How can I get a proper double form for a symbolic matrix?

1 次查看（过去 30 天）
PaoloV
PaoloV 2016-6-24
编辑： PaoloV 2016-6-24
How can I get a proper double form from this symbolic Matrix in MatLab? I've tried everything but I prefer not using feval or inline function as they're not recommended
This is the code to get the matrix
function T = Romberg (a, b, m, f)
T = zeros(m, m);
T = sym(T);
syms f(x) c h;
f(x) = f;
c = (subs(f,a)+subs(f,b)) / 2;
h = b - a;
T(1,1) = h * c;
som = 0 ;
n = 2;
for i = 2 : m
h = h / 2;
for r = 1 : n/2
som = som + subs(f,(a + 2*(r-1)*h));
T(i,1) = h * (c + som);
n = 2*n;
end
end
r = 1;
for j = 2 : m
r = 4*r;
for i = j : m
T(i,j) = (r * T(i, j-1) - T(i-1,j-1)/(r-1));
end
end
end
And with an input like this
Romberg(0, 1, 4, '2*x')
I get a symbolic matrix output with all the
3 * f(3)/2 + f(1)/2 + f(5)/2
I would like to have a double output.
Can you please help me? Thank you very much in advance!

请先登录，再回答此问题。

采纳的回答

Steven Lord
Steven Lord 2016-6-24
Rather than perform the calculations symbolically, why not just write a numeric Romberg integration function? Pass your f input argument as a function handle:
f = @(x) 2*x;
Romberg(0, 1, 4, f)
You'd need to replace your symbolic subs calls with function handle evaluation like f(1) but at first glance it looks like that's the only change you would need to make.
  1 个评论
PaoloV
PaoloV 2016-6-24
编辑：PaoloV 2016-6-24
Didn't know function handle! Thank you very much!
This is the final version of the function hoping this may help someone having the same problem.
I used str2func in order to pass the function as a normal string.
function T = Romberg (a, b, m, f)
%pass the function as string
f = str2func(['@(x) ' f]);
T = zeros(m, m);
c = (f(a)+f(b)) / 2;
h = b - a;
T(1,1) = h * c;
som = 0 ;
n = 2;
for i = 2 : m
h = h / 2;
for r = 1 : n/2
som = som + subs(f,(a + 2*(r-1)*h));
T(i,1) = h * (c + som);
n = 2*n;
end
end
r = 1;
for j = 2 : m
r = 4*r;
for i = j : m
T(i,j) = (r * T(i, j-1) - T(i-1,j-1)/(r-1));
end
end
end

请先登录，再进行评论。

更多回答（2 个）

Kiran Prasad
Kiran Prasad 2016-6-24
Just from my limited experience using symbolic equations to get double answers, I would suggest maybe using the double function on each of the elements at the end if using double on the whole thing won't work. If that doesn't work I would create a small new function that just converts T to numeric. You can try using sym2cell and then cell2mat as that has worked for me before. Hopefully, this helps you-I'm by no means an expert.
  1 个评论
PaoloV
PaoloV 2016-6-24
Thanks for your answer,
I tried at the end of the function writing
T = cell2mat(sym2cell(T));
but MatLab prompted me
Error using cell2mat (line 52)
CELL2MAT does not support cell arrays containing cell arrays or objects.
Error in Romberg (line 47)
T = cell2mat(sym2cell(T));

请先登录，再进行评论。

Walter Roberson
Walter Roberson 2016-6-24
You have an input parameter named f, and then you have
syms f(x) c h;
The first part of that,
syms f(x)
is equivalent to
f = sym('f(x)');
x = sym('x');
which clobbers the meaning of f as being from the input parameter and redefines it as being symbolic. After, places where you thought you were referring to the input parameter become references to the symbolic function.
If you are deliberately ignoring the input parameter then you should use ~ instead of giving it a name, as you are going to confuse readers. And if you are not deliberately ignoring the input parameter then you should be using a different name for f(x) compared to f.
If the idea is to indicate that the input is already a symbolic function then do not declare it with syms: MATLAB would already know it is a symbolic function because it knows the data type of the value that was passed in. But in that case you might still want to syms x

类别

在 Help Center 和 File Exchange 中查找有关 Common Operations 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by