argmax - Developer IT

posmax: like argmax but gives the position(s) of the element x for which f[x] is maximal

- by dreeves

Mathematica has a built-in function ArgMax for functions over infinite domains, based on the standard mathematical definition. The analog for finite domains is a handy utility function. Given a function and a list (call it the domain of the function), return the element(s) of the list that maximize the function. Here's an example of finite argmax in action: http://stackoverflow.com/questions/471029/canonicalize-nfl-team-names/472213#472213 And here's my implementation of it (along with argmin for good measure): (* argmax[f, domain] returns the element of domain for which f of that element is maximal -- breaks ties in favor of first occurrence. *) SetAttributes[{argmax, argmin}, HoldFirst]; argmax[f_, dom_List] := Fold[If[f[#1]>=f[#2], #1, #2]&, First[dom], Rest[dom]] argmin[f_, dom_List] := argmax[-f[#]&, dom] First, is that the most efficient way to implement argmax? What if you want the list of all maximal elements instead of just the first one? Second, how about the related function posmax that, instead of returning the maximal element(s), returns the position(s) of the maximal elements?

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How can I extend Scala collections with an argmax method?

- by Lukasz Lew

I would like to add to all collections where it makes sense, an argMax method. How to do it? Use implicits?

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C++: select argmax over vector of classes w.r.t. arbitrary expression

- by karpathy

Hello, I have trouble describing my problem so I'll give an example: I have a class description that has a couple of variables in it, for example: class A{ float a, b, c, d; } Now, I maintain a vector<A> that contains many of these classes. What I need to do very very often is to find the object inside this vector that satisfies that one of it's parameters is maximal w.r.t to the others. i.e code looks something like: int maxi=-1; float maxa=-1000; for(int i=0;i<vec.size();i++){ res= vec[i].a; if(res > maxa) { maxa= res; maxi=i; } } return vec[maxi]; However, sometimes I need to find class with maximal a, sometimes with maximal b, sometimes the class with maximal 0.8*a + 0.2*b, sometimes I want a maximal a*VAR + b, where VAR is some variable that is assigned in front, etc. In other words, I need to evaluate an expression for every class, and take the max. I find myself copy-pasting this everywhere, and only changing the single line that defines res. What makes it even more complicated is that even the name of the vector changes. Sometimes it's vec, sometimes it can be something else. I have many vectors that contain A's. This could be changed if this makes the problem too hard. Is there some nice way to avoid this insanity in C++? What's the neatest way to handle this? Thank you!

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choose the best class if 2 class have same P (c|d), naive bayes

- by ryandi

Hello I have some question about naive bayes classifier . In my project I have to classify a text into a class from 4 available class. In naive bayes we have formula like cmap=argmax.P(d|c).P(c) I have standarize the amount of training document of each class, so I got a same P(c) value for each class (0.25). Here's my question: What if a testing document token doesn't have any token which belong to any of those 4 class(in document training)? Resulted to all of the class have same value of P(d|c).P(c). Which class should i pick? What if the token exist, and 2 class or more have same value of P(d|c).P(c) what should I do? Thank you..

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fit a ellipse in Python given a set of points xi=(xi,yi)

- by Gianni

I am computing a series of index from a 2D points (x,y). One index is the ratio between minor and major axis. To fit the ellipse i am using the following post when i run these function the final results looks strange because the center and the axis length are not in scale with the 2D points center = [ 560415.53298363+0.j 6368878.84576771+0.j] angle of rotation = (-0.0528033467597-5.55111512313e-17j) axes = [0.00000000-557.21553487j 6817.76933256 +0.j] thanks in advance for help import numpy as np from numpy.linalg import eig, inv def fitEllipse(x,y): x = x[:,np.newaxis] y = y[:,np.newaxis] D = np.hstack((x*x, x*y, y*y, x, y, np.ones_like(x))) S = np.dot(D.T,D) C = np.zeros([6,6]) C[0,2] = C[2,0] = 2; C[1,1] = -1 E, V = eig(np.dot(inv(S), C)) n = np.argmax(np.abs(E)) a = V[:,n] return a def ellipse_center(a): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] num = b*b-a*c x0=(c*d-b*f)/num y0=(a*f-b*d)/num return np.array([x0,y0]) def ellipse_angle_of_rotation( a ): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] return 0.5*np.arctan(2*b/(a-c)) def ellipse_axis_length( a ): b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0] up = 2*(a*f*f+c*d*d+g*b*b-2*b*d*f-a*c*g) down1=(b*b-a*c)*( (c-a)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a)) down2=(b*b-a*c)*( (a-c)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a)) res1=np.sqrt(up/down1) res2=np.sqrt(up/down2) return np.array([res1, res2]) if __name__ == '__main__': points = [(560036.4495758876, 6362071.890493258), (560036.4495758876, 6362070.890493258), (560036.9495758876, 6362070.890493258), (560036.9495758876, 6362070.390493258), (560037.4495758876, 6362070.390493258), (560037.4495758876, 6362064.890493258), (560036.4495758876, 6362064.890493258), (560036.4495758876, 6362063.390493258), (560035.4495758876, 6362063.390493258), (560035.4495758876, 6362062.390493258), (560034.9495758876, 6362062.390493258), (560034.9495758876, 6362061.390493258), (560032.9495758876, 6362061.390493258), (560032.9495758876, 6362061.890493258), (560030.4495758876, 6362061.890493258), (560030.4495758876, 6362061.390493258), (560029.9495758876, 6362061.390493258), (560029.9495758876, 6362060.390493258), (560029.4495758876, 6362060.390493258), (560029.4495758876, 6362059.890493258), (560028.9495758876, 6362059.890493258), (560028.9495758876, 6362059.390493258), (560028.4495758876, 6362059.390493258), (560028.4495758876, 6362058.890493258), (560027.4495758876, 6362058.890493258), (560027.4495758876, 6362058.390493258), (560026.9495758876, 6362058.390493258), (560026.9495758876, 6362057.890493258), (560025.4495758876, 6362057.890493258), (560025.4495758876, 6362057.390493258), (560023.4495758876, 6362057.390493258), (560023.4495758876, 6362060.390493258), (560023.9495758876, 6362060.390493258), (560023.9495758876, 6362061.890493258), (560024.4495758876, 6362061.890493258), (560024.4495758876, 6362063.390493258), (560024.9495758876, 6362063.390493258), (560024.9495758876, 6362064.390493258), (560025.4495758876, 6362064.390493258), (560025.4495758876, 6362065.390493258), (560025.9495758876, 6362065.390493258), (560025.9495758876, 6362065.890493258), (560026.4495758876, 6362065.890493258), (560026.4495758876, 6362066.890493258), (560026.9495758876, 6362066.890493258), (560026.9495758876, 6362068.390493258), (560027.4495758876, 6362068.390493258), (560027.4495758876, 6362068.890493258), (560027.9495758876, 6362068.890493258), (560027.9495758876, 6362069.390493258), (560028.4495758876, 6362069.390493258), (560028.4495758876, 6362069.890493258), (560033.4495758876, 6362069.890493258), (560033.4495758876, 6362070.390493258), (560033.9495758876, 6362070.390493258), (560033.9495758876, 6362070.890493258), (560034.4495758876, 6362070.890493258), (560034.4495758876, 6362071.390493258), (560034.9495758876, 6362071.390493258), (560034.9495758876, 6362071.890493258), (560036.4495758876, 6362071.890493258)] a_points = np.array(points) x = a_points[:, 0] y = a_points[:, 1] from pylab import * plot(x,y) show() a = fitEllipse(x,y) center = ellipse_center(a) phi = ellipse_angle_of_rotation(a) axes = ellipse_axis_length(a) print "center = ", center print "angle of rotation = ", phi print "axes = ", axes from pylab import * plot(x,y) plot(center[0:1],center[1:], color = 'red') show() each vertex is a xi,y,i point plot of 2D point and center of fit ellipse

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