I am currently taking Andrew Nguyen's coursera machine learning course and I am on week 2. For a cost function assignment, my function keeps on returning "ans = 0" when it should be returning "ans= 32.07:
My code is below (The variables have been defined in the command window):
%COMPUTECOST Compute cost for linear regression
% J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
% parameter for linear regression to fit the data points in X and y
% Initialize some useful values
% number of training examples
m = length(y);
% You need to return the following variables correctly
J =0;
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
% You should set J to the cos
h = X * theta;
J = (1/(2m)*(sum(h-y).^2));
% =========================================================================
end
Related
I have written a function plus a script to determine the variables. My variables name are "S E I1 I2 R Q H" which I named them in my function as x(1) to x(7). The total number of population equals to N which also equals to x(1)+x(2)+x(3)+x(4)+x(5). The problem is that when I try to run the script MATLAB gives me error and can not solve the linear system of ordinary differential equations. The worse problem is that MATLAB does not tell me where I'm wrong. It just tell me that the error comes from the eight line of my function. Can anyone help me with it ?
function Variables_rate = COVID_FUN(t,x) %#ok
NV = 7; % Number of Variables
global beta1 beta2 kessi ro1 ro2 alpha theta1 theta2 gamma1 gamma2 say phi lambda delta
% The Whole Number of community (N) equals to : N = S + E + I + R
N = x(1) + x(2) + x(3) + x(4) + x(5); % Total Number of people
%% This function will Model the COVID-19 Dynamical System Based on input Variables which are as follows :
% S: Suceptible Class corrosponds to {x1}
% E : Exposed Corrosponds to {x2}
% I1 : Infectious without intervention Corrosponds to {x3}
% I2 : Infectious with intervention corrosponds to {x4}
% R : Recovered corrosponds to {x5}
% Q : Quarantined corrosponds to {x6}
% H : Hospitalized corrosponds to {x7}
%% Model The Dynamic of the System with Differential Equations
Variables_rate = zeros(NV,1);
Variables_rate(1) = (-x(1)./N)*(beta1*x(3)+beta2*x(4)+kessi*x(2))+ro1*x(6)-ro2*x(1)+alpha*x(5); % Sdot
Variables_rate(2) = (x(1)./N)*(beta1*x(3)+beta2*x(4)+kessi*x(2))-theta1*x(2)-theta2*x(2); % Edot
Variables_rate(3) = theta1*x(2)-gamma1*x(3); % I1dot
Variables_rate(4) = theta2*x(2)-gamma2*x(4)-say*x(4)+lambda*(delta+x(6)); % I2dot
Variables_rate(5) = gamma1*x(3)+gamma2*x(4)+phi*x(7)-alpha*x(5); % Rdot
Variables_rate(6) = say*x(4)-phi*x(7); % Qdot
Variables_rate(7) = delta+ro2*x(1)-lambda*(delta+x(6))-ro1*x(6); % Hdot
end
Also the following is my main script :
clc;clear;close all;
% { COVID-19 Main Script Based on the written function }
global beta1 beta2 kessi ro1 ro2 alpha theta1 theta2 gamma1 gamma2 phi lambda delta say
%% According to TABLE 5 the Values of the Global Parameters are as follows :
beta1 = 1.0538*1e-1; % Contact rate of transmission per contact with infected class
beta2 = beta1; % Infection rate of transmission per contact with infected class
kessi = 1.6221*1e-1; % Probability of transmission per contact from exposed individuals
ro1 = 2.8133*1e-3; % Transition rate of quarantined exposed between the quarantined infected class and wider community
ro2 = 1.2668*1e-1; % Transition rate of quarantined exposed between the quarantined infected class and wider community
alpha = 1.2048*1e-4; % Temporary Immunity Rate
theta1 = 9.5*1e-4; % Transition rate of exposed individuals to the infected class
theta2 = 3.5412*1e-2; % Transition rate of exposed individuals to the infected class
gamma1 = 8.5*1e-3; % Recovery rate of symptomatic Infected Individuals to recovered
gamma2 =1.0037*1e-3; % Recovery rate of symptomatic Infected Individuals to recovered
say = 0.291; % Rate of Infectious with symptoms Hospitalized
phi = 0.0107; % Recovered rate of Quarantined infected individuals
lambda = 9.4522*1e-2; % Recovered rate of Quarantined Class to the recovered class
delta = 10; % External Input from the foreign countries
%% Time Vector and Initial Conditions
t = linspace(0,5,5);
Ics = [59717.71 5077 7.29 729 32 4711 658]';
%% Solve the Linear System Using ODE45 function
[~,States] = ode45(#(t,x)COVID_FUN,t,Ics)
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
% theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by
% taking num_iters gradient steps with learning rate alpha
% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);
for iter = 1:num_iters
% ====================== YOUR CODE HERE ======================
% Instructions: Perform a single gradient step on the parameter vector
% theta.
%
% Hint: While debugging, it can be useful to print out the values
% of the cost function (computeCost) and gradient here.
%
%theta(iter)=theta(iter)-0.01*(1/m)*(((theta(1)+theta(2))*X-y)*X(iter,2))
theta=theta-(alpha*(1/m)*(X*theta-y)*X(iter,2);
% ============================================================
% Save the cost J in every iteration
J_history(iter) = computeCost(X, y, theta);
end
end
theta=theta-(alpha*(1/m)*(X*theta-y)*X(iter,2);
The parentheses are not balanced as far as I can tell?
You're missing a closing parenthesis ) are you not?
I would like to smooth an Impulse Response audio file. The FFT of the file shows that it is very spikey. I would like to smooth out the audio file, not just its plot, so that I have a smoother IR file.
I have found a function that shows the FFT plot smoothed out. How could this smoothing be applied to the actual FFT data and not just to the plot of it?
[y,Fs] = audioread('test\test IR.wav');
function x_oct = smoothSpectrum(X,f,Noct)
%SMOOTHSPECTRUM Apply 1/N-octave smoothing to a frequency spectrum
%% Input checking
assert(isvector(X), 'smoothSpectrum:invalidX', 'X must be a vector.');
assert(isvector(f), 'smoothSpectrum:invalidF', 'F must be a vector.');
assert(isscalar(Noct), 'smoothSpectrum:invalidNoct', 'NOCT must be a scalar.');
assert(isreal(X), 'smoothSpectrum:invalidX', 'X must be real.');
assert(all(f>=0), 'smoothSpectrum:invalidF', 'F must contain positive values.');
assert(Noct>=0, 'smoothSpectrum:invalidNoct', 'NOCT must be greater than or equal to 0.');
assert(isequal(size(X),size(f)), 'smoothSpectrum:invalidInput', 'X and F must be the same size.');
%% Smoothing
% calculates a Gaussian function for each frequency, deriving a
% bandwidth for that frequency
x_oct = X; % initial spectrum
if Noct > 0 % don't bother if no smoothing
for i = find(f>0,1,'first'):length(f)
g = gauss_f(f,f(i),Noct);
x_oct(i) = sum(g.*X); % calculate smoothed spectral coefficient
end
% remove undershoot when X is positive
if all(X>=0)
x_oct(x_oct<0) = 0;
end
end
endfunction
function g = gauss_f(f_x,F,Noct)
% GAUSS_F calculate frequency-domain Gaussian with unity gain
%
% G = GAUSS_F(F_X,F,NOCT) calculates a frequency-domain Gaussian function
% for frequencies F_X, with centre frequency F and bandwidth F/NOCT.
sigma = (F/Noct)/pi; % standard deviation
g = exp(-(((f_x-F).^2)./(2.*(sigma^2)))); % Gaussian
g = g./sum(g); % normalise magnitude
endfunction
% take fft
Y = fft(y);
% keep only meaningful frequencies
NFFT = length(y);
if mod(NFFT,2)==0
Nout = (NFFT/2)+1;
else
Nout = (NFFT+1)/2;
end
Y = Y(1:Nout);
f = ((0:Nout-1)'./NFFT).*Fs;
% put into dB
Y = 20*log10(abs(Y)./NFFT);
% smooth
Noct = 12;
Z = smoothSpectrum(Y,f,Noct);
% plot
semilogx(f,Y,'LineWidth',0.7,f,Z,'LineWidth',2.2);
xlim([20,20000])
grid on
PS. I have Octave GNU, so I don't have the functions that are available with Matlab Toolboxes.
Here is the test IR audio file.
I think I found it. Since the FFT of the audio file (which is real numbers) is symmetric, with the same real part on both sides but opposite imaginary part, I thought of doing this:
take the FFT, keep the half of it, and apply the smoothing function without converting the magnitudes to dB
then make a copy of that smoothed FFT, and invert just the imaginary part
combine the two parts so that I have the same symmetric FFT as I had in the beginning, but now it is smoothed
apply inverse FFT to this and take the real part and write it to file.
Here is the code:
[y,Fs] = audioread('test IR.wav');
function x_oct = smoothSpectrum(X,f,Noct)
x_oct = X; % initial spectrum
if Noct > 0 % don't bother if no smoothing
for i = find(f>0,1,'first'):length(f)
g = gauss_f(f,f(i),Noct);
x_oct(i) = sum(g.*X); % calculate smoothed spectral coefficient
end
% remove undershoot when X is positive
if all(X>=0)
x_oct(x_oct<0) = 0;
end
end
endfunction
function g = gauss_f(f_x,F,Noct)
sigma = (F/Noct)/pi; % standard deviation
g = exp(-(((f_x-F).^2)./(2.*(sigma^2)))); % Gaussian
g = g./sum(g); % normalise magnitude
endfunction
% take fft
Y = fft(y);
% keep only meaningful frequencies
NFFT = length(y);
if mod(NFFT,2)==0
Nout = (NFFT/2)+1;
else
Nout = (NFFT+1)/2;
end
Y = Y(1:Nout);
f = ((0:Nout-1)'./NFFT).*Fs;
% smooth
Noct = 12;
Z = smoothSpectrum(Y,f,Noct);
% plot
semilogx(f,Y,'LineWidth',0.7,f,Z,'LineWidth',2.2);
xlim([20,20000])
grid on
#Apply the smoothing to the actual data
Zreal = real(Z); # real part
Zimag_neg = Zreal - Z; # opposite of imaginary part
Zneg = Zreal + Zimag_neg; # will be used for the symmetric Z
# Z + its symmetry with same real part but opposite imaginary part
reconstructed = [Z ; Zneg(end-1:-1:2)];
# Take the real part of the inverse FFT
reconstructed = real(ifft(reconstructed));
#Write to file
audiowrite ('smoothIR.wav', reconstructed, Fs, 'BitsPerSample', 24);
Seems to work! :) It would be nice if someone more knowledgeable could confirm that the thinking and code are good :)
I have to solve the following boundary value problem which is
also it is defined in my Matlab code below, but my code doesn't work. I mean I didn't get the approximate solution of my system.
I want to know where is the problem in my code or just the version of matlab that I have can't compile the kind of function I have used , Thanks
Explanation of method I have used : I have used the finite element method or what we called Galerkin Method based on investigation about assembly matrix and stiffness matrix. I have multiplied the system by weight function which satisfies the boundary condition then I have integrated over elements (integration of elementary matrix over the range ]-1,1[). I have four elementary matrix. For more information about that Method I used please check this paper(page:6,7,8)
Note The error I have got upon the compilation of my code is
The current use of "MatElt2Nd" is inconsistent with it previous use or definition in line 7
Code
function [U] = EquaDiff2(n)
% ----------------------------------
% -d²u/dx² + 6*u = (-4*x^2-6)exp(x^2)
% u(-1) = 0 u(1)= 0
%----------------------------------
function [Ke, Fe] = MatElt2Nd(x1,x2)
% déclaration de la fonction,
% function of computing matrix and elementary matrix (assembly matrix)
% ----------------------------------
x = [-1:2/n:1]'; % modification d1 of bound d’intégration
K = zeros(n+1) ;
F = zeros(n+1,1) ;
for i = 1:n
j = i+1;
t = [i j];
x1 = x(i);
x2 = x(j);
[Ke,Fe] = MatElt2Nd(x1,x2);
K(t,t) = K(t,t) + Ke;
F(t) = F(t) + Fe;
end;
K(1,:) = [];
K(:,1) = [];
F(1) = [];
U = K\F;
U = [0.0;U];
t = 0:0.01:1;
return
%-------------------------------------------
% calculation of matrix Ke and vector Fe
%-------------------------------------------
function [Ke,Fe] = MatElt2Nd0(x1,x2)
% NEWly named nested function is introduced
Ke1 = 1/(x2-x1)*[ 1 -1 % no modification done
-1 1 ] ; % essentiellement que les matrices
Ke2 =(x2-x1)* [ 2 1 % élémentaires
1 2 ] ;
N = [(x-x2)/(x1-x2) (x-x1)/(x2-x1)] % function of form
Fe =simple( int(N' * (-4*x^2-6)*exp(x^2) , x, x1, x2) ) % vecteur Fe ;
Ke = Ke1 + 6*Ke2 ;
return
Edit I have got a general code for that but I can't do changes in the general code to solve my system , Any help ?
General Code
% au'(x)+bu"(x)=0 for 0<=x<=d
% BC: u(0)=0 and u(d)=h
%==============================================================
% ======Example======
% Finding an approximate solution to the following BVP using 4 elements of
% equal length.
% u'(x)-u"(x)=0 : 0<=x<=1
% BC: u(0)=0 and u(1)=1
% Solution:
% >> Galerkin(4,1,-1,1,1)
% ==============================================================
% The output of this program is
% 1- The approximate solution (plotted in blue)
% 2- The exact solution (plotted in red)
% 3- The percentage error (plotted in magenta)
%=======================Program Begin==========================
function Galerkin(ne1,a,b,d,h) % Declare function
clc % Clear workspace
% Define the Coefficients of the exact solution
% The Exact solution is : u(x)=C1+C2*exp(-ax/b)
% where C2=h/(exp(-a*d/b)-1)and C1=-C2
C2=h/((exp(-a*d/b))-1);
C1=-C2;
% Define element length
le = d/ne1;
% Define x matrix
x = zeros (ne1+1,1); %
for i=2:ne1 +1
x(i,1) = x(i-1,1)+le;
end
% K1 matrix corresponding to the diffusion term (u"(x))
K1 = (b/le) * [1,-1;-1,1]
% K2 matrix corresponding to the convection term (u'(x))
K2 = a*[-1/2 1/2;-1/2 1/2]
% Element stiffness Matrix
Ke = K1+K2
% Global stiffness matrix
%********************Begin Assembly***************************
k = zeros(ne1+1);
for i=1:ne1+1
for j=1:ne1 +1
if (i==j)
if(i==1)
k(i,j)=Ke(1,1);
elseif(i==ne1+1)
k(i,j)=Ke(2,2);
else
k(i,j)=Ke(1,1)+Ke(2,2);
end
elseif(i==j+1)
k(i,j)=Ke(1,2);
elseif(j==i+1)
k(i,j)=Ke(2,1);
else
k(i,j)=0;
end
end
end
%********************End Assembly*****************************
%The Global f Matrix
f = zeros(ne1+1,1);
%BC apply u(0) = 0
f(1,1) = 0;
%BC apply u(d) = h
f(ne1+1,1) = h;
% Display the Global stifness matrix before striking row
K_Global=k
%Striking first row (u1=0)
k(1,1) = 1;
for i=2:ne1+1
k(1,i) = 0;
k(ne1+1,i) = 0;
end
k(ne1+1,ne1+1) = 1;
% Display the solvable stifness matrix
K_strike=k
%solving the result and finding the displacement matrix, {u}
u=inv(k)*f
hold on
% ======Calculating Approximate Solution and plotting============
syms X
U_sym=sym(zeros(ne1,1));
dU_sym=sym(zeros(ne1,1));
for i=1:ne1
N1x=1-((X-x(i))/le);
N2x=(X-x(i))/le;
U_X=(u(i)*N1x)+(u(i+1)*N2x);
U_sym(i)=U_X;
dU_sym(i)=diff(U_sym(i));
subplot(3,1,1)
hold on
ezplot(U_sym(i),[x(i) x(i+1)])
subplot(3,1,2)
hold on
% du/dx approximate
ezplot(dU_sym(i),[x(i) x(i+1)])
end
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
% theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by
% taking num_iters gradient steps with learning rate alpha
% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);
for iter = 1:num_iters
% ====================== YOUR CODE HERE ======================
% Instructions: Perform a single gradient step on the parameter vector
% theta.
%
% Hint: While debugging, it can be useful to print out the values
% of the cost function (computeCost) and gradient here.
%
hypothesis = x*theta;
theta_0 = theta(1) - alpha(1/m)*sum((hypothesis-y)*x);
theta_1 = theta(2) - alpha(1/m)*sum((hypothesis-y)*x);
theta(1) = theta_0;
theta(2) = theta_1;
% ============================================================
% Save the cost J in every iteration
J_history(iter) = computeCost(X, y, theta);
end
end
I keep getting this error
error: gradientDescent: subscript indices must be either positive integers less than 2^31 or logicals
on this line right in-between the first theta and =
theta_0 = theta(1) - alpha(1/m)*sum((hypothesis-y)*x);
I'm very new to octave so please go easy on me, and
thank you in advance.
This is from the coursera course on Machine Learning from Week 2
99% sure your error is on the line pointed out by topsig, where you have alpha(1/m)
it would help if you gave an example of input values to your function and what you hoped to see as an output, but I'm assuming from your comment
% taking num_iters gradient steps with learning rate alpha
that alpha is a constant, not a function. as such, you have the line alpha(1/m) without any operator in between. octave sees this as you indexing alpha with the value of 1/m.
i.e., if you had an array
x = [3 4 5]
x*(2) = [6 8 10] %% two times each element in the array
x(2) = [4] %% second element in the array
what you did doesn't seem to make sense, as 'm = length(y)' which will output a scalar, so
x = [3 4 5]; m = 3;
x*(1/m) = x*(1/3) = [1 1.3333 1.6666] %% element / 3
x(1/m) = ___error___ %% the 1/3 element in the array makes no sense
note that for certain errors it always indicates that the location of the error is at the assignment operator (the equal sign at the start of the line). if it points there, you usually have to look elsewhere in the line for the actual error. here, it was yelling at you for trying to apply a non-integer subscript (1/m)