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implement other variants

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This commit is contained in:
Gael Guennebaud 2010-06-17 10:11:38 +02:00
parent db160f2e0b
commit 43086d12d2
2 changed files with 49 additions and 19 deletions
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64
Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
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@ -43,7 +43,7 @@
* This class solves the generalized eigenvalue problem * This class solves the generalized eigenvalue problem
* \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be * \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be
* selfadjoint and the matrix \f$ B \f$ should be positive definite. * selfadjoint and the matrix \f$ B \f$ should be positive definite.
* *
* Only the \b lower \b triangular \b part of the input matrix is referenced. * Only the \b lower \b triangular \b part of the input matrix is referenced.
* *
* Call the function compute() to compute the eigenvalues and eigenvectors of * Call the function compute() to compute the eigenvalues and eigenvectors of
@ -138,7 +138,7 @@ class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixT
* Only the lower triangular part of the matrix is referenced. * Only the lower triangular part of the matrix is referenced.
* \param[in] options A or-ed set of flags {ComputeEigenvectors,EigenvaluesOnly} | {Ax_lBx,ABx_lx,BAx_lx}. * \param[in] options A or-ed set of flags {ComputeEigenvectors,EigenvaluesOnly} | {Ax_lBx,ABx_lx,BAx_lx}.
* Default is ComputeEigenvectors|Ax_lBx. * Default is ComputeEigenvectors|Ax_lBx.
* *
* \returns Reference to \c *this * \returns Reference to \c *this
* *
* If \p options contains Ax_lBx (the default), this function computes eigenvalues * If \p options contains Ax_lBx (the default), this function computes eigenvalues
@ -147,7 +147,7 @@ class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixT
* matrix \f$ A \f$ and \a matB the positive definite * matrix \f$ A \f$ and \a matB the positive definite
* matrix \f$ B \f$. In addition, each eigenvector \f$ x \f$ * matrix \f$ B \f$. In addition, each eigenvector \f$ x \f$
* satisfies the property \f$ x^* B x = 1 \f$. * satisfies the property \f$ x^* B x = 1 \f$.
* *
* In addition, the two following variants can be solved via \p options: * In addition, the two following variants can be solved via \p options:
* - \c ABx_lx: \f$ ABx = \lambda x \f$ * - \c ABx_lx: \f$ ABx = \lambda x \f$
* - \c BAx_lx: \f$ BAx = \lambda x \f$ * - \c BAx_lx: \f$ BAx = \lambda x \f$
@ -185,28 +185,58 @@ compute(const MatrixType& matA, const MatrixType& matB, int options)
ei_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows()); ei_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows());
ei_assert((options&~(EigVecMask|GenEigMask))==0 ei_assert((options&~(EigVecMask|GenEigMask))==0
&& (options&EigVecMask)!=EigVecMask && (options&EigVecMask)!=EigVecMask
&& ((options&GenEigMask)==Ax_lBx || (options&GenEigMask)==ABx_lx || (options&GenEigMask)==BAx_lx) && ((options&GenEigMask)==0 || (options&GenEigMask)==Ax_lBx
|| (options&GenEigMask)==ABx_lx || (options&GenEigMask)==BAx_lx)
&& "invalid option parameter"); && "invalid option parameter");
ei_assert((options&GenEigMask)==Ax_lBx && "other variants are not implemented yet, sorry."); bool computeEigVecs = ((options&EigVecMask)==0) || ((options&EigVecMask)==ComputeEigenvectors);
// TODO implements other variants !!
bool computeEigVecs = (options&EigVecMask)==ComputeEigenvectors;
// Compute the cholesky decomposition of matB = L L' = U'U // Compute the cholesky decomposition of matB = L L' = U'U
LLT<MatrixType> cholB(matB); LLT<MatrixType> cholB(matB);
// compute C = inv(L) A inv(L') int type = (options&GenEigMask);
MatrixType matC = matA.template selfadjointView<Lower>(); if(type==0)
cholB.matrixL().template solveInPlace<OnTheLeft>(matC); type = Ax_lBx;
cholB.matrixU().template solveInPlace<OnTheRight>(matC);
Base::compute(matC, options&EigVecMask); if(type==Ax_lBx)
{
// compute C = inv(L) A inv(L')
MatrixType matC = matA.template selfadjointView<Lower>();
cholB.matrixL().template solveInPlace<OnTheLeft>(matC);
cholB.matrixU().template solveInPlace<OnTheRight>(matC);
// transform back the eigen vectors: evecs = inv(U) * evecs Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly );
if(computeEigVecs)
cholB.matrixU().solveInPlace(Base::m_eivec); // transform back the eigen vectors: evecs = inv(U) * evecs
if(computeEigVecs)
cholB.matrixU().solveInPlace(Base::m_eivec);
}
else if(type==ABx_lx)
{
// compute C = L' A L
MatrixType matC = matA.template selfadjointView<Lower>();
matC = matC * cholB.matrixL();
matC = cholB.matrixU() * matC;
Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);
// transform back the eigen vectors: evecs = inv(U) * evecs
if(computeEigVecs)
cholB.matrixU().solveInPlace(Base::m_eivec);
}
else if(type==BAx_lx)
{
// compute C = L' A L
MatrixType matC = matA.template selfadjointView<Lower>();
matC = matC * cholB.matrixL();
matC = cholB.matrixU() * matC;
Base::compute(matC, computeEigVecs ? ComputeEigenvectors : EigenvaluesOnly);
// transform back the eigen vectors: evecs = L * evecs
if(computeEigVecs)
Base::m_eivec = cholB.matrixL() * Base::m_eivec;
}
return *this; return *this;
} }

4
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library // This file is part of Eigen, a lightweight C++ template library
// for linear algebra. // for linear algebra.
// //
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> // Copyright (C) 2008-2010 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk> // Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
// //
// Eigen is free software; you can redistribute it and/or // Eigen is free software; you can redistribute it and/or
@ -66,7 +66,7 @@
* *
* The documentation for SelfAdjointEigenSolver(const MatrixType&, bool) * The documentation for SelfAdjointEigenSolver(const MatrixType&, bool)
* contains an example of the typical use of this class. * contains an example of the typical use of this class.
* *
* To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and * To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and
* the like see the class GeneralizedSelfAdjointEigenSolver. * the like see the class GeneralizedSelfAdjointEigenSolver.
* *