How to solve an overdetermined set of equations using non-linear lest squares in Matlab -



How to solve an overdetermined set of equations using non-linear lest squares in Matlab -

a11 = cos(x)*cos(y) (1) a12 = cos(x)*sin(y) (2) a13 = -sin(y) (3) a21 = sin(z)*sin(x)*cos(y) - cos(z)*sin(y) (4) a22 = sin(z)*sin(y)*sin(x) + cos(z)*cos(y) (5) a23 = cos(x)*sin(z) (6) a31 = cos(z)*sin(x)*cos(z) + sin(z)*sin(x) (7) a32 = cos(z)*sin(x)*sin(y) - sin(z)*cos(y) (8) a33 = cos(x)*cos(z) (9)

i have set of 9 equations , 3 unknowns. unknowns x, y , z. know values of a11, a12, a13 ....... a33. these values might have noise , hence have utilize optimization algorithm find best fit values of x,y, , z.

how solve above set of overdetermined equations in matlab?

i have been searching online , came across few functions notably one .

but i'm confused what's best way approach problem. little direction needed....

my favorite lsqcurvefit optimization toolbox.

from documentation see requires:

function handle (fun) starting values parameters (x0) additional non-fitted parameters (xdata) in case not exist data values (ydata)

options can set optimset can specify 1 of several tested algorithms. maximal number of iterations or minimal threshold on function tolerance or parameter value tolerance can set there.

if chance should not have optimization toolbox, can utilize fminsearch , minimize to the lowest degree squares sum((ydata-fun(x)).^2) directly.

and illustration of writing function fun (also see documentation) in case here , using code question be:

function r = fun(p, xdata) x = p(1); y = p(2); z = p(3); % code here a11 = cos(x)*cos(y) a12 = cos(x)*sin(y) a13 = -sin(y) a21 = sin(z)*sin(x)*cos(y) - cos(z)*sin(y) a22 = sin(z)*sin(y)*sin(x) + cos(z)*cos(y) a23 = cos(x)*sin(z) a31 = cos(z)*sin(x)*cos(z) + sin(z)*sin(x) a32 = cos(z)*sin(x)*sin(y) - sin(z)*cos(y) a33 = cos(x)*cos(z) % in 1 matrix r = [a11, a12, a13, a21, a22, a23, a31, a32, a33]; end

one sees there no real difference between scalar , vectorial valued function. matlab automatically computes difference info , sums on it.

matlab least-squares nonlinear-optimization

Comments

Post a Comment

Popular posts from this blog

php - Android app custom user registration and login with cookie using facebook sdk -

php - Android app custom user registration and login with cookie using facebook sdk - i developing android application in users need register , log in using facebook. approximately, flow. open app first time, authenticate facebook, data, send info server create them business relationship in application, start session new business relationship in server, cookie perform later interactions. so far good. what need know wich info have send server, can able identify users when log in seccond time. because need start session in server , send cookie android app farther interactions. i'm using php server side language. i thinking getting getaccesstoken() in android facebook sdk, pass server on business relationship creation , storing in android app. but can't manage how login users on sec time utilize app. any suggestions ? in advance ! to uniquely identify user within app, should create request /me , user's id. guaranteed unique , remain con
Read more

django - Access session in user model .save() -

django - Access session in user model .save() - is possible access current session in user model .save()? pseudo code of want achieve: # users.models.py def save(self, *args, **kwargs): created = true if self.pk: created = false super(abstractuser, self).save(*args, **kwargs) # post-save if created: look_for_invite_in_session_and_register_if_found(self, session) seems wrong in architecture. shouldn't access request in models layer. work request must done in view. can this: user, created = abstractuser.objects.get_or_create(name=name) if created: look_for_invite_in_session_and_register_if_found(user, request.session) django session
Read more

php - .htaccess Multiple Rewrite Rules / Prioritizing -

php - .htaccess Multiple Rewrite Rules / Prioritizing - here current htaccess file: rewriteengine on rewritecond %{http_host} !^www\.website\.com [nc] rewritecond %{http_host} ([^.]+)\.website\.com [nc] rewriterule ^(.*)$ http://www.website.com/gotourl.php?urlid=?%1 [l] rewriterule ^(\w+)$ ./gotourl.php?urlid=$1 [nc,l] rewriterule ^(\w+)/$ ./gotourl.php?urlid=$1 [nc,l] the website in question url shortener i'm working on testing/developing , personal use. above code may not ideal i'm not familiar .htaccess , made via googling , testing. want url shortening aspect: http://website.com/1234 -> http://website.com/gotourl.php?urlid=1234 http://website.com/1234/ -> http://website.com/gotourl.php?urlid=1234 the problem cannot figure out how ignore directories. want specific directories go specific pages: http://website.com/img (or) http://website.com/img/ -> http://website.com/img.php http://website.com/img/1234 (or) http://website.com/
Read more