accessing single function from an array of functions

I have defined a matrix of functions:

a=@(t) (1+0.8*sin(2*pi*t));

b=@(t) .8*(1-0.8*sin(2*pi*t));

z = @(t) 0*t;

%T = matlabFunction(fmat);

T=@(t) [-3*a(t) a(t) a(t) a(t) z(t) z(t);...

a(t) -5*a(t) a(t) a(t) a(t) a(t); ...

a(t) a(t) -5*a(t) a(t) a(t) a(t); ...

b(t) b(t) b(t) -5*b(t) b(t) b(t); ...

b(t) b(t) b(t) b(t) -5*b(t) b(t); ...

a(t) a(t) a(t) b(t) 5*b(t) -3*a(t)-6*b(t)];

If I want to access just a single function from the matrix, how do I do it? I have tried several approaches and keep getting: Error: Invalid array indexing.

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/539642-is-it-possible-to-have-an-array-of-function-handles#comment_2020739

Answer 1

[Torsten]

f = {@(t) t, @(t) exp(t), @exp} % the second and third are equivalent
SecondFunction = f{2};
ValueOfSecondFunction = SecondFunction(1)

Does that help ?

[Barbara Margolius]

I have also tried defining the function in this way:

Tcell = {@(t) -3*a(t), a, a, a, z, z;...

a, @(t) -5*a(t), a, a, a, a; ...

a, a, @(t) -5*a(t), a, a, a; ...

b, b, b, @(t) -5*b(t), b, b; ...

b, b, b, b, @(t) -5*b(t), b; ...

a, a, a, b, @(t) 5*b(t), @(t)-3*a(t)-6*b(t)};

The trouble is that I want to exponentiate the matrix for fixed values of t and define a new function in terms of that. Something like

myLT = @(s)eye(mysize);

% temporary definition***

C=eye(mysize);

for k=0:n-1

tobeexp = T(k*deltat)*deltat;

myLT = @(s) myLT(s)*expm(tobeexp-s*C);

end

This does work, but I can't figure out how to get to a particular function within the matrix of functions.

[Torsten]

myLT = @(s)eye(mysize);

Why does eye(mysize) depend on a parameter s ?

This does work, but I can't figure out how to get to a particular function within the matrix of functions.

Within which matrix of functions ?

The trouble is that I want to exponentiate the matrix for fixed values of t and define a new function in terms of that.

Why trouble ?

a=@(t) (1+0.8*sin(2*pi*t));
b=@(t) .8*(1-0.8*sin(2*pi*t));
z = @(t) 0*t;
Tcell =  @(t){ -3*a(t), a(t), a(t), a(t), z(t), z(t);...
                a(t),  -5*a(t), a(t), a(t), a(t), a(t); ...
                a(t), a(t),  -5*a(t), a(t), a(t), a(t); ...
                b(t), b(t), b(t),  -5*b(t), b(t), b(t); ...
                b(t), b(t), b(t), b(t),  -5*b(t), b(t); ...
                a(t), a(t), a(t), b(t),  5*b(t), -3*a(t)-6*b(t)};
Tcell_45_at_t_eq_2 = Tcell(2)(4,5);

Please include a piece of code and explain comprehensively what you are trying to do.

[Barbara Margolius]

Sorry, it is a code snippet. mysize is just 6. It does not depend on s. It is so the loop definition of the function will work.

[Barbara Margolius]

a = @(t)(1+0.8*sin(2*pi*t));

b = @(t)0.8*(1-0.8*sin(2*pi*t));

z = @(t)0*t;

n = 10;

%T = matlabFunction(fmat);

% T is a function of t which returns a 6-by-6 matrix.

% Each element of T is derived from the outputs of functions a, b, and z,

% which are also functions of t.

T = @(t)[ ...

-3*a(t) a(t) a(t) a(t) z(t) z(t);...

a(t) -5*a(t) a(t) a(t) a(t) a(t); ...

a(t) a(t) -5*a(t) a(t) a(t) a(t); ...

b(t) b(t) b(t) -5*b(t) b(t) b(t); ...

b(t) b(t) b(t) b(t) -5*b(t) b(t); ...

a(t) a(t) a(t) b(t) 5*b(t) -3*a(t)-6*b(t); ...

];

mysize = max(size(T(0)));

myLT = @(s)eye(mysize);

C=diag([1 2 3 -4 -3 0]);

deltat = 1/n;

mysize = max(size(T(0)));

myLT = @(s)eye(mysize);

C=diag([1 2 3 -4 -3 0]);

for k=0:n-1

tobeexp = T(k*deltat)*deltat;

myLT = @(s) myLT(s)*expm(tobeexp-s*C);

end

myLT = @(s)det(eye(mysize)-myLT(s));

myLT(.4)

28.0296

h=0:.01:.99;

plot(myLT(h));

Error using *

Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix

matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'.

[Torsten]

h=0:.01:.99;
myLTh = arrayfun(myLT,h);
plot(h,myLTh)

But to be honest: I can't decipher what you are doing in your code.

[Barbara Margolius]

thanks!

Answer 2

[Voss]

a = @(t)(1+0.8*sin(2*pi*t));
b = @(t)0.8*(1-0.8*sin(2*pi*t));
z = @(t)0*t;

%T = matlabFunction(fmat);

% T is a function of t which returns a 6-by-6 matrix.
% Each element of T is derived from the outputs of functions a, b, and z,
% which are also functions of t.
T = @(t)[ ...
    -3*a(t)    a(t)    a(t)    a(t)    z(t)           z(t);...
       a(t) -5*a(t)    a(t)    a(t)    a(t)           a(t); ...
       a(t)    a(t) -5*a(t)    a(t)    a(t)           a(t); ...
       b(t)    b(t)    b(t) -5*b(t)    b(t)           b(t); ...
       b(t)    b(t)    b(t)    b(t) -5*b(t)           b(t); ...
       a(t)    a(t)    a(t)    b(t)  5*b(t) -3*a(t)-6*b(t); ...
    ];

% the 6-by-6 matrix returned from the function T when it is called with 
% input 1:
result = T(1)
% get some element of the result (the result is the matrix returned from 
% calling the function T with input 1):
result(4,5)
% trying to do the same with the output of the function T called with 
% input 1 directly doesn't work in MATLAB (the output from T should be 
% stored in a variable first, i.e., 'result' here):
try
    T(1)(4,5);
catch ME
    disp(ME.message);
    % but you can index T(1) without storing in a variable, if you really
    % want to:
    subsref(T(1),substruct('()',{4,5}))
end