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22 <p class=
"p1">// The J programming language is a successor of APL.
<http://www.jsoftware.com
></p>
23 <p class=
"p1">// These languages are made for processing arrays of data and are able to express
</p>
24 <p class=
"p1">// complex notions of iteration implicitly.
</p>
25 <p class=
"p1">// The following are some concepts borrowed from or inspired by J.
</p>
26 <p class=
"p1">// Thinking about multidimensional arrays can be both mind bending and mind expanding.
</p>
27 <p class=
"p1">// It may take some effort to grasp what is happening in these examples.
</p>
28 <p class=
"p2"><br></p>
29 <p class=
"p1">// iota fills an array with a counter
</p>
30 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
2,
3,
3);
</p>
31 <p class=
"p1"><span class=
"s2">z.rank;
</span>//
3 dimensions
</p>
32 <p class=
"p1"><span class=
"s2">z.shape;
</span>// gives the sizes of the dimensions
</p>
33 <p class=
"p1"><span class=
"s2">z = z.reshape(
3,
2,
3);
</span>// reshape changes the dimensions of an array
</p>
34 <p class=
"p1"><span class=
"s2">z.rank;
</span>//
3 dimensions
</p>
35 <p class=
"p3">z.shape;
</p>
36 <p class=
"p2"><br></p>
37 <p class=
"p1">// fill a
2D array
</p>
38 <p class=
"p3"><span class=
"s1">Array
</span>.fill2D(
3,
3,{
1.0.rand.round(
0.01)});
</p>
39 <p class=
"p2"><br></p>
40 <p class=
"p3"><span class=
"s1">Array
</span>.fill2D(
2,
3,{
<span class=
"s1">|i,j|
</span> i@j});
</p>
41 <p class=
"p2"><br></p>
42 <p class=
"p1">// fill a
3D array
</p>
43 <p class=
"p3"><span class=
"s1">Array
</span>.fill3D(
2,
2,
2,{
1.0.rand.round(
0.01)});
</p>
44 <p class=
"p2"><br></p>
45 <p class=
"p3"><span class=
"s1">Array
</span>.fill3D(
2,
2,
2,{
<span class=
"s1">|i,j,k|
</span> `[i,j,k]});
</p>
46 <p class=
"p2"><br></p>
47 <p class=
"p2"><br></p>
48 <p class=
"p1">// using dup to create arrays
</p>
49 <p class=
"p3">(
1.
.4) dup:
3;
</p>
50 <p class=
"p3">100.rand dup:
10;
</p>
51 <p class=
"p3">{
100.rand} dup:
10;
</p>
52 <p class=
"p3">{
100.rand} dup:
3 dup:
4;
</p>
53 <p class=
"p3">{{
100.rand} dup:
3} dup:
4;
</p>
54 <p class=
"p3">{
<span class=
"s1">|i|
</span> i.squared} dup:
10;
</p>
55 <p class=
"p3">{
<span class=
"s1">|i|
</span> i.nthPrime} dup:
10;
</p>
56 <p class=
"p2"><br></p>
57 <p class=
"p1">// ! is an abbreviation of dup
</p>
58 <p class=
"p3">(
1.
.4) !
3;
</p>
59 <p class=
"p3">100.rand !
10;
</p>
60 <p class=
"p3">{
100.rand} !
10;
</p>
61 <p class=
"p3">{
100.rand} !
3 !
4;
</p>
62 <p class=
"p3">{{
100.rand} !
3} !
4;
</p>
63 <p class=
"p3">{
<span class=
"s1">|i|
</span> i.squared} !
10;
</p>
64 <p class=
"p3">{
<span class=
"s1">|i|
</span> i.nthPrime} !
10;
</p>
65 <p class=
"p2"><br></p>
66 <p class=
"p1">// other ways to do the same thing:
</p>
67 <p class=
"p1"><span class=
"Apple-tab-span"> </span>// partial application
</p>
68 <p class=
"p3"><span class=
"s1">_
</span>.squared !
10;
</p>
69 <p class=
"p3"><span class=
"s1">_
</span>.nthPrime !
10;
</p>
70 <p class=
"p2"><br></p>
71 <p class=
"p1"><span class=
"Apple-tab-span"> </span>// operating on a list
</p>
72 <p class=
"p3">(
0.
.9).squared;
</p>
73 <p class=
"p3">(
0.
.9).nthPrime;
</p>
74 <p class=
"p2"><br></p>
75 <p class=
"p1">// operator adverbs
</p>
76 <p class=
"p1">// Adverbs are a third argument passed to binary operators that modifies how they iterate over
</p>
77 <p class=
"p1">// SequenceableCollections or Streams.
</p>
78 <p class=
"p1">// see the Adverbs help file
</p>
79 <p class=
"p3">[
10,
20,
30,
40,
50] + [
1,
2,
3];
<span class=
"s3">// normal
</span></p>
80 <p class=
"p3">[
10,
20,
30,
40,
50] +.f [
1,
2,
3];
<span class=
"s3">// folded
</span></p>
81 <p class=
"p3">[
10,
20,
30,
40,
50] +.s [
1,
2,
3];
<span class=
"s3">// shorter
</span></p>
82 <p class=
"p3">[
10,
20,
30,
40,
50] +.x [
1,
2,
3];
<span class=
"s3">// cross
</span></p>
83 <p class=
"p3">[
10,
20,
30,
40,
50] +.t [
1,
2,
3];
<span class=
"s3">// table
</span></p>
84 <p class=
"p2"><br></p>
85 <p class=
"p1">// operator depth.
</p>
86 <p class=
"p1">// J has a concept called verb rank, which is probably too complex to understand and implement
<span class=
"Apple-converted-space"> </span></p>
87 <p class=
"p1">// in SC, but operator depth is similar and simpler.
</p>
88 <p class=
"p1">// A binary operator can be given a depth at which to operate
</p>
89 <p class=
"p1">// negative depths iterate the opposite operand.
</p>
90 <p class=
"p1">// These are better understood by example.
</p>
91 <p class=
"p1">// It is not currently possible to combine adverb and depth.
</p>
92 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
3,
3);
</p>
93 <p class=
"p3">y = [
100,
200,
300];
</p>
94 <p class=
"p3">z + y;
</p>
95 <p class=
"p1"><span class=
"s2">z +
.0 y;
</span>// same as the above. y added to each row of z
</p>
96 <p class=
"p1"><span class=
"s2">z +
.1 y;
</span>// y added to each column of z
</p>
97 <p class=
"p1"><span class=
"s2">z +
.2 y;
</span>// y added to each element of z
</p>
98 <p class=
"p1"><span class=
"s2">z +.-
1 y;
</span>// z added to each element of y
</p>
99 <p class=
"p2"><br></p>
100 <p class=
"p1">// deepCollect operates a function at different dimensions or depths in an array.
</p>
101 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
3,
2,
3);
</p>
102 <p class=
"p3">f = {
<span class=
"s1">|item|
</span> item.reverse };
</p>
103 <p class=
"p3">z.deepCollect(
0, f);
</p>
104 <p class=
"p3">z.deepCollect(
1, f);
</p>
105 <p class=
"p3">z.deepCollect(
2, f);
</p>
106 <p class=
"p2"><br></p>
107 <p class=
"p3">f = {
<span class=
"s1">|item|
</span> item.stutter };
</p>
108 <p class=
"p3">z.deepCollect(
0, f);
</p>
109 <p class=
"p3">z.deepCollect(
1, f);
</p>
110 <p class=
"p3">z.deepCollect(
2, f);
</p>
111 <p class=
"p2"><br></p>
112 <p class=
"p1">// slice can get sections of multidimensional arrays.
</p>
113 <p class=
"p1">// nil gets all the indices of a dimension
</p>
114 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
4,
5);
</p>
115 <p class=
"p3">z.slice(
<span class=
"s1">nil
</span>, (
1.
.3));
</p>
116 <p class=
"p3">z.slice(
2, (
1.
.3));
</p>
117 <p class=
"p3">z.slice((
2.
.3), (
0.
.2));
</p>
118 <p class=
"p3">z.slice((
1.
.3),
3);
</p>
119 <p class=
"p3">z.slice(
2,
3);
</p>
120 <p class=
"p2"><br></p>
121 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
3,
3,
3);
</p>
122 <p class=
"p3">z.slice([
0,
1],[
1,
2],[
0,
2]);
</p>
123 <p class=
"p3">z.slice(
<span class=
"s1">nil
</span>,
<span class=
"s1">nil
</span>,[
0,
2]);
</p>
124 <p class=
"p3">z.slice(
1);
</p>
125 <p class=
"p3">z.slice(
<span class=
"s1">nil
</span>,
1);
</p>
126 <p class=
"p3">z.slice(
<span class=
"s1">nil
</span>,
<span class=
"s1">nil
</span>,
1);
</p>
127 <p class=
"p3">z.slice(
<span class=
"s1">nil
</span>,
2,
1);
</p>
128 <p class=
"p3">z.slice(
<span class=
"s1">nil
</span>,
1,(
1.
.2));
</p>
129 <p class=
"p3">z.slice(
1,[
0,
1]);
</p>
130 <p class=
"p3">z.flop;
</p>
131 <p class=
"p2"><br></p>
132 <p class=
"p1">// sorting order
</p>
133 <p class=
"p2"><br></p>
134 <p class=
"p1"><span class=
"s2">z = {
100.rand}.dup(
10);
</span>// generate a random array;
</p>
135 <p class=
"p1">// order returns an array of indices representing what would be the sorted order of the array.
</p>
136 <p class=
"p3">o = z.order;
<span class=
"Apple-converted-space"> </span></p>
137 <p class=
"p1"><span class=
"s2">y = z[o];
</span>// using the order as an index returns the sorted array
</p>
138 <p class=
"p2"><br></p>
139 <p class=
"p1">// calling order on the order returns an array of indices that returns the sorted array to the
<span class=
"Apple-converted-space"> </span></p>
140 <p class=
"p1">// original scrambled order
</p>
141 <p class=
"p3">p = o.order;
<span class=
"Apple-converted-space"> </span></p>
142 <p class=
"p3">x = y[p];
</p>
143 <p class=
"p2"><br></p>
144 <p class=
"p1">// bubbling wraps an item in an array of one element. it takes the depth and levels as arguments.
</p>
145 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
4,
4);
</p>
146 <p class=
"p3">z.bubble;
</p>
147 <p class=
"p3">z.bubble(
1);
</p>
148 <p class=
"p3">z.bubble(
2);
</p>
149 <p class=
"p3">z.bubble(
0,
2);
</p>
150 <p class=
"p3">z.bubble(
1,
2);
</p>
151 <p class=
"p3">z.bubble(
2,
2);
</p>
152 <p class=
"p1">// similarly, unbubble unwraps an Array if it contains a single element.
</p>
153 <p class=
"p3">5.unbubble;
</p>
154 <p class=
"p3">[
5].unbubble;
</p>
155 <p class=
"p3">[[
5]].unbubble;
</p>
156 <p class=
"p3">[[
5]].unbubble(
0,
2);
</p>
157 <p class=
"p3">[
4,
5].unbubble;
</p>
158 <p class=
"p3">[[
4],[
5]].unbubble;
</p>
159 <p class=
"p3">[[
4],[
5]].unbubble(
1);
</p>
160 <p class=
"p3">z.bubble.unbubble;
</p>
161 <p class=
"p3">z.bubble(
1).unbubble(
1);
</p>
162 <p class=
"p3">z.bubble(
2).unbubble(
2);
</p>
163 <p class=
"p2"><br></p>
164 <p class=
"p1">// laminating with the +++ operator
</p>
165 <p class=
"p1">// the +++ operator takes each item from the second list and appends it to the corresponding item
</p>
166 <p class=
"p1">// in the first list. If the second list is shorter, it wraps.
</p>
167 <p class=
"p3">z =
<span class=
"s1">Array
</span>.iota(
5,
2);
</p>
168 <p class=
"p3">z +++ [
77,
88,
99];
</p>
169 <p class=
"p3">z +++ [[
77,
88,
99]];
</p>
170 <p class=
"p3">z +++ [[[
77,
88,
99]]];
</p>
171 <p class=
"p3">z +++ [ [[
77]],[[
88]],[[
99]] ];
</p>
172 <p class=
"p1">// same as:
</p>
173 <p class=
"p3">z +++ [
77,
88,
99].bubble;
</p>
174 <p class=
"p3">z +++ [
77,
88,
99].bubble(
0,
2);
</p>
175 <p class=
"p3">z +++ [
77,
88,
99].bubble(
1,
2);
</p>
176 <p class=
"p2"><br></p>
177 <p class=
"p3">z +++ [
11,
22,
33].pyramidg;
</p>
178 <p class=
"p3">z +++ [
11,
22,
33].pyramidg.bubble;
</p>
179 <p class=
"p3">z +++ [[
11,
22,
33].pyramidg];
</p>
180 <p class=
"p3">z +++ [[[
11,
22,
33].pyramidg]];
</p>
181 <p class=
"p2"><br></p>
182 <p class=
"p2"><br></p>
184 <p class=
"p3">z = (
1.
.4);
</p>
185 <p class=
"p3">10.do {
<span class=
"s1">|i|
</span><span class=
"Apple-converted-space"> </span></p>
186 <p class=
"p3"><span class=
"Apple-tab-span"> </span><span class=
"Apple-tab-span"> </span><span class=
"Apple-tab-span"> </span>z.pyramid(i+
1).postln;
</p>
187 <p class=
"p3"><span class=
"Apple-tab-span"> </span><span class=
"Apple-tab-span"> </span><span class=
"Apple-tab-span"> </span>z.pyramidg(i+
1).postln;
</p>
188 <p class=
"p3"><span class=
"Apple-tab-span"> </span><span class=
"Apple-tab-span"> </span><span class=
"Apple-tab-span"> </span><span class=
"s4">""</span>.postln;
</p>
191 <p class=
"p2"><br></p>
192 <p class=
"p1">// reshapeLike allows you to make one nested array be restructured in the same manner as another.
</p>
193 <p class=
"p2"><br></p>
194 <p class=
"p3">a = [[
10,
20],[
30,
40,
50],
60,
70, [
80,
90]];
</p>
195 <p class=
"p3">b = [[
1,
2, [
3,
4], [[
5],
6],
7],
8, [[
9]]];
</p>
196 <p class=
"p3">a.reshapeLike(b);
</p>
197 <p class=
"p3">b.reshapeLike(a);
</p>
198 <p class=
"p2"><br></p>
199 <p class=
"p1">// If the lengths are different, the default behaviour is to wrap:
</p>
200 <p class=
"p2"><br></p>
201 <p class=
"p3">a = [[
10,
20],[
30,
40,
50]];
</p>
202 <p class=
"p3">b = [[
1,
2, [
3,
4], [[
5],
6],
7],
8, [[
9]]];
</p>
203 <p class=
"p3">a.reshapeLike(b);
</p>
204 <p class=
"p2"><br></p>
205 <p class=
"p1">// but you can specify other index operators:
</p>
206 <p class=
"p2"><br></p>
207 <p class=
"p3">a.reshapeLike(b,
<span class=
"s5">\foldAt
</span>);
</p>
208 <p class=
"p2"><br></p>
209 <p class=
"p3">a.reshapeLike(b,
<span class=
"s5">\clipAt
</span>);
</p>
210 <p class=
"p2"><br></p>
211 <p class=
"p3">a.reshapeLike(b,
<span class=
"s5">\at
</span>);
</p>
212 <p class=
"p2"><br></p>
213 <p class=
"p1">// allTuples will generate all combinations of the sub arrays
</p>
214 <p class=
"p3">[[
1,
2,
3], [
4,
5],
6].allTuples;
</p>
215 <p class=
"p3">[[
1,
2,
3], [
4,
5,
6,
7], [
8,
9]].allTuples;
</p>
216 <p class=
"p2"><br></p>
217 <p class=
"p2"><br></p>
218 <p class=
"p2"><br></p>
