Multivariate Newthon’s Method
Dear All,
I am trying to solve a multivariate function by using the Newthon’s Method. However, I get an error message in the lwhen I run my code (exactly in newtons_method file), and I could not figure out what is going on. Here is the files that I am using:
%This file is the one that appears here: Multivariate Newton’s Method (newtons_method_n)
function [x,k,x_all] = newtons_method_n(f,J,x0,opts)
if (nargin < 4) || isempty(opts) || ~isfield(opts,’k_max’)
k_max = 200;
else
k_max = opts.k_max;
end
if (nargin < 4) || isempty(opts) || ~isfield(opts,’return_all’)
return_all = false;
else
return_all = opts.return_all;
end
if (nargin < 4) || isempty(opts) || ~isfield(opts,’TOL’)
TOL = 1e-10;
else
TOL = opts.TOL;
end
n = length(x0);
if f(x0) == zeros(n,1)
x = x0;
return
end
x_curr = x0;
x_next = zeros(n,1);
if return_all
x_all = zeros(n,k_max+1);
end
for k = 1:k_max
if return_all
x_all(:,k) = x_curr;
end
y = J(x_curr)(-f(x_curr));
x_next = x_curr+y;
if (norm(y) < TOL)
break;
end
x_curr = x_next;
end
x = x_next;
if return_all
x_all(:,k+1) = x;
x_all = x_all(:,1:(k+1));
end
end
This is the main.n file:
clear all
clc
% Global variables are only parameters which do not change
global a b theta t d n L Y g
load DATA
n = 19; % Number of countries
a = 0.134813590592666;
b = 0.21221;
theta = 8.28; % Shape of Pareto dist
relaw = aw./aw(n,1); % Relative wage to US
t = exp( b*(S+theta*(log(relaw))) ); % Technology: see Table VI
d = D; % Geographic barriers dni^(-theta)
L = l; % Labor
Y = y; % Income
elast = 0.1; % Elasticity of wage adjustment
% Gamma constant (as in the original code)
g = (b^(-b))*((1-b)^(-(1-b)));
g = g^(theta);
disp(‘Newton iterative procedure starts here’)
w = aw; % Set initial wages at data
% Set bounds (implied by the model) for prices
pbounds = bounds(w);
p0 = 0.5*(pbounds(:,1)+pbounds(:,2)); % Half way between min and max
[pval,fval] = newtons_method(@(p) prices(p,w),p0);
And finally the prices.m file:
function [fval,fjac] = prices(p,w)
global b theta t d n g
aux1 = g*t.*(w.^(-theta*b));
aux2 = repmat(aux1,1,n)’;
G = d.*aux2;
fval = Gp -p.^(1-b);
fjac = inv(G) – (1-b)*diag(p.^(-b));
With all this on hand, any idea about why is there an error?
Thank you in advanced!Dear All,
I am trying to solve a multivariate function by using the Newthon’s Method. However, I get an error message in the lwhen I run my code (exactly in newtons_method file), and I could not figure out what is going on. Here is the files that I am using:
%This file is the one that appears here: Multivariate Newton’s Method (newtons_method_n)
function [x,k,x_all] = newtons_method_n(f,J,x0,opts)
if (nargin < 4) || isempty(opts) || ~isfield(opts,’k_max’)
k_max = 200;
else
k_max = opts.k_max;
end
if (nargin < 4) || isempty(opts) || ~isfield(opts,’return_all’)
return_all = false;
else
return_all = opts.return_all;
end
if (nargin < 4) || isempty(opts) || ~isfield(opts,’TOL’)
TOL = 1e-10;
else
TOL = opts.TOL;
end
n = length(x0);
if f(x0) == zeros(n,1)
x = x0;
return
end
x_curr = x0;
x_next = zeros(n,1);
if return_all
x_all = zeros(n,k_max+1);
end
for k = 1:k_max
if return_all
x_all(:,k) = x_curr;
end
y = J(x_curr)(-f(x_curr));
x_next = x_curr+y;
if (norm(y) < TOL)
break;
end
x_curr = x_next;
end
x = x_next;
if return_all
x_all(:,k+1) = x;
x_all = x_all(:,1:(k+1));
end
end
This is the main.n file:
clear all
clc
% Global variables are only parameters which do not change
global a b theta t d n L Y g
load DATA
n = 19; % Number of countries
a = 0.134813590592666;
b = 0.21221;
theta = 8.28; % Shape of Pareto dist
relaw = aw./aw(n,1); % Relative wage to US
t = exp( b*(S+theta*(log(relaw))) ); % Technology: see Table VI
d = D; % Geographic barriers dni^(-theta)
L = l; % Labor
Y = y; % Income
elast = 0.1; % Elasticity of wage adjustment
% Gamma constant (as in the original code)
g = (b^(-b))*((1-b)^(-(1-b)));
g = g^(theta);
disp(‘Newton iterative procedure starts here’)
w = aw; % Set initial wages at data
% Set bounds (implied by the model) for prices
pbounds = bounds(w);
p0 = 0.5*(pbounds(:,1)+pbounds(:,2)); % Half way between min and max
[pval,fval] = newtons_method(@(p) prices(p,w),p0);
And finally the prices.m file:
function [fval,fjac] = prices(p,w)
global b theta t d n g
aux1 = g*t.*(w.^(-theta*b));
aux2 = repmat(aux1,1,n)’;
G = d.*aux2;
fval = Gp -p.^(1-b);
fjac = inv(G) – (1-b)*diag(p.^(-b));
With all this on hand, any idea about why is there an error?
Thank you in advanced! Dear All,
I am trying to solve a multivariate function by using the Newthon’s Method. However, I get an error message in the lwhen I run my code (exactly in newtons_method file), and I could not figure out what is going on. Here is the files that I am using:
%This file is the one that appears here: Multivariate Newton’s Method (newtons_method_n)
function [x,k,x_all] = newtons_method_n(f,J,x0,opts)
if (nargin < 4) || isempty(opts) || ~isfield(opts,’k_max’)
k_max = 200;
else
k_max = opts.k_max;
end
if (nargin < 4) || isempty(opts) || ~isfield(opts,’return_all’)
return_all = false;
else
return_all = opts.return_all;
end
if (nargin < 4) || isempty(opts) || ~isfield(opts,’TOL’)
TOL = 1e-10;
else
TOL = opts.TOL;
end
n = length(x0);
if f(x0) == zeros(n,1)
x = x0;
return
end
x_curr = x0;
x_next = zeros(n,1);
if return_all
x_all = zeros(n,k_max+1);
end
for k = 1:k_max
if return_all
x_all(:,k) = x_curr;
end
y = J(x_curr)(-f(x_curr));
x_next = x_curr+y;
if (norm(y) < TOL)
break;
end
x_curr = x_next;
end
x = x_next;
if return_all
x_all(:,k+1) = x;
x_all = x_all(:,1:(k+1));
end
end
This is the main.n file:
clear all
clc
% Global variables are only parameters which do not change
global a b theta t d n L Y g
load DATA
n = 19; % Number of countries
a = 0.134813590592666;
b = 0.21221;
theta = 8.28; % Shape of Pareto dist
relaw = aw./aw(n,1); % Relative wage to US
t = exp( b*(S+theta*(log(relaw))) ); % Technology: see Table VI
d = D; % Geographic barriers dni^(-theta)
L = l; % Labor
Y = y; % Income
elast = 0.1; % Elasticity of wage adjustment
% Gamma constant (as in the original code)
g = (b^(-b))*((1-b)^(-(1-b)));
g = g^(theta);
disp(‘Newton iterative procedure starts here’)
w = aw; % Set initial wages at data
% Set bounds (implied by the model) for prices
pbounds = bounds(w);
p0 = 0.5*(pbounds(:,1)+pbounds(:,2)); % Half way between min and max
[pval,fval] = newtons_method(@(p) prices(p,w),p0);
And finally the prices.m file:
function [fval,fjac] = prices(p,w)
global b theta t d n g
aux1 = g*t.*(w.^(-theta*b));
aux2 = repmat(aux1,1,n)’;
G = d.*aux2;
fval = Gp -p.^(1-b);
fjac = inv(G) – (1-b)*diag(p.^(-b));
With all this on hand, any idea about why is there an error?
Thank you in advanced! optimization, functions MATLAB Answers — New Questions
