In J dictionary, verb The shape of a result is the frame (relative to the cells to which the verb applies) catenated with the shape produced by applying the verb to the individual cells. Commonly these individual shapes agree, but if not, they are first brought to a common rank by introducing leading unit axes to any of lower rank, and are then brought to a common shape by *padding* with an appropriate *fill* element: space for a character array, 0 for a numeric array, and a boxed empty list for a boxed array. For example:
i."0 s=: 2 3 4 >'I';'was';'here' 0 1 0 0 I 0 1 2 0 was 0 1 2 3 here On Dec 13, 2017 7:59 AM, "TongKe Xue" <[email protected]> wrote: > Both explanations are great. Unfortunately, I asked an XY problem. Let > me re-ask as follows: > > I am trying to write a mini interpreter for J. > > How do we execute "i. (2 2 $ 1 2 3 4)" ? > > After parsing, and evaluating the (), we are left with: > > 1. execute monad "i." on tensor of (shape: [2 2], data: [[1 2] [3 4]]) > > 2. Next, we look up the rank of "i." and see that it is [1 _ _] > > 3. Therefore, we split [[1 2] [3 4]] into a frame, containing two cells: > cell1 = [1 2] > cell2 = [3 4] > > 4. We execute i. on each cell, getting: > cell1-output = [0 1] > cell2-output = [[0 1 2 3] [4 5 6 7] [8 9 10 11]] > > 5. At this point, I am expecting: error! tensor shape mismatch > > 6. Instead, J appears to just 0 pad the cells until they are of the same > size. > > Is there some fundamental principle why the 0 padding is happening, or > does J have a hard coded piece of logic that says: > when merging the output-cells of a frame, if the output-cells are of > different shape, 0-pad them all until they are of the same shape ? > > Thanks, > --TongKe > > > > On Tue, Dec 12, 2017 at 4:35 PM, Brian Schott <[email protected]> > wrote: > > The rank of monadic i. is 1 as determined by the following. > > i. b. 0 > > 1 _ _ > > > > Consider the following where the rows and column lengths of i. 1 2 are > > made to match those of i. 3 4. > > > > (i. 1 2),:i. 3 4 > > 0 1 0 0 > > 0 0 0 0 > > 0 0 0 0 > > > > 0 1 2 3 > > 4 5 6 7 > > 8 9 10 11 > > > > But that may not be explanation enough. > > > > On Tue, Dec 12, 2017 at 5:49 PM, TongKe Xue <[email protected]> wrote: > > > >> Hi, > >> > >> > >> I understand what (2 2 $ 1 2 3 4) does. > >> I understand what i. 1 2 does > >> I understand what i. 3 4 does. > >> > >> I have read http://www.jsoftware.com/help/ > jforc/loopless_code_i_verbs_ > >> have_r.htm#_Toc191734331 > >> > >> I understand the concept of verb-rank, of frames + cells, of > >> "promoting one frame to another if they share the same prefix." > >> > >> I don't understand how the 0 padding in > >> > >> i. (2 2 $ 1 2 3 4) works > >> > >> > >> What is the mechanism by which 0-padding is happening? > >> > >> > >> Thanks, > >> --TongKe > >> > >> > >> ==== > >> > >> 2 2 $ 1 2 3 4 > >> > >> 1 2 > >> > >> 3 4 > >> > >> i. 1 2 > >> > >> 0 1 > >> > >> i. 3 4 > >> > >> 0 1 2 3 > >> > >> 4 5 6 7 > >> > >> 8 9 10 11 > >> > >> i. (2 2 $ 1 2 3 4) > >> > >> 0 1 0 0 > >> > >> 0 0 0 0 > >> > >> 0 0 0 0 > >> > >> > >> 0 1 2 3 > >> > >> 4 5 6 7 > >> > >> 8 9 10 11 > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > > > > > -- > > (B=) <-----my sig > > Brian Schott > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
