Kahan

For any pair \((\phi,\zeta)\) such that \(|\phi|^2+|\zeta|^2=1\), the corresponding \(n \times n\) Kahan matrix is given by:

\[\begin{split}K = \text{diag}(1,\phi,\ldots,\phi^{n-1}) \begin{pmatrix} 1 & -\zeta & -\zeta & \cdots & -\zeta \\ 0 & 1 & -\zeta & \cdots & -\zeta \\ & \ddots & & \vdots & \vdots \\ \vdots & & & 1 & -\zeta \\ 0 & & \cdots & & 1 \end{pmatrix}\end{split}\]

C++ API

void Kahan(Matrix<F> &A, Int n, F phi)

void Kahan(AbstractDistMatrix<F> &A, Int n, F phi)

Sets the matrix A equal to the \(n \times n\) Kahan matrix with the specified value for \(\phi\).

C API

ElError ElKahan_s(ElMatrix_s A, ElInt n, float phi)

ElError ElKahan_d(ElMatrix_d A, ElInt n, double phi)

ElError ElKahan_c(ElMatrix_c A, ElInt n, complex_float phi)

ElError ElKahan_z(ElMatrix_z A, ElInt n, complex_double phi)

ElError ElKahanDist_s(ElDistMatrix_s A, ElInt n, float phi)

ElError ElKahanDist_d(ElDistMatrix_d A, ElInt n, double phi)

ElError ElKahanDist_c(ElDistMatrix_c A, ElInt n, complex_float phi)

ElError ElKahanDist_z(ElDistMatrix_z A, ElInt n, complex_double phi)

Python API

Kahan(A, n, phi)