Spectral cloud

The following routines return the norms of the shifted inverses in the vector invNorms for a given set of shifts. The returned integer vector is a list of the number of iterations required for convergence of each shift.

Python API

SpectralCloud(A, shifts[, ctrl=None])

C++ API

Matrix<int> SpectralCloud(const Matrix<F> &A, const Matrix<Complex<Base<F>>> &shifts, Matrix<Base<F>> &invNorms, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int, VR, STAR> SpectralCloud(const AbstractDistMatrix<F> &A, const AbstractDistMatrix<Complex<Base<F>>> &shifts, AbstractDistMatrix<Base<F>> &invNorms, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

Matrix<int> TriangularSpectralCloud(const Matrix<F> &U, const Matrix<Complex<Base<F>>> &shifts, Matrix<Base<F>> &invNorms, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int, VR, STAR> TriangularSpectralCloud(const AbstractDistMatrix<F> &U, const AbstractDistMatrix<Complex<Base<F>>> &shifts, AbstractDistMatrix<Base<F>> &invNorms, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int, VR, STAR> QuasiTriangularSpectralCloud(const AbstractDistMatrix<Real> &U, const AbstractDistMatrix<Complex<Real>> &shifts, AbstractDistMatrix<Real> &invNorms, PseudospecCtrl<Real> psCtrl = PseudospecCtrl<Real>())

Matrix<int> HessenbergSpectralCloud(const Matrix<F> &H, const Matrix<Complex<Base<F>>> &shifts, Matrix<Base<F>> &invNorms, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int, VR, STAR> HessenbergSpectralCloud(const AbstractDistMatrix<F> &H, const AbstractDistMatrix<Complex<Base<F>>> &shifts, AbstractDistMatrix<Base<F>> &invNorms, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

C API

Single-precision

ElError ElSpectralCloud_s(ElConstMatrix_s A, ElConstMatrix_c shifts, ElMatrix_s invNormMap)

ElError ElSpectralCloudDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_c shifts, ElDistMatrix_s invNormMap)

ElError ElSpectralCloudX_s(ElConstMatrix_s A, ElConstMatrix_c shifts, ElMatrix_s invNormMap, ElPseudospecCtrl_s ctrl)

ElError ElSpectralCloudXDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_c shifts, ElDistMatrix_s invNormMap, ElPseudospecCtrl_s ctrl)

Double-precision

ElError ElSpectralCloud_d(ElConstMatrix_d A, ElConstMatrix_z shifts, ElMatrix_d invNormMap)

ElError ElSpectralCloudDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_z shifts, ElDistMatrix_d invNormMap)

ElError ElSpectralCloudX_d(ElConstMatrix_d A, ElConstMatrix_z shifts, ElMatrix_d invNormMap, ElPseudospecCtrl_d ctrl)

ElError ElSpectralCloudXDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_z shifts, ElDistMatrix_d invNormMap, ElPseudospecCtrl_d ctrl)

Single-precision complex

ElError ElSpectralCloud_c(ElConstMatrix_c A, ElConstMatrix_c shifts, ElMatrix_s invNormMap)

ElError ElSpectralCloudDist_c(ElConstDistMatrix_c A, ElConstDistMatrix_c shifts, ElDistMatrix_s invNormMap)

ElError ElSpectralCloudX_c(ElConstMatrix_c A, ElConstMatrix_c shifts, ElMatrix_s invNormMap, ElPseudospecCtrl_s ctrl)

ElError ElSpectralCloudXDist_c(ElConstDistMatrix_c A, ElConstDistMatrix_c shifts, ElDistMatrix_s invNormMap, ElPseudospecCtrl_s ctrl)

Double-precision complex

ElError ElSpectralCloud_z(ElConstMatrix_z A, ElConstMatrix_z shifts, ElMatrix_d invNormMap)

ElError ElSpectralCloudDist_z(ElConstDistMatrix_z A, ElConstDistMatrix_z shifts, ElDistMatrix_d invNormMap)

ElError ElSpectralCloudX_z(ElConstMatrix_z A, ElConstMatrix_z shifts, ElMatrix_d invNormMap, ElPseudospecCtrl_d ctrl)

ElError ElSpectralCloudXDist_z(ElConstDistMatrix_z A, ElConstDistMatrix_z shifts, ElDistMatrix_d invNormMap, ElPseudospecCtrl_d ctrl)