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Replace local variables by member variables in compute() methods.

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This is to avoid dynamic memory allocations in the compute() methods of
ComplexEigenSolver, EigenSolver, and SelfAdjointEigenSolver where possible.
As a result, Tridiagonalization::decomposeInPlace() is no longer used.
Biggest remaining issue is the allocation in HouseholderSequence::evalTo().
This commit is contained in:
Jitse Niesen 2010-05-24 17:43:06 +01:00
parent 68820fd4e8
commit 7a43a4408b
4 changed files with 101 additions and 81 deletions
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23
Eigen/src/Eigenvalues/ComplexEigenSolver.h
View File

@ -3,6 +3,7 @@
//
// Copyright (C) 2009 Claire Maurice
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@ -99,7 +100,8 @@ template<typename _MatrixType> class ComplexEigenSolver
: m_eivec(),
m_eivalues(),
m_schur(),
m_isInitialized(false)
m_isInitialized(false),
m_matX()
{}
/** \brief Default Constructor with memory preallocation
@ -112,7 +114,8 @@ template<typename _MatrixType> class ComplexEigenSolver
: m_eivec(size, size),
m_eivalues(size),
m_schur(size),
m_isInitialized(false)
m_isInitialized(false),
m_matX(size, size)
{}
/** \brief Constructor; computes eigendecomposition of given matrix.
@ -125,7 +128,8 @@ template<typename _MatrixType> class ComplexEigenSolver
: m_eivec(matrix.rows(),matrix.cols()),
m_eivalues(matrix.cols()),
m_schur(matrix.rows()),
m_isInitialized(false)
m_isInitialized(false),
m_matX(matrix.rows(),matrix.cols())
{
compute(matrix);
}
@ -199,6 +203,7 @@ template<typename _MatrixType> class ComplexEigenSolver
EigenvalueType m_eivalues;
ComplexSchur<MatrixType> m_schur;
bool m_isInitialized;
EigenvectorType m_matX;
};
@ -217,16 +222,16 @@ void ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix)
// Step 2: Compute X such that T = X D X^(-1), where D is the diagonal of T.
// The matrix X is unit triangular.
EigenvectorType X = EigenvectorType::Zero(n, n);
m_matX = EigenvectorType::Zero(n, n);
for(int k=n-1 ; k>=0 ; k--)
{
X.coeffRef(k,k) = ComplexScalar(1.0,0.0);
m_matX.coeffRef(k,k) = ComplexScalar(1.0,0.0);
// Compute X(i,k) using the (i,k) entry of the equation X T = D X
for(int i=k-1 ; i>=0 ; i--)
{
X.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
m_matX.coeffRef(i,k) = -m_schur.matrixT().coeff(i,k);
if(k-i-1>0)
X.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * X.col(k).segment(i+1,k-i-1)).value();
m_matX.coeffRef(i,k) -= (m_schur.matrixT().row(i).segment(i+1,k-i-1) * m_matX.col(k).segment(i+1,k-i-1)).value();
ComplexScalar z = m_schur.matrixT().coeff(i,i) - m_schur.matrixT().coeff(k,k);
if(z==ComplexScalar(0))
{
@ -234,12 +239,12 @@ void ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix)
// Use a small value instead, to prevent division by zero.
ei_real_ref(z) = NumTraits<RealScalar>::epsilon() * matrixnorm;
}
X.coeffRef(i,k) = X.coeff(i,k) / z;
m_matX.coeffRef(i,k) = m_matX.coeff(i,k) / z;
}
}
// Step 3: Compute V as V = U X; now A = U T U^* = U X D X^(-1) U^* = V D V^(-1)
m_eivec = m_schur.matrixU() * X;
m_eivec.noalias() = m_schur.matrixU() * m_matX;
// .. and normalize the eigenvectors
for(int k=0 ; k<n ; k++)
{

119
Eigen/src/Eigenvalues/EigenSolver.h
View File

@ -120,7 +120,7 @@ template<typename _MatrixType> class EigenSolver
*
* \sa compute() for an example.
*/
EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false) {}
EigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_realSchur(), m_matT(), m_tmp() {}
/** \brief Default Constructor with memory preallocation
*
@ -131,7 +131,11 @@ template<typename _MatrixType> class EigenSolver
EigenSolver(int size)
: m_eivec(size, size),
m_eivalues(size),
m_isInitialized(false) {}
m_isInitialized(false),
m_realSchur(size),
m_matT(size, size),
m_tmp(size)
{}
/** \brief Constructor; computes eigendecomposition of given matrix.
*
@ -148,7 +152,10 @@ template<typename _MatrixType> class EigenSolver
EigenSolver(const MatrixType& matrix)
: m_eivec(matrix.rows(), matrix.cols()),
m_eivalues(matrix.cols()),
m_isInitialized(false)
m_isInitialized(false),
m_realSchur(matrix.cols()),
m_matT(matrix.rows(), matrix.cols()),
m_tmp(matrix.cols())
{
compute(matrix);
}
@ -261,12 +268,17 @@ template<typename _MatrixType> class EigenSolver
EigenSolver& compute(const MatrixType& matrix);
private:
void computeEigenvectors(MatrixType& matH);
void computeEigenvectors();
protected:
MatrixType m_eivec;
EigenvalueType m_eivalues;
bool m_isInitialized;
RealSchur<MatrixType> m_realSchur;
MatrixType m_matT;
typedef Matrix<Scalar, ColsAtCompileTime, 1, Options & ~RowMajor, MaxColsAtCompileTime, 1> ColumnVectorType;
ColumnVectorType m_tmp;
};
template<typename MatrixType>
@ -324,32 +336,32 @@ EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matr
assert(matrix.cols() == matrix.rows());
// Reduce to real Schur form.
RealSchur<MatrixType> rs(matrix);
MatrixType matT = rs.matrixT();
m_eivec = rs.matrixU();
m_realSchur.compute(matrix);
m_matT = m_realSchur.matrixT();
m_eivec = m_realSchur.matrixU();
// Compute eigenvalues from matT
m_eivalues.resize(matrix.cols());
int i = 0;
while (i < matrix.cols())
{
if (i == matrix.cols() - 1 || matT.coeff(i+1, i) == Scalar(0))
if (i == matrix.cols() - 1 || m_matT.coeff(i+1, i) == Scalar(0))
{
m_eivalues.coeffRef(i) = matT.coeff(i, i);
m_eivalues.coeffRef(i) = m_matT.coeff(i, i);
++i;
}
else
{
Scalar p = Scalar(0.5) * (matT.coeff(i, i) - matT.coeff(i+1, i+1));
Scalar z = ei_sqrt(ei_abs(p * p + matT.coeff(i+1, i) * matT.coeff(i, i+1)));
m_eivalues.coeffRef(i) = ComplexScalar(matT.coeff(i+1, i+1) + p, z);
m_eivalues.coeffRef(i+1) = ComplexScalar(matT.coeff(i+1, i+1) + p, -z);
Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));
Scalar z = ei_sqrt(ei_abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));
m_eivalues.coeffRef(i) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);
m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);
i += 2;
}
}
// Compute eigenvectors.
computeEigenvectors(matT);
computeEigenvectors();
m_isInitialized = true;
return *this;
@ -376,7 +388,7 @@ std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)
template<typename MatrixType>
void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
void EigenSolver<MatrixType>::computeEigenvectors()
{
const int size = m_eivec.cols();
const Scalar eps = NumTraits<Scalar>::epsilon();
@ -385,7 +397,7 @@ void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
Scalar norm = 0.0;
for (int j = 0; j < size; ++j)
{
norm += matH.row(j).segment(std::max(j-1,0), size-std::max(j-1,0)).cwiseAbs().sum();
norm += m_matT.row(j).segment(std::max(j-1,0), size-std::max(j-1,0)).cwiseAbs().sum();
}
// Backsubstitute to find vectors of upper triangular form
@ -405,11 +417,11 @@ void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
Scalar lastr=0, lastw=0;
int l = n;
matH.coeffRef(n,n) = 1.0;
m_matT.coeffRef(n,n) = 1.0;
for (int i = n-1; i >= 0; i--)
{
Scalar w = matH.coeff(i,i) - p;
Scalar r = matH.row(i).segment(l,n-l+1).dot(matH.col(n).segment(l, n-l+1));
Scalar w = m_matT.coeff(i,i) - p;
Scalar r = m_matT.row(i).segment(l,n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
if (m_eivalues.coeff(i).imag() < 0.0)
{
@ -422,27 +434,27 @@ void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
if (m_eivalues.coeff(i).imag() == 0.0)
{
if (w != 0.0)
matH.coeffRef(i,n) = -r / w;
m_matT.coeffRef(i,n) = -r / w;
else
matH.coeffRef(i,n) = -r / (eps * norm);
m_matT.coeffRef(i,n) = -r / (eps * norm);
}
else // Solve real equations
{
Scalar x = matH.coeff(i,i+1);
Scalar y = matH.coeff(i+1,i);
Scalar x = m_matT.coeff(i,i+1);
Scalar y = m_matT.coeff(i+1,i);
Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();
Scalar t = (x * lastr - lastw * r) / denom;
matH.coeffRef(i,n) = t;
m_matT.coeffRef(i,n) = t;
if (ei_abs(x) > ei_abs(lastw))
matH.coeffRef(i+1,n) = (-r - w * t) / x;
m_matT.coeffRef(i+1,n) = (-r - w * t) / x;
else
matH.coeffRef(i+1,n) = (-lastr - y * t) / lastw;
m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;
}
// Overflow control
Scalar t = ei_abs(matH.coeff(i,n));
Scalar t = ei_abs(m_matT.coeff(i,n));
if ((eps * t) * t > 1)
matH.col(n).tail(size-i) /= t;
m_matT.col(n).tail(size-i) /= t;
}
}
}
@ -452,24 +464,24 @@ void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
int l = n-1;
// Last vector component imaginary so matrix is triangular
if (ei_abs(matH.coeff(n,n-1)) > ei_abs(matH.coeff(n-1,n)))
if (ei_abs(m_matT.coeff(n,n-1)) > ei_abs(m_matT.coeff(n-1,n)))
{
matH.coeffRef(n-1,n-1) = q / matH.coeff(n,n-1);
matH.coeffRef(n-1,n) = -(matH.coeff(n,n) - p) / matH.coeff(n,n-1);
m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);
m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);
}
else
{
std::complex<Scalar> cc = cdiv<Scalar>(0.0,-matH.coeff(n-1,n),matH.coeff(n-1,n-1)-p,q);
matH.coeffRef(n-1,n-1) = ei_real(cc);
matH.coeffRef(n-1,n) = ei_imag(cc);
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) = ei_real(cc);
m_matT.coeffRef(n-1,n) = ei_imag(cc);
}
matH.coeffRef(n,n-1) = 0.0;
matH.coeffRef(n,n) = 1.0;
m_matT.coeffRef(n,n-1) = 0.0;
m_matT.coeffRef(n,n) = 1.0;
for (int i = n-2; i >= 0; i--)
{
Scalar ra = matH.row(i).segment(l, n-l+1).dot(matH.col(n-1).segment(l, n-l+1));
Scalar sa = matH.row(i).segment(l, n-l+1).dot(matH.col(n).segment(l, n-l+1));
Scalar w = matH.coeff(i,i) - p;
Scalar ra = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n-1).segment(l, n-l+1));
Scalar sa = m_matT.row(i).segment(l, n-l+1).dot(m_matT.col(n).segment(l, n-l+1));
Scalar w = m_matT.coeff(i,i) - p;
if (m_eivalues.coeff(i).imag() < 0.0)
{
@ -483,39 +495,39 @@ void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
if (m_eivalues.coeff(i).imag() == 0)
{
std::complex<Scalar> cc = cdiv(-ra,-sa,w,q);
matH.coeffRef(i,n-1) = ei_real(cc);
matH.coeffRef(i,n) = ei_imag(cc);
m_matT.coeffRef(i,n-1) = ei_real(cc);
m_matT.coeffRef(i,n) = ei_imag(cc);
}
else
{
// Solve complex equations
Scalar x = matH.coeff(i,i+1);
Scalar y = matH.coeff(i+1,i);
Scalar x = m_matT.coeff(i,i+1);
Scalar y = m_matT.coeff(i+1,i);
Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;
Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;
if ((vr == 0.0) && (vi == 0.0))
vr = eps * norm * (ei_abs(w) + ei_abs(q) + ei_abs(x) + ei_abs(y) + ei_abs(lastw));
std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
matH.coeffRef(i,n-1) = ei_real(cc);
matH.coeffRef(i,n) = ei_imag(cc);
m_matT.coeffRef(i,n-1) = ei_real(cc);
m_matT.coeffRef(i,n) = ei_imag(cc);
if (ei_abs(x) > (ei_abs(lastw) + ei_abs(q)))
{
matH.coeffRef(i+1,n-1) = (-ra - w * matH.coeff(i,n-1) + q * matH.coeff(i,n)) / x;
matH.coeffRef(i+1,n) = (-sa - w * matH.coeff(i,n) - q * matH.coeff(i,n-1)) / x;
m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;
}
else
{
cc = cdiv(-lastra-y*matH.coeff(i,n-1),-lastsa-y*matH.coeff(i,n),lastw,q);
matH.coeffRef(i+1,n-1) = ei_real(cc);
matH.coeffRef(i+1,n) = ei_imag(cc);
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) = ei_real(cc);
m_matT.coeffRef(i+1,n) = ei_imag(cc);
}
}
// Overflow control
Scalar t = std::max(ei_abs(matH.coeff(i,n-1)),ei_abs(matH.coeff(i,n)));
Scalar t = std::max(ei_abs(m_matT.coeff(i,n-1)),ei_abs(m_matT.coeff(i,n)));
if ((eps * t) * t > 1)
matH.block(i, n-1, size-i, 2) /= t;
m_matT.block(i, n-1, size-i, 2) /= t;
}
}
@ -525,7 +537,8 @@ void EigenSolver<MatrixType>::computeEigenvectors(MatrixType& matH)
// Back transformation to get eigenvectors of original matrix
for (int j = size-1; j >= 0; j--)
{
m_eivec.col(j).segment(0, size) = m_eivec.leftCols(j+1) * matH.col(j).segment(0, j+1);
m_tmp.noalias() = m_eivec.leftCols(j+1) * m_matT.col(j).segment(0, j+1);
m_eivec.col(j) = m_tmp;
}
}

32
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
View File

@ -2,6 +2,7 @@
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@ -110,9 +111,10 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
* Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver.out
*/
SelfAdjointEigenSolver()
: m_eivec(int(Size), int(Size)),
m_eivalues(int(Size)),
m_subdiag(int(TridiagonalizationType::SizeMinusOne))
: m_eivec(),
m_eivalues(),
m_tridiag(),
m_subdiag()
{
ei_assert(Size!=Dynamic);
}
@ -133,7 +135,8 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
SelfAdjointEigenSolver(int size)
: m_eivec(size, size),
m_eivalues(size),
m_subdiag(TridiagonalizationType::SizeMinusOne)
m_tridiag(size),
m_subdiag(size > 1 ? size - 1 : 1)
{}
/** \brief Constructor; computes eigendecomposition of given matrix.
@ -157,9 +160,9 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
SelfAdjointEigenSolver(const MatrixType& matrix, bool computeEigenvectors = true)
: m_eivec(matrix.rows(), matrix.cols()),
m_eivalues(matrix.cols()),
m_subdiag()
m_tridiag(matrix.rows()),
m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1)
{
if (matrix.rows() > 1) m_subdiag.resize(matrix.rows() - 1);
compute(matrix, computeEigenvectors);
}
@ -187,9 +190,9 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
SelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors = true)
: m_eivec(matA.rows(), matA.cols()),
m_eivalues(matA.cols()),
m_subdiag()
m_tridiag(matA.rows()),
m_subdiag(matA.rows() > 1 ? matA.rows() - 1 : 1)
{
if (matA.rows() > 1) m_subdiag.resize(matA.rows() - 1);
compute(matA, matB, computeEigenvectors);
}
@ -351,6 +354,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
protected:
MatrixType m_eivec;
RealVectorType m_eivalues;
TridiagonalizationType m_tridiag;
typename TridiagonalizationType::SubDiagonalType m_subdiag;
#ifndef NDEBUG
bool m_eigenvectorsOk;
@ -396,14 +400,12 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
return *this;
}
m_eivec = matrix;
// FIXME, should tridiag be a local variable of this function or an attribute of SelfAdjointEigenSolver ?
// the latter avoids multiple memory allocation when the same SelfAdjointEigenSolver is used multiple times...
// (same for diag and subdiag)
m_tridiag.compute(matrix);
RealVectorType& diag = m_eivalues;
m_subdiag.resize(n-1);
TridiagonalizationType::decomposeInPlace(m_eivec, diag, m_subdiag, computeEigenvectors);
diag = m_tridiag.diagonal();
m_subdiag = m_tridiag.subDiagonal();
if (computeEigenvectors)
m_eivec = m_tridiag.matrixQ();
int end = n-1;
int start = 0;

8
Eigen/src/Eigenvalues/Tridiagonalization.h
View File

@ -70,10 +70,10 @@ template<typename _MatrixType> class Tridiagonalization
enum {
Size = MatrixType::RowsAtCompileTime,
SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1,
SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1),
Options = MatrixType::Options,
MaxSize = MatrixType::MaxRowsAtCompileTime,
MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1
MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1)
};
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> CoeffVectorType;
@ -108,7 +108,7 @@ template<typename _MatrixType> class Tridiagonalization
* \sa compute() for an example.
*/
Tridiagonalization(int size = Size==Dynamic ? 2 : Size)
: m_matrix(size,size), m_hCoeffs(size-1)
: m_matrix(size,size), m_hCoeffs(size > 1 ? size-1 : 1)
{}
/** \brief Constructor; computes tridiagonal decomposition of given matrix.
@ -122,7 +122,7 @@ template<typename _MatrixType> class Tridiagonalization
* Output: \verbinclude Tridiagonalization_Tridiagonalization_MatrixType.out
*/
Tridiagonalization(const MatrixType& matrix)
: m_matrix(matrix), m_hCoeffs(matrix.cols()-1)
: m_matrix(matrix), m_hCoeffs(matrix.cols() > 1 ? matrix.cols()-1 : 1)
{
_compute(m_matrix, m_hCoeffs);
}