I use anonymous functions in my code. For example:
G = #(x) [norm(A*x-b);A'*(A*x-b)];
norm(Ax-b) is the objective function and A'*(Ax-b) the gradient.
Then,
Algo( G,varagin );
etc
What I would like to do is to define f with a loop:
n = 9;
k = 2;
t = 1 - x.^k;
f = 0;
for i=1:n
f = f + x(i,1)*prod(t(1:i-1));
end
grad_f = zeros(n,1);
for i0=1:n
s = t;
s(i0) = [];
for i=i0+1:n
grad_f(i0) = grad_f(i0) + x(i)*prod(s(1:i0-1));
end
grad_f(i0) = -k*x(i0)^(k-1)*grad_f(i0);
grad_f(i0) = grad_f(i0) + prod(t(1:i0-1));
end
Then I would like to do something like:
" G = #(x) [f,grad_f] "
Thanks a lot for your help!
Found the answer:
create F(x) and GRAD_F(x) as functions in matlab computing f and grad_f respectively.
Then:
G = #(x) [F(x);GRAD_F(x)];
Algo(G,varargin);
Related
I'm trying to write a function that sums a bunch of functions and I have no idea what I'm doing wrong. My code:
function [f_max,x_max] = ftot(l,a,E,J,F)
% a and F are arrays
f_max = 0;
b = l-a;
n = length(F);
f1 = 0;
syms x
for j=1:n
y1 = piecewise(x<=a(j),1,x>a(j),0);
y2 = piecewise(x<=a(j),0,x>a(j),1);
f = (F(j)*b(j)*x)*y1 + (F(j)*b(j)*x^3)*y2;
f1 = f1 + f;
end
Basically I want to create a function that is the sum of F(j)*b(j)*x for j=1:n when x<=a and F(j)*b(j)*x^3 when x>a. How can I accomplish that?
I want the function P to look like this:
-1 + 0.6366*(x+pi/2) + (-0.000)*(x + pi/2)*(x)
and right now it looks like this
(5734161139222659*x)/9007199254740992 + (5734161139222659*pi)/18014398509481984 - (8131029572207409*x*(x + pi/2))/324518553658426726783156020576256 - 1.
How to convert S array so that the values are not symbolic?
syms P x
f = sin(x);
f = matlabFunction(f);
X = [-pi/2, 0, pi/2];
Y = f(sym(X));
P = MetN(X,Y,x)
P = matlabFunction(P);
function [P] = MetN(X,Y,x)
n = length(X);
for i = 1:n
A(i,1) = 1;
end
for i = 2:n
for j = 2: n
if i >= j
produs = 1;
for k =1:j-1
produs = produs * (X(i) - X(k));
end
A(i,j) = produs;
end
end
end
S = SubsAsc(A, Y);
S = double(S);
disp(S);
sym produs
P = double(sym(S(1)));
for i = 2:n
produs = 1;
for j = 1:i-1
produs = produs * (x - sym(X(j)));
end
disp(produs);
P = P + double(S(i))*produs;
end
end
function [x] = SubsAsc(A,b)
n = length(b);
x(1) = (1/A(1,1))*b(1);
for k = 2:n
s = 0;
for j = 1:k-1
s = s + A(k,j)*x(j);
end
x(k) = (1/A(k,k))*(b(k)-s);
end
end
The output you currently have is because symbolic uses exact arithmetic, so it outputs it as a rational number (hence the ugly fraction).
To have it output P using decimals, use vpa(). For instance output P using decimals to 5 significant digits
>> vpa(P, 5)
ans =
0.63662*x - 2.5056e-17*x*(x + 1.5708)
This will, however, also round pi, so you can't really have the best of both worlds here.
I am attempting to write a function called expSeries which uses another function factFunc to evaluate e^x. I have already written the function factFunc, as shown below:
function fact = factFunc(n)
f = 1;
for a = 1:b
f = f*a;
end
fact = f;
end
I am now attempting to write the function expSeries which evaulates e^x using the Taylor series. This is what I have so far:
function expo = exponentialFunc(x)
terms = input('Enter the number of terms');
b = 0;
for i = 1:terms
b = x/factFunc(terms);
end
expo = b;
end
And in the main program, I have
n = exponentialFunc(4);
disp(n);
Where in this instance I am trying to find e^4. However, the output is not what expected. Does anyone have any idea where I am going wrong?
Fix to factFunc:
function fact = factFunc(n)
f = 1;
for a = 1:n
f = f*a;
end
fact = f;
end
Fix to exponentialFunc
function expo = exponentialFunc(x)
terms = input('Enter the number of terms');
b = 0;
for i = 0:terms-1
b = b + x^i/factFunc(i);
end
expo = b;
end
Example
>> exponentialFunc(4)
Enter the number of terms10
ans =
54.1541
Note exp(4) = 54.59815...
I am currently trying to run a script that calls a particular function, but want to call the function inside a loop that halfs one of the input variables for roughly 4 iterations.
in the code below the function has been replaced for another for loop and the inputs stated above.
the for loop is running an Euler method on the function, and works fine, its just trying to run it with the repeated smaller step size im having trouble with.
any help is welcomed.
f = '3*exp(-x)-0.4*y';
xa = 0;
xb = 3;
ya = 5;
n = 2;
h=(xb-xa)/n;
x = xa:h:xb;
% h = zeros(1,4);
y = zeros(1,length(x));
F = inline(f);
y(1) = ya;
for j = 1:4
hOld = h;
hNew = hOld*0.5;
hOld = subs(y(1),'h',hNew);
for i = 1:(length(x)-1)
k1 = F(x(i),y(i));
y(i+1,j+1) = y(i) + h*k1;
end
end
disp(h)
after your comment, something like this
for j = 1:4
h=h/2;
x = xa:h:xb;
y = zeros(1,length(x));
y(1) = ya;
for i = 1:(length(x)-1)
k1 = F(x(i),y(i));
y(i+1,j+1) = y(i) + h*k1;
end
end
I am coding a QR decomposition algorithm in MATLAB, just to make sure I have the mechanics correct. Here is the code for the main function:
function [Q,R] = QRgivens(A)
n = length(A(:,1));
Q = eye(n);
R = A;
for j = 1:(n-1)
for i = n:(-1):(j+1)
G = eye(n);
[c,s] = GivensRotation( A(i-1,j),A(i,j) );
G(i-1,(i-1):i) = [c s];
G(i,(i-1):i) = [-s c];
Q = Q*G';
R = G*R;
end
end
end
The sub function GivensRotation is given below:
function [c,s] = GivensRotation(a,b)
if b == 0
c = 1;
s = 0;
else
if abs(b) > abs(a)
r = -a / b;
s = 1 / sqrt(1 + r^2);
c = s*r;
else
r = -b / a;
c = 1 / sqrt(1 + r^2);
s = c*r;
end
end
end
I've done research and I'm pretty sure this is one of the most straightforward ways to implement this decomposition, in MATLAB especially. But when I test it on a matrix A, the R produced is not right triangular as it should be. The Q is orthogonal, and Q*R = A, so the algorithm is doing some things right, but it is not producing exactly the correct factorization. Perhaps I've just been staring at the problem too long, but any insight as to what I've overlooked would be appreciated.
this seems to have more bugs,
what I see:
You should rather use [c,s] = GivensRotation( R(i-1,j),R(i,j) ); (note, R instead of A)
The original multiplications Q = Q*G'; R = G*R are correct.
r = a/b and r = b/a (without minus, not sure if it's important)
G([i-1, i],[i-1, i]) = [c -s; s c];
Here is an example code, seems to work.
First file,
% qrgivens.m
function [Q,R] = qrgivens(A)
[m,n] = size(A);
Q = eye(m);
R = A;
for j = 1:n
for i = m:-1:(j+1)
G = eye(m);
[c,s] = givensrotation( R(i-1,j),R(i,j) );
G([i-1, i],[i-1, i]) = [c -s; s c];
R = G'*R;
Q = Q*G;
end
end
end
and the second
% givensrotation.m
function [c,s] = givensrotation(a,b)
if b == 0
c = 1;
s = 0;
else
if abs(b) > abs(a)
r = a / b;
s = 1 / sqrt(1 + r^2);
c = s*r;
else
r = b / a;
c = 1 / sqrt(1 + r^2);
s = c*r;
end
end
end