diff options
-rw-r--r-- | unsupported/Eigen/MatrixFunctions | 4 | ||||
-rw-r--r-- | unsupported/doc/examples/MatrixPower_failure.cpp | 20 |
2 files changed, 24 insertions, 0 deletions
diff --git a/unsupported/Eigen/MatrixFunctions b/unsupported/Eigen/MatrixFunctions index 41dfab390..ff466a519 100644 --- a/unsupported/Eigen/MatrixFunctions +++ b/unsupported/Eigen/MatrixFunctions @@ -262,6 +262,10 @@ where \f$ T_1 \f$ is invertible. Then \f$ T^p \f$ is given by 0 & 0 \end{array}. \right] \f] +\warning Fractional power of a matrix with a non-semisimple zero +eigenvalue is not well-defined. We introduce an assertion failure +against inaccurate result, e.g. \include MatrixPower_failure.cpp + Details of the algorithm can be found in: Nicholas J. Higham and Lijing Lin, "A Schur-Padé algorithm for fractional powers of a matrix," <em>SIAM J. %Matrix Anal. Applic.</em>, diff --git a/unsupported/doc/examples/MatrixPower_failure.cpp b/unsupported/doc/examples/MatrixPower_failure.cpp new file mode 100644 index 000000000..d20de78a0 --- /dev/null +++ b/unsupported/doc/examples/MatrixPower_failure.cpp @@ -0,0 +1,20 @@ +#include <unsupported/Eigen/MatrixFunctions> +#include <iostream> + +int main() +{ + Eigen::Matrix4d A; + A << 0, 0, 2, 3, + 0, 0, 4, 5, + 0, 0, 6, 7, + 0, 0, 8, 9; + std::cout << A.pow(0.37) << std::endl; + + // The 1 makes eigenvalue 0 non-semisimple. + A.coeffRef(0, 1) = 1; + + // This fails if EIGEN_NO_DEBUG is undefined. + std::cout << A.pow(0.37) << std::endl; + + return 0; +} |