Empty Arrays

Empty arrays can function as a kind of null element for certain general operations such as concatenation operations or general formulations of certain kinds of equation systems. An empty array can not be constructed by { } or [ ]. Instead an empty array is created using some other constructor from which the type can be deduced, or explicilty declared as a variable. Array variables of unspecified size can be set equal to or assigned empty array values.

1 Empty Arrays

class Empty Real f[0] = fill(1.,0); //An empty vector of type Real[0] since 1. is Real Real x[0]; // An empty vector variable x of type Real[0] Real[0, 3] A; // An empty matrix variable A Real B[5, 0], C[0, 0]; // Empty matrices B and C //Real A[:, :] = fill(0.0, 0, 1); // A Real 0 x 1 matrix //Boolean B[:, :, :] = fill (false, 0, 1, 0); // A Boolean 0 x 1 x 0 array //The code used the previous two lines, and the omc compiler gave errors //due to declaration of variables with same name with different type. //After changing the variable names to A2 and B2 the problem was fixed. Real A2[:, :] = fill(0.0, 0, 1); // A Real 0 x 1 matrix Boolean B2[:, :, :] = fill (false, 0, 1, 0); // A Boolean 0 x 1 x 0 end Empty;

1.1 Simulation of Empty

simulate( Empty )

2 Adding Empty Arrays

class AddEmpty Real[3, 0] A, B; Real[0, 0] C; Real ab[3, 0] = A + B; // Fine, the result is an empty matrix of type Real[3, 0] //Real ac = A + C; // Error, incompatible types Real[3, 0] and Real[0, 0] end AddEmpty;

2.1 Simulation of AddEmpty

simulate( AddEmpty )

3 Using Empty Arrays

The ABCDsystem model below shows how the equation section will shrink to y = D*u when some variables are empty arrays.

model ABCDsystem parameter Integer n = 0; Real u[5] = {15, 4, 3, 9, 11}; Real x[n]; Real y[3]; Real A[n, n], B[n, 5], C[3, n]; Real D[3, 5] = fill(1, 3, 5); equation der(x) = A*x + B*u; // This will disappear since x is empty y = C*x + D*u; // Which is: y = D*u end ABCDsystem;

3.1 Simulation of ABCDsystem

simulate( ABCDsystem)
plot({y[2],n})

Take a look at the results at time=0:

val(D[2, 2],0)
val(y[2],0)
val(u[1],0)