Undefined operator '*' for input arguments of type 'function_handle' error in Integral2. Kindly help me clear this error.

CODE:

for  d=0.1:0.1:1
    
   A=0
     
r1=@(ai,aj) sqrt((x+ai).^2+(y+aj).^2+z.^2)
r2=@(ai,aj) sqrt((ai-x).^2+(y+aj).^2+z.^2)
r3=@(ai,aj) sqrt((ai-x).^2+(y-aj).^2+z.^2)
r4=@(ai,aj) sqrt((x+ai).^2+(y-aj).^2+z.^2)
C1=@(ai) ai+x
C4=@(ai) -C1
C2=@(ai) ai-x
C3=@(ai) -C2
d1=@(aj) y+aj
d2=@(aj) d1
d3=@(aj) y-aj
d4=@(aj) d3

Bz= @(ai,aj) (u0/(4*pi))*(((((-1)^1*d1)/(r1*(r1+((-1)^(1+1))*C1)))-(C1/(r1*(r1+d1))))+((((-1)^2*d2)/(r2*(r2+((-1)^(2+1))*C2)))-(C2/(r2*(r2+d2))))+((((-1)^3*d3)/(r3*(r3+((-1)^(3+1))*C3)))-(C3/(r3*(r3+d3))))+((((-1)^4*d4)/(r4*(r4+((-1)^(4+1))*C4)))-(C4/(r4*(r4+d4)))))
 
for  ai=[a-2*(N-1)*wd-2*(N-1)*s a-2*(N-2)*wd-2*(N-2)*s a-2*(N-3)*wd-2*(N-3)*s a-2*(N-4)*wd-2*(N-4)*s a-2*(N-5)*wd-2*(N-5)*s]
     for  aj=[a-2*(N-1)*wd-2*(N-1)*s a-2*(N-2)*wd-2*(N-2)*s a-2*(N-3)*wd-2*(N-3)*s a-2*(N-4)*wd-2*(N-4)*s a-2*(N-5)*wd-2*(N-5)*s]
       M=integral2(Bz,0,ai,0,aj) 
       A=A+M
       hold on
        end
     end
      
end

ERROR: Undefined operator '*' for input arguments of type 'function_handle'.

Error in FPSSConlyM3 (line 62)

M=integral2(Bz,0,ai,0,aj)

Answer 1

[Walter Roberson]

You have

d1=@(aj) y+aj

and

Bz= @(ai,aj) (u0/(4*pi))*(((((-1)^1*d1)/(r1*(r1+((-1)^(1+1))*C1)))-(C1/(r1*(r1+d1))))+((((-1)^2*d2)/(r2*(r2+((-1)^(2+1))*C2)))-(C2/(r2*(r2+d2))))+((((-1)^3*d3)/(r3*(r3+((-1)^(3+1))*C3)))-(C3/(r3*(r3+d3))))+((((-1)^4*d4)/(r4*(r4+((-1)^(4+1))*C4)))-(C4/(r4*(r4+d4)))))

When it reaches the sub-expression (-1)^1*d1 then it encounters a reference to d1, which is the handle to an anonymous function. d1 is after an * operator, so you are trying to multiply something by the anonymous function d1. Your code is not a request to execute d1 with some argument and multiply based upon the return value: it is a request to multiply the anonymous function itself. Which is not defined.

MATLAB will not look at the d1 and see that it was defined in terms of dummy argumented aj and so try to look to see if there is an active variable named aj that it should use as the argument for executing d1 .

Dummy argument names to an anonymous function are effectively in their own namespace, as if you had written something like.

function Q93277CEA4_result = Q93277CEA4(aj_of_function_Q93277CEA4)
  Q93277CEA4_result = y + aj_of_function_Q93277CEA4
end
d1 = @Q93277CEA4

and

function N76783_result = N76783(ai_of_function_N76783, aj_of_function_N76783)
  N76783_result = (u0/(4*pi))*(((((-1)^1*d1)/(r1*(r1+((-1)^(1+1))*C1)))-(C1/(r1*(r1+d1))))+((((-1)^2*d2)/(r2*(r2+((-1)^(2+1))*C2)))-(C2/(r2*(r2+d2))))+((((-1)^3*d3)/(r3*(r3+((-1)^(3+1))*C3)))-(C3/(r3*(r3+d3))))+((((-1)^4*d4)/(r4*(r4+((-1)^(4+1))*C4)))-(C4/(r4*(r4+d4)))))
end
Bz = @N76783

Under no circumstances will N76783 associate aj_of_function_N76783 with aj_of_function_Q93277CEA4 by itself.

IF you want d1 to be invoked with a particular argument in Bz, then you need to say so specifically, like

Bz= @(ai,aj) (u0/(4*pi))*(((((-1)^1*d1(aj))/(r1(ai,aj)*(r1(ai,aj)+((-1)^(1+1))*C1(ai)))) and so on

[Swathi S]

Thank you, Sir for your explanation. The error is cleared. But now am getting an error as 'Matrix dimension must agree' at M=integral2(Bz,0,ai,0,aj). Can you guide me as where am making mistake?

[Torsten]

The ai and aj passed to your function by integral2 are vectors of the same length.

So multiplication, division and exponentiation in your function definition have to be done elementwise, e.g.

Bz= @(ai,aj) (u0/(4*pi))*(((((-1)^1*d1(aj))./(r1(ai,aj).*(r1(ai,aj)+((-1)^(1+1))*C1(ai))))

and so on.

[Swathi S]

Sir, I tried this already but still getting the same error.

[Torsten]

Please include the modified code.

[Swathi S]

CODE:

for  d=0.1:0.1:1
         A=0
 r1=@(ai,aj) sqrt((x+ai).^2+(y+aj).^2+z.^2)
r2=@(ai,aj) sqrt((ai-x).^2+(y+aj).^2+z.^2)
r3=@(ai,aj) sqrt((ai-x).^2+(y-aj).^2+z.^2)
r4=@(ai,aj) sqrt((x+ai).^2+(y-aj).^2+z.^2)
C1=@(ai) ai+x
C4=@(ai) -C1
C2=@(ai) ai-x
C3=@(ai) -C2
d1=@(aj) y+aj
d2=@(aj) d1
d3=@(aj) y-aj
d4=@(aj) d3


  Bz= @(ai,aj) ((u0./(4.*pi)).*((((((-1).^1).*d1(aj))./(r1(ai,aj).*(r1(ai,aj)+((-1).^(1+1)).*C1(ai))))-(C1(ai)./(r1(ai,aj).*(r1(ai,aj)+d1(aj)))))+(((((-1).^2).*d2(aj))./(r2(ai,aj).*(r2(ai,aj)+(((-1).^(2+1))).*C2(ai))))-(C2(ai)./(r2(ai,aj).*(r2(ai,aj)+d2(aj)))))+(((((-1).^3).*d3(aj))./(r3(ai,aj).*(r3(ai,aj)+(((-1).^(3+1))).*C3(ai))))-(C3(ai)./(r3(ai,aj).*(r3(ai,aj)+d3(aj)))))+(((((-1).^4).*d4)./(r4(ai,aj).*(r4(ai,aj)+((-1).^(4+1)).*C4(ai))))-(C4(ai)./(r4(ai,aj).*(r4(ai,aj)+d4(aj)))))))
   
for  ai=[a-2.*(N-1).*wd-2.*(N-1).*s a-2.*(N-2).*wd-2.*(N-2).*s a-2.*(N-3).*wd-2.*(N-3).*s a-2.*(N-4).*wd-2.*(N-4).*s a-2.*(N-5).*wd-2.*(N-5).*s]
    for  aj=[a-2.*(N-1).*wd-2.*(N-1).*s a-2.*(N-2).*wd-2.*(N-2).*s a-2.*(N-3).*wd-2.*(N-3).*s a-2.*(N-4).*wd-2.*(N-4).*s a-2.*(N-5).*wd-2.*(N-5).*s]
       M=integral2(Bz,0,ai,0,aj) 
       A=A+M
hold on
        end
     end
 end

ERROR:

Matrix dimensions must agree.
Error in FPSSConlyM3 (line 63)
       M=integral2(Bz,0,ai,0,aj)

[Torsten]

a, N, wd, s are undefined.

Where do you use d ?

[Swathi S]

clear all;
close all;
x=0
y=0
a=0.15;
N=5
wd=0.001
s=0.0006
   
for  z=0.1:0.1:1
         A=0
r1=@(ai,aj) sqrt((x+ai).^2+(y+aj).^2+z.^2)
r2=@(ai,aj) sqrt((ai-x).^2+(y+aj).^2+z.^2)
r3=@(ai,aj) sqrt((ai-x).^2+(y-aj).^2+z.^2)
r4=@(ai,aj) sqrt((x+ai).^2+(y-aj).^2+z.^2)
C1=@(ai) ai+x
C4=@(ai) -C1
C2=@(ai) ai-x
C3=@(ai) -C2
d1=@(aj) y+aj
d2=@(aj) d1
d3=@(aj) y-aj
d4=@(aj) d3
Bz= @(ai,aj) ((u0./(4.*pi)).*((((((-1).^1).*d1(aj))./(r1(ai,aj).*(r1(ai,aj)+((-1).^(1+1)).*C1(ai))))-(C1(ai)./(r1(ai,aj).*(r1(ai,aj)+d1(aj)))))+(((((-1).^2).*d2(aj))./(r2(ai,aj).*(r2(ai,aj)+(((-1).^(2+1))).*C2(ai))))-(C2(ai)./(r2(ai,aj).*(r2(ai,aj)+d2(aj)))))+(((((-1).^3).*d3(aj))./(r3(ai,aj).*(r3(ai,aj)+(((-1).^(3+1))).*C3(ai))))-(C3(ai)./(r3(ai,aj).*(r3(ai,aj)+d3(aj)))))+(((((-1).^4).*d4)./(r4(ai,aj).*(r4(ai,aj)+((-1).^(4+1)).*C4(ai))))-(C4(ai)./(r4(ai,aj).*(r4(ai,aj)+d4(aj)))))))
  
    for  ai=[a-2.*(N-1).*wd-2.*(N-1).*s a-2.*(N-2).*wd-2.*(N-2).*s a-2.*(N-3).*wd-2.*(N-3).*s a-2.*(N-4).*wd-2.*(N-4).*s a-2.*(N-5).*wd-2.*(N-5).*s]
    for  aj=[a-2.*(N-1).*wd-2.*(N-1).*s a-2.*(N-2).*wd-2.*(N-2).*s a-2.*(N-3).*wd-2.*(N-3).*s a-2.*(N-4).*wd-2.*(N-4).*s a-2.*(N-5).*wd-2.*(N-5).*s]
       M=integral2(Bz,0,ai,0,aj) 
       A=A+M
hold on
        end
     end
        plot(z,A)
end

ERROR:

Undefined operator '.*' for input arguments of type 'function_handle'.

Error in FPSSConlyM3 (line 57)

M=integral2(Bz,0,ai,0,aj)

[Walter Roberson]

C4=@(ai) -C1

This has the same problem we discussed: C1 is a function handle.

You have the same problem on other lines.

[Swathi S]

Yes, Sir. I could finally clear the error. Thank you, Walter Roberson Sir and Torsten Sir.