Why is element of matrix not numeric but value of element is?

Can someone help me explain this? I am testing an element of a matrix to see if it's numeric (the matrix also contains some symbolic variables).

>> T12test2(1)

ans =

4967757600021511/81129638414606681695789005144064

>> isnumeric(T12test2(1))

ans =

    logical

     0

>> isnumeric(4967757600021511/81129638414606681695789005144064)

ans =

    logical

     1

When I test the element of the matrix it is not numeric, but when I test the value of the element it is numeric. Puzzled.....

Answer 1

[Steven Lord]

Whether an array is numeric or not is a function of the class of the array, not the contents of the array.

The array T12test2 is of class sym so T12test2(1) is also of class sym, and sym objects are not numeric. They can contain numbers, but they are not themselves numeric.

syms x
z = sym(5);
isnumeric(x) % false
isnumeric(z) % false

When you divide two numbers like you did in your second isnumeric call, you receive a number that is stored as an array of class double. A double array contains numbers and is also numeric.

isnumeric(42) % true
isnumeric(1/2) % true
y = pi; isnumeric(y) % true

[S Crombie]

Thanks for the explanation.

It seems I can convert the element of the array to numeric using

double(T12test2(1))

and then isnumeric is true. But if I try to do this for all the elements of the array it throws an error when it comes to an element which is a symbolic variable.

Is there a way of testing the elements of a matrix to see whether they are symbolic variables so I can skip the conversion to double for those elements?

[Walter Roberson]

What is the purpose of testing for numeric? Is it something that could be solved by using vpa() ?

If an element contains (for example) sqrt(2) or sin(pi/8) in symbolic form, then are those to be considered numeric? If it contains factorial(1000) which is beyond the range of double but is still a numeric constant, then should it be considered numeric?

Is the question whether the expression contains any symbolic variables? Is the question whether the expression contains any unbound symbolic variables? For example in x + int(sin(y),y,0,1) then y is "bound" because it only appears in contexts that give it specific range of values, pretty much "defining" it locally, whereas x has no restrictions on it and is called "unbound". int(sin(y),y,0,1) is effectively a constant that could be evaluated if you double() it, but the x part cannot be resolved by double()

[S Crombie]

My matrix is a homogeneous rotation matrix generated from a function which takes four inputs (they are the Denavit-Hartenberg parameters for a robot joint to be exact, two are distances and two are angles in radians).

When I run the function with a mixture of numeric and symbolic inputs some of the output matrix elements appear as huge fractions, although these evaluate to zero effectively. For example the fraction in my original post above. The other matrix elements are numbers, or expressions which can be evaluated, eg 2^(1/2)/2 and others which can't eg d2 (which is a symbolic variable).

I want to go through the matrix, evaluating the elements, set any that are effectively zero to exactly zero to make the matrix easier to read, but leave other elements and any symbolic variables unchanged. My efforts so far have failed because any operation I can apply to the matrix elements which are numbers throws an error when applied to a matrix element which is a symbolic variable.

So ideally I want some way of distinguishing the symbolic variables in my matrix.

[Walter Roberson]

Determining whether a particular element of a matrix contains at least one symbolic variable is easy:

arrayfun( @(X) isempty(symvar(X)), YourMatrix )

However, you undoubtedly have a matrix that contains expressions in which you want to zero out the coefficients involved with some terms but not others. That is something that is difficult to impossible to do at the MATLAB level, but is possible to do having the MATLAB level telling the symbolic engine to run some code.