Getting Started with Simulations

To start numerical simulations, we first need the ability to set the initial condition. It will also be a good excercise for Paraiso building blocks, so let's give it a try. Please look at the example.

table :: Named (StaticValue TArray Double)
table = "table" `isNameOf` StaticValue TArray undefined

createBuilder :: Builder Vec2 Int Annotation ()
createBuilder = do
  x01 <- bind $ (cast $ loadIndex (Axis 0)) 
              / (cast $ broadcast $ loadSize (Axis 0))
  y01 <- bind $ (cast $ loadIndex (Axis 1)) 
              / (cast $ broadcast $ loadSize (Axis 1))
  x <- bind $ 4 * (x01-0.5)
  y <- bind $ 5 * (y01-0.5)
  z <- bind $ atan((1- x^2 - (y-(x^2)**(1/3))^2)*10)
  store table z

The Generator.hs makes a bit tedious use of casts and broadcasts we have just learned, to calculate x and y coordinates in real number inbetween 0 and 1 (they are namely x01 and y01.) See how input and output types for casts and broadcasts are inferred. The index and size are of type Int (as specified in the type annotation for createBuilder) while x01, y01, x, y and z are all of type (Builder of) Double because table has that type and we cannot convert type without an explicit cast. The careful reader also might have noticed that 1/3 is treated as Double instead of just being truncated to 0.

Now, Paraiso and the author give hearts to the readers! Thank you!