Look What We Made in Five Months!
It’s hard to believe we’ve been doing this for 35 years, building a taller and taller tower of ideas and technology that allow us to reach ever further. In earlier times we used to release the results of efforts only every few years. But in recent times we’ve started doing incremental (“.1”) releases that deliver our latest R&D achievements—both fully fleshed out, and partly as “coming attractions”—much more frequently.
We released Version 12.2 on December 16, 2020. And today, just five months later, we’re releasing Version 12.3. There are some breakthroughs and major new directions in 12.3. But much of what’s in 12.3 is just about making Wolfram Language and Mathematica better, smoother and more convenient to use. Things are faster. More “But what about ___?” cases are handled. Big frameworks are more completely filled out. And there are lots of new conveniences.
There are also the first pieces of what will become large-scale structures in the future. Early functions—already highly useful in their own right—that will in future releases be pieces of major systemwide frameworks.
One way to assess a release is to talk about how many new functions it contains. For Version 12.3 that number is 111 (or about 5 new functions per development-week). It’s a very impressive level of R&D productivity. But particularly for 12.3 it’s just part of the story; there are also 1190 bug fixes (about a quarter for externally reported bugs), and 105 substantially updated and enhanced functions.
Incremental releases are part of our commitment to open development. We’ve also been sharing more kinds of functionality in open-source form (including more than 300 new functions in the Wolfram Function Repository). And we’ve been doing our unique thing of livestreaming our internal design processes. For Version 12.3 it’s once again possible to see just where and how design decisions were made, and the reasoning behind them. And we’ve also had great input from our community (often in real time during livestreams)—that has significantly enhanced the Version 12.3 that we are delivering today.
By the way, when we say “Version 12.3” of Wolfram Language and Mathematica we mean desktop, cloud and engine: all three versions are being released today.
Lots of Little New Conveniences
What should “just work”? What should be made easier? Ever since Version 1.0 we’ve been working hard to figure out what little conveniences we can add to make the Wolfram Language ever more streamlined.
Version 12.3 has our latest batch of conveniences, scattered across many parts of the language. A new dynamic that’s emerged in this version is functions that have essentially been “prototyped” in the Wolfram Function Repository, and then “upgraded” to be built into the system.
Here’s a first example of a new convenience function: SolveValues. The function Solve—originally introduced in Version 1.0—has a very flexible way of representing its results, that allows for different numbers of variables, different numbers of solutions, etc.
✕
Solve[x^2 + 3 x + 1 == 0, x] |
But often you’re happy to assume a fixed structure for the solution, and you just want to know the values of variables. And that’s what SolveValues gives:
✕
SolveValues[x^2 + 3 x + 1 == 0, x] |
By the way, there’s also an NSolveValues that gives approximate numerical values:
✕
NSolveValues[x^2 + 3 x + 1 == 0, x] |
Another example of a new convenience function is NumberDigit. Let’s say you want the 10th digit of π. You can always use RealDigits and then pick out the digit you want:
✕
RealDigits[Pi, 10, 20] |
But now you can also just use NumberDigit (where now by “10th digit” we’re assuming you mean the coefficient of 10-10):
✕
NumberDigit[Pi, -10] |
Back in Version 1.0, we just had Sort. In Version 10.3 (2015) we added AlphabeticSort, and then in Version 11.1 (2017) we added NumericalSort. Now in Version 12.3—to round out this family of default types of sorting—we’re adding LexicographicSort. The default sorting sort (as produced by Sort) is:
✕
Subsets[{a, b, c, d}]
|
But here’s true lexicographic order, like you would find in a dictionary:
✕
LexicographicSort[Subsets[{a, b, c, d}]]
|
Another small new function in Version 12.3 is StringTakeDrop:
✕
StringTakeDrop["abcdefghijklmn", {2, 5}]
|
Having this as a single function makes it easier to use in functional programming constructs like this:
✕
FoldPairList[StringTakeDrop, "abcdefghijklmn", {2, 3, 4, 5}]
|
It’s always an important goal to make “standard workflows” as straightforward as possible. For example, in handling graphs we’ve had VertexOutComponent since Version 8.0 (2010). It gives a list of the vertices that can be reached from a given vertex. And for some things that’s exactly what one wants. But sometimes it’s much more convenient to get the subgraph (and in fact in the formalism of our Physics Project that subgraph—that we view as a “geodesic ball”—is a rather central construct). So in Version 12.3 we’ve added VertexOutComponentGraph:
✕
VertexOutComponentGraph[CloudGet["http://wolfr.am/VAs5QDwv"], 10, 4] |
Another example of a small “workflow improvement” is in HighlightImage. HighlightImage typically takes a list of regions of interest to highlight in the image. But functions like MorphologicalComponents don’t just make lists of regions in an image; instead they produce a “label matrix” that puts numbers to label different regions in an image. So to make the HighlightImage workflow smoother, in Version 12.3 we let it directly use a label matrix, assigning different colors to the differently labeled regions:
✕
HighlightImage[ CloudGet["http://wolfr.am/VAs6lxUj"], MorphologicalComponents] |
One thing we work hard to ensure in the Wolfram Language is coherence and interoperability. (And in fact, we have a whole initiative around this that we call “Language Completeness & Consistency”, whose weekly meetings we regularly livestream.) One of the various facets of interoperability is that we want functions to be able to “eat” any reasonable input and turn it into something they can “naturally” handle.
And as a small example of this, something we added in Version 12.3 is automatic conversion between color spaces. Red by default means the RGB color red (RGBColor[1,0,0]). But now
✕
Hue[Red] |
means turns that red into red in hue space:
✕
Hue[Red] // InputForm |
Let’s say you’re running a long computation. You often want to get some indication of the progress that’s being made. In Version 6.0 (2007) we added Monitor, and in subsequent versions we’ve added automatic built-in progress reporting for some functions, for example NetTrain. But now we have an initiative underway to systematically add progress reporting for all sorts of functions that can end up doing long computations. ($ProgressReporting = False globally switches it off.)
✕
VideoMap[ColorConvert[#Image, "Grayscale"] &, Video["ExampleData/bullfinch.mkv"]] |
We work hard in Wolfram Language to make sure that we pick good defaults, for example for how to display things. But sometimes you have to tell the system what kind of “look” you want. And in Version 12.3 we’ve added the option DatasetTheme to specify “themes” for how Dataset objects should be displayed.
Underneath, each theme is just setting specific options, which you could set yourself. But the theme is “bank switching” options in a convenient way. Here’s a basic dataset with default formatting:
✕
Dataset[IdentityMatrix[6]] |
Here it is looking more “lively” for the web:
✕
Dataset[IdentityMatrix[6], DatasetTheme -> "Web"] |
You can give various “theme directives” too:
✕
Dataset[IdentityMatrix[6], DatasetTheme -> "AlternatingColumnBackgrounds"] |
As well as additional hints:
✕
Dataset[IdentityMatrix[6],
DatasetTheme -> {"AlternatingColumnBackgrounds", LightGreen}]
|
I’m not sure why we didn’t think of it before, but in Version 11.3 (2018) we introduced a very nice “user interface innovation”: Iconize. And in Version 12.3 we’ve added another piece of polish to iconization. If you select a piece of an expression, then use Iconize in the context (“right-click”) menu, an appropriate subpart of the expression will get iconized, even if the selection you made might have included an extra comma, or been something that can’t be a strict subpart of the expression:
✕
Range[20] |
Let’s say you generate an object that takes a lot of memory to store:
✕
SparseArray[Range[10^7]] |
By default, the object is kept in your kernel session, but it’s not stored directly in your notebook—so it won’t persist after you end your current kernel session. In Version 12.3 we’ve added some options for where you can store the data:
✕
SparseArray[Range[10^7]] |
One important area where we put lots of effort into making things “just work” is in importing and exporting of data. The Wolfram Language now supports about 250 external data formats, with for example new statistical data formats like SAS7BDAT, DTA, POR and SAV being added in Version 12.3.
Lots of Things Got Faster
In addition to all the effort we put into creating new functionality for Wolfram Language, we’re also always trying to make existing functionality better, and faster. And in Version 12.3 there are lots of things that are now faster. One particularly large group of things got faster because of advances in our compiler technology that allow a broader range of Wolfram Language functionality to be compiled directly into optimized machine code. An example of a beneficiary of this is Around.
Here’s a computation with Around:
✕
Sin[Around[RandomReal[], 0.001]] |
In Version 12.2 doing this 10,000 times takes about 1.3 seconds on my computer:
✕
Do[Sin[Around[RandomReal[], 0.001]], 10^4] // Timing |
In Version 12.3, it’s roughly 100 times faster:
✕
Do[Sin[Around[RandomReal[], 0.001]], 10^4] // Timing |
There are lots of different reasons that things got faster in Version 12.3. In the case of Permanent, for example, we were able to use a new and much better algorithm. Here it is in 12.2:
✕
Permanent[Table[2.3 i/j, {i, 15}, {j, 15}]] // Timing
|
And now in 12.3:
✕
Permanent[Table[2.3 i/j, {i, 15}, {j, 15}]] // Timing
|
Another example is date parsing: converting dates from textual to internal form. The main advance here came from realizing that date parsing is often done in bulk, so it makes sense to adaptively cache parts of the operation. And the result, for example in parsing a million dates, is that what used to take many minutes now takes just a few seconds.
One more example is Rasterize, which in Version 12.3 is typically 2 to 4 times faster than in Version 12.2. The reason for this speedup is somewhat subtle. Back when Rasterize was first introduced in Version 6.0 (2007) data transfer speeds between processes were an issue, and so it was a good optimization to compress any data being transferred. But today transfer speeds are much higher, and we have better optimized array data structures—and so compression no longer makes sense, and removing it (together with other codepath optimization) allows Rasterize to be significantly faster.
An important advance in Version 12.1 was the introduction of DataStructure, allowing direct use of optimization data structures (implemented through our new compiler technology). Version 12.3 introduces several new data structures. There’s "ByteTrie" for fast prefix-based lookups (think Autocomplete and GenomeLookup), and there’s "KDTree" for fast geometric lookups (think Nearest). There’s also now "ImmutableVector", which is basically like an ordinary Wolfram Language list, except that it’s optimized for fast appending.
In addition to speed improvements in the computational kernel, Version 12.3 has user interface speed improvements too. Particularly notable is significantly faster rendering on Windows platforms, achieved by using DirectWrite and making use of GPU capabilities.
Pushing the Math Frontier
Version 1 of Mathematica was billed as “A System for Doing Mathematics by Computer”, and—for more than three decades—in every new version of Wolfram Language and Mathematica there’ve been innovations in “doing mathematics by computer”.
For Version 12.3 let’s talk first about symbolic equation solving. Back in Version 3 (1996) we introduced the idea of implicit “Root object” representations for roots of polynomials, allowing us to do exact, symbolic computations even without “explicit formulas” in terms of radicals. Version 7 (2008) then generalized Root to also work for transcendental equations.
What about systems of equations? For polynomials, elimination theory means that systems really aren’t a different story from individual equations; the same Root objects can be used. But for transcendental equations, this isn’t true anymore. But for Version 12.3 we’ve now figured out how to generalize Root objects so they can work with multivariate transcendental roots:
✕
Solve[Sin[x y] == x^2 + y &&
3 x E^y == 2 y E^x + 1 &&
-3 < x < 3 && -3 < y < 3, {x, y}, Reals]
|
And because these Root objects are exact, they can for example be evaluated to any precision:
✕
N[First[x /. %], 150] |
In Version 12.3 there are also some new equations, involving elliptic functions, where exact symbolic results can be given, even without Root objects:
✕
Reduce[JacobiSN[x, 2 y] == 1, x] |
A major advance in Version 12.3 is being able to solve symbolically any linear system of ODEs (ordinary differential equations) with rational function coefficients.
Sometimes the result involves explicit mathematical functions:
✕
DSolve[{Derivative[1][x][t] == -((4 x[t])/t) + (4 y[t])/t,
Derivative[1][y][t] == (4/t - t/4) x[t] - (4 y[t])/t}, {x[t], y[t]},
t]
|
Sometimes there are integrals—or differential roots—in the results:
✕
DSolveValue[{Derivative[1][y][x] + 2 Derivative[1][z][x] ==
z[x], (-3 + x) x^2 (y[x] + z[x]) +
Derivative[1][z][x] == (1 + 3 x^2) z[x]}, {y[x], z[x]},
x] // Simplify
|
Another ODE advance in Version 12.3 is full coverage of linear ODEs with q-rational function coefficients, in which variables can appear explicitly or implicitly in exponents. The results are exact, though they typically involve differential roots:
✕
DSolve[2^x y[x] + ((-1 + 2^x)
\!\(\*SuperscriptBox[\(y\),
TagBox[
RowBox[{"(", "4", ")"}],
Derivative],
MultilineFunction->None]\)[x])/(1 + 2^x) == 0, y[x], x]
|
What about PDEs? For Version 12.2 we introduced a major new framework for modeling with numerical PDEs. And now in Version 12.3 we’ve produced a whole 105-page monograph about symbolic solutions to PDEs:
Here’s an equation that in Version 12.2 could be solved numerically:
✕
eqns = {Laplacian[u[x, y],{x, y}] == 0,
u[x, 0] == Sin[x] && u[0, y] == Sin[y] && u[2, y] == Sin[2 y]};
|
Now it can be solved exactly and symbolically as well:
✕
DSolveValue[eqns, u[x, y], {x, y}]
|
In addition to linear PDEs, Version 12.3 extends the coverage of special solutions to nonlinear PDEs. Here’s one (with 4 variables) that uses Jacobi’s method:
✕
DSolveValue[(\!\(
\*SubscriptBox[\(\[PartialD]\), \(x\)]\(u[x, y, z, t]\)\))^4 == (\!\(
\*SubscriptBox[\(\[PartialD]\), \(y\)]\(u[x, y, z, t]\)\))^2 + (\!\(
\*SubscriptBox[\(\[PartialD]\), \(z\)]\(u[x, y, z, t]\)\))^3 \!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(u[x, y, z, t]\)\),
u[x, y, z, t], {x, y, z, t}]
|
Something added in 12.3 that both supports PDEs and provides new functionality for signal processing is bilateral Laplace transforms (i.e. integrating from –∞ to +∞, like a Fourier transform):
✕
BilateralLaplaceTransform[Sin[t] Exp[-t^2], t, s] |
Ever since Version 1, we’ve prided ourselves on our coverage of special functions. Over the years we’ve been able to progressively extend that coverage to more and more general special functions. Version 12.3 has several new long-sought classes of special functions. There are the Carlson elliptic integrals. And then there is the Fox H-function.
Back in Version 3 (1996) we introduced MeijerG which dramatically expanded the range of definite integrals that we could do in symbolic form. MeijerG is defined in terms of a Mellin–Barnes integral in the complex plane. It’s a small change in the integrand, but it’s taken 25 years to unravel the necessary mathematics and algorithms to bring us now in Version 12.3 FoxH.
FoxH is a very general function—that encompasses all hypergeometric pFq and Meijer G functions, and much beyond. And now that FoxH is in our language, we’re able to start the process of expanding our integration and other symbolic capabilities to make use of it.
Symbolic Optimization Breakthrough
A major step forward in Version 12.0 was the introduction of industrial-strength convex optimization, routinely handling problems involving millions of variables in the linear case and thousands in the nonlinear case. In Version 12.0 everything had to be numerical (in 12.1 we added integer optimization). In Version 12.3 we’re now adding the possibility for symbolic parameters in large-scale linear and quadratic problems, as in this small example:
✕
MinValue[{(x - 1)^2 + (2 y - 1)^2,
x + 2 y <= a + b && 2 x - y <= a - b + 1 &&
x - 2 y <= 2 a - b + 1}, {x, y}]
|
✕
Plot3D[%, {a, -5, 5}, {b, -5, 5}]
|
In typical convex optimization computations not involving symbolic parameters one aims only for approximate numerical results, and it wasn’t clear whether there was any general method for getting exact numerical results. But for Version 12.3 we’ve found one, and we’re now able to give exact numerical results which you can, for example, evaluate to any precision you want.
Here’s a geometric optimization problem—which can now be solved exactly in terms of transcendental root objects:
✕
MinValue[{x^(3/4) + 2 y^(4/5) + 3 z^(5/7),
x y z <= 1 && x^E y^\[Pi] z >= 2 && x > 0 && y > 0 && z > 0}, {x, y,
z}]
|
Given such an exact solution, it’s now possible to do numerical evaluation to any precision:
✕
N[%, 200] |
More with Graphs
In case one ever doubted that graphs are important, our Wolfram Physics Project has made it pretty clear over the past year that at the lowest level physics is all about graphs. And in fact our whole Physics Project was basically made possible by the rich graph functionality in the Wolfram Language.
In Version 12.3 we’ve continued to expand that functionality. Here, for example, is a new 3D visualization function for graphs:
✕
LayeredGraphPlot3D[KaryTree[255], BoxRatios -> {1, 1, 1}]
|
And here’s a new 3D graph embedding:
✕
Graph3D[GridGraph[{20, 20}], GraphLayout -> "SphericalEmbedding"]
|
We’ve been able to find spanning trees in graphs since Version 10 (2014). In Version 12.3, however, we’ve generalized FindSpanningTree to directly handle objects—like geo locations—that have some kind of coordinates. Here’s a spanning tree based on the positions of capital cities in Europe:
✕
FindSpanningTree[ EntityClass["Country", "Europe"][ EntityProperty["Country", "CapitalCity"]]] |
And now in Version 12.3 we can use the new GeoGraphPlot to plot this on a map:
✕
GeoGraphPlot[%] |
By the way, in a “geo graph” there are “geo” ways to route the edges. For example, you can specify that they follow (when possible) driving directions (as provided by TravelDirections):
✕
GeoGraphPlot[%%, GraphLayout -> "Driving"] |
Euclid Meets Descartes, and More
We’ve been doing a lot with geometry in the past few years, and there’s more to come. In Version 12.0 we introduced “Euclid-style” synthetic geometry. In Version 12.3 we’re connecting to “Descartes-style” analytic geometry, converting geometric descriptions to algebraic formulas.
Given three symbolically specified points, GeometricTest can give the algebraic condition for them to be collinear:
✕
GeometricTest[{{a, b}, {c, d}, {e, f}}, "Collinear"]
|
For the particular case of collinearity, there’s a specific function for doing the test:
✕
CollinearPoints[{{a, b}, {c, d}, {e, f}}]
|
But GeometricTest is much more general in scope—supporting more than 30 kinds of predicates. This gives the condition for a polygon to be convex:
✕
GeometricTest[Polygon[{{a, b}, {1, 2}, {3, 3}, {4, 7}}], "Convex"]
|
And this gives the condition for a polygon to be regular:
✕
GeometricTest[Polygon[{{a, b}, {c, d}, {1, 1}, {2, 3}}], "Regular"]
|
And here’s the condition for three circles to be mutually tangent (and, yes, that ∃ is a little “post Descartes”):
✕
GeometricTest[{Circle[{0, 0}, r], Circle[{a, b}, s],
Circle[{c, d}, t]}, "Tangent"]
|
Version 12.3 also has enhancements to core computational geometry. Most notable are RegionDilation and RegionErosion, that essentially convolve regions with each other. RegionDilation effectively finds the whole (“Minkowski sum”) “union region” obtained by translating one region to every point in another region.
Why is this useful? It turns out there are lots of reasons. One example is the “piano mover problem” (AKA the robot motion planning problem). Given, say, a rectangular shape, is there a way to maneuver it (in the simplest case, without rotation) through a house with certain obstacles (like walls)?
Basically what you need to do is take the rectangular shape and “dilate the room” (and the obstacles) with it:
✕
RegionDilation[\!\(\*
GraphicsBox[
TagBox[
DynamicModuleBox[{Typeset`mesh = HoldComplete[
BoundaryMeshRegion[{{0., 0.}, {0.11499999999999999`, 0.}, {
0.11499999999999999`, 0.22999999999999998`}, {0.,
0.22999999999999998`}}, {
Line[{{1, 2}, {2, 3}, {3, 4}, {4, 1}}]},
Method -> {
"EliminateUnusedCoordinates" -> True,
"DeleteDuplicateCoordinates" -> Automatic,
"DeleteDuplicateCells" -> Automatic, "VertexAlias" ->
Identity, "CheckOrientation" -> Automatic,
"CoplanarityTolerance" -> Automatic, "CheckIntersections" ->
Automatic, "BoundaryNesting" -> {{0, 0}},
"SeparateBoundaries" -> False, "TJunction" -> Automatic,
"PropagateMarkers" -> True, "ZeroTest" -> Automatic, "Hash" ->
740210533488462839}]]},
TagBox[GraphicsComplexBox[{{0., 0.}, {0.11499999999999999`, 0.}, {
0.11499999999999999`, 0.22999999999999998`}, {0.,
0.22999999999999998`}},
{Hue[0.6, 0.3, 0.95], EdgeForm[Hue[0.6, 0.3, 0.75]],
TagBox[PolygonBox[{{1, 2, 3, 4}}],
Annotation[#, "Geometry"]& ]}],
MouseAppearanceTag["LinkHand"]],
AllowKernelInitialization->False],
"MeshGraphics",
AutoDelete->True,
Editable->False,
Selectable->False],
DefaultBaseStyle->{
"MeshGraphics", FrontEnd`GraphicsHighlightColor ->
Hue[0.1, 1, 0.7]},
ImageSize->{27.866676879084963`, Automatic}]\),
CloudGet["http://wolfr.am/VAs8Qsr5"]]
|
Then if there’s a connected path “left over” from one point to another, then it’s possible to move the piano along that path. (And of course, the same kind of thing can be done for robots in a factory, etc. etc.)
RegionDilation is also useful for “smoothing out” or “offsetting” shapes, for example, for CAD applications:
✕
Region[RegionDilation[Triangle[], Disk[]]] |
At least in simple cases, one can “go Descartes” with it, and get explicit formulas:
✕
RegionDilation[Triangle[], Disk[]] |
And, by the way, this all works in any number of dimensions—providing a useful way to generate all sorts of “new shapes” (like a cylinder is the dilation of a disk by a line in 3D).
Yet More Visualization
The Wolfram Language has a huge collection of built-in visualization functions—but there always seem to be more that we figure out can be added. We’ve had ListPlot3D since Version 1.0 (1988); we added ListPointPlot3D in Version 6.0 (2007)—and now in Version 12.3 we’re adding ListLinePlot3D.
Here’s a 3D random walk rendered with ListLinePlot3D:
✕
ListLinePlot3D[
AnglePath3D[RandomReal[{0 \[Degree], 20 \[Degree]}, {1000, 3}]]]
|
If you give multiple lists of data, ListLinePlot3D plots them each separately:
✕
ListLinePlot3D[Table[Array[BitXor[#, n] &, 100], {n, 8}],
Filling -> Axis]
|
We first introduced plotting of vector fields in Version 7.0 (2008), with functions like VectorPlot and StreamPlot—that were substantially enhanced in Versions 12.1 and 12.2. In Version 12.3 we’re now adding StreamPlot3D (as well as ListStreamPlot3D). Here’s a plot of streamlines for a 3D vector field, colored by field strength:
✕
StreamPlot3D[{y + x, y - x, z}, {x, -2, 2}, {y, -2, 2}, {z, -3, 3}]
|
It’s one thing to make a plot; it’s another to give it axes. There’s a remarkable amount of subtlety in specifying how axes—and their ticks and labels—should be drawn. This is going to be a longer story, but in Version 12.3 we have the beginnings of symbolic axis specifications.
Axes work a bit like arrows: first you give the “core structure”, then you say how to annotate it. Here’s an axis that is linearly labeled from 0 to 100 on a line:
✕
Graphics[AxisObject[Line[{{-1, -1}, {1, 1}}], {0, 100}]]
|
And here’s a spiral axis (AKA labeling on a parametric curve):
✕
Graphics[
AxisObject[
Line[Table[{t Cos[t], t Sin[t]}, {t, 0, 5 Pi, 0.1}]], {0, 100}]]
|
And, yes, it works in more ornate cases as well:
✕
Graphics[AxisObject[HilbertCurve[3], {0, 100}, TickPositions -> 50]]
|
Among many subtle issues, there’s the question of how tick labels should be oriented with respect to the axis:
✕
Graphics[
AxisObject[
Line[Table[{t Cos[t], t Sin[t]}, {t, 0, 5 Pi, 0.1}]], {0, 100},
TickPositions -> 50, TickLabelOrientation -> "Parallel"]]
|
Talking of subtleties in graphics, here’s another one that’s addressed in Version 12.3. Say you’re making a dashed line:
✕
Graphics[{Dashing[{.2, .15}], Thickness[.05],
Line[{{0, 0}, {1, .1}}]}]
|
The numbers inside Dashing indicate the length of each dash, and between dashes. In Version 12.3 there’s an additional number you can give: the offset of the start of the first dash:
✕
Graphics[{Dashing[{.2, .15}, 0.1], Thickness[.05],
Line[{{0, 0}, {1, .1}}]}]
|
And something else is that you can control the “caps” on each dash, here making them rounded:
✕
Graphics[{Dashing[{.2, .15}, 0.1, "Round"], Thickness[.05],
Line[{{0, 0}, {1, .1}}]}]
|
These may all seem like micro-details—but they’re the kinds of things that are important in having Wolfram Language graphics look really good. Like, for example, if you have two dashed axes that cross, you probably want the “dashings” to line up:
✕
Graphics[{{Dashing[{0.1`, 0.05`}, 0.0195`],
Line[{{-1, 0}, {1, 0}}]}, {Dashing[{0.1`, 0.05`}, 0.0195`],
Line[{{0, -1}, {0, 1}}]}}, ImageSize -> 200]
|
Golden Knots, and Other Material Matters
We’ve talked about it almost since Version 1.0. And now finally in Version 12.3 it’s here! Realistic rendering of surfaces as materials. Here’s a knot, rendered as if it’s made of gold:
✕
Graphics3D[{MaterialShading["Gold"],
KnotData["SolomonSeal", "ImageData"]}]
|
Here’s a surface, in velvet:
✕
Plot3D[Sin[x + y^2], {x, -7, 7}, {y, -2, 2},
PlotStyle -> MaterialShading["Velvet"]]
|
In Version 12.3 we’re supporting a bit more than a dozen standard named materials (with more to come). But MaterialShading is also set up to allow you to specify in detail explicit physical and geometrical properties of materials—so you can get effects like this:
✕
Graphics3D[{MaterialShading[<|"BaseColor" -> Texture[\!\(\*
GraphicsBox[
TagBox[RasterBox[CompressedData["
1:eJzsvceSJEuSJNi7e9nj/sL+xVz3OEQ7NDPVVfXqocyMDODIMMbYMUaBEryq
7un/XGbRqKb9gsiLEXk6eVqYqamyKBGbmIiw/N+fzT89/O//8i//4v6f+PrT
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Lighting -> "ThreePoint"]
|
Notice, by the way, the new "ThreePoint" setting for Lighting—essentially a simulation of a standard placement of lights in a photography studio.
The story of modeling light interacting with surfaces—and “physically based rendering”—is a complicated one, that Version 12.3 has a whole monograph about:
Trees!
Based on the number of new built-in functions the clear winner for the largest new framework in Version 12.3 is the one for trees. We’ve been able to handle trees as a special case of graphs for more than a decade (and of course all symbolic expressions in the Wolfram Language are ultimately represented as trees). But in Version 12.3 we’re introducing trees as first-class objects in the system.
The fundamental object is Tree:
✕
Tree[a, {b, Tree[c, {d, e}], f, g}]
|
Tree takes two arguments: a “payload” (which can be any expression), and a list of subtrees. (And, yes, trees are by default rendered slightly green, in a nod to their botanical analogs.)
There are a variety of “*Tree” functions for constructing trees, and “Tree*” functions for converting trees to other things. RulesTree, for example, constructs a tree from a nested collection of rules:
✕
RulesTree[a -> {b, c -> {d, e}, f, g}]
|
And TreeRules goes the other way, converting a tree to a nested collection of rules:
✕
TreeRules[%] |
ExpressionTree creates a tree from the structure of an expression:
✕
ExpressionTree[Integrate[1/(x^2 - 1), x]] |
In a sense, this is a direct representation of a FullForm expression, as shown, for example, in TreeForm. But there are also ways to turn an expression into a tree. This takes the nodes of the tree to contain full subexpressions—so that the expressions on a given level in the tree are essentially what a function like Map would consider to be the expressions at that level (with Heads → True):
✕
ExpressionTree[Integrate[1/(x^2 - 1), x], "Subexpressions"] |
Here’s another version, now effectively removing the redundancy of nested subexpressions, and treating heads of expressions just like other parts (in “S-expression style”):
✕
ExpressionTree[Integrate[1/(x^2 - 1), x], "Atoms"] |
Why do we need Tree when we have Graph? The answer is that there are several special features of trees that are important. In a Graph, for example, every node has a name, and the names have to be unique. In a tree, nodes don’t have to be named, but they can have “payloads” that don’t have to be unique. In addition, in a graph, the edges at a given node don’t appear in any particular order; in a tree they do. Finally, a tree has a specific root node; a graph doesn’t necessarily have anything like this.
When we were designing Tree we at first thought we’d have to have separate symbolic representations of whole trees, subtrees and leaf nodes. But it turned out that we were able to make an elegant design with Tree alone. Nodes in a tree typically have the form Tree[payload, {child1, child2, …}] where the childi are subtrees. A node doesn’t necessarily have to have a payload, in which case it can just be given as Tree[{child1, child2, …}]. A leaf node is then Tree[expr, None] or Tree[None].
One very nice feature of this design is that trees can immediately be constructed from subtrees just by nesting expressions:
✕
Tree[{\!\(\*
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|
By the way, we can turn this into a generic Graph object with TreeGraph:
✕
TreeGraph[%] |
Notice that since Graph doesn’t pay attention to ordering of nodes, some nodes have effectively been flipped in this rendering. The nodes have also had to be given distinct names in order to preserve the tree structure:
✕
Graph[CloudGet["http://wolfr.am/VAsb0AqA"], VertexLabels -> Automatic] |
If there’s a generic graph that happens to be a tree, GraphTree converts it to explicit Tree form:
✕
GraphTree[KaryTree[20]] |
RandomTree produces a random tree of a given size:
✕
RandomTree[20] |
One can also make trees from nesting functions: NestTree produces a tree by nestedly generating payloads of child nodes from payloads of parent nodes:
✕
NestTree[{f[#], g[#]} &, x, 2]
|
OK, so given a tree, what can we do with it? There are a variety of tree functions that are direct analogs of functions for generic expressions. For example, TreeDepth gives the depth of a tree:
✕
TreeDepth[CloudGet["http://wolfr.am/VAsbf4XX"]] |
TreeLevel is directly analogous to Level. Here we’re getting subtrees that start at level 2 in the tree:
✕
TreeLevel[CloudGet["http://wolfr.am/VAsbnJeT"], {2}]
|
How do you get a particular subtree of a given tree? Basically it has a position, just as a subexpression would have a position in an ordinary expression:
✕
TreeExtract[CloudGet["http://wolfr.am/VAsbnJeT"], {2, 2}]
|
TreeSelect lets you select subtrees in a given tree:
✕
TreeSelect[CloudGet["http://wolfr.am/VAsbnJeT"], TreeDepth[#] > 2 &] |
TreeData picks out payloads, by default for the roots of trees (TreeChildren picks out subtrees):
✕
TreeData /@ % |
There are also TreeCases, TreeCount and TreePosition—which by default search for subtrees whose payloads match a specified pattern. One can do functional programming with trees just like with generic expressions. TreeMap maps a function over (the payloads in) a tree:
✕
TreeMap[f, CloudGet["http://wolfr.am/VAsbCysJ"]] |
TreeFold does a slightly more complicated operation. Here f is effectively “accumulating data” by scanning the tree, with g being applied to the payload of each leaf (to “initialize the accumulation”):
✕
TreeFold[{f, g}, CloudGet["http://wolfr.am/VAsbCysJ"]]
|
There are lots of things that can be represented by trees. A classic example is family trees. Here’s a case where there’s built-in data we can use:
✕
Entity["Person", "QueenElizabethII::f5243"][ EntityProperty["Person", "Children"]] |
This constructs a 2-level family tree:
✕
NestTree[#[EntityProperty["Person", "Children"]] &, Entity["Person", "QueenElizabethII::f5243"], 2] |
By the way, our Tree system is very scalable, and can happily handle trees with millions of nodes. But in Version 12.3 we’re really just starting out; in subsequent versions there’ll be all sorts of other tree functionality, as well as applications to parse trees, XML trees, etc.
Dates, Times and How Fast Is the Earth Turning?
Dates and times are complicated. Not only does one have to deal with different calendar systems, and different time zones, but there are also different conventions in different languages and regions. Version 12.3 adds support for date and time conventions for more than 700 different “locales”.
Here’s a date with the standard conventions used in Swedish:
✕
DateString[Entity["Language", "Swedish::557qk"]] |
And this shows the difference between British and American conventions, both for English:
✕
{DateString[Entity["LanguageLocale", "en-GB"] ],
DateString[Entity["LanguageLocale", "en-US"] ]}
|
In Version 12.3, there’s a new detailed specification for how date formats should be constructed:
✕
DateString[<|"Elements" -> {"Year", "Month", "Day", "DayName"},
"Delimiters" -> "-",
"Language" -> Entity["Language", "Armenian::f964n"]|>]
|
What about going the other way: from a date string to a date object? The new FromDateString does that:
✕
FromDateString["2021-05-05-??????????", <|
"Elements" -> {"Year", "Month", "Day", "DayName"},
"Delimiters" -> "-",
"Language" -> Entity["Language", "Armenian::f964n"]|>]
|
Beyond questions of how to display dates and times, there’s also the question of how exactly times are determined. Since the 1950s there’s been a core standard of “atomic time” (itself complicated by relativistic and gravitational effects). But before then, and still for a variety of applications, one wants to determine time either from the Sun or the stars.
We introduced sidereal (star-based) time in Version 10.0 (2014):
✕
SiderealTime[] |
And now in Version 12.3 we’re adding solar time, which is based on the position of the Sun in the sky:
✕
SolarTime[] |
This doesn’t quite align with ordinary time, basically because of Daylight Saving Time and because of the longitude of the observer:
✕
TimeObject[] |
Things get even more complicated if we want to get precise times in astronomy. And one of the big issues there is knowing the precise orientation of the Earth. In Version 12.3—in preparation for more extensive coverage of astronomy—we’ve added GeoOrientationData.
This tells how much longer than 24 hours the day currently is:
✕
GeoOrientationData[Now, "DayDurationExcess"] |
In 1800, the day was shorter:
✕
GeoOrientationData[
DateObject[{1800}, "Year", "Gregorian", -4.`], "DayDurationExcess"]
|
The Leading Edge of Machine Learning & Neural Nets
We first introduced automated machine learning (with Predict and Classify) back in Version 10.0 (2014)—and we’ve been continuing to develop leading-edge machine learning capabilities ever since. Version 12.3 introduces several new much-requested features, particularly aimed at greater analysis and control of machine learning.
Train a predictor to predict “wine quality” from the chemical content of a wine:
✕
p = Predict[ ResourceData["Sample Data: Wine Quality"] -> "WineQuality"] |
Use the predictor for a particular wine:
✕
p[<|"FixedAcidity" -> 6.`, "VolatileAcidity" -> 0.21`, "CitricAcid" -> 0.38`, "ResidualSugar" -> 0.8`, "Chlorides" -> 0.02`, "FreeSulfurDioxide" -> 22.`, "TotalSulfurDioxide" -> 98.`, "Density" -> 0.98941`, "PH" -> 3.26`, "Sulphates" -> 0.32`, "Alcohol" -> 11.8`|>] |
A common question is then: “How did it get that result?”, or, more specifically, “How important were the different features of the wine in getting this result?” In Version 12.3 you can use SHAP values to see the relative importance of different features:
✕
p[<|"FixedAcidity" -> 6., "VolatileAcidity" -> 0.21`, "CitricAcid" -> 0.38`, "ResidualSugar" -> 0.8`, "Chlorides" -> 0.02`, "FreeSulfurDioxide" -> 22.`, "TotalSulfurDioxide" -> 98.`, "Density" -> 0.98941`, "PH" -> 3.26`, "Sulphates" -> 0.32`, "Alcohol" -> 11.8`|>, "SHAPValues"] |
Here’s a visual version of this “explanation”:
✕
BarChart[%, BarOrigin -> Left, ChartLabels -> Placed[Automatic, Before]] |
The way SHAP values are computed is basically to see how much results change if different features in the data are dropped. In Version 12.3 we’ve added new options to functions like Predict and Classify to control how in general missing (or dropped) elements in data are handled both for training and evaluation—giving a way to determine, for example, what the uncertainty in a result might be from missing data.
A subtle but important issue in machine learning is calibrating the “confidence” of classifiers. If a classifier says that certain images have 60% probability to be cats, does this mean that 60% of them actually are cats? A raw neural net won’t typically get this right. But one can get closer by recalibrating probabilities using a calibration curve. And in Version 12.3, in addition to automatic recalibration, functions like Classify support the new RecalibrationFunction option that allows you to specify how the recalibration should be done.
An important part of our machine learning framework is in-depth symbolic support for neural nets. And we’ve continued to put the latest neural nets from the research literature into our Neural Net Repository, making them immediately accessible in our framework using NetModel.
In Version 12.3 we’ve added a few extra features to our framework, for example “swish” and “hardswish” activation functions for ElementwiseLayer. “Under the hood” a lot has been going on. We’ve enhanced ONNX import and export, we’ve greatly streamlined the software engineering of our MXNet integration, and we’ve almost finished a native version of our framework for Apple Silicon (in 12.3.0 the framework runs through Rosetta).
We’re always trying to make our machine learning framework as automated as possible. And in achieving this, it’s been very important that we’ve had so many curated net encoders and decoders that you can immediately use on different kinds of data. In Version 12.3 an extension to this is the use of an arbitrary feature extractor as a net encoder, that can be trained as part of your main training process. Why is this important? Well, it gives you a trainable way to feed into a neural net arbitrary collections of data of different kinds, even though there’s no pre-defined way of even knowing how the data can be turned into something like an array of numbers suitable for input to a neural net.
In addition to providing direct access to state-of-the-art machine learning, the Wolfram Language has an increasing number of built-in functions that make powerful internal use of machine learning. One such function is TextCases. And in Version 12.3 TextCases has become significantly stronger, especially in supporting less common text content types, like "Protein" and "BoardGame":
✕
TextCases["Candy Land became Milton Bradley's best selling game \ surpassing its previous top seller, Uncle Wiggily.", "BoardGame" -> "Interpretation"] |
New in Video
We first introduced video into the Wolfram Language in Version 12.1, and in 12.2 we added many additional video capabilities. In 12.3 we’re adding still more capabilities, with yet more to come.
A major group of new capabilities in 12.3 revolve around programmatic video generation. There are three basic new functions: FrameListVideo, SlideShowVideo and AnimationVideo.
FrameListVideo takes a raw list of images, and assembles a video by treating them as successive raw frames. SlideShowVideo similarly takes a list of images, but now it creates a “slide show video” in which each image is displayed for a specified duration. Here, for example, each image is displayed in the video for 1 second:
✕
SlideShowVideo[{\!\(\*
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ColorFunction->RGBColor],
BoxForm`ImageTag[
"Byte", ColorSpace -> "RGB", Interleaving -> True,
Magnification -> Automatic],
Selectable->False],
DefaultBaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{200., 113.},
PlotRange->{{0, 200.}, {0, 113.}}]\),
CloudGet["http://wolfr.am/VAscEWfy"]} -> 1]
|
SlideShowVideo can also do things like take a TimeSeries whose values are images, and turn this into a slide show video.
AnimationVideo doesn’t take existing images; instead it takes an expression and then evaluates it “Manipulate-style” for a range of values of a parameter. (In effect, it’s like a video-making analog of Animate.)
✕
AnimationVideo[
Plot[Sin[a x] + Sin[x], {x, 0, 10}, Sequence[
ImageSize -> 300, PlotRange -> {-2, 2}, Filling -> Axis,
FillingStyle -> LightOrange]], {a, 0, 3}]
|
What if you want to capture a video, say from a camera? Eventually there’ll be an interactive way to do this in a notebook. But in Version 12.3 we’ve added the underlying programmatic capabilities, and in particular the function VideoRecord. So this records 5 seconds from my default camera:
✕
sw = VideoRecord[$DefaultImagingDevice]; Pause[5]; VideoStop[]; |
And here’s the resulting video:
✕
swvid=Video[sw] |
But VideoRecord can also use other sources. For example, if you give it a NotebookObject, it will record what’s happening in that notebook. And if you give it a URL (say for a webcam), it’ll record frames that are streaming from that URL:
A much-requested feature that we’ve added in Version 12.3 is the ability to combine videos, for example compositing one video into another, or assembling each frame as a collage.
So, for example, here’s me green-screen composited with the stream above:
✕
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Notice that in doing this we’re using Parallelize—which newly works with VideoFrameMap in 12.3.
Version 12.3 also adds some new video-editing capabilities. VideoTimeStretch lets you “warp time” in a video by any specified function. VideoInsert lets you insert a video clip into a video, and VideoReplace lets you replace part of a video with another one.
One of the best things about video in the Wolfram Language is that it can immediately be analyzed using all of the tools in the language. This includes machine learning, and in Version 12.3 we’ve started the process of allowing videos to be encoded for neural net computation. Version 12.3 includes a simple frame-based net encoder for videos, as well as a couple of built-in feature extractors. More will be coming soon, including a variety of video processing and analysis nets in the Wolfram Neural Net Repository.
More in Chemistry
Chemistry is a major new area for Wolfram Language. In Version 12.0 we introduced Molecule as a symbolic representation of a molecule, and we’ve steadily been expanding what can be done with it.
In Version 12.3, for example, there are new properties for Molecule, like "TautomerList" (possible reconfigurations in solution):
✕
MoleculePlot /@ Molecule[{"C",
Atom["C", "HydrogenCount" -> 1], "C", "O", "N", "C", "C", "O", "O",
"N"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Single"],
Bond[{3, 4}, "Double"],
Bond[{3, 5}, "Single"],
Bond[{5, 6}, "Single"],
Bond[{6, 7}, "Single"],
Bond[{7, 8}, "Double"],
Bond[{7, 9}, "Single"],
Bond[{2, 10}, "Single"]}, {StereochemistryElements -> {
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 2, "Direction" ->
"Clockwise"]}}]["TautomerList"]
|
There are also convenience functions like MoleculeName:
✕
MoleculeName["CCCCCC(CC(CC)C)CCC"] |
And, yes, with MoleculeRecognize you can just clip a structure diagram from a publication and find the name of the molecule:
✕
MoleculeName[MoleculeRecognize[CloudGet["http://wolfr.am/VAsdfYsh"]]] |
Given a collection of molecules, a question one often wants to ask is “What’s in common between these molecules?” In Version 12.3 we now have the function MoleculeMaximumCommonSubstructure, which is the molecular structure analog of LongestCommonSubsequence:
✕
mcs = MoleculeMaximumCommonSubstructure[{Molecule[{
"N", "C", "N", "C", "N", "C", "C", "N", "C", "N", "C", "O", "C",
"C", "O", "C", "O", "C", "O", "H", "H", "H", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Aromatic"],
Bond[{3, 4}, "Aromatic"],
Bond[{4, 5}, "Aromatic"],
Bond[{5, 6}, "Aromatic"],
Bond[{6, 7}, "Aromatic"],
Bond[{7, 8}, "Aromatic"],
Bond[{8, 9}, "Aromatic"],
Bond[{9, 10}, "Aromatic"],
Bond[{10, 11}, "Single"],
Bond[{11, 12}, "Single"],
Bond[{12, 13}, "Single"],
Bond[{13, 14}, "Single"],
Bond[{14, 15}, "Single"],
Bond[{13, 16}, "Single"],
Bond[{16, 17}, "Single"],
Bond[{16, 18}, "Single"],
Bond[{18, 19}, "Single"],
Bond[{7, 2}, "Aromatic"],
Bond[{18, 11}, "Single"],
Bond[{10, 6}, "Aromatic"],
Bond[{1, 20}, "Single"],
Bond[{1, 21}, "Single"],
Bond[{4, 22}, "Single"],
Bond[{9, 23}, "Single"],
Bond[{11, 24}, "Single"],
Bond[{13, 25}, "Single"],
Bond[{14, 26}, "Single"],
Bond[{14, 27}, "Single"],
Bond[{15, 28}, "Single"],
Bond[{16, 29}, "Single"],
Bond[{17, 30}, "Single"],
Bond[{18, 31}, "Single"],
Bond[{19, 32}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{32, 3}, {CompressedData["
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"], "Angstroms", {{1}, {
2}}}]], StereochemistryElements -> {
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 11,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 13,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 16,
"Direction" -> "Clockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 18,
"Direction" -> "Clockwise"]}}],
Molecule[{
"N", "C", "N", "C", "N", "C", "C", "N", "C", "N", "C", "O", "C",
"C", "O", "P", "O", "O", "O", "P", "O", "O", "O", "P", "O", "O",
"O", "C", "O", "C", "O", "H", "H", "H", "H", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Aromatic"],
Bond[{3, 4}, "Aromatic"],
Bond[{4, 5}, "Aromatic"],
Bond[{5, 6}, "Aromatic"],
Bond[{6, 7}, "Aromatic"],
Bond[{7, 8}, "Aromatic"],
Bond[{8, 9}, "Aromatic"],
Bond[{9, 10}, "Aromatic"],
Bond[{10, 11}, "Single"],
Bond[{11, 12}, "Single"],
Bond[{12, 13}, "Single"],
Bond[{13, 14}, "Single"],
Bond[{14, 15}, "Single"],
Bond[{15, 16}, "Single"],
Bond[{16, 17}, "Double"],
Bond[{16, 18}, "Single"],
Bond[{16, 19}, "Single"],
Bond[{19, 20}, "Single"],
Bond[{20, 21}, "Double"],
Bond[{20, 22}, "Single"],
Bond[{20, 23}, "Single"],
Bond[{23, 24}, "Single"],
Bond[{24, 25}, "Double"],
Bond[{24, 26}, "Single"],
Bond[{24, 27}, "Single"],
Bond[{13, 28}, "Single"],
Bond[{28, 29}, "Single"],
Bond[{28, 30}, "Single"],
Bond[{30, 31}, "Single"],
Bond[{7, 2}, "Aromatic"],
Bond[{30, 11}, "Single"],
Bond[{10, 6}, "Aromatic"],
Bond[{1, 32}, "Single"],
Bond[{1, 33}, "Single"],
Bond[{4, 34}, "Single"],
Bond[{9, 35}, "Single"],
Bond[{11, 36}, "Single"],
Bond[{13, 37}, "Single"],
Bond[{14, 38}, "Single"],
Bond[{14, 39}, "Single"],
Bond[{18, 40}, "Single"],
Bond[{22, 41}, "Single"],
Bond[{26, 42}, "Single"],
Bond[{27, 43}, "Single"],
Bond[{28, 44}, "Single"],
Bond[{29, 45}, "Single"],
Bond[{30, 46}, "Single"],
Bond[{31, 47}, "Single"]}, {AtomCoordinates -> QuantityArray[
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StereochemistryElements -> {
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 11,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 13,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 28,
"Direction" -> "Clockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 30,
"Direction" -> "Clockwise"]}}]}]
|
Here’s a diagram of the common part:
✕
MoleculePlot[Molecule[{
"N", "C", "N", "C", "N", "C", "C", "N", "C", "N", "C", "O", "C",
"C", "O", "P", "O", "O", "O", "P", "O", "O", "O", "P", "O", "O",
"O", "C", "O", "C", "O", "H", "H", "H", "H", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Aromatic"],
Bond[{3, 4}, "Aromatic"],
Bond[{4, 5}, "Aromatic"],
Bond[{5, 6}, "Aromatic"],
Bond[{6, 7}, "Aromatic"],
Bond[{7, 8}, "Aromatic"],
Bond[{8, 9}, "Aromatic"],
Bond[{9, 10}, "Aromatic"],
Bond[{10, 11}, "Single"],
Bond[{11, 12}, "Single"],
Bond[{12, 13}, "Single"],
Bond[{13, 14}, "Single"],
Bond[{14, 15}, "Single"],
Bond[{15, 16}, "Single"],
Bond[{16, 17}, "Double"],
Bond[{16, 18}, "Single"],
Bond[{16, 19}, "Single"],
Bond[{19, 20}, "Single"],
Bond[{20, 21}, "Double"],
Bond[{20, 22}, "Single"],
Bond[{20, 23}, "Single"],
Bond[{23, 24}, "Single"],
Bond[{24, 25}, "Double"],
Bond[{24, 26}, "Single"],
Bond[{24, 27}, "Single"],
Bond[{13, 28}, "Single"],
Bond[{28, 29}, "Single"],
Bond[{28, 30}, "Single"],
Bond[{30, 31}, "Single"],
Bond[{7, 2}, "Aromatic"],
Bond[{30, 11}, "Single"],
Bond[{10, 6}, "Aromatic"],
Bond[{1, 32}, "Single"],
Bond[{1, 33}, "Single"],
Bond[{4, 34}, "Single"],
Bond[{9, 35}, "Single"],
Bond[{11, 36}, "Single"],
Bond[{13, 37}, "Single"],
Bond[{14, 38}, "Single"],
Bond[{14, 39}, "Single"],
Bond[{18, 40}, "Single"],
Bond[{22, 41}, "Single"],
Bond[{26, 42}, "Single"],
Bond[{27, 43}, "Single"],
Bond[{28, 44}, "Single"],
Bond[{29, 45}, "Single"],
Bond[{30, 46}, "Single"],
Bond[{31, 47}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{47, 3}, {CompressedData["
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"], "Angstroms", {{1}, {2}}}]],
StereochemistryElements -> {
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 11, "Direction" ->
"Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 13, "Direction" ->
"Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 28, "Direction" ->
"Clockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 30, "Direction" ->
"Clockwise"]}}], %]
|
And now with MoleculeAlign we can see how the molecules actually align in 3D:
✕
MoleculePlot3D[
MoleculeAlign[
Molecule[{
"N", "C", "N", "C", "N", "C", "C", "N", "C", "N", "C", "O", "C",
"C", "O", "C", "O", "C", "O", "H", "H", "H", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Aromatic"],
Bond[{3, 4}, "Aromatic"],
Bond[{4, 5}, "Aromatic"],
Bond[{5, 6}, "Aromatic"],
Bond[{6, 7}, "Aromatic"],
Bond[{7, 8}, "Aromatic"],
Bond[{8, 9}, "Aromatic"],
Bond[{9, 10}, "Aromatic"],
Bond[{10, 11}, "Single"],
Bond[{11, 12}, "Single"],
Bond[{12, 13}, "Single"],
Bond[{13, 14}, "Single"],
Bond[{14, 15}, "Single"],
Bond[{13, 16}, "Single"],
Bond[{16, 17}, "Single"],
Bond[{16, 18}, "Single"],
Bond[{18, 19}, "Single"],
Bond[{7, 2}, "Aromatic"],
Bond[{18, 11}, "Single"],
Bond[{10, 6}, "Aromatic"],
Bond[{1, 20}, "Single"],
Bond[{1, 21}, "Single"],
Bond[{4, 22}, "Single"],
Bond[{9, 23}, "Single"],
Bond[{11, 24}, "Single"],
Bond[{13, 25}, "Single"],
Bond[{14, 26}, "Single"],
Bond[{14, 27}, "Single"],
Bond[{15, 28}, "Single"],
Bond[{16, 29}, "Single"],
Bond[{17, 30}, "Single"],
Bond[{18, 31}, "Single"],
Bond[{19, 32}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{32, 3}, {CompressedData["
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BmT0DKh0EkDj//9YRV0KQE5p87JV+fI/7MqzIdT/AkAs7t9wlkkUQOephZBb
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0GEhQD7K4oiNKg/ACAq4pDl4F0DsKddgbC0eQF3TZifqyQJAVE3KLT9LBUCO
ndocBCkgQAOqLvTAq/M/jjFOtjmJCUA6Xxc9Q3oSQJYJ2UlbTAdAliQpYDKO
E0DISN/v3owUQGzE9tkdm9k/mDrvyHN1FkCTdFRPxkYTQI9UunG1dgBAmAPP
LnUdEEDsEQ+K7O8GQKKatQ8Gxf0/ZiqswoCQA0B/4ppszoAQQCwkltOHLtc/
2pLZFNux8z8KYh2IWgoXQKy13XD5NQNAuBxwEWSmCkDOWdFW+ScYQNCXWmaf
A+m/iGJlVhMj9T+9WsEe8PceQIzEjnFC2sC/yMJgeQ==
"], "Angstroms", {{1}, {
2}}}]], StereochemistryElements -> {
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 11,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 13,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 16,
"Direction" -> "Clockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 18,
"Direction" -> "Clockwise"]}}],
Molecule[{
"N", "C", "N", "C", "N", "C", "C", "N", "C", "N", "C", "O", "C",
"C", "O", "P", "O", "O", "O", "P", "O", "O", "O", "P", "O", "O",
"O", "C", "O", "C", "O", "H", "H", "H", "H", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Aromatic"],
Bond[{3, 4}, "Aromatic"],
Bond[{4, 5}, "Aromatic"],
Bond[{5, 6}, "Aromatic"],
Bond[{6, 7}, "Aromatic"],
Bond[{7, 8}, "Aromatic"],
Bond[{8, 9}, "Aromatic"],
Bond[{9, 10}, "Aromatic"],
Bond[{10, 11}, "Single"],
Bond[{11, 12}, "Single"],
Bond[{12, 13}, "Single"],
Bond[{13, 14}, "Single"],
Bond[{14, 15}, "Single"],
Bond[{15, 16}, "Single"],
Bond[{16, 17}, "Double"],
Bond[{16, 18}, "Single"],
Bond[{16, 19}, "Single"],
Bond[{19, 20}, "Single"],
Bond[{20, 21}, "Double"],
Bond[{20, 22}, "Single"],
Bond[{20, 23}, "Single"],
Bond[{23, 24}, "Single"],
Bond[{24, 25}, "Double"],
Bond[{24, 26}, "Single"],
Bond[{24, 27}, "Single"],
Bond[{13, 28}, "Single"],
Bond[{28, 29}, "Single"],
Bond[{28, 30}, "Single"],
Bond[{30, 31}, "Single"],
Bond[{7, 2}, "Aromatic"],
Bond[{30, 11}, "Single"],
Bond[{10, 6}, "Aromatic"],
Bond[{1, 32}, "Single"],
Bond[{1, 33}, "Single"],
Bond[{4, 34}, "Single"],
Bond[{9, 35}, "Single"],
Bond[{11, 36}, "Single"],
Bond[{13, 37}, "Single"],
Bond[{14, 38}, "Single"],
Bond[{14, 39}, "Single"],
Bond[{18, 40}, "Single"],
Bond[{22, 41}, "Single"],
Bond[{26, 42}, "Single"],
Bond[{27, 43}, "Single"],
Bond[{28, 44}, "Single"],
Bond[{29, 45}, "Single"],
Bond[{30, 46}, "Single"],
Bond[{31, 47}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{47, 3}, {CompressedData["
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ayxga8EWAd4e8iUxtBKs+kjmHb1CQ1b0IuPqRg5cr9rYTzURYOyoPc4ykLG+
oSl8+04WPhjyHlMviMHbdMno8YqPW2p1ReXgPHw1UiTQf6Sgp+14fWE6H2VR
nS/vWsyCfqMxIP4BFR7FF4vLpLOQokn6RvxuSvl5nTIjoYiF4PrgymPebCwl
DXXE/yKA8x3RuLuAD5J8ad6i7E/Kyo7dixOLOWjuWlMTYRbA0uSoG2+zwAdv
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3YoKHFBnTBmmFxF4E7PjTI2XI2ZXJKdSpgkER5bZDtVIYfVHteaGlINc29/3
vZ8rhvax+4vJKgVOdssD/YOcIJrYF/FEJoOmo9Quu3oBulKfZsfMEuH5dOWZ
9gsu6CX63h8pVYDIehS7ZISGGl/tw4D1QuyPYTU/o8twonwy3Wr4jXJE2abq
K+ahMzT3NCNajKah5cO/VdhCpjJOZ1E5iHNx5lOZYhzzUpjCT5LQVxF2LKPE
Fq29x8dSQwn8D14J2II=
"], "Angstroms", {{1}, {2}}}]],
StereochemistryElements -> {
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 11,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 13,
"Direction" -> "Counterclockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 28,
"Direction" -> "Clockwise"],
Association[
"StereoType" -> "Tetrahedral", "ChiralCenter" -> 30,
"Direction" -> "Clockwise"]}}], mcs], mcs]
|
Given our strength in chemistry and in machine learning, we’re now in an interesting position to bring these fields together. And in Version 12.3 we have the beginnings of built-in chemical machine learning. Here are samples of two classes of chemicals:
✕
acids = {Molecule[{
"S", "O", "O", "C", "C", "C", "C", "C", "C", "C", "B", "H", "H",
"H", "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 5}, "Single"],
Bond[{1, 10}, "Single"],
Bond[{2, 11}, "Single"],
Bond[{2, 19}, "Single"],
Bond[{3, 11}, "Single"],
Bond[{3, 20}, "Single"],
Bond[{4, 6}, "Aromatic"],
Bond[{4, 7}, "Aromatic"],
Bond[{4, 11}, "Single"],
Bond[{5, 6}, "Aromatic"],
Bond[{5, 8}, "Aromatic"],
Bond[{6, 12}, "Single"],
Bond[{7, 9}, "Aromatic"],
Bond[{7, 13}, "Single"],
Bond[{8, 9}, "Aromatic"],
Bond[{8, 14}, "Single"],
Bond[{9, 15}, "Single"],
Bond[{10, 16}, "Single"],
Bond[{10, 17}, "Single"],
Bond[{10, 18}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{20, 3}, {CompressedData["
1:eJwB8QEO/iFib1JlAgAAABQAAAADAAAAy+WqtmpOAUC0OlJvt4PxP9cVgoWt
lfS/h9BKaQDmD8DOBPTNy3Tov2n35zZnP+S/0NqgsP7pCsDj3TNLVWz6P4Pu
V5/CBt2/uFYfpon1978hvomBUvSxvyIA9rVBMaO/w9AGAEbU6z++t0VYNXfR
Pxd3axKxKNi/uiHIloWW3L92pdZmTkfhP8n8RNEWvOa/U3XfuugS9L/FKow2
L73uv/Ai+UwHdu8/x725Piuc8T9PorWGT9TjvxYteUZppuQ/GrVtulpeqj8n
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B8DMgkHwTSHOP3OgvXTQu9q/G9emxOAt5b+zkeT+2cHzPw3P58WrHvi/+XSF
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VxSVztsuzj+XsUBpHg3/v+XbSmRhEAFAccHkG82jDkDHM2Wgt6jCv+/VQo0a
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uyjsNvm/x3tMaXgrDcBpqdjxfur5v56R1Jz6Je6/0iEKSlhECMD5k62H4FoA
QHy0f4hhetk/zTQJLw==
"], "Angstroms", {{1}, {2}}}]],
AtomDiagramCoordinates -> CompressedData["
1:eJxTTMoPSmViYGAQAWIQDQUO3zRi+g99/bHf93NfcEmKkAPX9cUFtlz/7RU3
FGVMfMsG51eZrbYLv83roAlSrnEHLg/R/2E/jL9DrvV14I51cPNgfJh+dPtg
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5N8Eglzwdb8oyFiRb/Yw82H2QdRzHoC4gwVuP8x9UL4DzH8wPgAJz4iI
"]}],
Molecule[{
"O", "O", "O", "C", "C", "C", "C", "C", "C", "C", "C", "C", "B",
"H", "H", "H", "H", "H", "H", "H", "H", "H", "H", "H", "H",
"H"}, {
Bond[{1, 4}, "Single"],
Bond[{1, 6}, "Single"],
Bond[{2, 13}, "Single"],
Bond[{2, 25}, "Single"],
Bond[{3, 13}, "Single"],
Bond[{3, 26}, "Single"],
Bond[{4, 5}, "Single"],
Bond[{4, 14}, "Single"],
Bond[{4, 15}, "Single"],
Bond[{5, 8}, "Single"],
Bond[{5, 16}, "Single"],
Bond[{5, 17}, "Single"],
Bond[{6, 7}, "Aromatic"],
Bond[{6, 9}, "Aromatic"],
Bond[{7, 10}, "Aromatic"],
Bond[{7, 13}, "Single"],
Bond[{8, 18}, "Single"],
Bond[{8, 19}, "Single"],
Bond[{8, 20}, "Single"],
Bond[{9, 11}, "Aromatic"],
Bond[{9, 21}, "Single"],
Bond[{10, 12}, "Aromatic"],
Bond[{10, 22}, "Single"],
Bond[{11, 12}, "Aromatic"],
Bond[{11, 23}, "Single"],
Bond[{12, 24}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{26, 3}, {CompressedData["
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uLDO+b9eiB8rzvH5P16nRWPfLfC/XoUSZXSM/z8+HqCb9On1v1IjRqt1E6o/
EOsxk/Ea+T8IVJhzipbmv8c2eRvjmPo/0ipdjWAuD0DwwqZ4sXmwvzHZFcH3
7/A/R5C047hYBkBBbCplOZ70P8wIRyWjufU/9wwH2+QJBUBMSdZTJgnnP/4J
jjL47Pe/J9COrh6mEUBpsJvxYwjjP2ws3BZWj/C/SWiZk6bsC0AN/mrB1H4A
QPzEY9KryOS/4eNaqmAuyD+f+IwUubACwDu0XZ1Rheg/ccLo6qStDcBzCiLX
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CsBD42W3tw4FQOXYzMmWQvi/hvFLbw==
"], "Angstroms", {{1}, {2}}}]],
AtomDiagramCoordinates -> CompressedData["
1:eJxTTMoPSmViYGCQAmIQ7fu5L7gkRchhh1zr68Ad6/bPfia7/MUJGQeu64sL
bLm+28d5n2C3vS0K51eZrbYLv83r8CYQpOPhfsUNRRkT37LB9cPUw+TzFjPu
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vFUY6t6/+yNPGR3Z+E7OAeLNC3D3FYItYj0Ak4eph/kH6j8HWHjA+AD39scp
"]}], Molecule[{
"F", "O", "O", "O", "C", "C", "C", "C", "C", "C", "C", "C", "C",
"C", "B", "H", "H", "H", "H", "H", "H", "H", "H", "H", "H", "H",
"H", "H", "H"}, {
Bond[{1, 10}, "Single"],
Bond[{2, 7}, "Single"],
Bond[{2, 9}, "Single"],
Bond[{3, 15}, "Single"],
Bond[{3, 28}, "Single"],
Bond[{4, 15}, "Single"],
Bond[{4, 29}, "Single"],
Bond[{5, 6}, "Single"],
Bond[{5, 7}, "Single"],
Bond[{5, 16}, "Single"],
Bond[{5, 17}, "Single"],
Bond[{6, 8}, "Single"],
Bond[{6, 18}, "Single"],
Bond[{6, 19}, "Single"],
Bond[{7, 20}, "Single"],
Bond[{7, 21}, "Single"],
Bond[{8, 22}, "Single"],
Bond[{8, 23}, "Single"],
Bond[{8, 24}, "Single"],
Bond[{9, 10}, "Aromatic"],
Bond[{9, 11}, "Aromatic"],
Bond[{10, 13}, "Aromatic"],
Bond[{11, 14}, "Aromatic"],
Bond[{11, 25}, "Single"],
Bond[{12, 13}, "Aromatic"],
Bond[{12, 14}, "Aromatic"],
Bond[{12, 15}, "Single"],
Bond[{13, 26}, "Single"],
Bond[{14, 27}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{29, 3}, {CompressedData["
1:eJwByQI2/SFib1JlAgAAAB0AAAADAAAAUQZRdcCD8j86RJqTdcUFQLHjE4X5
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y3H6mfY//OA+B11HDsA8eKc3OVf5vy+kMmyaw9G/LrPpSJ2I97/sy0KKS1vc
v5N297TYaPM/p3KXLz8R97/RpShPzPvwv6NsofOj/t+/Z3E6kPigFcAhexvW
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DUCSeXt2ARcAQAckr+5tdOa/6OnJpUCMBkBqKMYoGa3+v9JnQ8y9m+M/7eD3
N33DFUCnvFZrbyD6P+PZfNb86t8/Ed13BV7rGEAHRt0zbYj7v2O1va8xndo/
OEh46g==
"], "Angstroms", {{1}, {2}}}]],
AtomDiagramCoordinates -> CompressedData["
1:eJxTTMoPSmViYGCQBWIQDQUOO+RaXwfuWLe/ymy1XfhtXodvGjH9h75+2O/7
uS+4JEXIASQr18rtoLihKGPiWzY4HyZfLbLO/WEVy4E47xPstrdFoXyOAzB5
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CkAiB+yXv/DQ+7+QyQESLX/sYfIwPsx/UP3w+IDxAbOMxbo=
"]}],
Molecule[{
"O", "O", "O", "C", "C", "C", "C", "C", "C", "B", "H", "H", "H",
"H", "H", "H", "H"}, {
Bond[{1, 7}, "Single"],
Bond[{1, 15}, "Single"],
Bond[{2, 10}, "Single"],
Bond[{2, 16}, "Single"],
Bond[{3, 10}, "Single"],
Bond[{3, 17}, "Single"],
Bond[{4, 5}, "Aromatic"],
Bond[{4, 6}, "Aromatic"],
Bond[{4, 10}, "Single"],
Bond[{5, 8}, "Aromatic"],
Bond[{5, 11}, "Single"],
Bond[{6, 9}, "Aromatic"],
Bond[{6, 12}, "Single"],
Bond[{7, 8}, "Aromatic"],
Bond[{7, 9}, "Aromatic"],
Bond[{8, 13}, "Single"],
Bond[{9, 14}, "Single"]}, {AtomCoordinates -> QuantityArray[
StructuredArray`StructuredData[{17, 3}, {CompressedData["
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"], "Angstroms", {{1}, {
2}}}]],
AtomDiagramCoordinates -> {{2.866, -2.405}, {3.7321, 2.095}, {2.,
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AtomDiagramCoordinates -> CompressedData["
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Molecule[{
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Bond[{1, 8}, "Single"],
Bond[{2, 14}, "Single"],
Bond[{2, 28}, "Single"],
Bond[{3, 14}, "Single"],
Bond[{3, 29}, "Single"],
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Bond[{4, 6}, "Single"],
Bond[{4, 15}, "Single"],
Bond[{4, 16}, "Single"],
Bond[{5, 7}, "Single"],
Bond[{5, 17}, "Single"],
Bond[{5, 18}, "Single"],
Bond[{6, 19}, "Single"],
Bond[{6, 20}, "Single"],
Bond[{7, 21}, "Single"],
Bond[{7, 22}, "Single"],
Bond[{7, 23}, "Single"],
Bond[{8, 9}, "Aromatic"],
Bond[{8, 11}, "Aromatic"],
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Bond[{10, 14}, "Single"],
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Bond[{11, 25}, "Single"],
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Bond[{12, 26}, "Single"],
Bond[{13, 27}, "Single"]}, {AtomCoordinates -> QuantityArray[
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AtomDiagramCoordinates -> CompressedData["
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Molecule[{
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Bond[{3, 22}, "Single"],
Bond[{4, 13}, "Single"],
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Bond[{6, 8}, "Aromatic"],
Bond[{6, 13}, "Single"],
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Bond[{12, 19}, "Single"],
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AtomDiagramCoordinates -> CompressedData["
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Bond[{3, 24}, "Single"],
Bond[{4, 14}, "Single"],
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Bond[{5, 6}, "Aromatic"],
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AtomDiagramCoordinates -> CompressedData["
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|
✕
bases = {Molecule[{
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Bond[{2, 3}, "Single"]}, {
AtomDiagramCoordinates -> {{2., 0.25}, {2.866, -0.25}, {3.403,
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Molecule[{
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AtomDiagramCoordinates -> CompressedData["
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Bond[{1, 2}, "Single"],
Bond[{1, 4}, "Single"],
Bond[{1, 5}, "Single"],
Bond[{2, 6}, "Single"],
Bond[{2, 7}, "Single"],
Bond[{2, 8}, "Single"]}, {
AtomDiagramCoordinates -> {{2.866, 0.}, {3.7321, 0.5}, {
2., -0.5}, {2.556, 0.5369}, {3.176, -0.5369}, {
4.0421, -0.0369}, {4.269, 0.81}, {3.4221, 1.0369}}}],
Molecule[{
Atom["C", "FormalCharge" -> -1], "C", "C", "C",
Atom["Li", "FormalCharge" -> 1], "H", "H", "H", "H", "H", "H", "H",
"H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{1, 3}, "Single"],
Bond[{1, 6}, "Single"],
Bond[{2, 4}, "Single"],
Bond[{2, 7}, "Single"],
Bond[{2, 8}, "Single"],
Bond[{3, 9}, "Single"],
Bond[{3, 10}, "Single"],
Bond[{3, 11}, "Single"],
Bond[{4, 12}, "Single"],
Bond[{4, 13}, "Single"],
Bond[{4, 14}, "Single"]}, {
AtomDiagramCoordinates -> {{2.866, -0.25}, {2.866, 0.75}, {
3.7321, -0.75}, {2., 1.25}, {2.866, -1.25}, {3.403, 0.06}, {
3.4766, 0.6423000000000001}, {3.0781, 1.3326}, {
3.4221, -1.2869}, {4.269, -1.06}, {
4.0421, -0.21310000000000004`}, {2.31, 1.7869}, {1.4631,
1.56}, {1.69, 0.7131000000000001}}}], Molecule[{
Atom["K", "FormalCharge" -> 1],
Atom["O", "FormalCharge" -> -1], "H"}, {
Bond[{2, 3}, "Single"]}, {
AtomDiagramCoordinates -> {{2., 0.25}, {2.866, -0.25}, {3.403,
0.06}}}], Molecule[{
Atom["O", "FormalCharge" -> -1], "C", "C", "C",
Atom["Li", "FormalCharge" -> 1], "H", "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Single"],
Bond[{2, 4}, "Single"],
Bond[{2, 6}, "Single"],
Bond[{3, 7}, "Single"],
Bond[{3, 8}, "Single"],
Bond[{3, 9}, "Single"],
Bond[{4, 10}, "Single"],
Bond[{4, 11}, "Single"],
Bond[{4, 12}, "Single"]}, {
AtomDiagramCoordinates -> {{3.7321, 0.75}, {2.866, 0.25}, {2.,
0.75}, {2.866, -0.75}, {4.5981, 0.25}, {2.866, 0.87}, {2.31,
1.2869}, {1.4631, 1.06}, {1.69, 0.21310000000000004`}, {
2.246, -0.75}, {2.866, -1.37}, {3.486, -0.75}}}],
Molecule[{"Ba", "O", "O", "O",
Atom["C", "MassNumber" -> 13], "H", "H"}, {
Bond[{2, 5}, "Single"],
Bond[{2, 6}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{3, 7}, "Single"],
Bond[{4, 5}, "Double"]}, {
AtomDiagramCoordinates -> {{1.153, 3.5}, {2.269, 1.5}, {0.5369,
1.5}, {1.4030000000000002`, 0.}, {1.4030000000000002`, 1.}, {
2.8059, 1.19}, {0., 1.19}}}], Molecule[{
Atom["O", "FormalCharge" -> -1],
Atom["N", "FormalCharge" -> 1], "C", "C", "C", "C", "H", "H", "H",
"H", "H", "H", "H", "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 19}, "Single"],
Bond[{2, 3}, "Single"],
Bond[{2, 4}, "Single"],
Bond[{2, 5}, "Single"],
Bond[{2, 6}, "Single"],
Bond[{3, 7}, "Single"],
Bond[{3, 8}, "Single"],
Bond[{3, 9}, "Single"],
Bond[{4, 10}, "Single"],
Bond[{4, 11}, "Single"],
Bond[{4, 12}, "Single"],
Bond[{5, 13}, "Single"],
Bond[{5, 14}, "Single"],
Bond[{5, 15}, "Single"],
Bond[{6, 16}, "Single"],
Bond[{6, 17}, "Single"],
Bond[{6, 18}, "Single"]}, {AtomDiagramCoordinates -> CompressedData["
1:eJxTTMoPSmViYGAQBmIQ7WPe6Zjw9I399qT6m7aWwg7LZx9R2FD0zR5Gf/l7
peKlGhNU/J/9c9nlLzz0HtrD9MFoXOpyj/7bVF3E5uCXJBBhuYXR4dMlXyDr
v72vaI/XqxZmh3yh5gOnFrI4OCc8vaB0+6v9G/3d6vzcZ+1naUlMvcL53Z4B
CsDSPx/ZX8qPZz8n+dqevXGqc3fOdbg6mDkwdTB7Yepg9qLbA3MXzB6Yu2D2
wPwDCx8ApKyMBQ==
"]}], Molecule[{
Atom["O", "FormalCharge" -> -1], "O",
Atom["Li", "FormalCharge" -> 1], "H", "H", "H"}, {
Bond[{1, 4}, "Single"],
Bond[{2, 5}, "Single"],
Bond[{2, 6}, "Single"]}, {
AtomDiagramCoordinates -> {{0.866, 2.5}, {0.7015000000000001,
0.}, {0., 3.}, {1.4030000000000002`, 2.81}, {1.2384, 0.31}, {
0.1645, 0.31}}}], Molecule[{
Atom["Rb", "FormalCharge" -> 1],
Atom["O", "FormalCharge" -> -1], "O", "H", "H", "H"}, {
Bond[{2, 4}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{3, 6}, "Single"]}, {
AtomDiagramCoordinates -> {{0., 0.5}, {0.866, 0.}, {
0.7015000000000001, 2.5}, {1.4030000000000002`, 0.31}, {1.2384,
2.81}, {0.1645, 2.81}}}], Molecule[{
Atom["O", "FormalCharge" -> -1],
Atom["N", "FormalCharge" -> 1], "H", "H", "H", "H", "H"}, {
Bond[{1, 7}, "Single"],
Bond[{2, 3}, "Single"],
Bond[{2, 4}, "Single"],
Bond[{2, 5}, "Single"],
Bond[{2, 6}, "Single"]}, {
AtomDiagramCoordinates -> {{0.0369, 3.0739}, {0.5369, 0.5369}, {
1.0739, 0.8469}, {0., 0.2269}, {0.2269, 1.0739}, {0.8469, 0.}, {
1.0369, 3.0739}}}], Molecule[{
Atom["K", "FormalCharge" -> 1],
Atom["O", "FormalCharge" -> -1], "C", "C", "C", "C", "H", "H", "H",
"H", "H", "H", "H", "H", "H"}, {
Bond[{2, 4}, "Single"],
Bond[{3, 4}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{3, 6}, "Single"],
Bond[{3, 7}, "Single"],
Bond[{4, 8}, "Single"],
Bond[{4, 9}, "Single"],
Bond[{5, 10}, "Single"],
Bond[{5, 11}, "Single"],
Bond[{5, 12}, "Single"],
Bond[{6, 13}, "Single"],
Bond[{6, 14}, "Single"],
Bond[{6, 15}, "Single"]}, {
AtomDiagramCoordinates -> {{5.4641, 0.75}, {4.5981, 0.25}, {2.866,
0.25}, {3.7321, 0.75}, {2., 0.75}, {2.866, -0.75}, {2.866,
0.87}, {4.1306, 1.225}, {3.3335, 1.225}, {2.31, 1.2869}, {
1.4631, 1.06}, {1.69, 0.21310000000000004`}, {2.246, -0.75}, {
2.866, -1.37}, {3.486, -0.75}}}], Molecule[{
Atom["O", "FormalCharge" -> -1], "C", "C", "C", "C",
Atom["Li", "FormalCharge" -> 1], "H", "H", "H", "H", "H", "H", "H",
"H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{2, 3}, "Single"],
Bond[{2, 4}, "Single"],
Bond[{2, 5}, "Single"],
Bond[{3, 7}, "Single"],
Bond[{3, 8}, "Single"],
Bond[{3, 9}, "Single"],
Bond[{4, 10}, "Single"],
Bond[{4, 11}, "Single"],
Bond[{4, 12}, "Single"],
Bond[{5, 13}, "Single"],
Bond[{5, 14}, "Single"],
Bond[{5, 15}, "Single"]}, {
AtomDiagramCoordinates -> {{3.7321, 0.5}, {2.866, 0.}, {
2., -0.5}, {2.366, 0.866}, {3.366, -0.866}, {4.5981, 0.}, {1.69,
0.0369}, {1.4631, -0.81}, {2.31, -1.0369}, {2.903, 1.176}, {
2.056, 1.4030000000000002`}, {1.8291, 0.556}, {
2.8291, -1.176}, {3.676, -1.4030000000000002`}, {
3.903, -0.556}}}], Molecule[{
Atom["Cl", "FormalCharge" -> -1],
Atom["Mg", "FormalCharge" -> 2],
Atom["C", "FormalCharge" -> -1], "C", "C", "C", "H", "H", "H", "H",
"H", "H", "H", "H", "H"}, {
Bond[{3, 4}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{3, 6}, "Single"],
Bond[{4, 7}, "Single"],
Bond[{4, 8}, "Single"],
Bond[{4, 9}, "Single"],
Bond[{5, 10}, "Single"],
Bond[{5, 11}, "Single"],
Bond[{5, 12}, "Single"],
Bond[{6, 13}, "Single"],
Bond[{6, 14}, "Single"],
Bond[{6, 15}, "Single"]}, {
AtomDiagramCoordinates -> {{4.5981, 0.}, {3.7321, 0.5}, {2.866,
0.}, {2., -0.5}, {2.366, 0.866}, {3.366, -0.866}, {1.69,
0.0369}, {1.4631, -0.81}, {2.31, -1.0369}, {2.903, 1.176}, {
2.056, 1.4030000000000002`}, {1.8291, 0.556}, {
2.8291, -1.176}, {3.676, -1.4030000000000002`}, {
3.903, -0.556}}}], Molecule[{
Atom["Br", "FormalCharge" -> -1],
Atom["Mg", "FormalCharge" -> 2],
Atom["C", "FormalCharge" -> -1], "C", "H", "H", "H", "H", "H"}, {
Bond[{3, 4}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{3, 6}, "Single"],
Bond[{4, 7}, "Single"],
Bond[{4, 8}, "Single"],
Bond[{4, 9}, "Single"]}, {
AtomDiagramCoordinates -> {{2., 1.25}, {2.866, 0.75}, {
2.866, -0.25}, {2.866, -1.25}, {3.403, -0.56}, {3.403, 0.06}, {
2.246, -1.25}, {2.866, -1.87}, {3.486, -1.25}}}], Molecule[{
Atom["N", "FormalCharge" -> -1], "C", "C",
Atom["Li", "FormalCharge" -> 1], "H", "H", "H", "H", "H", "H"}, {
Bond[{1, 2}, "Single"],
Bond[{1, 3}, "Single"],
Bond[{2, 5}, "Single"],
Bond[{2, 6}, "Single"],
Bond[{2, 7}, "Single"],
Bond[{3, 8}, "Single"],
Bond[{3, 9}, "Single"],
Bond[{3, 10}, "Single"]}, {
AtomDiagramCoordinates -> {{2.866, 0.25}, {3.7321, 0.75}, {
2.866, -0.75}, {2., 0.75}, {4.0421, 0.21310000000000004`}, {
4.269, 1.06}, {3.4221, 1.2869}, {2.246, -0.75}, {
2.866, -1.37}, {3.486, -0.75}}}], Molecule[{
Atom["Ca", "FormalCharge" -> 2],
Atom["O", "FormalCharge" -> -1],
Atom["O", "FormalCharge" -> -1], "O", "C"}, {
Bond[{2, 5}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{4, 5}, "Double"]}, {
AtomDiagramCoordinates -> {{0.8536, 2.}, {0.8536, 3.}, {-0.1464,
2.}, {-0.8536, 3.7071}, {-0.1464, 3.}}}],
Molecule[{"Ni", "Ni",
Atom["Ni", "FormalCharge" -> 2], "O", "O", "O", "O",
Atom["O", "FormalCharge" -> -1],
Atom["O", "FormalCharge" -> -1], "O", "O", "C", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H"}, {
Bond[{4, 13}, "Single"],
Bond[{4, 14}, "Single"],
Bond[{5, 15}, "Single"],
Bond[{5, 16}, "Single"],
Bond[{6, 17}, "Single"],
Bond[{6, 18}, "Single"],
Bond[{7, 19}, "Single"],
Bond[{7, 20}, "Single"],
Bond[{8, 12}, "Single"],
Bond[{9, 12}, "Single"],
Bond[{10, 12}, "Double"],
Bond[{11, 21}, "Single"],
Bond[{11, 22}, "Single"]}, {AtomDiagramCoordinates -> CompressedData["
1:eJxTTMoPSmViYGAQA2IQ7dKd8/z3SkGHxYx7WIWuCDlcX1xgy3X9sX39TdvK
iBU/7S/7JglE7ORz6GP7IOYR8Nu+8FzHpXsKolD1Ig4w/e7MFdwqK3jh+v9v
qv60IeCxve6mue+XH/tuf+DNPBudKwwOMPOkeR/oTljwzP6lmiHHmhhhuPm9
Gm959xmIOTBAgfLtn3VZe97Yy0alWN/vF3KAqYfpNz6yUS/vsbBDwtMLSrd/
ijmsuxFf5h8n5vBcdvkLj3VCDvvmS+nfVRGBu2/i2xp70zg+NPd+hrsXZi+M
b97pCDT6k73VlhNl++RZHSDu+WMvPS9O87TAT/vWmgubI79+swc5z/+ssENF
1VIdZ5nrcD4AUR2Ziw==
"]}], Molecule[{
Atom["Cl", "FormalCharge" -> -1],
Atom["Mg", "FormalCharge" -> 2], "C",
Atom["C", "FormalCharge" -> -1], "C", "C", "C", "H", "H", "H", "H",
"H", "H", "H", "H", "H", "H", "H"}, {
Bond[{3, 4}, "Single"],
Bond[{3, 5}, "Single"],
Bond[{3, 6}, "Single"],
Bond[{3, 7}, "Single"],
Bond[{4, 8}, "Single"],
Bond[{4, 9}, "Single"],
Bond[{5, 10}, "Single"],
Bond[{5, 11}, "Single"],
Bond[{5, 12}, "Single"],
Bond[{6, 13}, "Single"],
Bond[{6, 14}, "Single"],
Bond[{6, 15}, "Single"],
Bond[{7, 16}, "Single"],
Bond[{7, 17}, "Single"],
Bond[{7, 18}, "Single"]}, {
AtomDiagramCoordinates -> {{2., -0.4145}, {
2.866, -0.9145000000000001}, {4.5981, 0.0855}, {
3.7321, -0.4145}, {5.4641, 0.5855}, {
5.0981, -0.7806000000000001}, {4.0981, 0.9515000000000001}, {
3.4221, 0.12240000000000001`}, {4.0421, -0.9515000000000001}, {
5.7741, 0.04850000000000001}, {6.001, 0.8955}, {5.1541,
1.1224}, {4.5611, -1.0906}, {
5.408100000000001, -1.3175000000000001`}, {5.635, -0.4706}, {
4.635, 1.2615}, {3.7881, 1.4884000000000002`}, {3.5611,
0.6415}}}]};
|
FeatureSpacePlot now has a built-in feature extractor for molecules:
✕
FeatureSpacePlot[
Join[Thread[Style[acids, RGBColor[0.8, 0.2, 0.19215686274509805`]]],
Thread[
Style[bases, RGBColor[
0.2901960784313726, 0.4392156862745098, 0.8901960784313725]]]]]
|
Closing the Loop for Control Systems
It’s something we’ve been working towards for more than a decade. How do we connect our capabilities for representing and simulating large-scale engineering and other systems to our capabilities in control theory? Or, in particular, how can we use our control systems capabilities to create practical designs that can be directly deployed in engineering systems? Version 12.3 takes some important steps in answering this, and developing what’s increasingly a fully automated workflow for control systems design.
Let’s start by importing a model that was created in Wolfram System Modeler. In this particular case, it’s a simple model for a submarine:
✕
sys = Import["ExampleData/Submarine.mo"] |
Given the model (which in this case consists of more than 300 differential-algebraic equations) we can compute the behavior of the system in different situations. Like here’s a plot of how our model submarine responds to an impulse force—basically showing that the depth of the submarine exhibits damped oscillations:
✕
SystemModelPlot[sys, {"y"}, 40, <|
"Inputs" -> {"f" -> (10^7 UnitBox[0.5 - #] &), "deltarho" -> (0 &)}|>]
|
But now the question is: how can we control the submarine to prevent those oscillations? Basically we want to set up a closed loop in which a controller will take the observed behavior of the submarine and modify its dynamics to make it stable and well damped, say characterized by particular eigenvalues.
So given the underlying system model, how can we design that controller? Well, in Version 12.3 we’ve managed to get it down to just a couple of functions. First we give the model and parameters that are going to be controlled, and specify our design goal by giving the eigenvalues we want:
✕
cd = StateFeedbackGains[<|"InputModel" -> sys,
"FeedbackInputs" -> {"deltarho"}|>, {-0.75 + 0.2 I, -0.75 - 0.2 I},
"Data"]
|
Now we can take this controller and connect it into our system model:
✕
csys = ConnectSystemModelController[sys, cd] |
As the diagram indicates, this is now a closed-loop system (the original system model has been elided into the gray circle). So now we can look at the behavior of this closed-loop system, given for example the same input as before:
✕
SystemModelPlot[csys, {"y"}, 40, <|
"Inputs" -> {"f" -> (10^7 UnitBox[0.5 - #] &), "deltarho" -> (0 &)}|>,
PlotRange -> All]
|
Now there are no oscillations; our controller successfully damped them out and “rejected the disturbance”.
So how did this work? Well, as is typical in this type of control systems design, we first found a linearization of the underlying model, appropriate for the domain in which we were going to be operating:
✕
cd["DesignModel"] |
We can get out the eigenvalues of this linearized model:
✕
TransferFunctionPoles[TransferFunctionModel[cd["DesignModel"]]] |
The goal of the controller is to shift these to the desired design location:
✕
cd["ClosedLoopPoles"] |
So what actually is the controller that was found? Here it is as a nonlinear state space model:
✕
cd["ControllerModel"] |
And now it’s ready to actually deploy. And for example, we can compile the controller for an Arduino:
✕
Needs["MicrocontrollerKit`"]; |
✕
MicrocontrollerEmbedCode[ ToDiscreteTimeModel[cd["ControllerModel"], 0.1], <|"Target" -> "ArduinoUno", "Inputs" -> Table["Serial", 3], "Outputs" -> "Serial"|>, <|"ConnectionPort" -> None|>] |
And here’s the actual Arduino C source code:
✕
%["SourceCode"] |
Needless to say, for a real submarine, one wouldn’t use an Arduino Uno (though that would probably be just fine for a toy submarine). But the point here is that in Version 12.3 we now have a remarkably automated workflow for going from a sophisticated system model to a control system.
It’s Going to Get Easier to Type Code in Notebooks
Ever since Version 3.0 (1996) -> has automatically turned into → when you enter in code. And we’ve gradually added additional “input auto replacements”, the most recent being |-> turning into ↦ (\[Function]) in Version 12.2. In Version 12.3 we’re generalizing this whole mechanism (using the new AutoOperatorRenderings option), and we’re making <| ... |> automatically turn into <| ... |>, and [[ ... ]] turn into 〚 ... 〛.
So this means for example that instead of your code looking this
✕
Range[10][[
Nest[Flatten[RandomInteger[{1, 10}, {10, 2}][[#]]] &, 1, 5]]]
|
it’ll immediately turn into this more readable form right when you type it:
✕
Range[10][[
Nest[Flatten[RandomInteger[{1, 10}, {10, 2}][[#]]] &, 1, 5]]]
|
It might seem odd that it’s taken so many years to go from “automatic →” to “automatic 〚 〛”. But it’s a lot more subtle than you might think, and in fact it’s required a whole new as-you-type approach to code rendering. Back in Version 3.0, the idea was to replace -> with → when you type it. So, for example, if you then backspace one character, you’ll delete the whole →, rather than simply “removing the >” and reverting to -.
But if you’re dealing with [[ ... ]] you can’t just do this kind of “local replacement” without the potential for confusion with some ]] showing up as 〛 while others break apart into ]] as a result of routine editing.
In Version 12.3 what we’re doing is not to make replacements at all, but instead just to render specified sequences of characters (like ]]) in special ways. The result is that we can support very general “ligature-like” behavior, and that backspacing will always exactly reverse characters that were entered.
AutoOperatorRenderings will make code you type look nicer and be easier to read. But there’s a second, more significant change in the way you enter code that’s now available in Version 12.3. It’s still rather experimental, so it hasn’t been turned on by default, but you can explicitly turn it on if you want, just by evaluating
✕
CurrentValue[$FrontEnd, DelimiterAutoMatching] = True; |
or by checking the checkbox in the Interface tab of the Preferences:
The basic idea—as the name DelimiterAutoMatching might suggest—is that when you type code, the delimiters you enter are automatically matched, as you type.
So that means that if you type
what you’ll actually see is:
In other words, you’ll automatically get matched delimiters. (And by “delimiters”, we mean any of [ ... ], { ... }, ( ... ), " ... ", [[ ... ]], <| ... |> and (* ... *).)
So what happens to your old typing habits? Well, you can still use them. Because you can enter ] to “type through” the closing ]. And that means you’re typing the exact same characters as before. But the important point is that you don’t need to. The ] is already there for you.
Why is this important? Basically because it means you don’t have to think about matching your delimiters anymore. It’s done automatically for you. Ever since Version 3.0 (1996) we’ve had syntax coloring that indicates when delimiters haven't been closed—and to suggest that you should close them. But now the closing will just happen automatically. And in particular that means that expressions you’re typing will always “look complete”, and won’t have all kinds of structural changes happening as you enter each character.
Needless to say, this is all a lot trickier than it might at first appear. Let’s say you’ve already entered a complicated expression, and now you add an opening delimiter inside it, or, worse, several opening delimiters. Where do the closing delimiters go? How much of the code that’s already there should they enclose? Sometimes it’s fairly obvious, but sometimes it’s not. You can always delete an inappropriately added closing delimiter, but we’re working hard to use the appropriate heuristics to either add the closing delimiter in the right place, or not add it at all.
What’s Wrong with That Code? Code Analysis & Assistance
“Automate everything” is a big theme in what we’re trying to achieve with the Wolfram Language. So what about debugging? Is that something we can automate? We’ve been thinking about this for a long time, and in Version 12.3 we’ve introduced the first steps in our code analysis and assistance system.
We’ve had things like syntax coloring and ^ for missing arguments for decades. And these are extremely useful. But what we want is something more global. Something not so much like spellchecking as like being able to say whether a piece of text means the right thing.
One might think that there’s a kind of philosophical problem with this. In the Wolfram Language any piece of code—so long as it’s syntactically correct—is a symbolic expression which at some level means something. The question is whether that “something” is what you want. And the point is that by knowing the typical structure of “correct code” it’s often possible to make a very good guess. And that’s what our new code analysis system does.
Say you have this simple piece of code:
✕
If[x == y, f[e^2 + 4 e + 1], f[e^2 + 4 e + 1]] |
In Version 12.3 there’s a new context (“right-click”) menu item Analyze Cell. Here’s what it does:
Code Analysis has noticed that the expressions on the two branches of the If are the same (as might have happened if you’d copied and pasted them, intending to change one, but forgetting). It’s not strictly “wrong” to have the branches the same, but it’s almost certainly not what you wanted, and if you had always wanted to give the same expression, then your code would be much less obscure if you just gave the expression.
Here’s a marginally more complicated example:
✕
Switch[x,1,a,2,b,True,c] |
Now we’ve clicked the description, and got a suggestion about how to fix things—which we can immediately implement just by clicking the suggestion. (The Code Analysis box effectively gives you a preview; click Apply Edits to actually change your original code.)
Does Code Analysis catch real errors? Yes, and we’ve got evidence for that, because we’ve run it on our internal code, as well as on examples in our documentation. For example, in Version 12.2 the documentation for FitRegularization contained the example:
✕
Length[basis = Flatten[
Table[Exp[-((t - \[Tau])/\[Sigma])^2]
{1,
Table[{Cos[\[Omega] t], Sin[\[Omega] t]}, {\[Omega],
Drop[Subdivide[0., 150., n\[Omega]], 1]}]},
{\[Tau], Subdivide[0., 1., n\[Tau]]}]]]
|
Run Code Analysis and you’ll see
And, yes, that’s an error: there should be a comma in there.
The Code Analysis in Version 12.3 is just a beginning. We’ll be adding many more cases and suggestions, derived both from symbolic analysis and machine learning. And the interface for the analysis will become more automatic—like spellchecking. But I think Code Analysis is going to be very important for both novice and experienced users of Wolfram Language, injecting automation into yet another domain.
Advances in the Compiler: Portability and Librarying
We have a major long-term project of compiling Wolfram Language directly into efficient machine code. And as the project advances, it’s becoming possible to do more and more of our core development using the compiler. In addition, in things like the Wolfram Function Repository, more and more functions—or fragments of functions—are able to use the compiler.
In Version 12.3 we took an important step to make the workflow for this easier. Let’s say you compile a very simple function:
✕
fun = FunctionCompile[Function[Typed[x, "Integer64"], x + 1]] |
What is that output? Well, in Version 12.3 it’s a symbolic object that contains raw low-level code:
✕
fun[[1]]["CompiledIR"] |
But an important point is that everything is right there in this symbolic object. So you can just pick it up and use it:
✕
CompiledCodeFunction[
Association[
"Signature" -> TypeSpecifier[{"Integer64"} -> "Integer64"], "Input" ->
Compile`Program[{},
Function[
Typed[x, "Integer64"], x + 1]], "ErrorFunction" -> Automatic,
"InitializationName" ->
"Initialization_18398332_a4ff_43e1_bda5_14c193a2b3d6",
"ExpressionName" -> "Main_ExprInvocation", "CName" ->
"Main_CInvocation", "FunctionName" -> "Main", "SystemID" ->
"MacOSX-x86-64", "VersionData" -> {12.3, 0, 0}, "CompiledIR" ->
Association["MacOSX-x86-64" -> ByteArray[CompressedData["
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"]]], "orcInstance" ->
140467786380800, "orcModuleId" -> 1, "targetMachineId" ->
140467786361856], 4886855856, 4886855712, 4886855744, 4886855680,
"{\"Integer64\"} -> \"Integer64\""][50]
|
There’s a slight catch, however. By default, FunctionCompile will generate raw low-level code for the type of computer on which you’re running. But if you take the resulting CompiledCodeFunction to another type of computer, it won’t be able to use the low-level code. (It keeps a copy of the original expression before compilation, so it can still run, but won’t have the efficiency advantage of compiled code.)
In Version 12.3, there’s a new option to FunctionCompile: TargetSystem. And with TargetSystem → All you can tell FunctionCompile to create cross-compiled low-level code for all current systems:
✕
fun = FunctionCompile[Function[Typed[x, "Integer64"], x + 1], TargetSystem -> All] |
Needless to say, it’s slower to do all that compilation. But the result is a portable object that contains low-level code for all current platforms:
✕
fun[[1]]["CompiledIR"] |
So if you have a notebook—or a Wolfram Function Repository entry—that contains this kind of CompiledCodeFunction you can send it to anyone, and it will automatically run on their system.
There are a few other subtleties to this. The low-level code created by default in FunctionCompile is actually LLVM IR (intermediate representation) code, not pure machine code. The LLVM IR is optimized for each particular platform, but when the code is loaded on the platform, there’s the small additional step of locally converting to actual machine code. You can use UseEmbeddedLibrary → True to avoid this step, and pre-create a complete library that includes your code.
This will make it slightly faster to load compiled code on your platform, but the catch is that creating a complete library can only be done on a specific platform. We’ve built a prototype of a cloud-based compilation-as-a-service system, but it’s not yet clear if the speed improvement is worth the trouble.
Another new compiler feature for Version 12.3 is that FunctionCompile can now take a list or association of functions that are compiled together, optimizing with all their interdependencies.
The compiler continues to get stronger and broader, with more and more functions and types (like "Integer128") being supported. And to support larger-scale compilation projects, something added in Version 12.3 is CompilerEnvironmentObject. This is a symbolic object that represents a whole collection of compiled resources (for example defined by FunctionDeclaration) that act like a library and can immediately be used to provide an environment for additional compilation that is being done.
Shell, Java, ...: New Built-in External Connections
Over the past several versions we’ve added support for direct interactions with a sequence of external languages, both programmatically through functions like ExternalEvaluate, and as parts of notebooks. Version 12.3 adds support for several additional languages.
First, there’s the shell. Back in Version 1.0, there was the notion of “shell escapes”: type ! at the beginning of a line, and everything after it would be sent to your operating system shell. A third of a century later, it’s a bit more polished and sophisticated, though it’s the same basic idea.
Type > in a notebook, and select Shell, then type your shell command:
✕
date |
The stdout from the shell will be echoed as it’s generated, and then what comes back will be a symbolic object—from which it’s possible to extract things like exit code, or stdout:
✕
%["StandardOutput"] |
In earlier versions, we added capabilities for languages like Python, Julia, R, etc., as well as SQL. In this version, we’re also adding support for Octave (yes, the function names are not great):
✕
inv(1+eye(4)) |
But the important point here is that data structures have been connected so that an Octave array comes back as an appropriate expression, in this case a list of lists (containing approximate numbers, because that’s all Octave handles).
By the way, although external language cells in notebooks are nice, you definitely don’t have to use them, and you can use ExternalEvaluate—or ExternalFunction—to do things purely programmatically.
We’ve had tight integration with Java in Wolfram Language through J/Link for more than 20 years. But in Version 12.3 we’ve set things up so that instead of using J/Link’s sophisticated symbolic interface to Java, you can just enter Java code directly in ExternalEvaluate and external language cells:
✕
System.getProperty("java.version")
|
Basic Java data structures are returned as standard Wolfram Language expressions:
✕
new int [20] |
Java objects are represented symbolically through J/Link:
✕
new Object() |
Everything interacts seamlessly with J/Link. And for example, you can create Java objects directly using J/Link—that you can subsequently use with Java you enter in an external language cell:
✕
Needs["JLink`"]; fmt = JavaNew["java.text.DecimalFormat", "#.0000"] |
If you define a Java function it gets represented symbolically as an ExternalFunction object:
✕
import java.text.DecimalFormat;
String[] formatArray(double[] d, DecimalFormat fmt) {
String[] result = new String[d.length];
for (int i = 0; i < d.length; i++)
result[i] = fmt.format(d[i]);
return result;
}
|
This particular function takes a list of numbers, and a Java object—of the kind we created above with J/Link:
✕
%[{1, 2, 3}, fmt]
|
(Yes, this particular operation is extremely easy to do directly in Wolfram Language.)
Blockchain, Storage, Authentication & Cryptography
We first introduced blockchain functionality into Wolfram Language in Version 11.3 (2018), and in each successive version we’re adding more and more blockchain integration. Version 12.3 adds connectivity to the Tezos blockchain:
✕
BlockchainBlockData[-1, BlockchainBase -> "Tezos"] |
|
✕
<|"BlockHash" ->
"BKp9B8Z4zNpMDeSaFe2ZU6tywVUhady46Jji1oizxkRc4WGwpkf",
"BlockNumber" -> 1460305,
"PreviousBlockHash" ->
"BL8qGr1awP9RdeCMRExVvyiVadHJvzo9AJGMTfwnWEZDh8BAZf1",
"Protocol" -> "PtEdo2ZkT9oKpimTah6x2embF25oss54njMuPzkJTEi5RqfdZFA",
"NextProtocol" ->
"PtEdo2ZkT9oKpimTah6x2embF25oss54njMuPzkJTEi5RqfdZFA",
"Timestamp" ->
DateObject[{2021, 5, 6, 15, 23, 25.`}, "Instant",
"Gregorian", -4.`], "ValidationPass" -> 4,
"OperationsHash" ->
"LLoatzgmfL7B8dz5tdJu6RncRTXmPSBHxNpwbAuKyNc4daJw21m9V",
"Fitness" -> {"01", "00000000000c4851"},
"ContextHash" ->
"CoVdfkgRAo5QFd5iqhoKX34s4KcaZSTgSee7TsPwmCFaLch7TSnu",
"Priority" -> 0, "Nonce" -> "cbbfffdbf95d0300",
"Signature" -> DigitalSignature[
Association[
"Type" -> "EllipticCurve", "CurveName" -> "prime256v1", "R" ->
ByteArray[{63, 206, 128, 26, 8, 98, 13, 127, 155, 77, 28, 109,
127, 131, 181, 72, 12, 233, 255, 113, 50, 41, 68, 60, 176, 134,
219, 28, 96, 233, 234, 145}], "S" ->
ByteArray[{203, 169, 245, 106, 175, 234, 118, 156, 176, 232, 249,
67, 153, 193, 64, 177, 95, 75, 47, 32, 23, 90, 41, 184, 8, 242,
92, 126, 135, 75, 109, 18}], "SignatureType" -> "Deterministic",
"HashingMethod" -> None]], Sequence[
"ConsumedGas" -> 791549625, "Baker" ->
"tz3RB4aoyjov4KEVRbuhvQ1CKJgBJMWhaeB8", "BlockReward" ->
Quantity[40000000, "Mutez"], "BlockFees" ->
Quantity[452892, "Mutez"], "TotalTransactions" -> 61,
"TransactionList" -> {
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"TransactionListDetails" ->
Association[
"Endorsement" -> {
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"Reveal" -> {
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"Delegation" -> {
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"Transaction" -> {
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|
In addition to doing blockchain transactions and blockchain analytics with Wolfram Language, we’re also doing more and more with computational contracts—for which the full-scale computational language character of the Wolfram Language gives unique opportunities (an example being the creation of “oracles” based on our computational knowledge about the world).
In Version 12.1 we introduced ExternalStorageObject, initially supporting IPFS and Dropbox. In Version 12.3 we’ve added support for Amazon S3 (and, yes, you can store and retrieve a whole bucket of files at a time):
✕
ExternalStorageUpload["ExampleData/spikey2.png", "wolfram-bucket", ExternalStorageBase -> "AmazonS3"] |
A necessary step in all sorts of external interactions is authentication. And in Version 12.3 we’ve added support for OAuth 2.0 workflows. You create a SecuredAuthenticationKey:
✕
SecuredAuthenticationKey[<|"Name" -> "Reddit",
"OAuthType" -> "ThreeLegged",
"OAuthVersion" -> "2.0",
"ConsumerKey" -> "" (*Your key here*),
"ConsumerSecret" -> "" (*Your key here*), "ResponseType" -> "code",
"Scopes" -> {"read"}, "ScopeDelimiter" -> " ",
"VerifierInputFunction" -> "WolframConnectorChannel",
"AccessTokenURL" -> "https://www.reddit.com/api/v1/access_token",
"UserAuthorizationURL" ->
"https://www.reddit.com/api/v1/authorize",
"AdditionalParameters" -> <|
"AuthorizationRequest" -> {"duration" -> "permanent"}|>
|>]
|
Then you can make a request using this key:
✕
URLRead["https://oauth.reddit.com/api/search_subreddits" , Authentication -> %] |
You’ll get a browser window that asks you to log in with your account—and then you’ll be off and running.
For many common external services, we have “pre-packaged” ServiceConnect connections. Often these require authentication. And for OAuth-based APIs (like Reddit or Twitter) we have our WolframConnector app that brokers the external part of the authentication. A new feature of Version 12.3 is that you can also use your own external app to broker that authentication, so you’re not limited by the arrangements made with the external service for the WolframConnector app.
Under the hood for everything we’re talking about here is cryptography. And in Version 12.3 we’ve added some new cryptographic capabilities; in particular we now have support for all elliptic curves in the NIST Digital Signature FIPS 186-4 standard, as well as for Edwards curves that will be part of FIPS 186-5.
We’ve packaged all of this to make it very easy to create blockchain wallets, sign transactions, and encode data for blockchains:
✕
BlockchainKeyEncode[PublicKey[
Association[
"Type" -> "EdwardsCurve", "CurveName" -> "ed25519",
"PublicByteArray" ->
ByteArray[{129, 57, 198, 230, 91, 48, 63, 133, 232, 63, 173, 17,
49, 237, 190, 143, 151, 108, 127, 202, 73, 93, 64, 14, 198, 177,
194, 15, 13, 79, 120, 246}],
"PublicCurvePoint" -> {
299335060271590132066951334928298030649197201001541795411746200767\
72068584535,
53585483370699320092407628906864478900713122887718404470323110058\
487397628289}]], "Address", BlockchainBase -> "Tezos"]
|
✕
BlockchainAddressData[%, "DelegateData", BlockchainBase -> "Tezos"] |
Distributed Computing & Its Management
We first introduced parallel computation in Wolfram Language in the mid-1990s, and in Version 7.0 (2008) we introduced functions like ParallelMap and Parallelize. It’s always been straightforward to set up parallel computation on multiple cores of a single computer. But it’s been more complicated when one also wants to use remote computers.
In Version 12.2 we introduced RemoteKernelObject as a symbolic representation of remote Wolfram Language capabilities. Starting in Version 12.2, this was available for one-shot evaluations with RemoteEvaluate. In Version 12.3 we’ve integrated RemoteKernelObject into parallel computation.
Let’s try this for one of my machines. Here’s a remote kernel object that represents a single kernel on it:
✕
RemoteKernelObject["threadripper2"] |
Now we can do a computation there, here just asking for the number of processor cores:
✕
RemoteEvaluate[%, $ProcessorCount] |
Now let’s create a remote kernel object that uses all 64 cores on this machine:
✕
RemoteKernelObject["threadripper2", "KernelCount" -> 64] |
Now I can launch those kernels (and, yes, it’s much faster and more robust than before):
✕
LaunchKernels[%] |
Now I can use this to do parallel computations:
✕
ParallelEvaluate[$ProcessID, %] |
For someone like me who is often involved in doing parallel computations, the streamlining of these capabilities in Version 12.3 will make a big difference.
One feature of functions like ParallelMap is that they’re basically just sending pieces of a computation independently to different processors. Things can get quite complicated when there needs to be communication between processors and everything is happening asynchronously.
The basic science of this is deeply related to the story of multiway graphs and to the origins of quantum mechanics in our Physics Project. But at a practical level of software engineering, it’s about race conditions, thread safety, locking, etc. And in Version 12.3 we’ve added some capabilities around this.
In particular, we’ve added the function WithLock that can lock files (or local objects) during a computation, thereby preventing interference between different processes which attempt to write to the file. WithLock provides a low-level mechanism for ensuring atomicity and thread safety of operations.
There’s a higher-level version of this in LocalSymbol. Say one sets a local symbol to 0:
✕
LocalSymbol["/tmp/counter"] = 0 |
Then launch 40 local parallel kernels (they need to be local so they share files):
✕
LaunchKernels[40]; |
Now, because of locking, the counter will be forced to update sequentially on each kernel:
✕
ParallelEvaluate[LocalSymbol["/tmp/counter"]++] |
✕
LocalSymbol["/tmp/counter"] |
