Error using quad2d

Hello everyone,

I am trying to run the function Bivariate_Meijer_G_Ask, with the command :

close all;clear
am1=[0]; bn1 =[1.2]; ap1 =[];   bq1 =[];
dn2 =[1 ,1]; cp2 =[]; cm2 =[1]; dq2 =[0];
fn3 =[]; ep3 =[0]; em3 =[1.2 ,2.3 ,3.4]; fq3 =[];
x =2; y =3;
Bivariate_Meijer_G_Ask(am1, ap1, bn1, bq1, cm2,cp2, dn2, dq2, em3, ep3, fn3, fq3, x, y)

However, I get the following error:

Error using quad2d (line 114)
C must be a finite, scalar, floating point constant or a function handle.

Error in Bivariate_Meijer_G_Ask (line 11)
out = (-1/(2.*pi)^2).*quad2d(F,cs-1j.*W,cs+1j.*W,
ct-1j.*W,ct+1j.*W,'Singular',true); %Increase MaxFunEvals for higher W

>Can someone please help me figure out this issue?

Thank you in advance!

function out = Bivariate_Meijer_G_Ask(am1, ap1, bn1, bq1, cm2,cp2, dn2, dq2, em3, ep3, fn3, fq3, x, y)
%***** Integrand definition *****
F = @(s,t) (GammaProd(am1,s+t) .* GammaProd(1-cm2,s).* GammaProd(dn2,-s) .* GammaProd(1-em3,t).* GammaProd(fn3,-t) .* (x.^s) .* (y.^t))./(GammaProd(1-ap1,-(s+t)) .* GammaProd(bq1, s+t) .* GammaProd(cp2,-s) .* GammaProd(1-dq2,s).* GammaProd(ep3,-t) .* GammaProd(1-fq3,t));
%***** Contour definition *****
Sups = min(dn2); Infs = -max(1-cm2); % cs
cs = (Sups + Infs)/2;% s between Sups and Infs
Supt = min(fn3); Inft = max([-am1-cs em3-1]);% t>-am1-s, s=cs
ct = Supt - ((Supt-Inft)/10);%t betweeen Supt and Inft
W = 10; % W
%***** Bivariate Meijer G *****
out = (-1/(2.*pi)^2).*quad2d(F,cs-1j.*W,cs+1j.*W, ct-1j.*W,ct+1j.*W,'Singular',true); %Increase MaxFunEvals for higher W
%***** GammaProd subfunction *****
function output = GammaProd(p,z)
[pp zz] = meshgrid(p,z);
if (isempty(p)) output = ones(size(z));
else output = reshape(prod(gamma(pp+zz),2),size(z));
end
end
 
end
 
  
 
 
 

Answer 1

[Walter Roberson]

Your fn3 is empty because you assign [] to it. Supt is min(fn3) but fn3 is empty so Supt is empty. ct is calculated based on Supt but Supt is empty so ct is empty. ct+1j.*W is empty because ct is empty. So the fourth parameter you pass to quad2d is empty.

am1=[0]; bn1 =[1.2]; ap1 =[];   bq1 =[];
dn2 =[1 ,1]; cp2 =[]; cm2 =[1]; dq2 =[0];
fn3 =[]; ep3 =[0]; em3 =[1.2 ,2.3 ,3.4]; fq3 =[];
x =2; y =3;
Bivariate_Meijer_G_Ask(am1, ap1, bn1, bq1, cm2,cp2, dn2, dq2, em3, ep3, fn3, fq3, x, y)

  Name      Size            Bytes  Class              Attributes

  F         1x1                32  function_handle              
  Infs      1x1                 8  double                       
  Inft      1x1                 8  double                       
  Sups      1x1                 8  double                       
  Supt      0x0                 0  double                       
  W         1x1                 8  double                       
  am1       1x1                 8  double                       
  ap1       0x0                 0  double                       
  bn1       1x1                 8  double                       
  bq1       0x0                 0  double                       
  cm2       1x1                 8  double                       
  cp2       0x0                 0  double                       
  cs        1x1                 8  double                       
  ct        0x0                 0  double                       
  dn2       1x2                16  double                       
  dq2       1x1                 8  double                       
  em3       1x3                24  double                       
  ep3       1x1                 8  double                       
  fn3       0x0                 0  double                       
  fq3       0x0                 0  double                       
  x         1x1                 8  double                       
  y         1x1                 8  double                       

Error using quad2d (line 114)
C must be a finite, scalar, floating point constant or a function handle.

Error in solution>Bivariate_Meijer_G_Ask (line 21)
out = (-1/(2.*pi)^2).*quad2d(F,cs-1j.*W,cs+1j.*W, ct-1j.*W,ct+1j.*W,'Singular',true); %Increase MaxFunEvals for higher W

function out = Bivariate_Meijer_G_Ask(am1, ap1, bn1, bq1, cm2,cp2, dn2, dq2, em3, ep3, fn3, fq3, x, y)
%***** Integrand definition *****
F = @(s,t) (GammaProd(am1,s+t) .* GammaProd(1-cm2,s).* GammaProd(dn2,-s) .* GammaProd(1-em3,t).* GammaProd(fn3,-t) .* (x.^s) .* (y.^t))./(GammaProd(1-ap1,-(s+t)) .* GammaProd(bq1, s+t) .* GammaProd(cp2,-s) .* GammaProd(1-dq2,s).* GammaProd(ep3,-t) .* GammaProd(1-fq3,t));
%***** Contour definition *****
Sups = min(dn2); Infs = -max(1-cm2); % cs
cs = (Sups + Infs)/2;% s between Sups and Infs
Supt = min(fn3); Inft = max([-am1-cs em3-1]);% t>-am1-s, s=cs
ct = Supt - ((Supt-Inft)/10);%t betweeen Supt and Inft
W = 10; % W
%***** Bivariate Meijer G *****
whos
out = (-1/(2.*pi)^2).*quad2d(F,cs-1j.*W,cs+1j.*W, ct-1j.*W,ct+1j.*W,'Singular',true); %Increase MaxFunEvals for higher W
%***** GammaProd subfunction *****
function output = GammaProd(p,z)
[pp zz] = meshgrid(p,z);
if (isempty(p)) output = ones(size(z));
else output = reshape(prod(gamma(pp+zz),2),size(z));
end
end
 
end

[Soumen Mondal]

I am also facing same probelm

[Walter Roberson]

@Soumen Mondal

There are two common causes for that error message:

• people try to pass a numeric array as the first parameter to quad2d, expecting numeric integration of the data array (use trapz() for this situation.)
• people try to pass something from the Symbolic toolbox for one of the parameters. Even if it is the symbolic representation of a numeric constant, such as sym(1)/sym(2) --> then it will fail, as quad2d requires that the first parameter is a function handle, the second and third are numeric, and the fourth and fifth are either numeric or function handles.

There are other causes, such as the one above where it turned out that a parameter was empty, or cases where a vector is passed where a scalar is needed -- but the above are the most common cases.

[Soumen Mondal]

@Walter Roberson Can you provide a example for which the code is running.

[Walter Roberson]

F = @(x,y) sin(x) + cos(y) - atan2(y,x)

F = function_handle with value:
    @(x,y)sin(x)+cos(y)-atan2(y,x)

quad2d(F, -pi, 0, 0, pi)

ans = -29.5379