Compare for equality.

Compare for inequality.

Compare for ordering.

Compare for ordering.

Compare for ordering.

Compare for ordering.

Return the maximum.

Return the minimum.

Implement the if-then-else operator.

Return an integral with the specified derivative and initial value.

To create a loopback, you should use the recursive do-notation. It allows defining the differential equations unordered as in mathematics:

model = 
  mdo a <- integ (- ka * a) 100
      b <- integ (ka * a - kb * b) 0
      c <- integ (kb * b) 0
      let ka = 1
          kb = 1
      runDynamicsInStopTime $ sequence [a, b, c]

Like integ but allows either setting a new Left integral value, or integrating using the Right derivative directly within computation.

This function always uses Euler's method.

Return the first order exponential smooth.

To create a loopback, you should use the recursive do-notation with help of which the function itself is defined:

smoothI x t i =
  mdo y <- integ ((x - y) / t) i
      return y

Return the first order exponential smooth.

This is a simplified version of the smoothI function without specifing the initial value.

Return the third order exponential smooth.

To create a loopback, you should use the recursive do-notation with help of which the function itself is defined:

smooth3I x t i =
  mdo y  <- integ ((s2 - y) / t') i
      s2 <- integ ((s1 - s2) / t') i
      s1 <- integ ((x - s1) / t') i
      let t' = t / 3.0
      return y

Return the third order exponential smooth.

This is a simplified version of the smooth3I function without specifying the initial value.

Return the n'th order exponential smooth.

The result is not discrete in that sense that it may change within the integration time interval depending on the integration method used. Probably, you should apply the discreteDynamics function to the result if you want to achieve an effect when the value is not changed within the time interval, which is used sometimes.

Return the n'th order exponential smooth.

This is a simplified version of the smoothNI function without specifying the initial value.

Return the first order exponential delay.

To create a loopback, you should use the recursive do-notation with help of which the function itself is defined:

delay1I x t i =
  mdo y <- integ (x - y / t) (i * t)
      return $ y / t

Return the first order exponential delay.

This is a simplified version of the delay1I function without specifying the initial value.

Return the third order exponential delay.

Return the third order exponential delay.

This is a simplified version of the delay3I function without specifying the initial value.

Return the n'th order exponential delay.

Return the n'th order exponential delay.

This is a simplified version of the delayNI function without specifying the initial value.

Return the forecast.

The function has the following definition:

forecast x at hz =
  do y <- smooth x at
     return $ x * (1.0 + (x / y - 1.0) / at * hz)

Return the trend.

The function has the following definition:

trend x at i =
  do y <- smoothI x at (x / (1.0 + i * at))
     return $ (x / y - 1.0) / at

Retun the sum for the difference equation. It is like an integral returned by the integ function, only now the difference is used instead of derivative.

As usual, to create a loopback, you should use the recursive do-notation.

Like diffsum but allows either setting a new Left sum value, or adding the Right difference.

Lookup x in a table of pairs (x, y) using linear interpolation.

Lookup x in a table of pairs (x, y) using stepwise function.

Return the delayed value using the specified lag time. This function is less accurate than delayByDT.

Return the delayed value using the specified lag time and initial value. Because of the latter, it allows creating a loop back. This function is less accurate than delayIByDT.

Return the delayed value by the specified positive number of integration time steps used for calculating the lag time.

Return the delayed value by the specified initial value and a positive number of integration time steps used for calculating the lag time. It allows creating a loop back.

Computation that returns 0 until the step time and then returns the specified height.

Computation that returns 1, starting at the time start, and lasting for the interval width; 0 is returned at all other times.

Computation that returns 1, starting at the time start, and lasting for the interval width and then repeats this pattern with the specified period; 0 is returned at all other times.

Computation that returns 0 until the specified time start and then slopes upward until the end time and then holds constant.

Return the Net Present Value (NPV) of the stream computed using the specified discount rate, the initial value and some factor (usually 1).

It is defined in the following way:

npv stream rate init factor =
  mdo let dt' = liftParameter dt
      df <- integ (- df * rate) 1
      accum <- integ (stream * df) init
      return $ (accum + dt' * stream * df) * factor

Return the Net Present Value End of period (NPVE) of the stream computed using the specified discount rate, the initial value and some factor.

It is defined in the following way:

npve stream rate init factor =
  mdo let dt' = liftParameter dt
      df <- integ (- df * rate / (1 + rate * dt')) (1 / (1 + rate * dt'))
      accum <- integ (stream * df) init
      return $ (accum + dt' * stream * df) * factor