Could you help me a little bit
i have 2 subset binary image curve A and B ,How i resampling data A or B to Equally.
For Example
curve A, {(1,1),(1,2),(1,3),(1,4),(1,5)}
curve B, {(5,5),(5,4),(5,3)}
i would like resampling the number of element B to 5 for equally A
B( resampling )==> {(5,5),(5,4.5),(5,4),(5,3.5),(5,3)}
i done to implement this method in c++.
but I do not sure that is call linear interplolation method
and another problem i do not know how to write this method equally A and B in term of Math formular or in term of geometry discrete?
thank you very much
kitti
You can use Lagrange interpolation.
Related
I have the following problem. I have a N x N real matrix called Z(x; t), where x and t might be vectors in general. I have N_s observations (x_k, Z_k), k=1,..., N_s and I'd like to find the vector of parameters t that better approximates the data in the least square sense, which means I want t that minimizes
S(t) = \sum_{k=1}^{N_s} \sum_{i=1}^{N} \sum_{j=1}^N (Z_{k, i j} - Z(x_k; t))^2
This is in general a non-linear fitting of a matrix function. I'm only finding examples in which one has to fit scalar functions which are not immediately generalizable to a matrix function (nor a vector function). I tried using the scipy.optimize.leastsq function, the package symfit and lmfit, but still I don't manage to find a solution. Eventually, I'm ending up writing my own code...any help is appreciated!
You can do curve-fitting with multi-dimensional data. As far as I am aware, none of the low-level algorithms explicitly support multidimensional data, but they do minimize a one-dimensional array in the least-squares sense. And the fitting methods do not really care about the "independent variable(s)" x except in that they help you calculate the array to be minimized - perhaps to calculate a model function to match to y data.
That is to say: if you can write a function that would take the parameter values and calculate the matrix to be minimized, just flatten that 2-d (on n-d) array to one dimension. The fit will not mind.
I have a linear program of the form min(f*x) s.t. A1*x < d1; A2*x < d2. The form with one constraint is implemented in Matlab in command linprog. What command can I use to solve linear program with two constrraints?
I could of course create a block diagonal matrix, and double the size of the variable x, but if there is more efficient way I would like to use it, because the size of the matrix is quite large.
Possibly I don't understand the question right but can't you combine the matrixes A1 und A2 by A = [A1; A2]?
You maybe interested in Dantzig-Wolfe Decomposition algorithm for solving linear programming. It takes advantage of this block diagonal structure. However, I don't think there is an out-of-the box implementation of it in commercial softwares.
This is the link that explain to solve inverse kinematics using ANFIS
http://www.mathworks.com/help/fuzzy/examples/modeling-inverse-kinematics-in-a-robotic-arm.html
But the example is only for 2 DOFs Robot. How to make the data set if the robot using 4 motors?
Because there is always an error that says :"Error using meshgrid. Too many input arguments." when running the code:
a= 0:(1*pi/180):(180*pi/180);
b= 0:(1*pi/180):(180*pi/180);
c= 0:(1*pi/180):(180*pi/180);
d= (25*180/pi):(1*pi/180):(180*pi/180);
[THETA1, THETA2, THETA3, THETA4] = meshgrid(a, b, c, d);
Any Suggestion will be appreciated
Thanks!
meshgrid is specifically for 2D or 3D data. For arbitrary n-dimensional data, the appropriately-named ndgrid is the guy you want.
Note that meshgrid is intended for working intuitively with Cartesian X,Y{,Z} data, so swaps the first two dimensions in the shape of its output to reflect X,Y order rather than row,column. ndgrid, being more general, just gives you standard multidimensional matrix order.
I have a matlab script that performs curve fitting on a set of curves using polynomials of third, second and first order (using polyfit with the desired order) and also using DCT of 4,3 and 2 coefficients (invoking dct for the whole array and then truncating just the first 4,3 or 2 coeffs).
I'm able to get a graphical view of the accuracy of each curve fitting using polyval and idct for the 2 types of curve fitting, but I was wondering if there is any way of getting a numeric value of the accuracy that makes sense for both approaches (dct and polyfit).
I'm sure this is more a maths question rather than a Matlab question, but maybe there is some way to obtain a simple and elegant way in a array-based algorithm that I haven't thought of yet.
Thanks in advance for your comments!
EDIT: What about correlation? :D
In the cuve fitting tool there should be a residual that uses standard deviation. If you are interested in another way to do it maybe you should use rmse for the entire curve, scripting a function that does something like:
input args : y1 = (curve going to be fitted), y2 = (fitted curve)
For each value in y, sum up the difference y1-y2 squared
Divide with the number of entries
Provided you are now left with a number, return its square root
See http://en.wikipedia.org/wiki/Root-mean-square_deviation#Formula for more.
Starting from the plot of one curve, it is possible to obtain the parametric equation of that curve?
In particular, say x={1 2 3 4 5 6....} the x axis, and y = {a b c d e f....} the corresponding y axis. I have the plot(x,y).
Now, how i can obtain the equation that describe the plotted curve? it is possible to display the parametric equation starting from the spline interpolation?
Thank you
If you want to display a polynomial fit function alongside your graph, the following example should help:
x=-3:.1:3;
y=4*x.^3-5*x.^2-7.*x+2+10*rand(1,61);
p=polyfit(x,y,3); %# third order polynomial fit, p=[a,b,c,d] of ax^3+bx^2+cx+d
yfit=polyval(p,x); %# evaluate the curve fit over x
plot(x,y,'.')
hold on
plot(x,yfit,'-g')
equation=sprintf('y=%2.2gx^3+%2.2gx^2+%2.2gx+%2.2g',p); %# format string for equation
equation=strrep(equation,'+-','-'); %# replace any redundant signs
text(-1,-80,equation) %# place equation string on graph
legend('Data','Fit','Location','northwest')
Last year, I wrote up a set of three blogs for Loren, on the topic of modeling/interpolationg a curve. They may cover some of your questions, although I never did find the time to add another 3 blogs to finish the topic to my satisfaction. Perhaps one day I will get that done.
The problem is to recognize there are infinitely many curves that will interpolate a set of data points. A spline is a nice choice, because it can be made well behaved. However, that spline has no simple "equation" to write down. Instead, it has many polynomial segments, pieced together to be well behaved.
You're asking for the function/mapping between two data sets. Knowing the physics involved, the function can be derived by modeling the system. Write down the differential equations and solve it.
Left alone with just two data series, an input and an output with a 'black box' in between you may approximate the series with an arbitrary function. You may start with a polynomial function
y = a*x^2 + b*x + c
Given your input vector x and your output vector y, parameters a,b,c must be determined applying a fitness function.
There is an example of Polynomial Curve Fitting in the MathWorks documentation.
Curve Fitting Tool provides a flexible graphical user interfacewhere you can interactively fit curves and surfaces to data and viewplots. You can:
Create, plot, and compare multiple fits
Use linear or nonlinear regression, interpolation,local smoothing regression, or custom equations
View goodness-of-fit statistics, display confidenceintervals and residuals, remove outliers and assess fits with validationdata
Automatically generate code for fitting and plottingsurfaces, or export fits to workspace for further analysis