numerics - Does Mathematica have an equivalent of C's nextafter?

In C (and many other programming languages), there is a function

double nextafter(double x, double y)

which takes two (IEEE 754) floating-point numbers and returns the next representable floating-point number after x in the direction of y. What is the Mathematica equivalent of this function for MachinePrecision numbers?

EDIT: This issue has been brought up in the comments, but for the benefit of future readers, note that this is a substantially more subtle task than simply adding or subtracting $MachineEpsilon. The problem is that the distance between one floating-point value and the next changes with magnitude. $MachineEpsilon, by definition, is the smallest positive floating-point value such that 1.0 + $MachineEpsilon > 1.0. The distance between 1.0e-300 and the next number up will be much smaller, while the distance between 1.0e+300 and the next number up will be much greater. In addition, there are issues raised by the transitions between one order of magnitude and the next. Observe that 1.0 + $MachineEpsilon/2 == 1.0, while 1.0 - $MachineEpsilon/2 < 1.0.

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front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

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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...

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