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I am not really familiar with LISP macros but from what little I think I know these do not appear to be strongly related. Rather they appear to be utility functions for function authors; it seems that a number of recently added internal top-level definitions use them. Some of them clearly do use meta-programming type expansions so perhaps they are closer ...


6

Experimentation based on the documentation you quoted led to two valid Method options: MatrixExp[{{1.2, 5.6}, {3, 4}}, Method -> "Pade"] {{346.557, 661.735}, {354.501, 677.425}} MatrixExp[{{1.2, 5.6}, {3, 4}}, {1, 2}, Method -> "Krylov"] {1670.03, 1709.35} If "Krylov" is used for the single parameter syntax it complains: MatrixExp[{{1.2, ...


1

Properties for SparseArray and InterpolatingFunction objects SparseArray objects can accept a range of Properties (or Methods) that allow the efficient extraction of certain information, most commonly "AdjacencyLists" or "NonzeroPositions" as a frequently faster alternative to Position. I started this answer to detail them but as it grew I came to believe ...


14

Introduction This post is long overdue as I have been repeatedly asked to explain code of mine containing these things. As I see increased use of this construct by others perhaps it is past due also. SparseArray objects can behave as functions accepting certain arguments to return internal data or efficiently return data in certain forms. These are known ...


15

In addition to the error messages quoted in the question the line returns: GeneralUtilities`Benchmarking`PackagePrivate`plot[ IndexBy[{{{16, 9.37132*10^-6}, . . . IndexBy was removed from 10.1.0: Note that IndexBy will be removed in a future version of Mathematica. It was something that was considered for 10.0.0 but didn't make the cut. – Stefan R ...


7

Internal`PartitionRagged This one has a usage statement! Internal`PartitionRagged[Range[14], {3, 5, 2, 4}] {{1, 2, 3}, {4, 5, 6, 7, 8}, {9, 10}, {11, 12, 13, 14}} Note that Length[list] must equal n1 + ... + nk. (* changed the last 4 to 3 *) Internal`PartitionRagged[Range[14], {3, 5, 2, 3}] Internal`PartitionRagged[Range[14], {3, 5, 2, 3}] ...


11

Internal`InheritedBlock What does Internal`InheritedBlock do? Daniel's MathGroup post Strange behaviour of Internal`InheritedBlock How safe is the use of Block and Internal`InheritedBlock Internal`Localizedblock What is the purpose of Internal`LocalizedBlock? Internal`Bag Internal`Bag inside Compile Daniel Lichtblau's answer On the use of of ...


12

Compile`InnerDo This is the one that initially struck me as interesting since I use compiled functions quite a lot. From the documentation of Do: Unless an explicit Return is used, the value returned by Do is Null. But that doesn't seem to be the case for Compile`InnerDo! f1 = Compile[{{x}}, Module[{a}, a = x; Compile`InnerDo[a++, {i, 10^8}]] ...



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