Operator

4.1.1. Convolution

⎕ ← +/ 2 ¯5 8 9 2 4

equals to:

⎕ ← 2 + ¯5 + 8 + 9 + 2 + 4;
20

4.1.2. Inner Products

⎕ ← 4 2 5 +.× ¯3 8 2;

equals to:

⎕ ← (4 × ¯3) + (2 × 8) + (5 × 2);
14

4.1.3. Outer Products

⎕ ← 4 2 5 ×. ¯3 8;

equals to:

⎕ ← 3 2 ρ (4 × ¯3) (4 × 8) (2 × ¯3) (2 × 8) (5 × ¯3) (5 × 8);
¯12 32
¯6  16
¯15 40

4.1.4. Tensor Transposition with Axis

A ← 3 2 3 ρ 1 ¯5 8 9 2 4 2 ¯5 8 9 2 4 3 ¯5 8 9 2 4;
B ← 0⍉1 A;
C ← 0⍉2 A;
D ← 1⍉2 A;

⎕ ← "A: {ρA}, {A}";
⎕ ← "";
⎕ ← "B: {ρB}, {B}";
⎕ ← "";
⎕ ← "C: {ρC}, {C}";
⎕ ← "";
⎕ ← "D: {ρD}, {D}";
A: 3 2 3, 1 ¯5 8
          9  2 4

          2 ¯5 8
          9  2 4

          3 ¯5 8
          9  2 4
   
B: 2 3 3, 1 ¯5 8
          2 ¯5 8
          3 ¯5 8

          9  2 4
          9  2 4
          9  2 4

C: 3 2 3,  1  2  3
           9  9  9

          ¯5 ¯5 ¯5
           2  2  2

           8  8  8
           4  4  4

D: 3 3 2,  1 9 
          ¯5 2
           8 4

           2 9
          ¯5 2
           8 4

           3 9
          ¯5 2
           8 4
A 0⍉1 A 0⍉2 A 1⍉2 A
1 0 0 0 0 0 0 0 0 0 0 0 0
¯5 0 0 1 0 0 1 1 0 0 0 1 0
8 0 0 2 0 0 2 2 0 0 0 2 0
9 0 1 0 1 0 0 0 1 0 0 0 1
2 0 1 1 1 0 1 1 1 0 0 1 1
4 0 1 2 1 0 2 2 1 0 0 2 1
2 1 0 0 0 1 0 0 0 1 1 0 0
¯5 1 0 1 0 1 1 1 0 1 1 1 0
8 1 0 2 0 1 2 2 0 1 1 2 0
9 1 1 0 1 1 0 0 1 1 1 0 1
2 1 1 1 1 1 1 1 1 1 1 1 1
4 1 1 2 1 1 2 2 1 1 1 2 1
3 2 0 0 0 2 0 0 0 2 2 0 0
¯5 2 0 1 0 2 1 1 0 2 2 1 0
8 2 0 2 0 2 2 2 0 2 2 2 0
9 2 1 0 1 2 0 0 1 2 2 0 1
2 2 1 1 1 2 1 1 1 2 2 1 1
4 2 1 2 1 2 2 2 1 2 2 2 1

4.1.5. Ranked Each

A ← 3 4 ρ 8 9 4 3 9 7 ¯5 3 ¯9 ¯8 7 6;
B ← 3 4 ρ ¯4 3 8 5 ¯8 9 7 0 0 ¯16 ¯23 ¯36;
C ← A + B;
D ← A +⍤2 B;
E ← A +⍤1 B;
F ← A +⍤0 B;
⎕ ← "A: {ρA}, {A}";
⎕ ← "";
⎕ ← "B: {ρB}, {B}";
⎕ ← "";
⎕ ← "C: {ρC}, {C}";
⎕ ← "";
⎕ ← "D: {ρD}, {D}";
⎕ ← "";
⎕ ← "E: {ρE}, {E}";
⎕ ← "";
⎕ ← "F: {ρF}, {F}";
A: 3 4,  8  9  4 3
         9  7 ¯5 3
        ¯9 ¯8  7 6

B: 3 4, ¯4   3   8   5
        ¯8   9   7   0
         {0 ¯16 ¯23 ¯36

C: 3 4,  4  12  12   8
         1  16   2   3
        ¯9 ¯24 ¯16 ¯30

D: 3 4,  4  12  12   8
         1  16   2   3
        ¯9 ¯24 ¯16 ¯30

E: 3 3 4,   4   12  12   8
            5   10   3   8
          ¯13  ¯5   15  11

            0   18  11   3
            1   16   2   3
          ¯17    1  14   6

            8  ¯7  ¯16 ¯33
            9  ¯9  ¯28 ¯33
          ¯9   ¯24 ¯17 ¯30

F: 3 4 3 4,  4    5   0 ¯1
             5    3 ¯9  ¯1
            ¯13 ¯12   3   2

             11  12   7   6
             12  10 ¯2    6
            ¯6  ¯5   10   9

             16  17  12  11
             17  15   3  11
            ¯1    0  15  14

             13  14   9   8
             14  12   0   8
            ¯4  ¯3   12  11



              0   1 ¯4  ¯5
              1 ¯1  ¯13 ¯5
            ¯17 ¯16 ¯1  ¯2

             17  18  13  12
             18  16   4  12
              0   1  16  15

             15  16  11  10
             16  14   2  10
            ¯2  ¯1   14  13

              8   9   4   3
              9   7 ¯5    3
            ¯9  ¯8    7   6



              8   9   4   3
              9   7 ¯5    3
            ¯9  ¯8    7   6

            ¯8  ¯7  ¯12 ¯13
            ¯7  ¯9  ¯21 ¯13
            ¯25 ¯24  ¯9 ¯10

            ¯15 ¯14 ¯19 ¯20
            ¯14 ¯16 ¯28 ¯20
            ¯32 ¯31 ¯16 ¯17

            ¯28 ¯27 ¯32 ¯33
            ¯27 ¯29 ¯41 ¯33
            ¯45 ¯44 ¯29 ¯30

4.1.6. Stencil