ellipticNome
Elliptic nome function
Syntax
Description
ellipticNome(
returns the Elliptic Nome of
m
)m
. If m
is an array, then
ellipticNome
acts element-wise.
Examples
Calculate Elliptic Nome for Numeric Inputs
ellipticNome(1.3)
ans = 0.0881 - 0.2012i
Call ellipticNome
on array inputs.
ellipticNome
acts element-wise when
m
is an array.
ellipticNome([2 1 -3/2])
ans = 0.0000 - 0.2079i 1.0000 + 0.0000i -0.0570 + 0.0000i
Calculate Elliptic Nome for Symbolic Numbers
Convert numeric input to symbolic form using
sym
, and find the elliptic nome. For symbolic input
where m = 0
, 1/2
, or 1
,
ellipticNome
returns exact symbolic output.
ellipticNome([0 1/2 1])
ans = 0 0.0432 1.0000
Show that for any other symbolic values of m
,
ellipticNome
returns an unevaluated function
call.
ellipticNome(sym(2))
ans = ellipticNome(2)
Find Elliptic Nome for Symbolic Variables or Expressions
For symbolic variables or expressions,
ellipticNome
returns the unevaluated function
call.
syms x f = ellipticNome(x)
f = ellipticNome(x)
Substitute values for the variables by using subs
,
and convert values to double by using double
.
f = subs(f, x, 5)
f = ellipticNome(5)
fVal = double(f)
fVal = -0.1008 - 0.1992i
Calculate f
to higher precision using
vpa
.
fVal = vpa(f)
fVal = - 0.10080189716733475056506021415746 - 0.19922973618609837873340100821425i
Plot Elliptic Nome
Plot the real and imaginary values of the elliptic nome using fcontour
. Fill plot contours by setting Fill
to on
.
syms m f = ellipticNome(m); subplot(2,2,1) fcontour(real(f),'Fill','on') title('Real Values of Elliptic Nome') xlabel('m') subplot(2,2,2) fcontour(imag(f),'Fill','on') title('Imaginary Values of Elliptic Nome') xlabel('m')
Input Arguments
m
— Input
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression
Input, specified as a number, vector, matrix, or multidimensional array, or a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.
More About
Elliptic Nome
The elliptic nome is
where K is the complete elliptic integral of the first kind, implemented
as ellipticK
.
holds for all .
Version History
Introduced in R2017b
MATLAB 명령
다음 MATLAB 명령에 해당하는 링크를 클릭했습니다.
명령을 실행하려면 MATLAB 명령 창에 입력하십시오. 웹 브라우저는 MATLAB 명령을 지원하지 않습니다.
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