Partition

Classic Edition

The symbol ⊆ (Left Shoe Underbar) is not available in Classic Edition, and Partition is instead represented by ⎕U2286.

Y may be any non-scalar array.

X must be a simple scalar or vector of non-negative integers.

The axis specification is optional. If present, it must be a simple integer scalar or one element array representing an axis of Y. If absent, the last axis is implied.

R is an array of the elements of Y partitioned according to X.

A new partition is started in the result whenever the corresponding element in X is greater than the previous one. Items in Y corresponding to 0s in X are not included in the result.

Note that if ⎕ML≥3, the symbol ⊂ means the same as ⊆.

Examples

      ⎕ML←3

      ]display 1 1 1 2 2 3 3 3⊆'NOWISTHE'
┌→─────────────────┐
│ ┌→──┐ ┌→─┐ ┌→──┐ │
│ │NOW│ │IS│ │THE│ │
│ └───┘ └──┘ └───┘ │
└∊─────────────────┘

      ]display 1 1 1 0 0 3 3 3⊆'NOWISTHE'
┌→────────────┐
│ ┌→──┐ ┌→──┐ │
│ │NOW│ │THE│ │
│ └───┘ └───┘ │
└∊────────────┘

      TEXT←'   NOW     IS      THE      TIME    '
      ]display (' '≠TEXT)⊆TEXT
┌→────────────────────────┐
│ ┌→──┐ ┌→─┐ ┌→──┐ ┌→───┐ │
│ │NOW│ │IS│ │THE│ │TIME│ │
│ └───┘ └──┘ └───┘ └────┘ │
└∊────────────────────────┘

      ]display CMAT←⎕FMT(' ',ROWS),COLS⍪NMAT
┌→─────────────────────────┐
↓           Jan   Feb  Mar │
│ Cakes       0   100  150 │
│ Biscuits    0     0  350 │
│ Buns        0  1000  500 │
└──────────────────────────┘

      ]display (∨⌿' '≠CMAT)⊆CMAT   ⍝ Split at blank cols.
┌→──────────────────────────────┐
↓ ┌→───────┐ ┌→──┐ ┌→───┐ ┌→──┐ │
│ │        │ │Jan│ │ Feb│ │Mar│ │
│ └────────┘ └───┘ └────┘ └───┘ │
│ ┌→───────┐ ┌→──┐ ┌→───┐ ┌→──┐ │
│ │Cakes   │ │  0│ │ 100│ │150│ │
│ └────────┘ └───┘ └────┘ └───┘ │
│ ┌→───────┐ ┌→──┐ ┌→───┐ ┌→──┐ │
│ │Biscuits│ │  0│ │   0│ │350│ │
│ └────────┘ └───┘ └────┘ └───┘ │
│ ┌→───────┐ ┌→──┐ ┌→───┐ ┌→──┐ │
│ │Buns    │ │  0│ │1000│ │500│ │
│ └────────┘ └───┘ └────┘ └───┘ │
└∊──────────────────────────────┘

      ]display N←4 4⍴⍳16
┌→──────────┐
↓ 1  2  3  4│
│ 5  6  7  8│
│ 9 10 11 12│
│13 14 15 16│
└~──────────┘

      ]display 1 1 0 1⊆N
┌→─────────────┐
↓ ┌→──┐   ┌→┐  │
│ │1 2│   │4│  │
│ └~──┘   └~┘  │
│ ┌→──┐   ┌→┐  │
│ │5 6│   │8│  │
│ └~──┘   └~┘  │
│ ┌→───┐  ┌→─┐ │
│ │9 10│  │12│ │
│ └~───┘  └~─┘ │
│ ┌→────┐ ┌→─┐ │
│ │13 14│ │16│ │
│ └~────┘ └~─┘ │
└∊─────────────┘

      ]display 1 1 0 1⊆[1]N
┌→────────────────────────┐
↓ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ │
│ │1 5│ │2 6│ │3 7│ │4 8│ │
│ └~──┘ └~──┘ └~──┘ └~──┘ │
│ ┌→─┐  ┌→─┐  ┌→─┐  ┌→─┐  │
│ │13│  │14│  │15│  │16│  │
│ └~─┘  └~─┘  └~─┘  └~─┘  │
└∊────────────────────────┘