Oh... attachment...
On 13.04.21 19:30, Ralf Hemmecke wrote:
> Welcome Thejasvi,
>
> I cannot probably give you full help, but I modified your .input file a bit.
>
> Note that ++ is for docstrings in .spad files. The usual comment starts
> with --.
>
> The first thing that I have noticed is that legendreP requires its first
> argument to be a NonNegativeInteger. Unfortunately, FriCAS does not know
> that n-1 for n: PositiveInteger would be of type NonNegativeInteger. You
> have to help FriCAS here, i.e.,
>
> (n-1)::NonNegativeInteger
>
> (See start of the notebook. I have defined a few macros that I usually use.)
>
> Still there is a problem with the aromberg function, but that comes from
> the fact that its first argument must be of type F->F.
>
> https://fricas.github.io/api/NumericalQuadrature.html#l4e756d65726963616c51756164726174757265-61726f6d62657267
>
> You, however, give a type DoubleFloat -> Complex(DoubleFloat).
> That cannot work.
>
> Sorry, I have no time now to analyxe further, but according to
>
> F: FloatingPointSystem
>
> for NumericalQuadrature(F), it will probably not work to use
> Complex(DoubleFloat) since
>
> (9) -> Complex(DoubleFloat) has FloatingPointSystem
>
> (9) false
>
> In other words, aromberg is not available for Complex(DF).
>
> Sorry that I cannot be more clear.
>
> Ralf
>
> PS: Please subscribe to fricas-devel for further discussion.
>
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)version
setFormat!(FormatMathJax)$JFriCASSupport
Z ==> Integer
N ==> NonNegativeInteger
P ==> PositiveInteger
DF ==> DoubleFloat
CDF ==> Complex DF
F ==> Float
-- Some of the constant values required for the rest of the functions below
-- These correspond to the acoustics of the problem.
freq := 50000;
k := 2*%pi/(330/freq);
ka := 5 ;
a := ka/k;
alpha := %pi/3;
R:= a/sin(alpha);
R := numeric(R)::DF;
r1 := R*cos(alpha)/cos(theta);
NN := 3 ;--12 + 2*ka/sin(alpha)--
-- I couldn't find inbuilt spherical bessel's functions, and so had to make
custom functions
-- spherical bessel function--
sphBessel(n: P,z: DF): CDF == besselJ(n+0.5,z)*sqrt(%pi/(2*z));
-- spherical neumann function --
sphNeumann(n: P, z: DF): CDF == besselY(n+0.5,z)*sqrt(%pi/(2*z));
sphHankel2(n: Z, z: DF): CDF == sphBessel(n,z) - %i*sphNeumann(n,z);
alternate_hankels(n: P,theta: DF): CDF ==
r1 := R*cos(alpha)/cos(theta)
legendreP(n::N,cos(theta))*cos(theta) + (n+1)*sphHankel2(n+1,k*r1)
alternate_legendres(n: P, theta: DF): CDF ==
r1 := R*cos(alpha)/cos(theta)
n*(n+1)*sphHankel2(n,k*r1)*(legendreP((n-1)::N,cos(theta)-legendreP(n+1,cos(theta))))/(k*r1)
legendretan(m: P, theta: DF): CDF ==
r1 := R*cos(alpha)/cos(theta)
legendreP(m,cos(theta))*(r1^2/R^2)*tan(theta)
one_imn_term(m: P, n: P, theta: DF): CDF ==
r1 := R*cos(alpha)/cos(theta)
(alternate_hankels(n,theta)+alternate_legendres(m,theta))*legendretan(m,theta)
intg_imn_m10n20(theta: DF): CDF == one_imn_term(10,20,theta)
-- Check that the output for the Imn term works
intg_imn_m10n20(0.2)
aromberg(intg_imn_m10n20,0$DF,alpha::DF,0.99::DF,(10^(-12))::DF,10::Z,50::Z,30::Z)
