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Description
The Simulation window contains an O-Matrix function that simulates values for the State vector . The Simulation window is an O-Matrix editor and as such you can perform standard editing commands within the window and using the Edit option from the O-Matrix menu bar. A specification of the Simulation function follows:


sim
The return value is a double-precision matrix containing the simulated State vector values. The column dimension of the return value must be equal to the number of elements in the initial state estimate . The row dimension of the return value determines the number of time points in the simulation. The (k,i)th element of the return value is the ith element of the State vector at the kth time index.

Example
The following is a picture of the Simulation window for the example in EXAMPLE.KBF .



function sim() begin
This line begins the definition of the O-Matrix sim function which has no parameters.

nk        = 10
amplitude = 20d0
These two lines set the number of time points and the amplitude of the sine wave in the simulation. points and the

#
east      = 50d0 + seq(nk)
This sets east to the double-precision column vector of length nk. The first value is 51, the second value is 52 and so on. Note that, in O-Matrix, a binary operation between an integer value and a double-precision value has a double-precision result.

theta     = seq(nk) * 2 * PI / nk
This sets theta to the double-precision column vector of length nk. The first value is pi / nk, the second value is pi / nk and so on.

north     = amplitude * sin(theta)
This sets north to a double-precision column vector of length nk. The kth element is equal to
	amplitude sin(k 2 pi / nk)

deast     = fill(1., nk, 1)
This sets deast to a single-precision column vector of length nk that has all its element equal to one. This is equal to the derivative of east with respect to time. (The single-precision data type is referred to as real in O-Matrix.)

dnorth    = amplitude * 2 * pi * cos(theta) / nk
This sets dnorth to a double-precision column vector of length nk. The kth element of dnorth is equal to the derivative of the function
	amplitude sin( (t - 50) 2 pi / nk)
with respect to t evaluated at t = k.

return [east, north, deast, dnorth]
This sets the return value of the sim function to a double-precision matrix with nk rows and 4 columns. The first column contains the values in east, the second north, the third deast, and the fourth dnorth.

end
This statement terminates the sim function definition.