Stencil too heavy

[Yves]

Dear All,
To solve a problem, i use stencil, very elegant.

With

      rank ← 10
      cut ← { ⊃,/ ×/ ⍵ (⌽⍵) (⊖⍵) (⌽⊖⍵) }
      corner ← { ⍵< (⍳2×⍵) ∘.+ (⍳2×⍵) }
      M ← cut corner rank

i produce a base to find neighbors at the east of each one.

      East ← { ×/ ⍵[2;2 3] }
      possible ← East ⌺ 3 3 ⊣ M

and i have WS Full with rank = 821, shape of M is (1642 1642).

But with a standard APL method :

      possible ← { (1↑⍴M)↑[2] (1↓[2]⍵) × (¯1↓[2]⍵) } M

the message WS Full come when rank=3898 and shape of M go up to (7796 7796).

Stencil is very elegant, but too greedy with wide matrice.

A chance ! at this point, rank=1,000 is enough.

Regards,
Yves

[Roger|Dyalog]

If your computation is as simple as you described, you are better off using the standard APL solution.

If there is some benefit to considering the problem as a computation on 3-by-3 neighborhoods, then stencil is worthwhile. Stencil has special code for certain left operand functions and the special code can make a difference in performance. In this case, the applicable special code is:

      ⊢ A←3 3⍴0 0 0 0 1 1 0 0 0
0 0 0
0 1 1
0 0 0
      Est←{+/,A×⍵}

For example:

      M ← cut corner 400 
                              
      cmpx'2=Est⌺3 3⊢M' 'East⌺3 3⊢M'
  2=Est⌺3 3⊢M → 1.50E¯2 |      0%                               
  East⌺3 3⊢M  → 4.55E0  | +30213% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕

That is, 2=Est⌺3 3⊢M gives the same answer as East⌺3 3⊢M but is faster by a factor of 303.

      M←1=?8000 8000⍴2
      cmpx '2=Est⌺3 3⊢M'
1.54E0

I don't know what your workspace size is, but an 8000 8000 boolean matrix takes 8 MB and stencil with Est should work with a reasonable workspace size.

[Yves]

Dear Roger,
Thank you for your light in APL.

If your computation is as simple as you described, you are better off using the standard APL solution.

Of course, you're right.
But stencil is really elegant, and now i use it in handwrite, naturally.

i work in macOS with Daylog APL 64bits v16.0.30781 unicode edition

      ⎕wa
243902952

impossible at this time to change it.

Stencil has special code for certain left operand functions

How can we discover special code or special case ?

Your solution is very efficient. WS is Full with rank = 3845.

Thank You Roger,
Yves

[AndyS|Dyalog]

By default Dyalog APL sets MAXWS to 256MB in version 16.0 (with the exception of the Pi where it's still 64MB).

To set it to a different value (in this example I'm setting it to 1GB):
edit ~/.dyalog/dyalog.config

add the line
export MAXWS=1G

and restart APL .. you should now see ⎕wa return a value close to 1072754280.

Rather than 1G, you could use 1024M for the same size.

[Phil Last]

[...] To set it to a different value (in this example I'm setting it to 1GB):
[...] close to 1072754280.
Rather than 1G, you could use 1024M for the same size.

Surely you mean 1GiB Andy?

But then if you did mean 1GB why 1024M? Wouldn't 1000M be nearer the mark?

IEC 60027-2 - ISO/IEC 80000

[Roger|Dyalog]

Stencil has special code for certain left operand functions

How can we discover special code or special case ?

It is our intention to document all the special codes, but this one may have slipped through the cracks for now. In any case, the special codes for stencil are:

Code: Select all

  {⊢⍵}      {,⍵}      {⊂⍵}

  {+/,⍵}
  {∧/,⍵}    {∨/,⍵}    {=/,⍵}    {≠/,⍵}
       
  {  +/,A×⍵}    {  +/⍪A×⍤2⊢⍵}
  {C<+/,A×⍵}    {C<+/⍪A×⍤2⊢⍵}

C: a single number or a variable whose value is a single number
A: a variable whose value is a rank-2 or -3 array

The comparison can be < ≤ ≥ > = ≠

odd window size; movement 1; matrix argument

You can use the cmpx (compare expression, from dfns workspace) to confirm the presence of special code. For example:

Code: Select all

      M←1=?200 200⍴2

      cmpx '{ +/,⍵}⌺3 3⊢M' '{⊢+/,⍵}⌺3 3⊢M'
  { +/,⍵}⌺3 3⊢M → 6.25E¯5 |       0%                               
  {⊢+/,⍵}⌺3 3⊢M → 1.10E¯1 | +175950% ⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕⎕


The extra ⊢ in the second expression defeats the special code recognizer. As a result the more general code is used and you can see the difference in execution time.

[Yves]

Dear Roger, Andy & All,
Thank you for your help.

Special codes are very intesresting.
Can you explain more about { +/ ⍪ A × ⍤2 ⊢⍵ } ?
i try it with

      ⊢ A ← ? 5 5 ⍴ 9
7 7 8 3 3
2 8 1 4 4
6 8 8 1 6
3 9 3 2 7
3 9 4 2 4
      { +/ ⍪ A × ⍤2 ⊢ ⍵ } ⌺ 3 3 ⊢ A
RANK ERROR
      {+/⍪A×⍤2⊢⍵}⌺3 3⊢A
     ∧

i am not sure to understand why this formula.

Regards,
Yves

[Roger|Dyalog]

{+/⍪A×⍤2⊢⍵}⌺ is like {+/,A×⍵}⌺ but you get to do a whole bunch of matrices all at once. For example:

      b←1=?97 113⍴5

      A←?5 5⍴9
      ⍴ {+/,A×⍤2⊢⍵}⌺5 5 ⊢b
97 113

      A3←?3 5 5⍴9
      ⍴ {+/⍪A3×⍤2⊢⍵}⌺5 5 ⊢b
97 113 3