least-squares

Anyone here that could help me with the following problem? The following code calculates the best polynomial fit to a given data-set, that is; a polynomial of a specified degree. Unfortunately, whatever the data-set may be, usually at degree 6 or higher, MATLAB gets a totally wrong fit. Usually the fit curves totally away from the data in a sort of exponantial-looking-manner downwards. (see the example: degree = 8). x=[1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5] % experimental x-values y=[4.3 6.2 10.1 13.5 19.8 22.6 24.7 29.2] % experimental y-values degree=8; % specify the degree A = zeros(length(x)

So I want to solve the equation z= a + b*y +c*x ,. getting a,b,c . ie: making a (plane) surface fit to a load of scatter points in 3D space. But I can't seem to find anything! I thought there would be a simple module for such a simple problem. I have tried, where x,y,z are arrays; ys=zip(x,y) (coeffs, residuals, rank, sing_vals) = np.linalg.lstsq(ys,z) am I right in thinking coeffs = b,c? Or am I going completely in the wrong direction. I just can't seem to find anything else that will work in 3d... I think you're on the right track. You could still try following the example of the scipy

I used a linear regression on data I have, using the lm function. Everything works (no error message), but I'm somehow surprised by the result: I am under the impression R "misses" a group of points, i.e. the intercept and slope are not the best fit. For instance, I am referring to the group of points at coordinates x=15-25,y=0-20. My questions: is there a function to compare fit with "expected" coefficients and "lm-calculated" coefficients? have I made a silly mistake when coding, leading the lm to do that? Following some answers: additionnal information on x and y x and y are both visual

I'm trying to perform a constrained least-squares estimation using Scipy such that all of the coefficients are in the range (0,1) and sum to 1 (this functionality is implemented in Matlab's LSQLIN function). Does anybody have tips for setting up this calculation using Python/Scipy. I believe I should be using scipy.optimize.fmin_slsqp() , but am not entirely sure what parameters I should be passing to it.[1] Many thanks for the help, Nick [1] The one example in the documentation for fmin_slsqp is a bit difficult for me to parse without the referenced text -- and I'm new to using Scipy. denis

I need to solve a system of linear equations Lx=b, where x is always a vector (3x1 array), L is an Nx3 array, and b is an Nx1 vector. N usually ranges from 4 to something like 10. I have no problems solving this using scipy.linalg.lstsq(L,b) However, I need to do this many times (something like 200x200=40000 times) as x is actually something associated with each pixel in an image. So x is actually stored in an PxQx3 array where P and Q is something like 200-300, and the last number '3' refers to the vector x. Right now I just loop through each column and row and solve the equation one-by-one

I am fitting data points using a logistic model. As I sometimes have data with a ydata error, I first used curve_fit and its sigma argument to include my individual standard deviations in the fit. Now I switched to leastsq, because I needed also some Goodness of Fit estimation that curve_fit could not provide. Everything works well, but now I miss the possibility to weigh the least sqares as "sigma" does with curve_fit. Has someone some code example as to how I could weight the least squares also in leastsq? Thanks, Woodpicker I just found that it is possible to combine the best of both worlds

I'm looking for an algorithm to find the best fit between a cloud of points and a sphere. That is, I want to minimise where C is the centre of the sphere, r its radius, and each P a point in my set of n points. The variables are obviously Cx , Cy , Cz , and r . In my case, I can obtain a known r beforehand, leaving only the components of C as variables. I really don't want to have to use any kind of iterative minimisation (e.g. Newton's method, Levenberg-Marquardt, etc) - I'd prefer a set of linear equations or a solution explicitly using SVD. There are no matrix equations forthcoming. Your