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Дата изменения: Mon Feb 13 12:59:10 2006 Дата индексирования: Mon Oct 1 23:23:09 2012 Кодировка: Windows-1251 |
| Lib-DVM interface description (contents) | Part 1 (1-5) |
Part 2 (6-7) |
Part 3 (8-11) |
Part 4 (12-13) |
Part 5 (14-15) |
Part 6 (16-18) |
Part 7 (19) |
| created: february, 2001 | - last edited 03.05.01 - |
12 Renewing shadow edges of distributed array
Let the local part of the distributed array be represented as an aggregate of its elements defined as a set of the index tuples:
{I1 О M1:
I1,init ? I1 ? I1,last }
? . . . ? {Im О Mm:
Im,init ? Im ? Im,last} ? . . . ?
{In О Mn:
In,init ? In ? In,last} ,
where:
| ? | - | symbol of Cartesian product; |
| n | - | rank of the array; |
| Im | - | index variable of the m-th dimension (1 ? m ? n); |
| Im,init | - | the initial value of the index variable of the m-th dimension; |
| Im,last | - | the last value of the index variable of the m-th dimension; |
| Mm | - | the range of values of the index variable of the m-th dimension. |
Suppose that the local part is entirely inside the array (for simplicity). Then low shadow edge of the local part of distributed array of k-th dimension is a set of its elements, defined by a set of the index corteges:
LSBk =
| { I1 | О M1 | : | I1,init | - | FS*LW1 | ? I1 | ? I1,last | + | FS*HW1 | } ? | |||
| . . . | . . . . . . . | . . . . . | . . . . . . . . | . . . . . | . . . . . . . . . | . . . . . . . . | |||||||
| { Ik-1 | О Mk-1 | : | Ik-1,init | - | FS*LWk-1 | ? Ik-1 | ? Ik-1,last | + | FS*HWk-1 | } ? | |||
| { Ik | О Mlow,k | : | Ik,init | - | LWk | ? Ik | ? Ik,last | - | 1 | } ? | |||
| { Ik+1 | О Mk+1 | : | Ik+1,init | - | FS*LWk+1 | ? Ik+1 | ? Ik+1,last | + | FS*HWk+1 | } ? | |||
| . . . | . . . . . . . | . . . . . | . . . . . . . . | . . . . . | . . . . . . . . . | . . . . . . . . | |||||||
| { In | О Mn | : | In,init | - | FS*LWn | ? In | ? In,last | + | FS*HWn | } | |||
| Here: | LWi | - | width of the low part of the shadow edge of i-th dimension; | ||||||||||
| HWi | - | width of the high part of the shadow edge of i-th dimension (parameters LowShdWidthArray and HiShdWidthArray of the functions crtda_ , section 6, and inssh_ , section12.2); | |||||||||||
| FS | - | flag of full edge (parameter *FullShdSignPtr of the function inssh_, section 12.2). | |||||||||||
Similarly high shadow edge of the local part of the distributed array of k-th dimension is defined by the set of index corteges:
HSBk =
| { I1 | О M1 | : | I1,init | - | FS*LW1 | ? I1 | ? I1,last | + | FS*HW1 | } ? |
| . . . | . . . . . . . | . . . . . | . . . . . . . . | . . . . . | . . . . . . . . . | . . . . . . . . | ||||
| { Ik-1 | О Mk-1 | : | Ik-1,init | - | FS*LWk-1 | ? Ik-1 | ? Ik-1,last | + | FS*HWk-1 | } ? |
| { Ik | О Mhigh,k | : | Ik,last | + | 1 | ? Ik | ? Ik,last | + | HWk | } ? |
| { Ik+1 | О Mk+1 | : | Ik+1,init | - | FS*LWk+1 | ? Ik+1 | ? Ik+1,last | + | FS*HWk+1 | } ? |
| . . . | . . . . . . . | . . . . . | . . . . . . . . | . . . . . | . . . . . . . . . | . . . . . . . . | ||||
| { In | О Mn | : | In,init | - | FS*LWn | ? In | ? In,last | + | FS*HWn | } |
The low (high) shadow edge of k-th dimension is called full, if FS=1, and is called low (high) shadow bound, if FS=0. The union of full shadow edges of all dimensions is called full shadow edge of the local part of the distributed array:
FSB = |
n U k = 1 |
( LSBk,FS=1 U HSBk,FS=1 ) = |
||||||||
| n | ||||||||||
| U ( | { I1 | О M1 | : I1,init | - LW1 | ? I1 | ? I1,last | + HW1 | } ? | ||
| k = 1 | …. | .....….. | ........ | ………. | .......... | ........……. | ..........… | |||
| { Ik-1 | О Mk-1 | : Ik-1,init | - LWk-1 | ? Ik-1 | ? Ik-1,last | + HWk-1 | } ? | |||
| { Ik | О Mk | : Ik,init | - LWk | ? Ik | ? Ik,init | - 1 ; | ||||