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(Sparse matrices, continued fimpage 10.) to be currently active in the sparse matrix. OUTOF-SARRAY unwires the element from the sparse matrix and places it on the available list. Ofcourse, actually manipulating matrix members means your code has to locate a particular element within the matrix. You accomplish this with the word S [ I, which accepts row and column coordinates atop the stack. S [ ] will return the sparse-matrix identifier of the element at that location, or NIL if the coordinates are empty. S [ 1 is only as smart as it can be. Notice that the structure I've described allows you to locate a member of a sparse array by walking either the row-based linked list to that member or the column-based linked list. S [ 1 would be really smart if it followed : ZAP-SMATRIX ( -- ) ROWS ARRAY @ DISPOSPTR COLS-ARRAY @ DISPOSPTR SMATRIX - BASE @ - DISPOSPTR \ .................................................... \ Place a sparse matrix element on the available list. : ON SMATRIX AVAIL ( i -- ) I . 2DROP SGTRIX AVAIL-BASE @ \ Fetch old head OVER & SMATRIX . RIGHT w ! \ Store it SMATRIX AVAIL BASE ! - - \ Element is new head \ .................................................... \ Fetch a matrix array element from the available list : FROM SMATRIX-AVAIL (--i) SMATRIX AVAIL-BASE @ \ Fetch head of list DUP NIL= \ List empty ABORT" No more array space" DUP &SMATRIX.RIGHT W@ \ Fetch pointer to next SMATRIX AVAIL BASE ! - - \ Return the element number of an element at index idx in a \ vector. \ Returns i=element # if found, NIL otherwise. This word \ also sets the PREV ELEM variable for attaching/detaching \ elements from vectors. : ( idx -- i ) R/C BASE @ W@ \ Fetch base of vector DUP-PREV - ELEM W ! \ Initial previous element / 1 BEGIN DUP NIL = \ At end? IF SWAP DROP EXIT \ Return NIL if so whatever list had the fewest ENDIF 2DUP &SMATRIX.IDX C@ \ Fetch index number of elements between the list head and the target element. of course, there's no j way S [ 1 can know this precisely without actually counting the intervening membersbut to do that would mean S [ I would have to walk both lists to the target and compare 2DUP = \ Did we find a match? IF 2DROP SWAP DROP \ Clear stack if so EXIT ENDIF > \ Are we past where we should look? WHILE DUP PREV ELEM W! \ Save wrevious element &SMATRIX:NEXT W@ \ Fetch next element REPEAT NIL \ Didn't find it ... return NIL . \ ............................................................. the results. So S [ 1 simply chooses the path most likely to be shortest, which is the path \ Prepare to place a sparse matrix element in a vector. \ i is the sparse matrix element. We assume that &SMATRIX.NEXT \ and &SMATRIX.IDX have been set properly. \ Returns: identified by the smaller coordinate. (I.e., if the row coordinate specified is smaller than \ flag = 0 if i is NOT in the vector \ flag = 1 if i is in the vector \ flag = 2 if someone else is in the vector where i wants to be \ n = predecessor of i in the vector, NIL if i is or should be the column coordinate, s [ ] searches the row list.) I Conclusion As mentioned above, there are plenty of opportunities for ( \ the head member of the vector. : WHERE IN VECTOR ( i -- n flag ) DUP &SMATRIX. IDX C@ \ Search the vector PREV ELEM W@ -ROT \ Save previous element DUP NIL = \ Was i found? IF 2DROP 0 \ Nope ELSE = \ Yes..izzit me? Or someone else? IF 1 \ It's me! extending the code. Increasing the row and column compo- ENDIF ELSE 2 ENDIF \ It's someone else! November 1993 December 38 Forth Dimensions
\ Locate i in row. \ See WHERE-IN-VECTOR for results on parameter stack. : WHERE IN-ROW ( i -- n flag ) NEXT-IS RIGHT \ Set NEXT function IDX IS ?OL \ Index to modify is COL W H E ~ - IN-VECTOR \ Find him \ Locate i in column. \ See WHERE-IN-VECTOR for results on parameter stack. : WHERE IN COL ( i -- n flag ) NEXT-7s %WN \ Set NEXT function IDX IS ROW \ Index to modify is ROW WHERE - YN - VECTOR \ Find him \ ........................................ \ ** INSERTING/REMOVING MATRIX ELEMENTS ** \ ........................................ \ Wire a sparse matrix element into a row or column vector. \ i is the sparse matrix element, n is the predecessor in the \ vector. n = NIL if i is to be wired in at the head of the list : WIRE-IN ( n i -- ) OVER NIL = \ Wiring in at head? IFSWAP DROP \ Discard NIL R/C BASE @ W@ \ Get old head OVER &SMATRIX .NEXT w ! \ Old head is our next R/C BASE @ W! \ We are new head ELSE OVER &SMATRIX.NEXT W@ \ Fix our next OVER &SMATRIX.NEXT W! SWAP &SMATRIX.NEXT W! \ Fix predecessor next ENDIF \ Unwire a sparse matrix element from a row or column vector. \ Stack acts same as WIRE-IN. : UNWIRE ( n i -- ) OVER NIL = \ Are we head? IFSWAP DROP \ Discard NIL &SMATRIX.NEXT W@ \ Our next is new head R/C BASE @ W! ELSE &SMATRIX .NEXT W@ \ Our next ... SWAP &SMATRIX.NEXT W! \ ... is predecessor's next ENDIF \ Given i -- index to a sparse matrix element -- link this \ element into the sparse matrix at row,col. : INTO - SMATRIX ( row col i -- ) >R \ Save i \ Set the row & column members OVER R@ &SMATRIX.ROW C! \ Set row DUP R@ &SMATRIX. COL C ! \ Set column \ Wire element into row SWAP SET ROW BASE \ Set the row base address R@ WHERETIN - %W \ Locate where to wire in O= \ Flag=O means slot is free IF R@ WIRE-IN \ Wire him in ELSE ." Error attaching to row" CR ABORT ENDIF \ Wire new element into column SET - COL - BASE \ Set the column base addres nents of an element would allow for truly gargantuan sparse matrices. I suppose if you needed sparse multi- dimensional arrays, you could add the necessary anchoring arrays, extend the element structure, and add the necessary words for access to element components. Off the top of my head, I can't imagine an application for such structures.. . but I'll bet there's one out there somewhere. Rick Grehan is the Technical Director of BYTE Labs. He wrole the code for this article with CreativeSolutions' MacForth. Forth Dimensions 39 November 1993 December
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