Skip to main content

bugs - Terrible accuracy of DawsonF


DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message,



General::munfl: Exp[-900.] is too small to represent as a normalized
machine number; precision may be lost.

I am on Mathematica 11.3.


The problem is that DawsonF[x] is being computed as Exp(-x^2) * Erfi[x] (times constant factors), which in this case is a product of a very small quantity times a very large one, resulting in under/overflow. This is a VERY bad algorithm. The point of having a DawsonF in the first place is to bypass this multiplication and return the result without under/overflow (see the section on Numerical Recipes book, for example).


I know I can use N[DawsonF[30], 20] to obtain an accurate result, but this can be slower, and there is no reason why DawsonF could not work in machine precision.


I will submit a bug report to Wolfram, but I wanted to post this here to get some feedback before. If the community agrees please tag this as a bug.



Are there other examples like this in Mathematica of special functions that just don't work in machine precision?


Update: I submitted a bug report and they replied (see my answer). See J.M.'s answer for a workaround.



Answer



I submitted a bug report and this is the relevant line from what they replied:



Starting with Version 11.3 underflow in no longer trapped in machine arithmetic and Mathematica does not switch automatically to arbitrary precision. This provides a more efficient way to handle numerical calculations and brings Mathematica much more in line with the IEEE 754 standard for how floating point numbers are to be handled ( https://en.wikipedia.org/wiki/IEEE_754 )



This explains the origin of the bug. Apparently the bad machine precision algorithm was there all along, but in previous versions it fell back to arbitrary precision and thus went unnoticed (though it probably impacted performance).


Hope it gets fixed soon.


See @J.M. answer for a an algorithm that works in MachinePrecision.



Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more