Spectral window

The following routines return the norms of the shifted inverses over a user-specified 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

SpectralWindow(A[, center=0, realWidth=1, imagWidth=1, realSize=100, imagSize=100, ctrl=None])

C++ API

Matrix<int> SpectralWindow(const Matrix<F> &A, Matrix<Base<F>> &invNormMap, Complex<Base<F>> center, Base<F> realWidth, Base<F> imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int> SpectralWindow(const AbstractDistMatrix<F> &A, AbstractDistMatrix<Base<F>> &invNormMap, Complex<Base<F>> center, Base<F> realWidth, Base<F> imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

Matrix<int> TriangularSpectralWindow(const Matrix<F> &U, Matrix<Base<F>> &invNormMap, Complex<Base<F>> center, Base<F> realWidth, Base<F> imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int> TriangularSpectralWindow(const AbstractDistMatrix<F> &U, AbstractDistMatrix<Base<F>> &invNormMap, Complex<Base<F>> center, Base<F> realWidth, Base<F> imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

Matrix<int> QuasiTriangularSpectralWindow(const Matrix<Real> &U, Matrix<Real> &invNormMap, Complex<Real> center, Real realWidth, Real imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Real> psCtrl = PseudospecCtrl<Real>())

DistMatrix<int> QuasiTriangularSpectralWindow(const AbstractDistMatrix<Real> &U, AbstractDistMatrix<Real> &invNormMap, Complex<Real> center, Real realWidth, Real imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Real> psCtrl = PseudospecCtrl<Real>())

Matrix<int> HessenbergSpectralWindow(const Matrix<F> &H, Matrix<Base<F>> &invNormMap, Complex<Base<F>> center, Base<F> realWidth, Base<F> imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

DistMatrix<int> HessenbergSpectralWindow(const AbstractDistMatrix<F> &H, AbstractDistMatrix<Base<F>> &invNormMap, Complex<Base<F>> center, Base<F> realWidth, Base<F> imagWidth, Int realSize, Int imagSize, PseudospecCtrl<Base<F>> psCtrl = PseudospecCtrl<Base<F>>())

C API

Single-precision

ElError ElSpectralWindow_s(ElConstMatrix_s A, ElMatrix_s invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowDist_s(ElConstDistMatrix_s A, ElDistMatrix_s invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowX_s(ElConstMatrix_s A, ElMatrix_s invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

ElError ElSpectralWindowXDist_s(ElConstDistMatrix_s A, ElDistMatrix_s invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

Double-precision

ElError ElSpectralWindow_d(ElConstMatrix_d A, ElMatrix_d invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowDist_d(ElConstDistMatrix_d A, ElDistMatrix_d invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowX_d(ElConstMatrix_d A, ElMatrix_d invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)

ElError ElSpectralWindowXDist_d(ElConstDistMatrix_d A, ElDistMatrix_d invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)

Single-precision complex

ElError ElSpectralWindow_c(ElConstMatrix_c A, ElMatrix_c invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowDist_c(ElConstDistMatrix_c A, ElDistMatrix_c invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowX_c(ElConstMatrix_c A, ElMatrix_c invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

ElError ElSpectralWindowXDist_c(ElConstDistMatrix_c A, ElDistMatrix_c invNormMap, complex_float center, float realWidth, float imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_s ctrl)

Double-precision complex

ElError ElSpectralWindow_z(ElConstMatrix_z A, ElMatrix_z invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowDist_z(ElConstDistMatrix_z A, ElDistMatrix_z invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize)

ElError ElSpectralWindowX_z(ElConstMatrix_z A, ElMatrix_z invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)

ElError ElSpectralWindowXDist_z(ElConstDistMatrix_z A, ElDistMatrix_z invNormMap, complex_double center, double realWidth, double imagWidth, ElInt realSize, ElInt imagSize, ElPseudospecCtrl_d ctrl)