Forsythe

A Forsythe matrix is a Jordan block with the bottom-left entry replaced with an arbitrary value. In the below routines, the eigenvalue of the \(n \times n\) Jordan block is \(\lambda\), and the entry placed in the \((n-1,0)\) position is \(\alpha\).

C++ API

void Forsythe(Matrix<T> &J, Int n, T alpha, T lambda)
void Forsythe(AbstractDistMatrix<T> &J, Int n, T alpha, T lambda)

C API

ElError ElForsythe_i(ElMatrix_i J, ElInt n, ElInt alpha, ElInt lambda)
ElError ElForsythe_s(ElMatrix_s J, ElInt n, float alpha, float lambda)
ElError ElForsythe_d(ElMatrix_d J, ElInt n, double alpha, double lambda)
ElError ElForsythe_c(ElMatrix_c J, ElInt n, complex_float alpha, complex_float lambda)
ElError ElForsythe_z(ElMatrix_z J, ElInt n, complex_double alpha, complex_double lambda)
ElError ElForsytheDist_i(ElDistMatrix_i J, ElInt n, ElInt alpha, ElInt lambda)
ElError ElForsytheDist_s(ElDistMatrix_s J, ElInt n, float alpha, float lambda)
ElError ElForsytheDist_d(ElDistMatrix_d J, ElInt n, double alpha, double lambda)
ElError ElForsytheDist_c(ElDistMatrix_c J, ElInt n, complex_float alpha, complex_float lambda)
ElError ElForsytheDist_z(ElDistMatrix_z J, ElInt n, complex_double alpha, complex_double lambda)

Python API

Forsythe(J, n, alpha, lamb)