Mirror of forum.nim-lang.org

6465 :: Dual number type

• whiterock (orginal) [2020-06-22T15:26:03+02:00] view original

  I am trying to implement a dual number type in NIM, but struggling with with, for me, obscure error messages. Most likely I am missing something trivial, but after having poured in more than 2 hours in trying stuff and researching I still could not figure it out. Here's the minimum not working example:

  type
    Dual*[N: static[int], T: SomeFloat | Dual] = object
      real*: T
      dual*: array[N, T]
  
  proc dual*[N: static[int]; T: SomeFloat | Dual](real: T, dual: array[N, T]): Dual[N, T] =
    result.real = real
    result.dual = dual
  
  # scalar multiplication
  proc `*`*[N: static[int]; T: SomeFloat | Dual](x: SomeFloat; y: Dual[N, T]): Dual[N, T] =
    result.real = x * y.real
    for i in 0..N-1:
     result.dual[i] = x * y.dual[i]
  Run

  Testing this gives different errors which I put in the comments above the relevant lines of code.

  # Test
  #let a = dual[2, Dual[2, float]](
  #  dual[2, float](1.0, [0.0, 0.0]),
  #  [dual[2, float](0.0, [0.0, 0.0]), dual[2, float](1.0, [0.0, 0.0])]
  #)
  
  let a = dual(3.0, [1.0, 0.0])
  echo a # works as expected
  
  # Error: cannot instantiate 'Dual[N, T: float or float32 or float64 or Dual]' inside of type definition: '*'; Maybe generic arguments are missing?
  echo 183.0*a
  
  # Error: cannot instantiate: '*[2, float]'
  echo `*`[2, float](183.0, a)
  Run

  Thanks in advance, ~whiterock

---

• jyapayne (orginal) [2020-06-22T15:51:37+02:00] view original

  Replace x: SomeFloat; with x: T; in your multiplication proc definition. The nim compiler can't determine which T you are wanting when there are no parameters with T as the type, so it's telling you that with Maybe generic arguments are missing?.

---

• jyapayne (orginal) [2020-06-22T15:55:06+02:00] view original

  If you want just scalar, you can change the definition of T in this case to:

  # scalar multiplication
  proc `*`*[N: static[int]; T: SomeFloat](x: T; y: Dual[N, T]): Dual[N, T] =
    result.real = x * y.real
    for i in 0..N-1:
     result.dual[i] = x * y.dual[i]
  
  # non-scalar multiplication
  proc `*`*[N: static[int]; T: Dual](x: T; y: Dual[N, T]): Dual[N, T] =
    # implementation here
    discard
  Run

---

• whiterock (orginal) [2020-06-22T22:27:00+02:00] view original

  Thank you, this solves the first problem I had. I don't understand though, why it can infer N from Dual[N, T] but not T. Anyways, the problem remains that scalar multiplication should work for arbitrarily nested duals, i.e.

  let a = dual[2, Dual[2, float]](
    dual[2, float](1.0, [0.0, 0.0]),
    [dual[2, float](0.0, [0.0, 0.0]), dual[2, float](1.0, [0.0, 0.0])]
  )
  Run

  but assuming the type T in Dual[N, T] can only be inferred if provided as another argument, I don't know what the function signature needs to be, so this fails:

  
  # Error: type mismatch: got <float64, Dual[2, Dual[2, system.float]]>
  echo 183.0*a
  Run

  The wanted output is the following just propagating the scalar multiplication through. An analogy I could think of would be viewing matrices as a vector of vectors where one can also propagate the scalar multiplication to the vectors. To be more clear:

  let want_expect = dual[2, Dual[2, float]](
    dual[2, float](183.0, [0.0, 0.0]),
    [dual[2, float](0.0, [0.0, 0.0]), dual[2, float](183.0, [0.0, 0.0])]
  )
  Run

  Thanks in advance, ~whiterock

---

• whiterock (orginal) [2020-07-19T15:09:10+02:00] view original

  anybody? :)

---