Automatic substitution of a symbolic variable with a numerical value

Hello there,

I noticed that a variable inside symbolic expression is not automatically substituted with its numerical value.

Here is an example:

% syms a; % does not affect the error(s)
a = 1.0;
syms aa b c d;
exp = str2sym('c = a + b');
exp2 = str2sym('d = aa + b');
xx = double(subs(rhs(exp), [b], [2.0])); % error 1
% xx = double(subs(rhs(exp), [a b], [2.0 2.0])); % error 2
% xx = double(subs(rhs(exp2), [aa b], [2.0 2.0])); % no error
disp(xx);

if a variable a which is predefined by the value assignment is automatically applied at the expression definition labeled as 'error 1', the expression would yield the result of 3.0. Instead, MATLAB generated error message.

Thus, I'm wondering if a) if there is any mistake I did in this regard b) if there is an available way to do (or enforce) so.

Answer 1

[Torsten]

The a in the symbolic equation

exp = str2sym('c = a + b');

is not associated with the

a = 1

in the first line.

This would work, however:

syms a b
expr = str2sym('c == a + b');
double(subs(rhs(expr),[a b],[1 2]))

ans = 3

[IN KWON PARK]

Yes, your solution would work. The expression with the label 'no error' in my code tried to show that. Meanwhile, my question is when MATLAB symbolics can take in the pre-existing numerical value, 'a = 1' in my case, into the corresponding symbol inside another symbolic arithmatics definition, 'a' in my question. In my attempt that was not possible obviously. Thus I wanted to check whether that is really the case or perhaps there might be a way to do that.

Answer 2

[Dyuman Joshi]

When you define expressions/variables using str2sym, it does not create the variables defined in the input.

Also, it's not a good idea to use built-in functions as variables names - exp in your case.

% syms a; % does not affect the error(s)
%a = 1.0;
%syms aa b c d;
exp1 = str2sym('c = a + b');
exp2 = str2sym('d = aa + b');
syms

Your symbolic variables are:

exp1  exp2                                                                                                                                                                                      

whos

  Name        Size            Bytes  Class    Attributes

  cmdout      1x33               66  char               
  exp1        1x1                 8  sym                
  exp2        1x1                 8  sym                

As you can see, none of a, aa, b, c or d have been defined.

In order to use sub(), the variables to be subsituted must have been defined as symbolic variables.

In your code, aa and b have been defined as such but not a. Thus the substitution for aa and b is succesfull, but it does not take place for a, and that expression does not resolve to a symbolic number. And you can use double() only on a symbolic number.

Now you might ask - Why does defining variable a as a symbolic variables does not affect the error?

Because you over-write it by assinging a numerical value to it.

If you remove that particular line, then you will not get an error -

syms a; % does not affect the error(s)
%a = 1.0;
syms aa b c d;
exp1 = str2sym('c = a + b');
exp2 = str2sym('d = aa + b');

%Can't use double() on a symbolic variable
xx1 = subs(rhs(exp1), [b], [2.0])

xx1 = 

%Can use double() on a symbolic number
xx2 = double(subs(rhs(exp1), [a b], [2.0 2.0]))

xx2 = 4

xx3 = double(subs(rhs(exp2), [aa b], [2.0 2.0]))

xx3 = 4

Solution - Define a as a symbolic variable and do not over-write it.

[IN KWON PARK]

What you've explained was what I already expected. The comment at the first line, '% does not affect the error(s)', tried to show that. What I wanted to check is to see if that is what MATLAB symbolics can do (or cannot do) or there is a way to achieve what I wanted. Other symbolic math software (e.g., Maple) runs with the awareness of pre-defined numeric values and applies the value(s) when a subsequent symbolic arithmatics expression is defined.

[Dyuman Joshi]

"when a subsequent symbolic arithmatics expression is defined."

But you have not defined symbolic arithmatic expressions. The functionality of str2sym is not to define expressions, rather evaluate it.

You can directly substitute values into expressions like this -

a=1;
b=2;
eqn1 = str2sym('c=a+b')

eqn1 = 

eqn2 = subs(str2sym('c=a+b'))

eqn2 = 

Whichever variables have been assigned a numerical value, will be substituted when used subs() as above.

rhs(eqn2)

ans = 

3

[IN KWON PARK]

Thank you for your further note.

'The functionality of str2sym is not to define expressions, rather evaluate it.': I used it for define the expression, not for evalaution. Probably that is also obvious in what you presented: 'eqn1' carries the expression itself, not the evaluation result. If 'str2sym' evaluates the expression given at the 'eqn1' line, it shoild come up with 'c=3' instead of 'c=a+b'. I also looked at the help page of 'str2sym'. While the title carries the word 'evaluation', the body shows plenty of examples presenting the role of the function call, define an arithmatic expression. Or you may want to show me how to 'define' an expression, instead of using 'str2sym'.

Meanwhile, if 'str2sym' does evaluate an expression, my expectation is to bring in the pre-existing numerical value when it evaluates the given expression. Other software already offers such convenience.

[Walter Roberson]

The rule is pretty simple in MATLAB:

If a name has been associated with a value at the MATLAB level (whether numeric or symbolic) and you use the name in a symbolic expression outside of quotes then the value associated with the variable will be pulled into the expression at that point.

If, on the other hand, the reference to the name is inside of quotes then neither sym() nor str2sym() will pull in the value associated with the variable, and will instead insert a symbolic variable with that name.

This is not different than using ' ' or " " or ` ` expressions in Maple. For example,

Yes, evaluating b does give 5+1 the first time, but when ' ' delay-evaluation quotes were used, the value of a is not used in b itself. Evaluating b evaluates a+1 using the then-current value of a at the time of evaluation. If a is still 5 then that would be 5+1 but you can see from steps 6 and 7 that with the current value of a changed then evaluating b gets a result based on the now-current value of a .

In Maple, line 3 with "a + 2" is creating a string with the characters 'a', space, '+', space, '2' .

In Maple, line 4 with `a + 2` is creating an atomic name that happens to have spaces and other characters in it. Atomic names can be assigned values --- so it would be legal, for example, in Maple to say

`a + 2` := 17

and that would be creating a variable with a funny name... a name that had no relationship to whatever value might have been associated with a

The Maple "delay-quote" is a significant semantic difference compared to MATLAB, but inside delay quotes, any value associated with a named variable is not bound into the expression: instead, at the time of evaluation, the current value of the variable is looked up.

[Walter Roberson]

@IN KWON PARK

You are mistaken about the operation of Maple.

a has a pre-defined value, but the result of converting the string "a + 5" to an expression does not involve evaluating a . In Maple, parse("a + 5") gives you the same as if you had entered 'a + 5' -- with delay quotes. If you were to assign the output of parse() to a variable and then change a and then evaluate the variable, you would get the result with the changed a not with the a as-was at the time you did the parse()

[Dyuman Joshi]

@IN KWON PARK

"I used it for define the expression, not for evalaution. "

You are misunderstanding here. It does not matter what you intend to do, or what you expect it to do.

Given an input, str2sym will evaluate it. If the expression evaluates to a symbolic number, the output will be the evaluated symbolic number, if not, it will return the input as it is.

That is how the function is defined and that is how it works.

"the body shows plenty of examples presenting the role of the function call, define an arithmatic expression"

As I said before, if str2sym can not evaluate the input to a symbolic number, it will return the input as it is.

Now, in your case, the input happens to be an arithmatic expression, thus so is the output.

"Or you may want to show me how to 'define' an expression, instead of using 'str2sym'."

syms a b c

eqn = c == a+b

eqn = 

xx = double(subs(rhs(eqn),[a b],[1 2]))

xx = 3

"Meanwhile, if 'str2sym' does evaluate an expression,"

The use of "if" is misplaced here, as evaluation is what it does.

"my expectation is to bring in the pre-existing numerical value when it evaluates the given expression."

I showed you how to do that.

"Other software already offers such convenience."

Can you show an example?

@Walter Roberson has already (comprehensively) showed you that your example of Maple is wrong.