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merge with main branch

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This commit is contained in:
Gael Guennebaud
2013-07-17 13:21:35 +02:00
parent 231d4a6fda 20e535e142
commit 2f593ee67c
245 changed files with 8361 additions and 2515 deletions
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2
Eigen/src/Eigenvalues/ComplexEigenSolver.h
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@@ -294,7 +294,7 @@ void ComplexEigenSolver<MatrixType>::doComputeEigenvectors(const RealScalar& mat
{
// If the i-th and k-th eigenvalue are equal, then z equals 0.
// Use a small value instead, to prevent division by zero.
internal::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
numext::real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
}
m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
}

10
Eigen/src/Eigenvalues/ComplexSchur.h
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@@ -263,8 +263,8 @@ template<typename _MatrixType> class ComplexSchur
template<typename MatrixType>
inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
{
RealScalar d = internal::norm1(m_matT.coeff(i,i)) + internal::norm1(m_matT.coeff(i+1,i+1));
RealScalar sd = internal::norm1(m_matT.coeff(i+1,i));
RealScalar d = numext::norm1(m_matT.coeff(i,i)) + numext::norm1(m_matT.coeff(i+1,i+1));
RealScalar sd = numext::norm1(m_matT.coeff(i+1,i));
if (internal::isMuchSmallerThan(sd, d, NumTraits<RealScalar>::epsilon()))
{
m_matT.coeffRef(i+1,i) = ComplexScalar(0);
@@ -282,7 +282,7 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
if (iter == 10 || iter == 20)
{
// exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
return abs(internal::real(m_matT.coeff(iu,iu-1))) + abs(internal::real(m_matT.coeff(iu-1,iu-2)));
return abs(numext::real(m_matT.coeff(iu,iu-1))) + abs(numext::real(m_matT.coeff(iu-1,iu-2)));
}
// compute the shift as one of the eigenvalues of t, the 2x2
@@ -299,13 +299,13 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
ComplexScalar eival1 = (trace + disc) / RealScalar(2);
ComplexScalar eival2 = (trace - disc) / RealScalar(2);
if(internal::norm1(eival1) > internal::norm1(eival2))
if(numext::norm1(eival1) > numext::norm1(eival2))
eival2 = det / eival1;
else
eival1 = det / eival2;
// choose the eigenvalue closest to the bottom entry of the diagonal
if(internal::norm1(eival1-t.coeff(1,1)) < internal::norm1(eival2-t.coeff(1,1)))
if(numext::norm1(eival1-t.coeff(1,1)) < numext::norm1(eival2-t.coeff(1,1)))
return normt * eival1;
else
return normt * eival2;

26
Eigen/src/Eigenvalues/EigenSolver.h
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@@ -317,12 +317,12 @@ MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
MatrixType matD = MatrixType::Zero(n,n);
for (Index i=0; i<n; ++i)
{
if (internal::isMuchSmallerThan(internal::imag(m_eivalues.coeff(i)), internal::real(m_eivalues.coeff(i))))
matD.coeffRef(i,i) = internal::real(m_eivalues.coeff(i));
if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i))))
matD.coeffRef(i,i) = numext::real(m_eivalues.coeff(i));
else
{
matD.template block<2,2>(i,i) << internal::real(m_eivalues.coeff(i)), internal::imag(m_eivalues.coeff(i)),
-internal::imag(m_eivalues.coeff(i)), internal::real(m_eivalues.coeff(i));
matD.template block<2,2>(i,i) << numext::real(m_eivalues.coeff(i)), numext::imag(m_eivalues.coeff(i)),
-numext::imag(m_eivalues.coeff(i)), numext::real(m_eivalues.coeff(i));
++i;
}
}
@@ -338,7 +338,7 @@ typename EigenSolver<MatrixType>::EigenvectorsType EigenSolver<MatrixType>::eige
EigenvectorsType matV(n,n);
for (Index j=0; j<n; ++j)
{
if (internal::isMuchSmallerThan(internal::imag(m_eivalues.coeff(j)), internal::real(m_eivalues.coeff(j))) || j+1==n)
if (internal::isMuchSmallerThan(numext::imag(m_eivalues.coeff(j)), numext::real(m_eivalues.coeff(j))) || j+1==n)
{
// we have a real eigen value
matV.col(j) = m_eivec.col(j).template cast<ComplexScalar>();
@@ -515,8 +515,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
else
{
std::complex<Scalar> cc = cdiv<Scalar>(0.0,-m_matT.coeff(n-1,n),m_matT.coeff(n-1,n-1)-p,q);
m_matT.coeffRef(n-1,n-1) = internal::real(cc);
m_matT.coeffRef(n-1,n) = internal::imag(cc);
m_matT.coeffRef(n-1,n-1) = numext::real(cc);
m_matT.coeffRef(n-1,n) = numext::imag(cc);
}
m_matT.coeffRef(n,n-1) = 0.0;
m_matT.coeffRef(n,n) = 1.0;
@@ -538,8 +538,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
if (m_eivalues.coeff(i).imag() == RealScalar(0))
{
std::complex<Scalar> cc = cdiv(-ra,-sa,w,q);
m_matT.coeffRef(i,n-1) = internal::real(cc);
m_matT.coeffRef(i,n) = internal::imag(cc);
m_matT.coeffRef(i,n-1) = numext::real(cc);
m_matT.coeffRef(i,n) = numext::imag(cc);
}
else
{
@@ -552,8 +552,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
m_matT.coeffRef(i,n-1) = internal::real(cc);
m_matT.coeffRef(i,n) = internal::imag(cc);
m_matT.coeffRef(i,n-1) = numext::real(cc);
m_matT.coeffRef(i,n) = numext::imag(cc);
if (abs(x) > (abs(lastw) + abs(q)))
{
m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
@@ -562,8 +562,8 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
else
{
cc = cdiv(-lastra-y*m_matT.coeff(i,n-1),-lastsa-y*m_matT.coeff(i,n),lastw,q);
m_matT.coeffRef(i+1,n-1) = internal::real(cc);
m_matT.coeffRef(i+1,n) = internal::imag(cc);
m_matT.coeffRef(i+1,n-1) = numext::real(cc);
m_matT.coeffRef(i+1,n) = numext::imag(cc);
}
}

4
Eigen/src/Eigenvalues/HessenbergDecomposition.h
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@@ -82,7 +82,7 @@ template<typename _MatrixType> class HessenbergDecomposition
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
/** \brief Return type of matrixQ() */
typedef typename HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType HouseholderSequenceType;
typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> MatrixHReturnType;
@@ -313,7 +313,7 @@ void HessenbergDecomposition<MatrixType>::_compute(MatrixType& matA, CoeffVector
// A = A H'
matA.rightCols(remainingSize)
.applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), internal::conj(h), &temp.coeffRef(0));
.applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1).conjugate(), numext::conj(h), &temp.coeffRef(0));
}
}

16
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@@ -395,7 +395,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
if(n==1)
{
m_eivalues.coeffRef(0,0) = internal::real(matrix.coeff(0,0));
m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0));
if(computeEigenvectors)
m_eivec.setOnes(n,n);
m_info = Success;
@@ -669,7 +669,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
static inline void computeRoots(const MatrixType& m, VectorType& roots)
{
using std::sqrt;
const Scalar t0 = Scalar(0.5) * sqrt( abs2(m(0,0)-m(1,1)) + Scalar(4)*m(1,0)*m(1,0));
const Scalar t0 = Scalar(0.5) * sqrt( numext::abs2(m(0,0)-m(1,1)) + Scalar(4)*m(1,0)*m(1,0));
const Scalar t1 = Scalar(0.5) * (m(0,0) + m(1,1));
roots(0) = t1 - t0;
roots(1) = t1 + t0;
@@ -699,9 +699,9 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
if(computeEigenvectors)
{
scaledMat.diagonal().array () -= eivals(1);
Scalar a2 = abs2(scaledMat(0,0));
Scalar c2 = abs2(scaledMat(1,1));
Scalar b2 = abs2(scaledMat(1,0));
Scalar a2 = numext::abs2(scaledMat(0,0));
Scalar c2 = numext::abs2(scaledMat(1,1));
Scalar b2 = numext::abs2(scaledMat(1,0));
if(a2>c2)
{
eivecs.col(1) << -scaledMat(1,0), scaledMat(0,0);
@@ -744,7 +744,7 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
RealScalar e = subdiag[end-1];
// Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still
// underflow thus leading to inf/NaN values when using the following commented code:
// RealScalar e2 = abs2(subdiag[end-1]);
// RealScalar e2 = numext::abs2(subdiag[end-1]);
// RealScalar mu = diag[end] - e2 / (td + (td>0 ? 1 : -1) * sqrt(td*td + e2));
// This explain the following, somewhat more complicated, version:
RealScalar mu = diag[end];
@@ -752,8 +752,8 @@ static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index sta
mu -= abs(e);
else
{
RealScalar e2 = abs2(subdiag[end-1]);
RealScalar h = hypot(td,e);
RealScalar e2 = numext::abs2(subdiag[end-1]);
RealScalar h = numext::hypot(td,e);
if(e2==0) mu -= (e / (td + (td>0 ? 1 : -1))) * (e / h);
else mu -= e2 / (td + (td>0 ? h : -h));
}

2
Eigen/src/Eigenvalues/SelfAdjointEigenSolver_MKL.h
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@@ -56,7 +56,7 @@ SelfAdjointEigenSolver<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(c
\
if(n==1) \
{ \
m_eivalues.coeffRef(0,0) = internal::real(matrix.coeff(0,0)); \
m_eivalues.coeffRef(0,0) = numext::real(matrix.coeff(0,0)); \
if(computeEigenvectors) m_eivec.setOnes(n,n); \
m_info = Success; \
m_isInitialized = true; \

10
Eigen/src/Eigenvalues/Tridiagonalization.h
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@@ -96,7 +96,7 @@ template<typename _MatrixType> class Tridiagonalization
>::type SubDiagonalReturnType;
/** \brief Return type of matrixQ() */
typedef typename HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType HouseholderSequenceType;
typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename CoeffVectorType::ConjugateReturnType>::type> HouseholderSequenceType;
/** \brief Default constructor.
*
@@ -345,7 +345,7 @@ namespace internal {
template<typename MatrixType, typename CoeffVectorType>
void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
{
using internal::conj;
using numext::conj;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
@@ -468,7 +468,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
{
using std::sqrt;
diag[0] = mat(0,0);
RealScalar v1norm2 = abs2(mat(2,0));
RealScalar v1norm2 = numext::abs2(mat(2,0));
if(v1norm2 == RealScalar(0))
{
diag[1] = mat(1,1);
@@ -480,7 +480,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
}
else
{
RealScalar beta = sqrt(abs2(mat(1,0)) + v1norm2);
RealScalar beta = sqrt(numext::abs2(mat(1,0)) + v1norm2);
RealScalar invBeta = RealScalar(1)/beta;
Scalar m01 = mat(1,0) * invBeta;
Scalar m02 = mat(2,0) * invBeta;
@@ -510,7 +510,7 @@ struct tridiagonalization_inplace_selector<MatrixType,1,IsComplex>
template<typename DiagonalType, typename SubDiagonalType>
static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType&, bool extractQ)
{
diag(0,0) = real(mat(0,0));
diag(0,0) = numext::real(mat(0,0));
if(extractQ)
mat(0,0) = Scalar(1);
}