numpy.polynomial.hermite_e.hermegauss¶
- numpy.polynomial.hermite_e.hermegauss(deg)[source]¶
Gauss-HermiteE quadrature.
Computes the sample points and weights for Gauss-HermiteE quadrature. These sample points and weights will correctly integrate polynomials of degree
System Message: WARNING/2 (2*deg - 1)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 ([-\inf, \inf])
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (f(x) = \exp(-x^2/2))
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.Parameters: deg : int
Number of sample points and weights. It must be >= 1.
Returns: x : ndarray
1-D ndarray containing the sample points.
y : ndarray
1-D ndarray containing the weights.
Notes
The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that
System Message: WARNING/2 (w_k = c / (He'_n(x_k) * He_{n-1}(x_k)) )
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.where
System Message: WARNING/2 (c)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (k)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (x_k)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.System Message: WARNING/2 (He_n)
latex exited with error [stdout] This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/TeX Live for SUSE Linux) (preloaded format=latex) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2015/01/01> patch level 2 Babel <3.9m> and hyphenation patterns for 79 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.173 \endinput ^^M No pages of output. Transcript written on math.log.