Introducing J-Language Function: ",." (Commma-dot)
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The document discusses the monadic and dyadic cases of the J symbol ",." (comma-dot). For the monadic case, ",." returns a matrix by raveling (flattening) its argument of any rank (scalar, vector, matrix, or higher-rank array) into a two-column matrix. For the dyadic case, ",." stitches together the items of its left and right arguments by placing their items side-by-side into a new matrix. The lengths of the arguments must match except when one is a scalar, which repeats to fit.
Introducing J-Language Function: ",." (Commma-dot)
- 1. J symbol “ ., ” (comma-dot) Group 6 Hikaru Sugiura
- 2. Outline • Monadic Case • Over 3-rank Array, Matrix, Vector, Scalar • Apply to empty list • Conclusion: Monadic • Dyadic Case • Matrix, Vector • Exception: special case • Error case • Conclusion : Dyadic
- 3. ,. : Monadic Case Items Matrix Ravel Items Definition: y ravels the items of y.
- 4. 18 19 20 21 22 23 24 25 26 Apply to rank-3 array Ravel Items returns the nx(m*o) Matrix for the nxmxo array. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 9 10 11 12 13 14 15 16 17 0 1 2 3 4 5 6 7 8 3rd 2nd 1st m*o m o n n ,. i.3 3 3 Matrix
- 5. Apply to matrix Ravel Items returns the Same Matrix for the matrix. 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 ,. n m 1st 2ndi.3 3
- 6. 0 1 2 Apply to vector Ravel Items returns a nx1 Matrix for the n vector. Shape : 3 1 0 1 2 ,. n 1st i.3
- 7. Apply to scaler Ravel Items returns a 1x1 Matrix for the scaler. 33,. No axis! Shape : 1 1
- 8. Ravel Items returns the Matrix for a scaler, vector, matrix and any size array. i.e. Arg:Rank Result Shape Rank Scalar : 0 1 1 2 n Vector : 1 n 1 2 nxm Matrix : 2 n m 2 nxmxo Array: 3 n m*o 2 Matrix! }
- 9. Apply to Empty list Result : ,. i. 0 0 0 → (empty) Ravel Items returns the 0x0 Matrix for the empty list. Rank : $$ ,. i. 0 0 0 → 2 Shape : $ ,. i. 0 0 0 → 0 0
- 10. Conclusion:Monadic Ravel Items returns the Matrix for the any list Arg:Rank Result Shape Rank Scalar : 0 1 1 2 n Vector : 1 n 1 2 nxm Matrix : 2 n m 2 nxmxo Array: 3 n m*o 2 nxmxo…xz n m*o*…*z 2 ※ n,m,…,z ≧ 0 Effective to over 4-rank Array. Make matrix and possible to process with other one.
- 11. ,. : Dyadic case Stitch Definition: x ,. y the items of x and stitched to the corresponding items of y. X Y,. X Y One Item
- 12. Example 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 ,. 0 1 2 0 1 2 3 4 5 3 4 5 6 7 8 6 7 8 3x6 Matrixi.3 3 i.3 3 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 ,. 0 1 2 3 0 1 2 4 5 6 7 3 4 5 8 9 10 11 6 7 8 i.3 4 i.3 3 • Matrices 3x7 Matrix
- 13. Example 0 1 2 3 4 5 6 7 8 0 1 2,. i.3 3 i.3 • Matrix and Vector 0 1 2 0 3 4 5 1 6 7 8 2 3x4 Matrix 0 1 2 ,. 0 0 1 1 2 2 • Vectors 2x3 Matrix 0 1 2 i.3 0 1 2 0 1 2not! i.3
- 14. Example ,.1 2 • Scalars 1 2 Vector • Scalar and Vector 0 1 2 i.3 3,. 0 3 1 3 2 3 Matrix Repeating to Fit!
- 15. Error Case • Length Error 0 1 2 3 4 5 6 7 8 0 1 3 4 ,. 0 1 2 ,. Matrix and Matrix The lengths of Y-axis Must be matched. Vector and Vector The length Must be matched. 0 1 2 3 ※Scaler automatically match to other item by repeating.
- 16. Conclusion:Dyadic Stitch returns Joint-Item made from (left) and (right). In over 1-rank items, The lengths must be matched. X Y,. X Y One Item