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Add a method to SelfAdjointEigenSolver for computing the matrix exponential

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Rasmus Munk Larsen
2025-10-05 15:06:04 +00:00
parent 32b0f386bc
commit 7eaf9ae68d
2 changed files with 27 additions and 0 deletions
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16
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@@ -325,6 +325,22 @@ class SelfAdjointEigenSolver {
return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint(); return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
} }
/** \brief Computes the matrix exponential the matrix.
*
* \returns the matrix exponential the matrix.
*
* \pre The eigenvalues and eigenvectors of a positive-definite matrix
* have been computed before.
*
* \sa operatorInverseSqrt(), operatorSqrt(),
* <a href="unsupported/group__MatrixFunctions__Module.html">MatrixFunctions Module</a>
*/
EIGEN_DEVICE_FUNC MatrixType operatorExp() const {
eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
return m_eivec * m_eivalues.array().exp().matrix().asDiagonal() * m_eivec.adjoint();
}
/** \brief Computes the inverse square root of the matrix. /** \brief Computes the inverse square root of the matrix.
* *
* \returns the inverse positive-definite square root of the matrix * \returns the inverse positive-definite square root of the matrix

11
test/eigensolver_selfadjoint.cpp
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@@ -13,6 +13,7 @@
#include <limits> #include <limits>
#include <Eigen/Eigenvalues> #include <Eigen/Eigenvalues>
#include <Eigen/SparseCore> #include <Eigen/SparseCore>
#include <unsupported/Eigen/MatrixFunctions>
template <typename MatrixType> template <typename MatrixType>
void selfadjointeigensolver_essential_check(const MatrixType& m) { void selfadjointeigensolver_essential_check(const MatrixType& m) {
@@ -135,11 +136,13 @@ void selfadjointeigensolver(const MatrixType& m) {
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorExp());
eiSymmUninitialized.compute(symmA, false); eiSymmUninitialized.compute(symmA, false);
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorExp());
// test Tridiagonalization's methods // test Tridiagonalization's methods
Tridiagonalization<MatrixType> tridiag(symmC); Tridiagonalization<MatrixType> tridiag(symmC);
@@ -167,6 +170,14 @@ void selfadjointeigensolver(const MatrixType& m) {
eiSymmTridiag.eigenvectors().real().transpose()); eiSymmTridiag.eigenvectors().real().transpose());
} }
// Test matrix expponential from eigendecomposition.
// First scale to avoid overflow.
symmB = symmB / symmB.norm();
eiSymm.compute(symmB);
MatrixType expSymmB = eiSymm.operatorExp();
symmB = symmB.template selfadjointView<Lower>();
VERIFY_IS_APPROX(expSymmB, symmB.exp());
if (rows > 1 && rows < 20) { if (rows > 1 && rows < 20) {
// Test matrix with NaN // Test matrix with NaN
symmC(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); symmC(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();