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I am doing some analysis to calculate the value of log_10(x) which is a negative number. I am now trying to plot these values, however, since the range of the answers is very large I would like to use a logarithmic scale for this. If I simply use plt.yscale('log') I get a message telling me UserWarning: Data has no positive values, and therefore cannot be log-scaled. I also cannot supply the values of x to plt.plot as the result of log_10(x) is so large and negative that the answer of x**(log_10(x)) is simply 0.
What might be the most straightforward way of plotting this data?
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A common technique for handling negative values is to add a constant value to the data prior to applying the log transform. The transformation is therefore log(Y+a) where a is the constant. Some people like to choose a so that min(Y+a) is a very small positive number (like 0.001). Others choose a so that min(Y+a) = 1.
The blue line represents the reflected line's function: y=-log_3(x). Although logarithms can not be negative, if a negative sign is put in front of a log function that still has its independent variable "x", it can produce a negative log graph. A flip across the x axis produces a negative log graph.
Why are negative values (and zero) missing from graphs using a logarithmic axis? The logarithm is simply not defined mathematically for zero or any negative value. Since a logarithmic axis essentially plots the logarithms of the values, it is only possible to plot positive values on logarithmic axes.
The logarithm of zero is not defined -- its mathematically impossible to plot zero on a log scale. Instead of entering zero, you can enter a low value (say -10 on the log scale), and then use custom ticks to label the graph correctly (so it is labeled "0" rather than "-10".
You can use
plt.yscale('symlog')
to set the scale to a symmetic log scale. This means that it will scale logarithmically to both sides of 0. Only using the negative part of the symlog scale would work just fine.
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