I cannot get my function to accept an input with a decimal and when the answer is displayed it displays an array of numbers.

I cannot get my function to accept an input with a decimal and when the answer is displayed it displays an array of numbers instead of just the answer.

Answer 1

[Walter Roberson]

You are confusing formulas and indexing. In MATLAB, there are two situations available:

A) If T is a numeric variable, then assigning to p(T) is always indexing, and T must be either logical or positive integer. The value of T gives the relative offset into the array (first location being index 1)

B) If T is an unresolved symbolic variable, such as syms T, then assigning to p(T) defines a symbolic function, equivalent to

p = symfun(EXPRESSION, T);

Later, p could then be invoked with a parameter that is an arbitrary number or possibly even symbolic value. The result of invoking p would be symbolic.

In MATLAB, if you want to define a formula that that returns a numeric value when passed a parameter, you need to create an anonymous function,

p = @(T) (999.83952 +(16.945176*T)-((7.9870401*10^-3)*T^2)-((46.170461*10^-6)*T^3)+((105.56302*10^-9)*T^4
-((280.54253*10^-12)*T^5)))/(1+((16.879850*10^-3)*T));

The result would be an unevaluated function handle, and you would need to invoke it on a particular numeric input in order to get a numeric result.

Remember, if you see something in a paper or textbook that looks like (for example)

then that is defining a formula, and if you want you can create a formula in MATLAB with

f = @(x) sin(exp(x));

but remember that this does not give a result for any particular x and you need to invoke the formula on your input to get a result.

fx = f(X);

Most of the time what you want to do is go directly to the result,

fx = sin(exp(X));

Notice there is not necessarily any () on the left hand side. There could be, for example,

for K = 1 : 10
    fx(K) = sin(exp(X(K)));
end

This would be indexing not formula.

[Nathan Stawasz]

why does the display of the answer then still include.....

[Walter Roberson]

When you have

p(T) = (999.83952 +(16.945176*T)-((7.9870401*10^-3)*T^2)-((46.170461*10^-6)*T^3)+((105.56302*10^-9)*T^4
-((280.54253*10^-12)*T^5)))/(1+((16.879850*10^-3)*T));

then, as I explained above, that is indexing. When T = 12, then the left hand side is p(12) -- assigning to the 12th element of the array p that did not exist before that point. MATLAB defines that if you assign past the last existing element of an array, that all of the elements between the existing end and the new location are filled with 0 for numeric arrays, so p(1), p(2), p(3), and so on up to p(11) would get assigned 0.

You need to decide whether you are coding a formula or an expression . If you are defining a formula then you need one of these two possibilities:

1)

p = @(T) (999.83952 +(16.945176*T)-((7.9870401*10^-3)*T^2)-((46.170461*10^-6)*T^3)+((105.56302*10^-9)*T^4
-((280.54253*10^-12)*T^5)))/(1+((16.879850*10^-3)*T));

or

2)

syms T
p(T) = (999.83952 +(16.945176*T)-((7.9870401*10^-3)*T^2)-((46.170461*10^-6)*T^3)+((105.56302*10^-9)*T^4
-((280.54253*10^-12)*T^5)))/(1+((16.879850*10^-3)*T));

If you are defining an expression the the p(T) on the left hand side is indexing and T becomes restricted to being a positive integer and you get those zeros like you are observing.

[Walter Roberson]

function f_density(T)
%f_density(T) calculates the value of p(T), the density of pure water at a given temperature T.
%Input arguments: 
T= input('Enter the temperature of the pure water:');
p =@(T) (999.83952 +(16.945176*T)-((7.9870401*10^-3)*T^2)-((46.170461*10^-6)*T^3)+((105.56302*10^-9)*T^4 -((280.54253*10^-12)*T^5)))/(1+((16.879850*10^-3)*T));
disp(' ') 
fprintf('The density of the pure water is %6.4f degrees celsius.\n',p(T));
end 

[Walter Roberson]

As I described in

https://www.mathworks.com/matlabcentral/answers/478604-assigning-a-name-for-a-function#answer_390112

the answer is NO, NEVER.

[Steven Lord]

Function names need to satisfy the same rules as variable names, as listed in the documentation for the isvarname function. The identifier f_density satisfies those rules. If you wanted to include (T) in the name [naming your function f_density(T)] that would not satisfy the rules, as ( is neither a letter, a number, nor an underscore.

[Walter Roberson]

If you could name it f_density(T) then the (T) would have to be included in every call to the function, so you would end up with constructs such as

f_density(T)(19.1)

and the parser would have to be made more intelligent to know that in

f = @(T) f_density(T)(T)

that the first (T) is to be part of the literal name but that the second (T) is the parameter.

There are some computer languages such as Maple that permit arbitrary characters to be included in function names, using syntaxes such as

`f_density(T)`(19.1)

however MATLAB is not one of those languages.

[Nathan Stawasz]

How would I edit this function to get it so you can input the temperature into the fuction name f_density (68.14) and get the answer when the function is called ?

[Walter Roberson]

Remove the line

T= input('Enter the temperature of the pure water:');