Spectral portrait

The following routines return the norms of the shifted inverses over an automatically-determined 2D window in the complex plane (in the matrix invNormMap) with the specified x and y resolutions. The returned integer matrix corresponds to the number of iterations required for convergence at each shift in the 2D grid.

Python API

SpectralPortrait(A[, realSize=100, imagSize=100, ctrl=None])

C++ API

Matrix<int> SpectralPortrait(const Matrix<F> &A, Matrix<Base<F>> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int> SpectralPortrait(const AbstractDistMatrix<F> &A, AbstractDistMatrix<Base<F>> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

Matrix<int> TriangularSpectralPortrait(const Matrix<F> &U, Matrix<Base<F>> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int> TriangularSpectralPortrait(const AbstractDistMatrix<F> &U, AbstractDistMatrix<Base<F>> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

Matrix<int> QuasiTriangularSpectralPortrait(const Matrix<Real> &U, Matrix<Real> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Real> psCtrl = PseudospecCtrl<Real>())

DistMatrix<int> QuasiTriangularSpectralPortrait(const AbstractDistMatrix<Real> &U, AbstractDistMatrix<Real> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Real> psCtrl = PseudospecCtrl<Real>())

Matrix<int> HessenbergSpectralPortrait(const Matrix<F> &H, Matrix<Base<F>> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int> HessenbergSpectralPortrait(const AbstractDistMatrix<F> &H, AbstractDistMatrix<Base<F>> &invNormMap, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

C API

Single-precision

ElError ElSpectralPortrait_s(ElConstMatrix_s A, ElMatrix_s invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitDist_s(ElConstDistMatrix_s A, ElDistMatrix_s invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitX_s(ElConstMatrix_s A, ElMatrix_s invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

ElError ElSpectralPortraitXDist_s(ElConstDistMatrix_s A, ElDistMatrix_s invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

Double-precision

ElError ElSpectralPortrait_d(ElConstMatrix_d A, ElMatrix_d invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitDist_d(ElConstDistMatrix_d A, ElDistMatrix_d invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitX_d(ElConstMatrix_d A, ElMatrix_d invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)

ElError ElSpectralPortraitXDist_d(ElConstDistMatrix_d A, ElDistMatrix_d invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)

Single-precision complex

ElError ElSpectralPortrait_c(ElConstMatrix_c A, ElMatrix_c invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitDist_c(ElConstDistMatrix_c A, ElDistMatrix_c invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitX_c(ElConstMatrix_c A, ElMatrix_c invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

ElError ElSpectralPortraitXDist_c(ElConstDistMatrix_c A, ElDistMatrix_c invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

Double-precision complex

ElError ElSpectralPortrait_z(ElConstMatrix_z A, ElMatrix_z invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitDist_z(ElConstDistMatrix_z A, ElDistMatrix_z invNormMap, ElInt realSize, ElInt imagSize)

ElError ElSpectralPortraitX_z(ElConstMatrix_z A, ElMatrix_z invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)

ElError ElSpectralPortraitXDist_z(ElConstDistMatrix_z A, ElDistMatrix_z invNormMap, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)