Java Number Cruncher: The Java Programmer’s Guide to Numerical Computing provides a solution using Newton’s Method. Source code from the book is available here. The following has been taken from chapter 12.5 Big Decimal Functions (p330 & p331): /** * Compute the natural logarithm of x to a given scale, x > 0. */ public … Read more
Notation As is the convention both in mathematics and programming, the “log” function is taken to be base-e. The “exp” function is the exponential function. Remember that these functions are inverses we take the functions as: exp : ℝ → ℝ+, and log : ℝ+ → ℝ. Solution You’re just solving a simple equation here: … Read more
If you are on a recent-ish x86 or x86-64 platform (and you probably are), use the bsr instruction which will return the position of the highest set bit in an unsigned integer. It turns out that this is exactly the same as log2(). Here is a short C or C++ function that invokes bsr using … Read more
In general, one doesn’t expand out log(a + b); you just deal with it as is. That said, there are occasionally circumstances where it makes sense to use the following identity: log(a + b) = log(a * (1 + b/a)) = log a + log(1 + b/a) (In fact, this identity is often used when … Read more
try plt.yscale(‘log’, nonposy=’clip’) http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.yscale The issue is with the bottom of bars being at y=0 and the default is to mask out in-valid points (log(0) -> undefined) when doing the log transformation (there was discussion of changing this, but I don’t remember which way it went) so when it tries to draw the rectangles for … Read more
let matplotlib take the log for you: fig = plt.figure() ax = plt.gca() ax.scatter(data[‘o_value’] ,data[‘time_diff_day’] , c=”blue”, alpha=0.05, edgecolors=”none”) ax.set_yscale(‘log’) ax.set_xscale(‘log’) If you are using all the same size and color markers, it is faster to use plot fig = plt.figure() ax = plt.gca() ax.plot(data[‘o_value’] ,data[‘time_diff_day’], ‘o’, c=”blue”, alpha=0.05, markeredgecolor=”none”) ax.set_yscale(‘log’) ax.set_xscale(‘log’)
A histogram is a poor-man’s density estimate. Note that in your call to hist() using default arguments, you get frequencies not probabilities — add ,prob=TRUE to the call if you want probabilities. As for the log axis problem, don’t use ‘x’ if you do not want the x-axis transformed: plot(mydata_hist$count, log=”y”, type=”h”, lwd=10, lend=2) gets … Read more
It means that the thing in question (usually running time) scales in a manner that is consistent with the logarithm of its input size. Big-O notation doesn’t mean an exact equation, but rather a bound. For instance, the output of the following functions is all O(n): f(x) = 3x g(x) = 0.5x m(x) = x … Read more
import matplotlib from matplotlib import pyplot as plt fig1, ax1 = plt.subplots() ax1.plot([10, 100, 1000], [1,2,3]) ax1.set_xscale(‘log’) ax1.set_xticks([20, 200, 500]) ax1.get_xaxis().set_major_formatter(matplotlib.ticker.ScalarFormatter()) or ax1.get_xaxis().get_major_formatter().labelOnlyBase = False plt.show()
You can use a function like this: function logslider(position) { // position will be between 0 and 100 var minp = 0; var maxp = 100; // The result should be between 100 an 10000000 var minv = Math.log(100); var maxv = Math.log(10000000); // calculate adjustment factor var scale = (maxv-minv) / (maxp-minp); return Math.exp(minv … Read more