# Defining a function for a vector of values, while keeping two variables unknown

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Laura Freitas
on 21 Oct 2021

Commented: Laura Freitas
on 22 Oct 2021

I have created a function on matlab dependent on three variables, say:

f= @(x,y,z) f(x,y,z)

I have a vector of values for x, let's call it A. My goal is to estimate function:

So what I am looking for is a Matlab command which will allow me to calculate f(x,y,z) for each value of vector A, and then sum them together. Here are a few things I have tried that failed:

% Attempt #1: returns g as a number (0), rather than a function.

g = @(y,z) sum(f(A,y,z))

% Attempt #2: returns g as a number (0), rather than as a function.

g = @(y,z) cumsum(f(A,y,z))

% Attempt #3: doesn't recognize A as an input.

function g = g(y,z)

g = f(A,y,z)

end

I have checked and the issue lies in estimating f(A,y,Z), which immediately turns all values to 0. I know that a possible alternative to this is doing a manual sum of f(a_1,y,z) + f(a_2,y,z) etc, but there are 175 different numbers in vector A and coding this manually would take forever. Does anyone have any other ideas?

##### 4 Comments

Walter Roberson
on 21 Oct 2021

elseif i==0 & ((y-x)/2571)==1

You are asking for the floating point calculation (y-x)/2571 to exactly equal an integer. That is risky because of floating point round-off. You would be better off rewriting it by multiplying it out,

elseif i==0 & (y-x)==2571*1

### Accepted Answer

Walter Roberson
on 22 Oct 2021

So I must achieve the function, EV(x,i), and then replace by the values of x and i

If you must achieve the function first, and then replace the placeholders later, then you need to use the symbolic toolbox and use piecewise()

The below is probably not correct. You say that you need to sum() but you did not define the dimension(s) you need to sum over.

theta_11 = 1

beta = 2

RC = 8

u_0 = @(y) -theta_11*0.001*y;

u_1 = @(y) -RC;

EV0 = @(y,j) 0;

V = @(y) log(exp(u_0(y)+beta*EV0(y,0))+exp(u_1(y)+beta*EV0(y,1)));

PV = @(y,x,i) Prob(y,x,i).*V(y); % use .* since V is also now a vector

% make up some example values just to try code

i = 0

x = 10

y = [0, 3*2571 + x, 2*2571+x, 2571+x]

[yG, xG, iG] = ndgrid(y, x, i);

pv = arrayfun(PV, yG, xG, iG)

sumPV = sum(pv, 1)

function P = Prob(Y,X,I)

y = sym(Y); x = sym(X); i = sym(I);

P = piecewise( ...

i == 0 & x == 442212 & y == 447354, ...

0.3621 + 0.0143, ...

i == 0 & x == 444783 & y == 447354, ...

0.5152 + 0.3621 + 0.0143, ...

i == 0 & x == 447354 & y == 447354, ...

1, ...

i == 1 & y == 0, ...

1, ...

i == 0 & (y-x) == 0*2571, ...

0.1071, ...

i == 0 & (y-x) == 1*2571, ...

0.5152, ...

i == 0 & i == 0 & (y-x) == 2*2571, ...

0.3621, ...

i == 0 & i == 0 & (y-x) == 3*2571, ...

0.0143, ...

symtrue, ...

0 );

end

##### 2 Comments

Walter Roberson
on 22 Oct 2021

### More Answers (3)

Sulaymon Eshkabilov
on 21 Oct 2021

Edited: Sulaymon Eshkabilov
on 21 Oct 2021

Supposedly, this is what you are trying to achieve:

syms y z

A = magic(3);

F = @(A, y, z) cumsum(A+y+z);

FF = (F(A, y,z))

Sulaymon Eshkabilov
on 21 Oct 2021

Edited: Sulaymon Eshkabilov
on 21 Oct 2021

% Here is the complete solution

syms y z

A =1:5;

F = @(A, y, z) sum(A+y+z);

FF = (F(A, y,z))

Jon
on 22 Oct 2021

One way to do what I think you want is to have the inner function, in your case PV(y,x,i) accept a vector argument for y and return a vector of values, pv. Then you can easily sum up the elements of pv using MATLAB's sum function.

Here is an attempt to illustrate this where I have appropriately modified your code snippet.

By the way your function EV0 seems to do nothing as it will always return zero, so then in your definition of your function V(y) the terms beta*EV0(y,0) are always zero. Doesn't seem to make much sense, but the main point is showing you how to have the function P accept and return a vector argument, and summing up the elements

% make up some example values just to try code

theta_11 = 1

beta = 2

RC = 8

u_0 = @(y) -theta_11*0.001*y;

u_1 = @(y) -RC;

EV0 = @(y,j) 0;

V = @(y) log(exp(u_0(y)+beta*EV0(y,0))+exp(u_1(y)+beta*EV0(y,1)));

PV = @(y,x,i) Prob(y,x,i).*V(y); % use .* since V is also now a vector

% make up some example values just to try code

i = 0

x = 10

y = [0, 3*2571 + x, 2*2571+x, 2571+x]

pv = PV(y,x,i)

sumPV = sum(pv)

% Define the probability matrix, to accept vector y

function P = Prob(y,x,i)

% preallocate output vector

P = zeros(size(y));

for k = 1:numel(P)

if i==0 && x== 442212 && y(k) == 447354

P(k) = 0.3621 + 0.0143;

elseif i==0 && x== 444783 && y(k)== 447354

P(k) = 0.5152 + 0.3621 + 0.0143;

elseif i==0 && x== 447354 && y(k)== 447354

P(k) = 1;

elseif i == 1 && y(k)==0

P(k) = 1;

elseif i==0 && (y(k)-x)==0*2571

P(k) = 0.1071;

elseif i==0 && (y(k)-x)==1*2571

P(k) = 0.5152;

elseif i==0 && i==0 && (y(k)-x)==2*2571

P(k) = 0.3621;

elseif i==0 && i==0 &&(y(k)-x)==3*2571

P(k) = 0.0143;

else

P(k) = 0;

end

end

end

##### 5 Comments

Jon
on 22 Oct 2021

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