Module: Mathpack::Functional

Defined in:
lib/mathpack/functional.rb

Constant Summary collapse

@@minus = 
-> f,g { -> x { f.(x) - g.(x) } }
@@div = 
-> f,g { -> x { f.(x) / g.(x) } }
@@mult = 
-> f,g { -> x { f.(x) * g.(x) } }
@@norm = 
-> f   { -> x { f.(x).abs } }
@@const = 
-> const { -> x { const} }
@@plus_eps = 
-> eps { -> f { -> x { f.(x + eps) } } }
@@min_eps = 
-> eps { -> f { -> x { f.(x - eps) } } }
@@inf = 
-> f,g { -> x { f.(x) < g.(x) } }
@@lim = 
-> f,eps,prec {
  -> x {
    @@inf.(@@norm.(@@minus.(@@plus_eps.(eps/2.0).(f), @@plus_eps.(eps).(f))) , @@const.(prec) ).(x) ? @@plus_eps.(eps).(f).(x) : @@lim.(f,eps/2.0,prec).(x)
  }
}
@@derivative_sheme = 
-> f {
  -> x {
    -> eps {
      @@div.( @@minus.(@@plus_eps.(eps).(f), @@min_eps.(eps).(f) ), @@mult.(@@const.(2), @@const.(eps))).(x)
    }
  }
}
@@derivate = 
-> f{
  -> x {
    @@lim.(@@derivative_sheme.(f).(x),1, 1e-16).(0)
  }
}
@@n_times = 
-> n,f {
  n == 1 ? f : -> x { f.(@@n_times.(n - 1,f).(x))}
}
@@nth_derivator = 
-> n {
  @@n_times.(n,@@derivate)
}

Class Method Summary collapse

Class Method Details

.derivative(n, &f) ⇒ Object 



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# File 'lib/mathpack/functional.rb', line 42

def self.derivative(n, &f)
  @@nth_derivator.(n).(f)
end