s *= -x2 / k;
delta = s / ((k + x1.val_) * (k + x1.val_));
}
T der1 = (u) * ( dig - l ) + exp( x1.val_ * l ) * S / g;
return fvar<typename
stan::return_type<T,double>::type>(u,x1.d_ * -der1);
}
inline
fvar<T>
gamma_p(const fvar<T>& x1, const fvar<T>& x2){
using stan::math::gamma_p;
using std::log;
using std::exp;
using std::pow;
using std::fabs;
using boost::math::tgamma;
using boost::math::digamma;
T u = gamma_p(x1.val_, x2.val_);
T S = 0;
T s = 1;
T l = log(x2.val_);
T g = tgamma(x1.val_);
T dig = digamma(x1.val_);
int k = 0;
T delta = s / (x1.val_ * x1.val_);
while (fabs(delta) > 1e-6) {
S += delta;
++k;
s *= -x2.val_ / k;
delta = s / ((k + x1.val_) * (k + x1.val_));
}
T der1 = (u) * ( dig - l ) + exp( x1.val_ * l ) * S / g;
T der2 = exp(-x2.val_) * pow(x2.val_, x1.val_ - 1.0) / g;
return fvar<T>(u,x1.d_ * -der1 + x2.d_ * der2);
}
static
double get_proper_norm(const BaseTopology& b_space, const rt_metric_type& rt_dist, const point_difference_type& dp) {
using std::fabs;
svp_reach_time_metric< base_time_topo, true > p_rt_dist(rt_dist);
double reach_time = p_rt_dist(dp.pt, b_space.get_space_topology());
return fabs(dp.time) + reach_time;
};
