I am trying to solve the equation below for array d. I have used the snippet below:
channel_size = 9e-3;
d = [11e-3, 12e-3];
sigma = 0.49;
ee = 727/9806.65;
alpha = d-channel_size;
sym('p',[1 2])
for i = 1:2
eqn = alpha == (4.3^(1/7))*(p^(3/11))*(((1-(sigma^2))/ee)^(7/5))/(d.^(1/6))
S = solve(eqn, p)*0.015;
vpa(S/13e-12)
end
In fact, I should get two number corresponding to d(1) and d(2), but it does not work and this error appears:
Error using mupadmex
Error in MuPAD command: Operands are invalid. [linalg::matlinsolve]
Error in sym/privBinaryOp (line 1693)
Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});
Error in sym/mrdivide (line 232)
X = privBinaryOp(A, B, 'symobj::mrdivide');
Declaring (d.^(1/6)) is wrong and instead (d(i)^(1/6)) should be used. In addition, as alpha = d-channel_size, in the equation, I should also declare alpha(i) instead of simple alpha.
I have x y z data which looks like the following:
How do i create a surface across the lines using z values in matlab (interpolated surface)?
I tried this method but i am getting following error:
[fn,pn] = uigetfile('*.xyz','Open the file');
I = importdata([pn,fn], ',', 16);
x = I.data(:,1);
y = I.data(:,2);
z = I.data(:,3);
%%
spX = min(x):3:max(x);
spY = min(y):3:max(y);
[xC,yC] = meshgrid(spX,spY);
Vq = interp2(x,y,z,xC,yC);
Error using griddedInterpolant
The grid vectors must be strictly monotonically increasing.
Error in interp2>makegriddedinterp (line 229)
F = griddedInterpolant(varargin{:});
Error in interp2 (line 129)
F = makegriddedinterp({X, Y}, V, method,extrap);
Try griddata
spX = min(x):3:max(x);
spY = min(y):3:max(y);
[xC,yC] = meshgrid(spX,spY);
zC = griddata(x,y,z,xC,yC);
surf(xC,yC,zC)
I = imread('data1.jpg');
imshow(I)
J = imnoise(I,'salt%pepper',0.02);
figure,imshow(J)
K = filter2(fspecial('average',3),J)/255;
figure,imshow(K)
L = medfilt2(J,[3,3]);
figure,imshow(L)
I got this error when I run above code
"??? Error using ==> imnoise>ParseInputs at 231
Unknown noise type: 'salt%pepper'.
Error in ==> imnoise at 85
[a, code, classIn, classChanged, p3, p4] = ParseInputs(varargin{:});
Error in ==> noisetry at 3
J = imnoise(I,'salt%pepper',0.02);"
Is your image black&white? If not convert it to B&W (JBW = rgb2gray(I)) and it should work. Function filter works only for 2 dimensional images.
I = imread('image.jpg');
imshow(I);
J = imnoise(I,'salt & pepper',0.02);
figure,imshow(J);
JBW = rgb2gray(I);
K = filter2(fspecial('average',3),JBW)/255;
figure,imshow(K);
L = medfilt2(JBW,[3,3]);
figure,imshow(L);
I am using numerical integration in MATLAB, with one varibale to integrate over but the function also contains a variable number of terms depending on the dimension of my data. Right now this looks like the following for the 2-dimensional case:
for t = 1:T
fxt = #(u) exp(-0.5*(x(t,1)-theta*norminv(u,0,1)).^2) .* ...
exp(-0.5*(x(t,2) -theta*norminv(u,0,1)).^2);
f(t) = integral(fxt,1e-4,1-1e-4,'AbsTol',1e-3);
end
I would like to have this function flexible in the sense that there could be any number of data points in, each in the following term:
exp(-0.5*(x(t,i) -theta*norminv(u,0,1)).^2);
I hope this is understandable.
If x and u have a valid dimension match (vector-vector or array-scalar) for the subtraction, you can put the whole matrix x into the handle and pass it to the integral function using the name-parameter pair ('ArrayValued',true):
fxt = #(u) exp(-0.5*(x - theta*norminv(u,0,1)).^2) .* ...
exp(-0.5*(x - theta*norminv(u,0,1)).^2);
f = integral(fxt,1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
[Documentation]
You may need a loop if integral ever passes a vector u into the handle.
But in looking at how the integral function is written, the integration nodes are entered as scalars for array-valued functions, so the loop shouldn't be necessary unless some weird dimension-mismatch error is thrown.
Array-Valued Output
In response to the comments below, you could try this function handle:
fx = #(u,t,k) prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1)).^2),2);
Then your current loop would look like
fx = #(u,t,k) prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1)).^2),2);
k = 2;
for t = 1:T
f(t) = integral(#(u)fx(u,t,k),1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
end
The ArrayValued flag is needed since x and u will have a dimension mismatch.
In this form, another loop would be needed to sweep through the k indexes.
However, we can improve this function by skipping the loop altogether since each iterate of the loop is independent by using the ArrayValued mode:
fx = #(u,k) prod(exp(-0.5*(x(:,1:k)-theta*norminv(u,0,1)).^2),2);
k = 2;
f = integral(#(u)fx(u,k),1e-4,1-1e-4,'AbsTol',1e-3,'ArrayValued',true);
Vector-Valued Output
If ArrayValued is not desired, which may be the case if the integration requires a lot of subdivisions and a vector-valued u is preferable, you can also try a recursive version of the handle using cell arrays:
% x has size [T,K]
fx = cell(K,1);
fx{1} = #(u,t) exp(-0.5*(x(t,1) - theta*norminv(u,0,1)).^2);
for k = 2:K
fx{k} = #(u,t) fx{k-1}(u,t).*exp(-0.5*(x(t,k) - theta*norminv(u,0,1)).^2);
end
f(T) = 0;
k = 2;
for t = 1:T
f(t) = integral(#(u)fx{k}(u,t),1e-4,1-1e-4,'AbsTol',1e-3);
end
ThanksTroy but now I run into the follwing:
x = [0.3,0.8;1.5,-0.7];
T = size(x,1);
k = size(x,2);
theta= 1;
fx = #(u,t,k) prod(exp(-0.5*(x(t,1:k) - theta*norminv(u,0,1))^2));
for t = 1,T
f(t) = integral(#(u)fx(u,t,k),1e-4,1-1e-4,'AbsTol',1e-3);
end
Error using -
Matrix dimensions must agree.
Error in #(u,t,k)prod(exp(-0.5*(x(t,1:k)-theta*norminv(u,0,1))^2))
Error in #(u)fx(u,t,k)
Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);
Error in integralCalc/vadapt (line 133)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);
Error in integralCalc (line 76)
[q,errbnd] = vadapt(#AtoBInvTransform,interval);
Error in integral (line 89)
Q = integralCalc(fun,a,b,opstruct);
I'm trying to write the code for quadrature phase-shift keying (QPSK) with zeroforcing when N=2, and I got an error.
Here is the code:
Modulation = 'QPSK'
Decode_Method = 'ZeroForcing'
switch Modulation
case {'QPSK'}
Symbols = [ 1+j 1-j -1+j -1-j ]';
end
Symbols = Symbols.';
nSymbols = length(Symbols);
SNR_Array = [0.3 0.7 1.2 2.5 5 6.2 10 15.4 22 45 75.7 100.0];
nSNR = length(SNR_Array);
Ntest = 20;
N = 2;
for iSNR = 1 : nSNR
SNR = SNR_Array(iSNR);
Nerror = 0;
for i = 1:Ntest
H = randn(N,N) + j*randn(N,N);
X = Symbols( ceil( nSymbols*rand(N,1) ) )';
Noise = (randn(N,1) + j*randn(N,1))/sqrt(2)/sqrt(SNR);
Y = H*X + Noise;
switch Decode_Method
case {'ZeroForcing'}
X_Decode = Zero_Forcing(Y,H,Symbols);
end
end
Nerror = Nerror + length( find( X ~= X_Decode) );
end
Symbol_Error_Rate(iSNR) = Nerror/Ntest/N;
figure(1)
loglog(SNR_Array, Symbol_Error_Rate,'b')
hold on
xlabel('SNR')
ylabel('Symbol Error Ratio')
title('Symbol Error Ratio for NxN MIMO System')
And the error is:
??? Undefined function or method 'Zero_Forcing' for input arguments of type 'double'.
Error in ==> Untitled2 at 33
X_Decode = Zero_Forcing(Y,H,Symbols);
How can I fix this error?
The error indicates that MATLAB cannot find the function Zero_Forcing. If you have a function of that name, you should make sure it's on the MATLAB path, that is, a directory MATLAB knows about. Otherwise, you should write the function. It seems rather important.
Also, you may want to not call your function 'Untitled2', but give it a more meaningful name.