typename EuclNorm<VectorType, MatrixType>::ScalarType
EuclNorm<VectorType, MatrixType>::operator()(const MatrixType &A) const {
return sqrt(nonnegativePart(
capd::matrixAlgorithms::spectralRadiusOfSymMatrix(Transpose(A) * A)
));
}
typename EuclLNorm<VectorType, MatrixType>::ScalarType
EuclLNorm<VectorType, MatrixType>::operator()(const VectorType &x) const {
ScalarType s(0.);
for(int i=0;i<x.dimension();++i)
s += power(x[i], 2);
return sqrt(nonnegativePart(s));
}
typename Object::ScalarType euclNorm(const Object& u){
typedef typename Object::ScalarType Scalar;
Scalar sum = TypeTraits<Scalar>::zero();
typename Object::const_iterator b=u.begin(), e=u.end();
while(b!=e)
{
sum += static_cast<Scalar>(power(*b,2));
++b;
}
return Scalar(sqrt(nonnegativePart(sum)));
}
typename MatrixType::ScalarType::BoundType OdeNum<MatrixType>::quadEscTime(Real a, Real b, Real c, Real r)
{
if(a>r) return -1;
else{
if( c == 0)
return OdeNum<MatrixType>::linEscTime(a,b,r);
else{
ScalarType ib = ScalarType(b);
ScalarType delta = power(ib,2)-4*ScalarType(c)*(ScalarType(a)-ScalarType(r));
// ScalarType delta=ib^2-4*ScalarType(c)*(ScalarType(a)-ScalarType(r));
if(c>0 || (delta > 0 && b > 0))
return ((-b+sqrt(nonnegativePart(delta)))/2/c).leftBound();
else
return OdeNum<MatrixType>::infty;
}
}
}
