leftimage for poohprod.ru

Gradient - calculate it with Matlab





We are going to include the concepts in our Derivative function created before, to develop a Matlab function to calculate the gradient of a multidimensional scalar function. The function is going to have the following functionality:


% Usage: g = Grad(fun, x0)
% fun: name of the multidimensional scalar function
% (string). This
function takes a vector argument of
% length n and returns a
scalar.
% x0: point of interest (vector of length n)
% g: column vector containing the gradient of fun at x0. The
% size(g) = size(x)

function g = Grad(fun, x0)
% |delta(i)| is relative to |x0(i)|
delta = x0 / 1000;
for i = 1 : length(x0)
if x0(i) == 0
% avoids delta(i) = 0 (**arbitrary value**)
delta(i) = 1e-12;
end
% recovers original x0
u = x0;
u(i) = x0(i) + delta(i);
% fun(x0(i-1), x0(i)+delta(i), x0(i+1), ...)
f1 = feval ( fun, u );
u(i) = x0(i) - delta(i);
% fun(x0(i-1), x0(i)-delta(i), x0(i+1), ...)
f2 = feval ( fun, u );

% partial derivatives in column vector
g(i,1) = (f1 - f2) / (2 * delta(i));
end

We can try this algorithm, creating a function bowl (which includes two variables) in an separate m-file, as follows:

function y = bowl(x)
y = (x(1)-6)^2 + (x(2)-4.5)^4 / 25;

Then, we can test it from the command window:

x = [0 0]
f = 'bowl'
Grad(f, x)
Expected: [-12 -14.58]' Obtained: [-12.0011 -14.5803]'

x = [1 1]
Grad(f, x)
Expected: [-10 -6.86]' Obtained: [-10.0000 -6.8600]'

x = [6 4.5]
Grad(f, x)
Expected: [0 0]' Obtained: [0 0]'

x = [2 1.5]
Grad(f, x)
Expected: [-8 -4.32]' Obtained: [-8.0000 -4.3200]'

Now, another test with a different multivariable function:

function y = semirosen(x)
y = 100 * ( x(2) - x(1)^2 ) + ( 1 - x(1) )^2 ;


x = [0 0]
f = 'semirosen'
Grad(f, x)
Expected: [-2 100]' Obtained: [-2.0]'

x = [1 1]
Grad(f, x)
Expected: [-200 100]' Obtained: [-200.0]'

x = [9 15]
Grad(f, x)
Expected: [-1784 100]' Obtained: 1.0e+003 *[-1.7840 0.1000]'


From 'Gradient' to home

From 'Gradient' to 'Matlab Cookbook'

Calculus

Top

Derivative

Curve Fitting

Math Optimization




footer for gradient page






Related pages


pascal's triangle examplematlab solve linear equationsoctal to binary conversion methodtriangle plot matlabalgorithm of tower of hanoidist matlabmatlab codes examplespoisson distribution on calculatorbisectional methodaverage rate of depreciation for a carseries expansion of sinxplotting function in matlabfactorial by recursionmagic square durersine wave matlabhow to find annual depreciation ratematlab programming tutorial for beginnersamortization table calculationexpansion of sinxsine series expansionintegrate in matlabused car salvage valueplotting circle in matlabmotorcycle depreciation rateascii code for alphabets and numbersexponential interpolation formulaevaluate double integral calculatorgray code to binary conversionsmith chart and its applicationsfourier sawtoothmatlab discountrecursive power functiongauss jorden methodsine series expansiontrendline matlabmatlab read excel filesolids of revolution examplesdurer magic squarepolar plot in control systembest fit curve matlabgraphing on matlabmaclaurin series expansionsexample of palindrome stringmaclaurin polynomial calculatorcosine series expansionmatlab 3d plotascii to binary chartformula for salvage valueprogram to find pascal triangle in cgui programming in matlabpermutations combinations calculator3dplot matlabcompass graphjordan matricesdomain of piecewise function5 band resistance calculatorsolve simultaneous equations matrixmatlab regressionbasic matlab tutorialbinary to grey code converterconvert decimal to binary converternon linear fit matlabto convert binary to decimaldecimal to gray code convertermatlab plot pdfmatlab bisection method codehobject matlabbinary to decimal conversion programplot legend matlabmatlab conditional statementintegration calculator with limitsgrey code to binaryconvert binary to grey code