I am new to matlab and want to calculate something like f(x)/f'(x). I want the user to input the function f(x), the parameter x and a value of x (suppose 5,so that I can evaluate f(5)/f'(5)) .Please suggest what I should do.
One approach is to use symbolic variables
function [ val ] = func( fun, num )
symfun = sym(fun);
dsymfun = diff(symfun);
y = symfun/dsymfun;
val = subs(y, num);
end
and then call it
e.g.
value = func('x^2', 5)
value =
5/2
Otherwise, you can provide your input as a symbolic variable:
function [ val ] = func( fun, num )
dfun = diff(fun);
y = fun/dfun;
val = subs(y, num);
end
and then write
syms x;
func(x^2, 5)
You can do this using polyder and polyval as follows:
f = input('Enter f(x): '); %e.g; Enter [1 3 4] if f(x)= x^2 + 3*x + 4
df = polyder(f); %f'(x)
x= input('Enter x: '); %Enter the value of 'x' e.g 5
fx_dfx= polyval(f,x)/ polyval(df,x) %f(x)/f'(x)
If you have Symbolic Math Toolbox, you can also do this using:
syms x; %Creating a symbolic variable x
f = input('Enter f(x): '); %Enter f(x) e.g: x^2 + 3*x + 4
f(x)= f; %Converting sym to symfun
df(x) = diff(f) %f'(x)
x_val= input('Enter x: '); %Enter the value of 'x' e.g 5
fx_dfx = double(f(x_val)/df(x_val)) %f(x)/f'(x)
Related
My goal is to compute the derivative of a function and use this result as another function. Clearly, it means :
f = #(x) (x-1)*(x-2); %A simple function
derivative = jacobian(f,x) %MATLAB output : "2*x - 3"
df = #(x) derivative %= #(x) 2*x - 3
df(2) %= "2*x -3" instead of 2*2 - 3
How can I do such a thing ? I tried syms x but it doesn't help.
You want matlabFunction:
g = matlabFunction(f) converts the symbolic expression or function f to a MATLAB function with handle g.
In your example:
>> syms x
>> f = #(x) (x-1)*(x-2);
>> derivative = jacobian(f,x);
>> df = matlabFunction(derivative)
df =
function_handle with value:
#(x)x.*2.0-3.0
>> df(2)
ans =
1
I am trying to compute the taylor series of ln(x) for any value of x.
What I have so far is:
clear
clc
n = input('Enter number of iiterations (n): ' );
x = input('enter value of x (x): ');
y = zeros(1,n);
for i = 0:n
y(i+1)=sum + (-1)^(n+1)*(x-1)^n/n;
end
But this code seems to be broken and I can't figure out why. Any suggestions on how to improve?
This is a one liner in addition to the for-loop answer provided by #farbiondriven
For 0<x<1 :
sumLn = #(x, n)(sum(((-1).^(0:n-1)).*((x-1).^(1:n))./(1:n)));
sumLn(0.5,10)
ans =
-0.6931
>> log(0.5)
ans =
-0.6931
For x>0.5 :
sumLn = #(x, n)(sum( ((x-1)/x).^(1:n) ./ (1:n) ));
sumLn(2,10)
ans =
0.6931
log(2) =
0.6931
Note: The variable x in this formula is bounded as mentioned in this link.
Try this:
clear
clc
n = input('Enter number of iterations (n): ' );
x = input('enter value of x with abs value < 1 (x): ');
y = zeros(1,n+1);
y(1)=0;
for i = 1:n
y(i+1)= y(i) + ((-1)^(i+1)*(x-1)^i/i);
end
txt = sprintf('The output is: %f', y(n+1))
I suggest using built-in function and hopefully there is one. taylor(f,var) approximates f with the Taylor series expansion of f up to the fifth order at the point var = 0.
Specify Expansion Point :
Find the Taylor series expansions at x = 1 for these functions. The default expansion point is 0. To specify a different expansion point, use 'ExpansionPoint':
syms x
taylor(log(x), x, 'ExpansionPoint', 1)
ans =
x - (x - 1)^2/2 + (x - 1)^3/3 - (x - 1)^4/4 + (x - 1)^5/5 - 1
Specify Truncation Order :
The default truncation order is 6.
syms x
f = log(x);
t6 = taylor(f, x);
Use 'Order' to control the truncation order. For example, approximate the same expression up to the orders 8.
syms x
taylor(log(x), x, 'ExpansionPoint', 1, 'Order', 8);
Is there anyway to use a loop index to call symbolic variables in Matlab? For example, consider the following code whose goal is to store the symbolic expression "x1+x2+x3" in "y".
syms x1 x2 x3
y = 0;
for i = 1:3
y = y + xi;
end
The code does not work because on each iteration Matlab reads "y = y + xi" and returns the error "xi is undefined", instead of reading "y = y + x1", "y = y + x2" and "y = y + x3", is there anyway around this?
Thanks.
I'd suggest this, provided that you can create your numbered symbolic variable slightly differently:
x = sym('x',[1 3]); % or: syms x1 x2 x3; x = [x1 x2 x3];
y = x(1);
for i = 2:numel(x)
y = y+x(i);
end
Of course in this simple example, the entire for loop and everything else can be replaced with:
y = sum(sym('x',[1 3]));
See the documentation on sym for more details.
EDIT: Note that, as #pm89 points out, by allocating the 1-by-3 symbolic vector x, you of course won't have direct access to the symbolic variables x1,x2, and x3 in your workspace, but will have to index them as shown. This is similar to working with arrays or cells and has many of the same benefits as my second vectorized example illustrates.
If your Matlab does not support the matrix declaration of symbolics directly (as sym('x',[3 1])) you can write your own function for that:
function out = Matrix_Sym(name, size) %#ok<STOUT>
rows = size(1);
cols = size(2);
S = '';
for k1 = 1:rows
for k2 = 1:cols
if rows == 1
S = [S name int2str(k2) ' '];
elseif cols == 1
S = [S name int2str(k1) ' '];
else
S = [S name int2str(k1) int2str(k2) ' '];
end
end
end
eval(['syms ' S]);
eval (['out = reshape([' S '], [rows, cols]);']);
Then you could get the same result with:
x = Matrix_Sym('x', [3 1])
...
I want to solve equations in matlab, eg.
100+a/2=173*cos(b)
sqrt(3)*a/2=173*sin(b）
and the code would be:
[a,b]=solve('100+a/2=173*cos(b)','sqrt(3)*a/2=173*sin(b)','a','b')
However, if I want to take 100 as a variable, like
for k=1:100
[a,b]=solve('k+a/2=173*cos(b)','sqrt(3)*a/2=173*sin(b)','a','b')
end
There would be an error, how to make it?
degree=140/1000000;
p=42164000;
a=6378136.5;
b=6356751.8;
x_1=0;
y_1=p;
z_1=0;
for i=451:550
for j=451:550
alpha=(1145-i)*degree;
beta=(1145-j)*degree;
x_2=p/cos(alpha)*tan(beta);
y_2=0;
z_2=p*tan(alpha);
syms x y z x_1 x_2 y_1 y_2 z_1 z_2 a b
eq = [(x-x_1)*(y2-y_1)-(x_2-x_1)*(y-y_1),(x-x_1)*(z_2-z_1)-(x_2-x_1)*(z-z_1), b^2*(x^2+y^2)+a^2*(y^2)-a^2*b^2 ];
sol = solve(eq(1),x,eq(2),y, eq(3),z);
sol.x
sol.y
sol.z
end
end
I got the expression value, how do I get the numeric value of x,y,z?
[['x(1)=';'x(2)='],num2str(double(sol.x))]
not work ,shows
??? Error using ==> mupadmex
Error in MuPAD command: DOUBLE cannot convert the input expression into a double array.
If the input expression contains a symbolic variable, use the VPA function instead.
Error in ==> sym.sym>sym.double at 927
Xstr = mupadmex('mllib::double', S.s, 0);
Error in ==> f2 at 38
[['x(1)=';'x(2)='],num2str(double(sol.x))]
If you have access to the Symbolic Toolkit then you do the following:
syms a b k
eq = [k+a/2-173*cos(b), sqrt(3)*a/2-173*sin(b)];
sol = solve(eq(1),a,eq(2),b);
sol.a = simplify(sol.a);
sol.b = simplify(sol.b);
% There are two solutions for 'a' and 'b'
% check residuals for example k=20
subs(subs(eq,{a,b},{sol.a(1),sol.b(1)}),k,20)
% ans = 0.2e-13
subs(subs(eq,{a,b},{sol.a(2),sol.b(2)}),k,20)
% ans = 0.2e-13
Edit 1
Based on new code by OP the matlab script to solve this is:
clear all
clc
syms alpha beta
degree=140/1000000;
p=42164000;
a=6378136.5;
b=6356751.8;
x_1=0;
y_1=p;
z_1=0;
x_2 = p/cos(alpha)*tan(beta);
y_2 = 0;
z_2 = p*tan(alpha);
syms x y z
eq = [(x-x_1)*(y_2-y_1)-(x_2-x_1)*(y-y_1);...
(x-x_1)*(z_2-z_1)-(x_2-x_1)*(z-z_1); ...
b^2*(x^2+y^2)+a^2*(y^2)-a^2*b^2 ];
sol = solve(eq(1),x,eq(2),y,eq(3),z);
sol.x = simplify(sol.x);
sol.y = simplify(sol.y);
sol.z = simplify(sol.z);
pt_1 = [sol.x(1);sol.y(1);sol.z(1)] % First Solution Point
pt_2 = [sol.x(2);sol.y(2);sol.z(2)] % Second Solution Point
x = zeros(100,100);
y = zeros(100,100);
z = zeros(100,100);
for i=451:550
disp(['i=',num2str(i)])
for j=451:550
res = double(subs(pt_1,{alpha,beta},{(1145-i)*degree,(1145-j)*degree}));
x(i-450, j-450) = res(1);
y(i-450, j-450) = res(2);
z(i-450, j-450) = res(3);
end
end
disp('x=');
disp(x);
disp('y=');
disp(x);
disp('z=');
disp(x);
I would try
for i=1:100
k=num2str(i)
[a,b]=solve('100+a/2=173*cos(b)','sqrt(3)*a/2=173*sin(b)','a','b')
end
and then solve the equation
I want to seperate a rational function to num and denom:
i.e x*y/(2*z) ===> n = x*y d = 2*z
here is my code:
func = input('Enter the function: ');
[n d] = numden(func);
disp(n);
>> test
Enter the function: x*y/(2*z)
??? Error using ==> input
Undefined function or variable 'y'.
Error in ==> test at 1
func = input('Enter the function: ');
You have to use symbolic objects.
>> syms x y;
>> [n d] = numden(x*y/(x+y))
n =
x*y
d =
x + y
>>