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The APL Wiki logo consists of the following [[numeric]] [[matrix]], where each number indicates a circle radius: | The APL Wiki logo consists of the following [[numeric]] [[matrix]], where each number indicates a circle radius: | ||
< | <syntaxhighlight lang=apl> | ||
⎕IO←0 | ⎕IO←0 | ||
⌊∘.+⍨.5×4!⍨⍳5 | ⌊∘.+⍨.5×4!⍨⍳5 | ||
| Line 17: | Line 17: | ||
== Counting == | == Counting == | ||
=== From 1 or from 0? === | === From 1 or from 0? === | ||
[[File:Computer console.jpg|thumb|A computer console: < | [[File:Computer console.jpg|thumb|A computer console: <syntaxhighlight lang=apl inline>⎕</syntaxhighlight>]] | ||
Whether to count from 0 or from 1 is an old disagreement among programmers. Many APLs let you choose whichever convention you want, but they tend to use 1 by default. To switch convention, we set the variable < | Whether to count from 0 or from 1 is an old disagreement among programmers. Many APLs let you choose whichever convention you want, but they tend to use 1 by default. To switch convention, we set the variable <syntaxhighlight lang=apl inline>⎕IO</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
⎕IO←0 | ⎕IO←0 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| Line 27: | Line 27: | ||
We can already now observe a couple of APL's characteristics… | We can already now observe a couple of APL's characteristics… | ||
=== No reserved words === | === No reserved words === | ||
The name < | The name <syntaxhighlight lang=apl inline>⎕IO</syntaxhighlight> begins with the special ''Quad character'' (a stylised console) which symbolises the computer system itself. APL has no reserved words. Rather, all built-in constants, variables, functions and operators have the prefix <syntaxhighlight lang=apl inline>⎕</syntaxhighlight> indicating that they are part of the system. Because of this, we call them [[quad name]]s. | ||
=== Assignments === | === Assignments === | ||
[[Assignment]] is not done with < | [[Assignment]] is not done with <syntaxhighlight lang=apl inline>=</syntaxhighlight> like in many other programming languages, but rather with <syntaxhighlight lang=apl inline>←</syntaxhighlight> which also indicates the direction of the assignment: Whatever is on the right gets put into the name on the left. | ||
=== Generating indices === | === Generating indices === | ||
The < | The <syntaxhighlight lang=apl inline>⍳</syntaxhighlight> function takes a number ''N'' and [[index generator|generates indices]] until is has made ''N'' [[Index|indices]]. Since we set <syntaxhighlight lang=apl inline>⎕IO</syntaxhighlight> to 0, we count from 0 until right before ''N'': | ||
< | <syntaxhighlight lang=apl> | ||
⍳5 | ⍳5 | ||
0 1 2 3 4 | 0 1 2 3 4 | ||
| Line 42: | Line 42: | ||
== How many subsets? == | == How many subsets? == | ||
Consider a bag with four distinct items. If you stick your hand into the bag and pick two items out, how many different possibilities are there for which pair you get out? <math>\{(0,1), (0,2), (0,3), (1,2), (1,3), (2,3)\}</math>. APL can tell you this with the [[Binomial]] (< | Consider a bag with four distinct items. If you stick your hand into the bag and pick two items out, how many different possibilities are there for which pair you get out? <math>\{(0,1), (0,2), (0,3), (1,2), (1,3), (2,3)\}</math>. APL can tell you this with the [[Binomial]] (<syntaxhighlight lang=apl inline>!</syntaxhighlight>) function: | ||
< | <syntaxhighlight lang=apl> | ||
2!4 | 2!4 | ||
6 | 6 | ||
| Line 51: | Line 51: | ||
Anyway, how many sets of four could you pick? Obviously, only one; all the items: | Anyway, how many sets of four could you pick? Obviously, only one; all the items: | ||
< | <syntaxhighlight lang=apl> | ||
4!4 | 4!4 | ||
1 | 1 | ||
| Line 57: | Line 57: | ||
=== Automatic mapping === | === Automatic mapping === | ||
A really nice feature of APL is its [[Array model|array]]-orientation. For computations which are defined on single elements ([[scalar functions]]), [[wikipedia:map (higher-order function)|map]]ping is implicit: | A really nice feature of APL is its [[Array model|array]]-orientation. For computations which are defined on single elements ([[scalar functions]]), [[wikipedia:map (higher-order function)|map]]ping is implicit: | ||
< | <syntaxhighlight lang=apl> | ||
0 1 2 3 4!4 | 0 1 2 3 4!4 | ||
1 4 6 4 1 | 1 4 6 4 1 | ||
| Line 64: | Line 64: | ||
== Order of evaluation == | == Order of evaluation == | ||
We want to generate the indices using [[Iota]] (< | We want to generate the indices using [[Iota]] (<syntaxhighlight lang=apl inline>⍳</syntaxhighlight>)… | ||
< | <syntaxhighlight lang=apl> ⍳5!4 | ||
| | ||
</syntaxhighlight> | </syntaxhighlight> | ||
That didn't work! This is because APL dispenses with traditional mathematics' confusing and inconsistent [[precedence]] order<ref>[[Ken Iverson|K.E. Iverson]], Appendix A: [https://www.jsoftware.com/papers/EvalOrder.htm Conventions Governing Order of Evaluation], Elementary Functions: An Algorithmic Treatment). Science Research Associates, 1966</ref>, replacing it with a simple right-to-left rule: | That didn't work! This is because APL dispenses with traditional mathematics' confusing and inconsistent [[precedence]] order<ref>[[Ken Iverson|K.E. Iverson]], Appendix A: [https://www.jsoftware.com/papers/EvalOrder.htm Conventions Governing Order of Evaluation], Elementary Functions: An Algorithmic Treatment). Science Research Associates, 1966</ref>, replacing it with a simple right-to-left rule: | ||
< | <syntaxhighlight lang=apl> | ||
(⍳5)!4 | (⍳5)!4 | ||
1 4 6 4 1 | 1 4 6 4 1 | ||
| Line 75: | Line 75: | ||
== Swapping arguments == | == Swapping arguments == | ||
If the arguments of < | If the arguments of <syntaxhighlight lang=apl inline>!</syntaxhighlight> were swapped, we wouldn't need that parenthesis. Enter the [[operator]] (higher-order function) [[swap]] (<syntaxhighlight lang=apl inline>⍨</syntaxhighlight>) which takes a [[dyadic]] function on its left and creates a new [[derived function]] which is identical to the original, but has swapped arguments: | ||
< | <syntaxhighlight lang=apl> | ||
4!⍨⍳5 | 4!⍨⍳5 | ||
1 4 6 4 1 | 1 4 6 4 1 | ||
| Line 83: | Line 83: | ||
== A number is a number == | == A number is a number == | ||
The next step is to halve everything: | The next step is to halve everything: | ||
< | <syntaxhighlight lang=apl> | ||
.5×4!⍨⍳5 | .5×4!⍨⍳5 | ||
0.5 2 3 2 0.5 | 0.5 2 3 2 0.5 | ||
| Line 93: | Line 93: | ||
== Tables == | == Tables == | ||
Remember the multiplication table from school? | Remember the multiplication table from school? | ||
< | <syntaxhighlight lang=apl> | ||
1 2 3 4 5∘.×1 2 3 4 5 | 1 2 3 4 5∘.×1 2 3 4 5 | ||
1 2 3 4 5 | 1 2 3 4 5 | ||
| Line 102: | Line 102: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Any function can be made into a table with the [[Outer Product]]: | Any function can be made into a table with the [[Outer Product]]: | ||
< | <syntaxhighlight lang=apl> | ||
1 2 3 4 5∘.+1 2 3 4 5 | 1 2 3 4 5∘.+1 2 3 4 5 | ||
2 3 4 5 6 | 2 3 4 5 6 | ||
| Line 112: | Line 112: | ||
=== Using an argument twice === | === Using an argument twice === | ||
It gets tedious to type the same argument twice. Enter the [[self]]ie operator which shares its [[Glyph|symbol]] with the above-mentioned [[swap]] operator. There's no ambiguity here. ''Swap'' swaps the two arguments, while ''selfie'' uses a single argument twice: | It gets tedious to type the same argument twice. Enter the [[self]]ie operator which shares its [[Glyph|symbol]] with the above-mentioned [[swap]] operator. There's no ambiguity here. ''Swap'' swaps the two arguments, while ''selfie'' uses a single argument twice: | ||
< | <syntaxhighlight lang=apl> | ||
∘.+⍨1 2 3 4 5 | ∘.+⍨1 2 3 4 5 | ||
2 3 4 5 6 | 2 3 4 5 6 | ||
| Line 121: | Line 121: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
We'll use this in our logo expression: | We'll use this in our logo expression: | ||
< | <syntaxhighlight lang=apl> | ||
∘.+⍨.5×4!⍨⍳5 | ∘.+⍨.5×4!⍨⍳5 | ||
1 2.5 3.5 2.5 1 | 1 2.5 3.5 2.5 1 | ||
| Line 130: | Line 130: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
== Rounding == | == Rounding == | ||
The last step is to round these numbers down. Traditional mathematics writes ''floor'' as <math>\lfloor x \rfloor</math> but APL is regular, so no function is denoted by two separated symbols. If the function takes a single argument, then the symbol will be on the left, so we write [[floor]] as < | The last step is to round these numbers down. Traditional mathematics writes ''floor'' as <math>\lfloor x \rfloor</math> but APL is regular, so no function is denoted by two separated symbols. If the function takes a single argument, then the symbol will be on the left, so we write [[floor]] as <syntaxhighlight lang=apl inline>⌊x</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
⌊∘.+⍨.5×4!⍨⍳5 | ⌊∘.+⍨.5×4!⍨⍳5 | ||
1 2 3 2 1 | 1 2 3 2 1 | ||
| Line 140: | Line 140: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Those are our radii! Let's save them: | Those are our radii! Let's save them: | ||
< | <syntaxhighlight lang=apl> | ||
sizes←⌊∘.+⍨.5×4!⍨⍳5 | sizes←⌊∘.+⍨.5×4!⍨⍳5 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| Line 146: | Line 146: | ||
== Placing the circles == | == Placing the circles == | ||
=== Pairwise summation === | === Pairwise summation === | ||
Now that we have our radii, we need to figure out where to put our circles. The horizontal pair-wise sum shows how much adjacent circles "reach out" towards each other. [[N-wise Reduce]] solves that. Here, < | Now that we have our radii, we need to figure out where to put our circles. The horizontal pair-wise sum shows how much adjacent circles "reach out" towards each other. [[N-wise Reduce]] solves that. Here, <syntaxhighlight lang=apl inline>/</syntaxhighlight> is an operator which takes the plus function and applies it in-between the elements of each horizontal run of length ''N'' (the left argument) in the right argument: | ||
< | <syntaxhighlight lang=apl> | ||
2+/sizes | 2+/sizes | ||
3 5 5 3 | 3 5 5 3 | ||
| Line 156: | Line 156: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
=== Finding maxima === | === Finding maxima === | ||
Since the circles line up on a grid, we need the maximum for each horizontal space, that is for each column. APL uses [[dyad]]ic < | Since the circles line up on a grid, we need the maximum for each horizontal space, that is for each column. APL uses [[dyad]]ic <syntaxhighlight lang=apl inline>a⌈b</syntaxhighlight> as the [[maximum]] of ''a'' and ''b''. <syntaxhighlight lang=apl inline>⌈⌿</syntaxhighlight> is the columnar maximum-[[reduce|reduction]]: | ||
< | <syntaxhighlight lang=apl> | ||
⌈⌿2+/sizes | ⌈⌿2+/sizes | ||
8 11 11 8 | 8 11 11 8 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
But obviously, we can't let the circles touch, so we add 1. This gives us all the centre-to-centre distances from the neighbours on the left (or above): | But obviously, we can't let the circles touch, so we add 1. This gives us all the centre-to-centre distances from the neighbours on the left (or above): | ||
< | <syntaxhighlight lang=apl> | ||
1+⌈⌿2+/sizes | 1+⌈⌿2+/sizes | ||
9 12 12 9 | 9 12 12 9 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
We also need an "offset" of the left/top-most circles which don't have any neighbours, so we prepend a 0: | We also need an "offset" of the left/top-most circles which don't have any neighbours, so we prepend a 0: | ||
< | <syntaxhighlight lang=apl> | ||
0,1+⌈⌿2+/sizes | 0,1+⌈⌿2+/sizes | ||
0 9 12 12 9 | 0 9 12 12 9 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Finally, we compute the total offset for each column/row by finding the running total of the offsets: | Finally, we compute the total offset for each column/row by finding the running total of the offsets: | ||
< | <syntaxhighlight lang=apl> | ||
⎕←offsets←0,+\1+⌈⌿2+/sizes | ⎕←offsets←0,+\1+⌈⌿2+/sizes | ||
0 9 21 33 42 | 0 9 21 33 42 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Assigning to the special ''Quad character'' (the stylised console, < | Assigning to the special ''Quad character'' (the stylised console, <syntaxhighlight lang=apl inline>⎕</syntaxhighlight>) sends the the pass-though value from the assignment to the console (the screen), as it would otherwise be hidden. (We call assignment ''[[shy]]''.) <syntaxhighlight lang=apl inline>\</syntaxhighlight> is just like <syntaxhighlight lang=apl inline>/</syntaxhighlight> but gives us the intermediate values. | ||
=== Combining arrays === | === Combining arrays === | ||
We need our offsets in two dimensions. So we need to combine the elements of < | We need our offsets in two dimensions. So we need to combine the elements of <syntaxhighlight lang=apl inline>offset</syntaxhighlight> with themselves in all possible combinations. | ||
The [[Rank operator]] (< | The [[Rank operator]] (<syntaxhighlight lang=apl inline>⍤</syntaxhighlight>) allows you to specify what you want paired up with what. In our case, we want individual numbers (which have zero [[axes]]) paired up with other individual numbers. As pairing up the numbers in <syntaxhighlight lang=apl inline>3 1 4</syntaxhighlight> with those in <syntaxhighlight lang=apl inline>2 7 1</syntaxhighlight>: | ||
< | <syntaxhighlight lang=apl> | ||
3 1 4(,⍤0)2 7 1 | 3 1 4(,⍤0)2 7 1 | ||
3 2 | 3 2 | ||
| Line 189: | Line 189: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
But we want to pair up each of the individual offsets with each of all the offsets. The offsets form a list, so we want to apply this pair-wise pairing function between each number and the entire list, as in: | But we want to pair up each of the individual offsets with each of all the offsets. The offsets form a list, so we want to apply this pair-wise pairing function between each number and the entire list, as in: | ||
< | <syntaxhighlight lang=apl> | ||
3 1 4(,⍤0⍤0 1)2 7 1 | 3 1 4(,⍤0⍤0 1)2 7 1 | ||
3 2 | 3 2 | ||
| Line 203: | Line 203: | ||
4 1 | 4 1 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Since we want the offsets paired up with themselves, we can use < | Since we want the offsets paired up with themselves, we can use <syntaxhighlight lang=apl inline>⍨</syntaxhighlight> again: | ||
< | <syntaxhighlight lang=apl> | ||
,⍤0⍤0 1⍨⍳3 | ,⍤0⍤0 1⍨⍳3 | ||
0 0 | 0 0 | ||
| Line 219: | Line 219: | ||
</syntaxhighlight> | </syntaxhighlight> | ||
The offset pairs form our circle locations: | The offset pairs form our circle locations: | ||
< | <syntaxhighlight lang=apl> | ||
⍴locs←,⍤0⍤0 1⍨offsets | ⍴locs←,⍤0⍤0 1⍨offsets | ||
5 5 2 | 5 5 2 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
that is, it is a 3D array with 5 layers, 5 rows in each layer, and 2 columns in each row. Each row of our result represents an <math>(x,y)</math> value. The first and last layers, which represents the leftmost and rightmost columns of the logo, are: | that is, it is a 3D array with 5 layers, 5 rows in each layer, and 2 columns in each row. Each row of our result represents an <math>(x,y)</math> value. The first and last layers, which represents the leftmost and rightmost columns of the logo, are: | ||
< | <syntaxhighlight lang=apl> | ||
(1↑locs) (¯1↑locs) | (1↑locs) (¯1↑locs) | ||
┌────┬─────┐ | ┌────┬─────┐ | ||
| Line 234: | Line 234: | ||
└────┴─────┘ | └────┴─────┘ | ||
</syntaxhighlight> | </syntaxhighlight> | ||
For example, the second row in the first layer is <math>(x,y)=(0,9)</math>. < | For example, the second row in the first layer is <math>(x,y)=(0,9)</math>. <syntaxhighlight lang=apl inline>↑</syntaxhighlight> is the [[Take]] function, that is, it takes the first ''N'' cells of an array, and a negative value simply means taking from the rear. | ||
== Making <code><circle/></code> tags == | == Making <code><circle/></code> tags == | ||
To help us create our SVG <code><circle/></code> tags, well set up a couple of helper functions. The first function will help us create tag attributes. | To help us create our SVG <code><circle/></code> tags, well set up a couple of helper functions. The first function will help us create tag attributes. | ||
=== Formatting attributes === | === Formatting attributes === | ||
APL uses a [[high minus]] (< | APL uses a [[high minus]] (<syntaxhighlight lang=apl inline>¯</syntaxhighlight>), to indicate that a number is negative. This avoids confusion with the [[negate]] function <syntaxhighlight lang=apl inline>-</syntaxhighlight>. However, SVG uses a regular dash, so we need to change our numeric arrays into character representations (using the [[format]] function, <syntaxhighlight lang=apl inline>⍕</syntaxhighlight>), and [[replace]] all occurrences of the symbol: | ||
< | <syntaxhighlight lang=apl> | ||
'¯'⎕R'-'⍕3 ¯1 2 ¯7 | '¯'⎕R'-'⍕3 ¯1 2 ¯7 | ||
3 -1 2 -7 | 3 -1 2 -7 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
The attribute value needs to be quoted, so we [[catenate|prepend]] (< | The attribute value needs to be quoted, so we [[catenate|prepend]] (<syntaxhighlight lang=apl inline>,</syntaxhighlight>) two quotation marks, and then we [[rotate]] the text one step (left), thereby pushing the first one to the end: | ||
< | <syntaxhighlight lang=apl> | ||
1⌽'""','¯'⎕R'-'⍕3 ¯1 2 ¯7 | 1⌽'""','¯'⎕R'-'⍕3 ¯1 2 ¯7 | ||
"3 -1 2 -7" | "3 -1 2 -7" | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Finally, create the full attribute phrase: | Finally, create the full attribute phrase: | ||
< | <syntaxhighlight lang=apl> | ||
' ','test','=',1⌽'""','¯'⎕R'-'⍕3 ¯1 2 ¯7 | ' ','test','=',1⌽'""','¯'⎕R'-'⍕3 ¯1 2 ¯7 | ||
test="3 -1 2 -7" | test="3 -1 2 -7" | ||
</syntaxhighlight> | </syntaxhighlight> | ||
=== Our first function === | === Our first function === | ||
In the most basic form, a [[dfn]] ("dee fun") is just an expression in curly braces with < | In the most basic form, a [[dfn]] ("dee fun") is just an expression in curly braces with <syntaxhighlight lang=apl inline>⍺</syntaxhighlight> and <syntaxhighlight lang=apl inline>⍵</syntaxhighlight> representing the left and right arguments, just like they are the leftmost and rightmost letters of the [[wikipedia:Greek alphabet|Greek alphabet]]: | ||
< | <syntaxhighlight lang=apl> | ||
Attr←{' ',⍺,'=',1⌽'""','¯'⎕R'-'⍕⍵} | Attr←{' ',⍺,'=',1⌽'""','¯'⎕R'-'⍕⍵} | ||
'test' Attr 3 ¯1 2 ¯7 | 'test' Attr 3 ¯1 2 ¯7 | ||
test="3 -1 2 -7" | test="3 -1 2 -7" | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Notice that assignment works for functions too! Remember the [[#Automatic_mapping|automatic mapping]]? It doesn't apply to user-defined functions, but we can use the [[Each]] operator (< | Notice that assignment works for functions too! Remember the [[#Automatic_mapping|automatic mapping]]? It doesn't apply to user-defined functions, but we can use the [[Each]] operator (<syntaxhighlight lang=apl inline>¨</syntaxhighlight>) instead: | ||
< | <syntaxhighlight lang=apl> | ||
'test' 'foo' Attr¨ 3 ¯1 | 'test' 'foo' Attr¨ 3 ¯1 | ||
┌─────────┬─────────┐ | ┌─────────┬─────────┐ | ||
| Line 270: | Line 270: | ||
=== Flattening enclosed things and enclosing flat things === | === Flattening enclosed things and enclosing flat things === | ||
Next, we make this list of strings (each of which is actually just a character list) into a simple list with the [[enlist]] function (< | Next, we make this list of strings (each of which is actually just a character list) into a simple list with the [[enlist]] function (<syntaxhighlight lang=apl inline>∊</syntaxhighlight>), and use above same concatenation and rotation techniques to finalise our tag: | ||
< | <syntaxhighlight lang=apl> | ||
2⌽'/><tag',∊'test' 'foo'Attr¨ 3 ¯1 | 2⌽'/><tag',∊'test' 'foo'Attr¨ 3 ¯1 | ||
<tag test="3" foo="-1"/> | <tag test="3" foo="-1"/> | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Let's create a dfn for that too: | Let's create a dfn for that too: | ||
< | <syntaxhighlight lang=apl> | ||
Circle←{⊂2⌽'/><circle',∊'cx' 'cy' 'r'Attr¨⍵} | Circle←{⊂2⌽'/><circle',∊'cx' 'cy' 'r'Attr¨⍵} | ||
Circle 3 1 4 | Circle 3 1 4 | ||
| Line 283: | Line 283: | ||
└─────────────────────────────┘ | └─────────────────────────────┘ | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Notice that a put in < | Notice that a put in <syntaxhighlight lang=apl inline>⊂</syntaxhighlight>) which [[enclose]]s the result. This is because I want to deal with these tags as [[scalar]] elements. Now we can create our circles (and show the first three: | ||
< | <syntaxhighlight lang=apl> | ||
3↑circles←,Circle⍤1⊢locs,sizes | 3↑circles←,Circle⍤1⊢locs,sizes | ||
┌─────────────────────────────┬─────────────────────────────┬──────────────────────────────┐ | ┌─────────────────────────────┬─────────────────────────────┬──────────────────────────────┐ | ||
| Line 290: | Line 290: | ||
└─────────────────────────────┴─────────────────────────────┴──────────────────────────────┘ | └─────────────────────────────┴─────────────────────────────┴──────────────────────────────┘ | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Here we're using < | Here we're using <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> again, but this time only with a single argument, so we only specify one rank — the rank of the sub-arrays we want <syntaxhighlight lang=apl inline>Circle</syntaxhighlight> called on. Rows are vector (list), so that's rank 1. The <syntaxhighlight lang=apl inline>⊢</syntaxhighlight> doesn't do anything other than separate <syntaxhighlight lang=apl inline>1</syntaxhighlight> from <syntaxhighlight lang=apl inline>locs</syntaxhighlight>, so the <syntaxhighlight lang=apl inline>⍤</syntaxhighlight> knows what is its right operand (which specifies on what sub-arrays the function left [[operand]] is to be called) and what is its right [[argument]] (which contains the arguments for that function in its sub-arrays). | ||
[[Monad]]ic < | [[Monad]]ic <syntaxhighlight lang=apl inline>,</syntaxhighlight> is called [[Ravel]] as it unravels an array into a vector, but unlike <syntaxhighlight lang=apl inline>∊</syntaxhighlight> it doesn't flatten enclosed elements. | ||
== The <code><svg></code> container == | == The <code><svg></code> container == | ||
[[APL Wiki]] is a [[wikipedia:MediaWiki|MediaWiki]] which has strict requirements on the dimensions of the site logo: | [[APL Wiki]] is a [[wikipedia:MediaWiki|MediaWiki]] which has strict requirements on the dimensions of the site logo: | ||
< | <syntaxhighlight lang=apl> | ||
⎕←dims←∊'width' 'height'Attr¨130 | ⎕←dims←∊'width' 'height'Attr¨130 | ||
width="130" height="130" | width="130" height="130" | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Since the circles on the first row and in the first column are at position 0, we need our SVG to begin a bit further to the top left. Similarly, it needs to end a bit further to the bottom right than the last circle. How much? Well, the maximum radius (which would extend up and to the left) in the first row (and column) is: | Since the circles on the first row and in the first column are at position 0, we need our SVG to begin a bit further to the top left. Similarly, it needs to end a bit further to the bottom right than the last circle. How much? Well, the maximum radius (which would extend up and to the left) in the first row (and column) is: | ||
< | <syntaxhighlight lang=apl> | ||
⌈/1↑sizes | ⌈/1↑sizes | ||
3 | 3 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
But let's add a bit more so the circles don't touch the image edge: | But let's add a bit more so the circles don't touch the image edge: | ||
< | <syntaxhighlight lang=apl> | ||
⎕←pad←2+⌈/1↑sizes | ⎕←pad←2+⌈/1↑sizes | ||
5 | 5 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
=== Taking things to a higher dimension === | === Taking things to a higher dimension === | ||
Finding the centres of the first and last circles with < | Finding the centres of the first and last circles with <syntaxhighlight lang=apl inline>Circle</syntaxhighlight> but this time with a 2-element left argument (this [[take]]s the first 1 layer and the first 1 row of that, etc.), we can find out where to begin, and the size of our image, which makes up the "viewBox" attribute: | ||
< | <syntaxhighlight lang=apl> | ||
⎕←first←1 1↑locs | ⎕←first←1 1↑locs | ||
0 0 | 0 0 | ||
| Line 324: | Line 324: | ||
viewBox="-5 -5 52 52" | viewBox="-5 -5 52 52" | ||
</syntaxhighlight> | </syntaxhighlight> | ||
The extra ravel < | The extra ravel <syntaxhighlight lang=apl inline>,</syntaxhighlight> is because <syntaxhighlight lang=apl inline>begin</syntaxhighlight> and <syntaxhighlight lang=apl inline>size</syntaxhighlight> are matrices, while <syntaxhighlight lang=apl inline>Attr</syntaxhighlight> needs a vector. | ||
Now we construct the opening tag: | Now we construct the opening tag: | ||
< | <syntaxhighlight lang=apl> | ||
⎕←svg←'<svg',dims,viewBox,' xmlns="http://www.w3.org/2000/svg">' | ⎕←svg←'<svg',dims,viewBox,' xmlns="http://www.w3.org/2000/svg">' | ||
<svg width="130" height="130" viewBox="-5 -5 52 52" xmlns="http://www.w3.org/2000/svg"> | <svg width="130" height="130" viewBox="-5 -5 52 52" xmlns="http://www.w3.org/2000/svg"> | ||
| Line 333: | Line 333: | ||
=== In-place modification through assignment === | === In-place modification through assignment === | ||
We can do in-place concatenations to add all the circle tags and the closing tag: | We can do in-place concatenations to add all the circle tags and the closing tag: | ||
< | <syntaxhighlight lang=apl> | ||
100↑svg,←∊circles | 100↑svg,←∊circles | ||
<circle cx="0" cy="0" r="1"/><circle cx="0" cy="9" r="2"/><circle cx="0" cy="21" r="3"/><circle cx=" | <circle cx="0" cy="0" r="1"/><circle cx="0" cy="9" r="2"/><circle cx="0" cy="21" r="3"/><circle cx=" | ||
svg,←'</svg>' | svg,←'</svg>' | ||
</syntaxhighlight> | </syntaxhighlight> | ||
You may recognise the pattern here as [[wikipedia:augmented assignment|augmented assignment]] from C and related programming languages. APL allows you to use any function to modify values in-place. If you are not familiar with this, then just think of < | You may recognise the pattern here as [[wikipedia:augmented assignment|augmented assignment]] from C and related programming languages. APL allows you to use any function to modify values in-place. If you are not familiar with this, then just think of <syntaxhighlight lang=apl inline>name,←value</syntaxhighlight> as <syntaxhighlight lang=apl inline>name←name,value</syntaxhighlight> (but the pass-though value is whatever is on the right of the assignment arrow). | ||
== Doing something with what we made == | == Doing something with what we made == | ||
Now we we can put the SVG data into a native (OS) file: | Now we we can put the SVG data into a native (OS) file: | ||
< | <syntaxhighlight lang=apl> | ||
⎕←svg ⎕NPUT '/tmp/aplwiki.svg' | ⎕←svg ⎕NPUT '/tmp/aplwiki.svg' | ||
850 | 850 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
The result is the number of bytes written (which can vary due to line ending standards). Alternatively, flatten the svg and we can show it in an embedded HTML window: | The result is the number of bytes written (which can vary due to line ending standards). Alternatively, flatten the svg and we can show it in an embedded HTML window: | ||
< | <syntaxhighlight lang=apl> | ||
]html svg | ]html svg | ||
</syntaxhighlight> | </syntaxhighlight> | ||
| Line 353: | Line 353: | ||
== Code == | == Code == | ||
{{Collapse|The function below contains all the code from above. It takes a file name as argument.| | {{Collapse|The function below contains all the code from above. It takes a file name as argument.| | ||
< | <syntaxhighlight lang=apl> | ||
Logo←{ | Logo←{ | ||
sizes←⌊∘.+⍨0.5×4!⍨⍳5 | sizes←⌊∘.+⍨0.5×4!⍨⍳5 | ||