Generate a Hermite series with the given roots.
Return the array of coefficients for the P-series whose roots (a.k.a.
“zeros”) are given by roots. The returned array of coefficients is
ordered from lowest order “term” to highest, and zeros of multiplicity
greater than one must be included in roots a number of times equal
to their multiplicity (e.g., if 2 is a root of multiplicity three,
then [2,2,2] must be in roots).
| Parameters : | roots : array_like
Sequence containing the roots.
|
|---|
| Returns : | out : ndarray
1-d array of the Hermite series coefficients, ordered from low to
high. If all roots are real, out.dtype is a float type;
otherwise, out.dtype is a complex type, even if all the
coefficients in the result are real (see Examples below).
|
|---|
See also
polyfromroots, chebfromroots
Notes
What is returned are the
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ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma
rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian,
kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn
orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia
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such that:
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LaTeX2e <2011/06/27>
Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge
rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi
c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis
h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis
h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h
ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma
rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian,
kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn
orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia
nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb
ian, welsh, loaded.
(/usr/share/texmf/tex/latex/base/article.cls
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where n == len(roots) and
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LaTeX2e <2011/06/27>
Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge
rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi
c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis
h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis
h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h
ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma
rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian,
kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn
orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia
nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb
ian, welsh, loaded.
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is the i-th Hermite
(basis) polynomial over the domain [-1,1]. Note that, unlike
polyfromroots, due to the nature of the Hermite basis set, the
above identity does not imply
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restricted \write18 enabled.
entering extended mode
(./math.tex
LaTeX2e <2011/06/27>
Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge
rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi
c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis
h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis
h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h
ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma
rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian,
kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn
orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia
nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb
ian, welsh, loaded.
(/usr/share/texmf/tex/latex/base/article.cls
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(/usr/share/texmf/tex/latex/base/size12.clo))
(/usr/share/texmf/tex/latex/base/inputenc.sty
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identically (see
Examples).
Examples
>>> from numpy.polynomial.hermite import hermfromroots, hermval
>>> coef = hermfromroots((-1, 0, 1))
>>> hermval((-1, 0, 1), coef)
array([ 0., 0., 0.])
>>> coef = hermfromroots((-1j, 1j))
>>> hermval((-1j, 1j), coef)
array([ 0.+0.j, 0.+0.j])
