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Fix bug #314:

Browse Source 
- remove most of the metaprogramming kung fu in MathFunctions.h (only keep functions that differs from the std)
- remove the overloads for array expression that were in the std namespace
This commit is contained in:
Gael Guennebaud
2012-11-06 15:25:50 +01:00
parent 959ef37006
commit a76fbbf397
88 changed files with 496 additions and 468 deletions
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2
unsupported/Eigen/src/FFT/ei_kissfft_impl.h
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@@ -28,6 +28,7 @@ struct kiss_cpx_fft
inline
void make_twiddles(int nfft,bool inverse)
{
using std::acos;
m_inverse = inverse;
m_twiddles.resize(nfft);
Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft;
@@ -399,6 +400,7 @@ struct kissfft_impl
inline
Complex * real_twiddles(int ncfft2)
{
using std::acos;
std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
if ( (int)twidref.size() != ncfft2 ) {
twidref.resize(ncfft2);

3
unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
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@@ -116,6 +116,7 @@ template<typename Scalar, int _UpLo, typename OrderingType>
template<typename _MatrixType>
void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType& mat)
{
using std::sqrt;
eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
// FIXME Stability: We should probably compute the scaling factors and the shifts that are needed to ensure a succesful LLT factorization and an efficient preconditioner.
@@ -182,7 +183,7 @@ void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType
m_info = NumericalIssue;
return;
}
RealScalar rdiag = internal::sqrt(RealScalar(diag));
RealScalar rdiag = sqrt(RealScalar(diag));
Scalar scal = Scalar(1)/rdiag;
vals[colPtr[j]] = rdiag;
// Insert the largest p elements in the matrix and scale them meanwhile

3
unsupported/Eigen/src/IterativeSolvers/IterationController.h
View File

@@ -129,7 +129,8 @@ class IterationController
bool converged() const { return m_res <= m_rhsn * m_resmax; }
bool converged(double nr)
{
m_res = internal::abs(nr);
using std::abs;
m_res = abs(nr);
m_resminreach = (std::min)(m_resminreach, m_res);
return converged();
}

1
unsupported/Eigen/src/IterativeSolvers/MINRES.h
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@@ -32,6 +32,7 @@ namespace Eigen {
const Preconditioner& precond, int& iters,
typename Dest::RealScalar& tol_error)
{
using std::sqrt;
typedef typename Dest::RealScalar RealScalar;
typedef typename Dest::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,1> VectorType;

17
unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
View File

@@ -235,6 +235,7 @@ void MatrixFunction<MatrixType,AtomicType,1>::computeSchurDecomposition()
template <typename MatrixType, typename AtomicType>
void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
{
using std::abs;
const Index rows = m_T.rows();
VectorType diag = m_T.diagonal(); // contains eigenvalues of A
@@ -251,14 +252,14 @@ void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
// Look for other element to add to the set
for (Index j=i+1; j<rows; ++j) {
if (internal::abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {
typename ListOfClusters::iterator qj = findCluster(diag(j));
if (qj == m_clusters.end()) {
qi->push_back(diag(j));
} else {
qi->insert(qi->end(), qj->begin(), qj->end());
m_clusters.erase(qj);
}
if (abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {
typename ListOfClusters::iterator qj = findCluster(diag(j));
if (qj == m_clusters.end()) {
qi->push_back(diag(j));
} else {
qi->insert(qi->end(), qj->begin(), qj->end());
m_clusters.erase(qj);
}
}
}
}

3
unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
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@@ -125,6 +125,7 @@ void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixTy
template <typename MatrixType>
void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result)
{
using std::pow;
int numberOfSquareRoots = 0;
int numberOfExtraSquareRoots = 0;
int degree;
@@ -141,7 +142,7 @@ void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixTy
degree = getPadeDegree(normTminusI);
int degree2 = getPadeDegree(normTminusI / RealScalar(2));
if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1))
break;
break;
++numberOfExtraSquareRoots;
}
MatrixType sqrtT;

6
unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
View File

@@ -99,11 +99,12 @@ template <typename MatrixType>
void MatrixSquareRootQuasiTriangular<MatrixType>::computeDiagonalPartOfSqrt(MatrixType& sqrtT,
const MatrixType& T)
{
using std::sqrt;
const Index size = m_A.rows();
for (Index i = 0; i < size; i++) {
if (i == size - 1 || T.coeff(i+1, i) == 0) {
eigen_assert(T(i,i) > 0);
sqrtT.coeffRef(i,i) = internal::sqrt(T.coeff(i,i));
sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));
}
else {
compute2x2diagonalBlock(sqrtT, T, i);
@@ -289,6 +290,7 @@ template <typename MatrixType>
template <typename ResultType>
void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
{
using std::sqrt;
// Compute Schur decomposition of m_A
const ComplexSchur<MatrixType> schurOfA(m_A);
const MatrixType& T = schurOfA.matrixT();
@@ -299,7 +301,7 @@ void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
result.resize(m_A.rows(), m_A.cols());
typedef typename MatrixType::Index Index;
for (Index i = 0; i < m_A.rows(); i++) {
result.coeffRef(i,i) = internal::sqrt(T.coeff(i,i));
result.coeffRef(i,i) = sqrt(T.coeff(i,i));
}
for (Index j = 1; j < m_A.cols(); j++) {
for (Index i = j-1; i >= 0; i--) {

15
unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
View File

@@ -52,7 +52,7 @@ public:
Parameters()
: factor(Scalar(100.))
, maxfev(1000)
, xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
, xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
, nb_of_subdiagonals(-1)
, nb_of_superdiagonals(-1)
, epsfcn(Scalar(0.)) {}
@@ -70,7 +70,7 @@ public:
HybridNonLinearSolverSpace::Status hybrj1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
HybridNonLinearSolverSpace::Status solveInit(FVectorType &x);
@@ -79,7 +79,7 @@ public:
HybridNonLinearSolverSpace::Status hybrd1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType &x);
@@ -185,6 +185,8 @@ template<typename FunctorType, typename Scalar>
HybridNonLinearSolverSpace::Status
HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)
{
using std::abs;
assert(x.size()==n); // check the caller is not cheating us
Index j;
@@ -276,7 +278,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)
++ncsuc;
if (ratio >= Scalar(.5) || ncsuc > 1)
delta = (std::max)(delta, pnorm / Scalar(.5));
if (internal::abs(ratio - 1.) <= Scalar(.1)) {
if (abs(ratio - 1.) <= Scalar(.1)) {
delta = pnorm / Scalar(.5);
}
}
@@ -423,6 +425,9 @@ template<typename FunctorType, typename Scalar>
HybridNonLinearSolverSpace::Status
HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType &x)
{
using std::sqrt;
using std::abs;
assert(x.size()==n); // check the caller is not cheating us
Index j;
@@ -516,7 +521,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
++ncsuc;
if (ratio >= Scalar(.5) || ncsuc > 1)
delta = (std::max)(delta, pnorm / Scalar(.5));
if (internal::abs(ratio - 1.) <= Scalar(.1)) {
if (abs(ratio - 1.) <= Scalar(.1)) {
delta = pnorm / Scalar(.5);
}
}

36
unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
View File

@@ -55,8 +55,8 @@ public:
Parameters()
: factor(Scalar(100.))
, maxfev(400)
, ftol(internal::sqrt(NumTraits<Scalar>::epsilon()))
, xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
, ftol(std::sqrt(NumTraits<Scalar>::epsilon()))
, xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
, gtol(Scalar(0.))
, epsfcn(Scalar(0.)) {}
Scalar factor;
@@ -72,7 +72,7 @@ public:
LevenbergMarquardtSpace::Status lmder1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@@ -83,12 +83,12 @@ public:
FunctorType &functor,
FVectorType &x,
Index *nfev,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
LevenbergMarquardtSpace::Status lmstr1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x);
@@ -206,6 +206,9 @@ template<typename FunctorType, typename Scalar>
LevenbergMarquardtSpace::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
{
using std::abs;
using std::sqrt;
assert(x.size()==n); // check the caller is not cheating us
/* calculate the jacobian matrix. */
@@ -249,7 +252,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
if (fnorm != 0.)
for (Index j = 0; j < n; ++j)
if (wa2[permutation.indices()[j]] != 0.)
gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (gnorm <= parameters.gtol)
@@ -288,7 +291,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
/* the scaled directional derivative. */
wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
temp1 = internal::abs2(wa3.stableNorm() / fnorm);
temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
temp2 = internal::abs2(sqrt(par) * pnorm / fnorm);
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
@@ -326,9 +329,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
}
/* tests for convergence. */
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::RelativeReductionTooSmall;
if (delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@@ -336,7 +339,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
/* tests for termination and stringent tolerances. */
if (nfev >= parameters.maxfev)
return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::FtolTooSmall;
if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
return LevenbergMarquardtSpace::XtolTooSmall;
@@ -423,6 +426,9 @@ template<typename FunctorType, typename Scalar>
LevenbergMarquardtSpace::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x)
{
using std::abs;
using std::sqrt;
assert(x.size()==n); // check the caller is not cheating us
Index i, j;
@@ -496,7 +502,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
if (fnorm != 0.)
for (j = 0; j < n; ++j)
if (wa2[permutation.indices()[j]] != 0.)
gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (gnorm <= parameters.gtol)
@@ -535,7 +541,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
/* the scaled directional derivative. */
wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
temp1 = internal::abs2(wa3.stableNorm() / fnorm);
temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
temp2 = internal::abs2(sqrt(par) * pnorm / fnorm);
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
@@ -573,9 +579,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
}
/* tests for convergence. */
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::RelativeReductionTooSmall;
if (delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@@ -583,7 +589,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
/* tests for termination and stringent tolerances. */
if (nfev >= parameters.maxfev)
return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::FtolTooSmall;
if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
return LevenbergMarquardtSpace::XtolTooSmall;

4
unsupported/Eigen/src/NonLinearOptimization/chkder.h
View File

@@ -16,6 +16,10 @@ void chkder(
Matrix< Scalar, Dynamic, 1 > &err
)
{
using std::sqrt;
using std::abs;
using std::log;
typedef DenseIndex Index;
const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());

3
unsupported/Eigen/src/NonLinearOptimization/covar.h
View File

@@ -6,8 +6,9 @@ template <typename Scalar>
void covar(
Matrix< Scalar, Dynamic, Dynamic > &r,
const VectorXi &ipvt,
Scalar tol = sqrt(NumTraits<Scalar>::epsilon()) )
Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
{
using std::abs;
typedef DenseIndex Index;
/* Local variables */

3
unsupported/Eigen/src/NonLinearOptimization/dogleg.h
View File

@@ -10,6 +10,9 @@ void dogleg(
Scalar delta,
Matrix< Scalar, Dynamic, 1 > &x)
{
using std::abs;
using std::sqrt;
typedef DenseIndex Index;
/* Local variables */

3
unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
View File

@@ -11,6 +11,9 @@ DenseIndex fdjac1(
DenseIndex ml, DenseIndex mu,
Scalar epsfcn)
{
using std::sqrt;
using std::abs;
typedef DenseIndex Index;
/* Local variables */

4
unsupported/Eigen/src/NonLinearOptimization/lmpar.h
View File

@@ -12,6 +12,8 @@ void lmpar(
Scalar &par,
Matrix< Scalar, Dynamic, 1 > &x)
{
using std::abs;
using std::sqrt;
typedef DenseIndex Index;
/* Local variables */
@@ -168,6 +170,8 @@ void lmpar2(
Matrix< Scalar, Dynamic, 1 > &x)
{
using std::sqrt;
using std::abs;
typedef DenseIndex Index;
/* Local variables */

6
unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
View File

@@ -63,11 +63,13 @@ public:
*/
int df(const InputType& _x, JacobianType &jac) const
{
using std::sqrt;
using std::abs;
/* Local variables */
Scalar h;
int nfev=0;
const typename InputType::Index n = _x.size();
const Scalar eps = internal::sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
ValueType val1, val2;
InputType x = _x;
// TODO : we should do this only if the size is not already known
@@ -89,7 +91,7 @@ public:
// Function Body
for (int j = 0; j < n; ++j) {
h = eps * internal::abs(x[j]);
h = eps * abs(x[j]);
if (h == 0.) {
h = eps;
}

1
unsupported/Eigen/src/Polynomials/Companion.h
View File

@@ -210,6 +210,7 @@ bool companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm,
template< typename _Scalar, int _Deg >
void companion<_Scalar,_Deg>::balance()
{
using std::abs;
EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );
const Index deg = m_monic.size();
const Index deg_1 = deg-1;

13
unsupported/Eigen/src/Polynomials/PolynomialSolver.h
View File

@@ -69,10 +69,11 @@ class PolynomialSolverBase
inline void realRoots( Stl_back_insertion_sequence& bi_seq,
const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
{
using std::abs;
bi_seq.clear();
for(Index i=0; i<m_roots.size(); ++i )
{
if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold ){
if( abs( m_roots[i].imag() ) < absImaginaryThreshold ){
bi_seq.push_back( m_roots[i].real() ); }
}
}
@@ -118,13 +119,14 @@ class PolynomialSolverBase
bool& hasArealRoot,
const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
{
using std::abs;
hasArealRoot = false;
Index res=0;
RealScalar abs2(0);
for( Index i=0; i<m_roots.size(); ++i )
{
if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold )
if( abs( m_roots[i].imag() ) < absImaginaryThreshold )
{
if( !hasArealRoot )
{
@@ -144,7 +146,7 @@ class PolynomialSolverBase
}
else
{
if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){
if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
res = i; }
}
}
@@ -158,13 +160,14 @@ class PolynomialSolverBase
bool& hasArealRoot,
const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
{
using std::abs;
hasArealRoot = false;
Index res=0;
RealScalar val(0);
for( Index i=0; i<m_roots.size(); ++i )
{
if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold )
if( abs( m_roots[i].imag() ) < absImaginaryThreshold )
{
if( !hasArealRoot )
{
@@ -184,7 +187,7 @@ class PolynomialSolverBase
}
else
{
if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){
if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
res = i; }
}
}

6
unsupported/Eigen/src/Polynomials/PolynomialUtils.h
View File

@@ -74,6 +74,7 @@ template <typename Polynomial>
inline
typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly )
{
using std::abs;
typedef typename Polynomial::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real Real;
@@ -82,7 +83,7 @@ typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Po
Real cb(0);
for( DenseIndex i=0; i<poly.size()-1; ++i ){
cb += internal::abs(poly[i]*inv_leading_coeff); }
cb += abs(poly[i]*inv_leading_coeff); }
return cb + Real(1);
}
@@ -96,6 +97,7 @@ template <typename Polynomial>
inline
typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly )
{
using std::abs;
typedef typename Polynomial::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real Real;
@@ -107,7 +109,7 @@ typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Po
const Scalar inv_min_coeff = Scalar(1)/poly[i];
Real cb(1);
for( DenseIndex j=i+1; j<poly.size(); ++j ){
cb += internal::abs(poly[j]*inv_min_coeff); }
cb += abs(poly[j]*inv_min_coeff); }
return Real(1)/cb;
}