Best least-squares line fit
I copied the best least squares line fit algorithm from Graphics Gems V book,
but now i'm having problems with vertical lines, although the book claims that
the algorithm can handle vertical lines.
For example using 0,0 and 0,2 as test points gives a=0 and b=0 and c=0 for the
line ax + by = c, although it should be something like a=1, b=0, c=0.
Here is my code:
void best_fit(void)
{
if(n_points<2)
{
a=1; // dummy values
b=1;
c=0;
return;
}
double sx=0;
double sy=0;
double sxx=0;
double syy=0;
double sxy=0;
for(point *p=points.first(); p; p=p->next)
{
sx += p->x;
sy += p->y;
}
double xmid = sx/n_points;
double ymid = sy/n_points;
for(p=points.first(); p; p=p->next)
{
double x1 = p->x-xmid;
double y1 = p->y-ymid;
sxx += x1*x1;
syy += y1*y1;
sxy += x1*y1;
}
double a1 = sxx-syy;
double b1 = sxy;
a = 2*b1;
b = - (a1 + sqrt(a1*a1 + 4*b1*b1));
c = - a*xmid - b*ymid;
if(a==0.0 && b==0.0) // try to solve the vertical line problem
{
a=1; c=-xmid;
}
}
ukram
comp.graphics.algorithms
6674 articles. 
1 followers.
1 Replies
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"Markku Poysti" <ukram@puosu.dna.fi_nospam> wrote in message news:3fba8264$0$6509$1b6aedd2@news.songnet.fi... > I copied the best least squares line fit algorithm from Graphics Gems V book, > but now i'm having problems with vertical lines, although the book claims that > the algorithm can handle vertical lines. <snip> The derivation has problems. For example, consider equation (3) which has x*sin(theta)+y*cos(theta)+p = 0. Figure 1 shows what p and theta mean. Now choose p = 0 and theta = 45 degrees. The figure indicates a line y = x. The equation says x + y = 0. Does this give you warm fuzzies about the rest of the construction? Let t = ((sxx+syy)-sqrt((sxx-syy)*(sxx-syy)+4*sxy*sxy))/2. The least squares line contains the average (xmid,ymid) of the points (using your notation). The direction is chosen to be either (-sxy, t-syy) or (t-sxx, -sxy), whichever has larger length. (The GG5 construction essentially chose the wrong direction that, as you noticed, was (0,0).) Grundgy details in http://www.magic-software.com/Documentation/LeastSquaresFitting.pdf -- Dave Eberly eberly@magic-software.com http://www.magic-software.com http://www.wild-magic.com
eberly
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I'm a total newbie at this guys. I have the following data in an .m file: x = 0:2:20; y = [0.02 0.26 0.35 0.53 0.66 0.78 0.88 0.96 1.03 1.06 1.14]; plot(x,y,'rx'); How would i fit a line of best fit to this graph? I know this is rudimentary stuff but as i said i'm a total newbie!!! Cheers for any help help polyfit /Johan Jamie Sutton wrote: > I'm a total newbie at this guys. > I have the following data in an .m file: > > x = 0:2:20; > y = [0.02 0.26 0.35 0.53 0.66 0.78 0.88 0.96 1.03 1.06 1.14]; > plot(x,y,'rx'); > > How would i fit...
Least square fitting
Hi, I have this graph: x = [0.000235 0.00025 0.0003 0.0004 0.0005 0.0006 0.00075] y = [54.9 43.1 62.7 86.3 86.3 90.2 96.1] plot (x, y) xlabel ('Amplitude') ylabel ('Correct Detection [%]') legend ('Psychometric Function') and I want to fit it to this equation: P(A, 'theta') = [1/sqrt(2*pi*sigma²)] * integral e^-[(A-'theta'²)/2*sigma²] how can i do this? thank you. "xety89 " <sow.chan@warwick.ac.uk> wrote in message <hqouqh$snf$1@fred.mathworks.com>... > Hi, > > I have this graph: > > x = [0.000235 0.00025 0.0003 0.0004 0.0005 0.0006 0.00075] > y = [54.9 43.1 62.7 86.3 86.3 90.2 96.1] > > plot (x, y) > xlabel ('Amplitude') > ylabel ('Correct Detection [%]') > legend ('Psychometric Function') > > and I want to fit it to this equation: > > P(A, 'theta') = [1/sqrt(2*pi*sigma²)] * integral e^-[(A-'theta'²)/2*sigma²] > > how can i do this? Hmm. I have a funny feeling that your expression is wrong. Everything about that expression is a simple, cumulative normal, except for that you square theta, as opposed to squaring the difference (A-theta). Beyond that, your expression is not meaningful in terms of the data that you have. You are talking about doing some sort of a nonlinear least squares fit to that expression, but that expression cannot ...
Least square fitting
Hi all, I have a problem with a rather complicated function depending on four parameters which I try to find using least square fitting and I don't know exactly how to do it. The basic problem is the following: I have an astronomical image of a star field and try to relate the sky coordinates (right ascension, declination) of the stars to the pixel coordinates (x, y). The function to relate the two depends on the not accurately known parameters focal length of the lens (f), the rotation of the field of view with respect of the north direction (beta) and the center sky coordinates of the...
Line of best fit
I am new to python so apologies for the ignorance with this question. How would I apply a line of best fit to a plot? My data are netCDF4 data files and this is essentially what I have done so far: swh1=netCDF4.Dataset('filename','r') hs1=swh1.variables['hs'] swh2=netCDF4.Dataset('filename'.'r') hs2=swh2.variables['hs'] plt.plot(hs1,hs2,'.') Cheers, Jamie --001a113a6020e6901104f5e5a9f1 Content-Type: text/plain; charset=UTF-8 None of these are in the standard library but why re-invent the wheel? Using numpy:...
Least squares fitting
Hello everybody, I am working on an inverse problem where I need to use least squares fitting. I am working on characterization of impedance of a piezoelectric crystal. A PZT crystal can be modeled as a series RLC circuit in parallel with a parasitic capacitor. Thus, I can derive the transfer function of its impedance and admittance and simulate it (see the code below) I am trying to extract R,L,C and C0 parameters from this simulated admittance curves using least squares fitting method.( Also, I need to inversely calculate these from the admittance curves that are constructed using ...
least squares fit
I'm trying to solve a system of 5+ equations for 3 unknowns, preferably using the least-squares method. I've Solve[] will not return solutions for more equations than you have unknowns. Fit[] does not work because my equations have 4 sets of data. Si=a*Ui + b*Vi + c*Wi, where i goes from 1 to 5 U, V, and W all come from a table, and S is from experimental data. I need to know how to solve for a,b,c given more than 3 equations. Background: The problem is actually trying to solve for Judd-Ofelt parameters of a laser crystal. S is the experimental line strength and U, V...
Least Square Fit
I tried to use lsqlin to do a least square fit with 3 constraints. I had 7 variables. However it didn't seem to take into account the last 2 cosntraints. I am trying to use fmincon but keep getting an error 'Inner matrix dimensions must agree'- I checked the dimensions of the constraint and Obj function matrices.but Ican't figure out why this is happening. Help! In article <eee31fe.-1@webx.raydaftYaTP>, "Shar P" <sprabhu@ieor.berkeley.edu> writes: >I tried to use lsqlin to do a least square fit with 3 constraints. I >had 7 variables. However it ...
Best fit line?
Hi. Is there a function to calculate/plot the best fit line given a few (approx 3) points? I don't have any toolboxes, nor can I afford any. Can any function in the basic matlab application do this? Thanks! "Amir " <amirschricker.DELETE@DELETE.gmail.DELETE.com> wrote in message <g4o8va$aa7$1@fred.mathworks.com>... > Hi. Is there a function to calculate/plot the best fit line > given a few (approx 3) points? I don't have any toolboxes, > nor can I afford any. > > Can any function in the basic matlab application do this? Yes. help polyfit J...
least square fitting
dear Gnuplot users, I am using the following command to fit a set of data: f(x)=a*x+b; fit f(x) 'dataset' via a,b then I get the value of a and b with only one decimal digit like a=0.1, b=0.9 how can I get five decimal digits like a=0.00001, b=0.91112 ? Thanks David <dagao@exchange.uta.edu> wrote: > dear Gnuplot users, > I am using the following command to fit a set of data: > f(x)=a*x+b; > fit f(x) 'dataset' via a,b > then I get the value of a and b with only one decimal digit like a=0.1, > b=0.9 "get the value" --- where? All the outputs of 'fit' I'm aware of print with a good deal more than 1 significant digit. Well, unless all the others following it *are* exactly zero, that is. -- Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de) Even if all the snow were burnt, ashes would remain. Below is the copy: Final set of parameters Asymptotic Standard Error ======================= ========================== a = 0.0751221 +/- 0.005317 (7.078%) b = -29512.8 +/- 0.001603 (5.432e-06%) correlation matrix of the fit parameters: a b a 1.000 b -0.905 1.000 you can notice b= -29512.8 only has one decimal value. How to change it to have more than 1 decimal digit? Thanks David <dagao@exchange.uta.edu> wrote: > Below is the c...
least square fit
I have the following data file: http://www.cs.kuleuven.ac.be/~bartv/gnuplot/sobol.dat Now I want to do a least square fit on the data of the first and second column. The data in the first-column represent the x-values, the data in the second column represent the y-values. I don't need the rest of the columns. Now I now that x and y are related somehow as: y = a/(x**b) and I want to find a and b as accurate as possible. The file that plots my data to an .eps file is at http://www.cs.kuleuven.ac.be/~bartv/gnuplot/relative_error.pl If I don't specify an initial value for b_sob, the fit fails. If I do specify a starting value of 0.9 the fit works, but the result is not satisfying as can be seen from the .eps file at http://www.cs.kuleuven.ac.be/~bartv/gnuplot/relative_error.eps I have also tried to fit on log($2)=a-b*log($1) and then plot exp(a)/(x**b) but this didn't give me satisfying results either. How can I increase the quality of my fit? Regards, Bart -- "Share what you know. Learn what you don't." Bart Vandewoestyne wrote: > I have the following data file: > > http://www.cs.kuleuven.ac.be/~bartv/gnuplot/sobol.dat > > Now I want to do a least square fit on the data of the first and > second column. The data in the first-column represent the x-values, the > data in the second column represent the y-values. I don't need the rest > of the columns. > &...
least square curve fit
I have an equation of y=k/a(1 -exp(-at)),and a set of data y=[1 2....];t=[2 3...]. is it possible to find the value of k and a by least square curve fitting? You could use something like: <http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=138&objectType=file> annie wrote: > > > I have an equation of y=k/a(1 -exp(-at)),and a set of data y=[1 > 2....];t=[2 3...]. is it possible to find the value of k and a by > least square curve fitting? In article <eeec072.-1@webx.raydaftYaTP>, annie <annie_e2004@yahoo.com> writes: >I have an...
Weighted Line of Best Fit
At the moment I am writing code to find the weighted line of best fit. I can calculate the line of best fit using the code given below, where sortWLAN corresponds to the entries in an array, which I want to extract. onedist = sortWLAN(3,1:100); onerssi = sortWLAN(4,1:100); onewgt = sortWLAN(5,1:100); coeffs = polyfit(onedist,onerssi, coefficient); curvefit = polyval(coeffs, distance); hold on plot(onedist, onerssi, 'o'); plot(distance,curvefit, 'r'); hold off Anybode have any ideas? Cheers Brad wrote: > At the moment I am writing code to find the weighted line of best &...
nonlinear best-fit line
Good afternoon, I am having trouble trying to figure out how to fit a nonlinear best fit line to my data in SAS. Any help would be greatly appreciated. Regards, Ligia ...
Web resources about - Best least-squares line fit - comp.graphics.algorithms
Least squares - Wikipedia, the free encyclopediaThe method of least squares is a standard approach to the approximate solution of overdetermined systems , i.e., sets of equations in which there ...
Least Squares for iPhone, iPod touch, and iPad on the iTunes App StoreGet Least Squares on the App Store. See screenshots and ratings, and read customer reviews.
How The Witcher 3’s economy was saved by polynomial least squares
For a game as complex and as huge as The Witcher 3 , it's hard to imagine that one of its core gameplay elements—one that ties the entire game ...
For a game as complex and as huge as The Witcher 3 , it's hard to imagine that one of its core gameplay elements—one that ties the entire game ...
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