problems with symbolic calculations

Hi, I'm getting an error while trying to do a calculation with a symbolic expression.

First I'll write the code so I can explain my question.

Earlier in the code I defined what the variable n is, n is a cell of size 2x1 where:

n{1}

is a symbolic expression with symbolic variable x and

n{2}

is the second symbolic expression with variable x.

Also the variable L has been defined before in the code, to simplify let's suppose that

L = [2 3];

Likewise the variable c has been defined before like this:

%Physical constants definition
c = 299792458; %Speed of light in [m/s] , needs to be converted to micrometer.
c = c.*10^6; %Conversion to micrometers.

Then my problem arises when I try to do the following calculations:

d = length(n);
t1 = zeros(1,d);
for i=1:d
    t1(i) = n{i}.*L(i)./c;
end

Then I get the following error from matlab:

The following error occurred converting from sym to double:
DOUBLE cannot convert the input expression into a double array.
If the input expression contains a symbolic variable, use VPA.

I have allready tried to use vpa like this:

for i=1:d
    t1(i) = vpa(n{i}.*L(i)./c);
end

but I get the same error.

Can someone tell me how to avoid this error and be able to complete the calculations?

Thanks in advance for the effort and time.

Answer 1

[John D'Errico]

Simple problem. Simple to fix too. Look in this loop.

t1 = zeros(1,d);
for i=1:d
    t1(i) = n{i}.*L(i)./c;
end

What is t1? What type is it? (Answer: Double precision.)

What is in the right hand side of that expression inside the loop? (Answer: symbolic stuff.)

What was the error message? Cannot convert sym to double. Why not? Because it contains a symbolic variable, x of course! You already said that n{i} was a function of x.

Instead, preallocate t1 as

t1 = zeros(1,d,'sym');

Now there will be no error, because the variable types will be compatible.

And, no, vpa cannot solve it, because vpa won't turn a symbolic expression that contains a variable into a double. vpa will still leave it symbolic.

If you don't believe me, TRY IT! Here is what you did.

t1 = zeros(1,2);
syms x

t1(1) = 3*x
The following error occurred converting from sym to double:
DOUBLE cannot convert the input expression into a double array.

Of course, vpa won't help, as I said, since 3*x is still symbolic, no matter what you do.

t1(1) = vpa(3*x)
The following error occurred converting from sym to double:
DOUBLE cannot convert the input expression into a double array.

Allocate t1 properly though...

t1 = zeros(1,2,'sym');
t1(1) = 3*x
t1 =
[ 3*x, 0]

And, finally, the last step is to show that had the result been in numeric form, it would have worked. Lets make t1 a double vector again, and try this:

t1 = zeros(1,2);
t1(1) = subs(3*x,x,pi)
t1 =
        9.42477796076938                         0

whos t1
Name      Size            Bytes  Class     Attributes
t1        1x2                16  double

As you can see, MATLAB still thinks that t1 is a double. So there was only a problem when you tried to stuff a square peg into a round hole.

[test run]

Thank you John D'Errico, I understand now how to handle the calculations correctly, your detailed explanation was great.

Answer 2

[Trang Nguyen]

Thank you so much John D'Errico. It helps me a lot in my working. You are completely great. Thanks ^^