Lauchli

An \(n+1 \times n\) Lauchli matrix has is a concatenation of a \(1 \times n\) row-vector of all ones with the \(n \times n\) matrix \(mu I\). The case where \(mu = \sqrt{\epsilon}\) is a prominent example of where the explicit formation of \(A^H A\) can be catastrophic.

C++ API

void Lauchli(Matrix<T> &A, Int n, T mu)

void Lauchli(ElementalMatrix<T> &A, Int n, T mu)

C API

ElError ElLauchli_i(ElMatrix_i A, ElInt n, ElInt mu)

ElError ElLauchli_s(ElMatrix_s A, ElInt n, float mu)

ElError ElLauchli_d(ElMatrix_d A, ElInt n, double mu)

ElError ElLauchli_c(ElMatrix_c A, ElInt n, complex_float mu)

ElError ElLauchli_z(ElMatrix_z A, ElInt n, complex_double mu)

ElError ElLauchliDist_i(ElDistMatrix_i A, ElInt n, ElInt mu)

ElError ElLauchliDist_s(ElDistMatrix_s A, ElInt n, float mu)

ElError ElLauchliDist_d(ElDistMatrix_d A, ElInt n, double mu)

ElError ElLauchliDist_c(ElDistMatrix_c A, ElInt n, complex_float mu)

ElError ElLauchliDist_z(ElDistMatrix_z A, ElInt n, complex_double mu)

Python API

Lauchli(A, n, mu)