imit_model / AnyLogic / UsersManual(AnyLogic)

AnyLogic V User’s Manual

Sometimes you may need to modify a submatrix. For instance, you have a block matrix X used in some equations. Blocks A, B, C, and D should be calculated in different ways (by different formulas).

The idea is to calculate the blocks separately and then combine them into one matrix using transforming matrices. To deal the problem with A and B blocks:

1.Define a matrix variable A with dimensions [3,4] and set a necessary formula to it.

2.Define a matrix variable Aleft with dimensions [6,3].

3.Type in the Initial Value property of Aleft the key word identity.

4.Define a matrix variable Aright with dimensions [4,6].

5.Type in the Initial Value property of Aright the keyword identity.

6.Set the formula for X: Aright*A*Aleft.

7.Now block A of X matrix gets the value from variable A and other blocks hold zeros. Block B does not lie on the main diagonal, so the right transforming matrix is not an identity one. We will initialize it in startup code.

8.Define a matrix variable B with dimensions [3,2] and set a necessary formula to it.

9.Define a matrix variable Bleft with dimensions [6,3].

10.Type in the Initial Value property of Bleft the keyword identity.

Table 7. Available operations for matrices

While generating code for a right-hand side, AnyLogic follows these rules:

•If all variables are scalars, the simple code like x*y+z is generated, and the result is treated as scalar.

•Otherwise AnyLogic assumes matrices and generates code like

Matrix.add(Matrix.mult(x,y),z).

To change the order of operations, use the round brackets. For instance, there is a matrix differential equation:

where A, B, X are square matrices n*n; C, D, E – vectors n*1.

The appropriate right-hand side expression of the integral equation is:

- D * ( 5*A + 1/B ) * C.transpose() * E[0]

You can explicitly notify AnyLogic that the equation is of scalar type by placing the ‘#’ symbol at the beginning of expression, e.g. a=#x*y+z. This may result in simulation performance improvement.

The right-hand side of a scalar variable may refer to matrices, if the result of the expression is scalar. In this example, real variable x could be calculated through the formula:

# - D * ( 5*A + 1/B ) * C.transpose()

There is an example. You should get a matrix that is the result of an expression such as:

Z = −D (5A + B−1 ) CT e0

where A, B, X are square matrices n*n; C, D, E – vectors n*1.

Type the following code to create such a matrix:

Matrix Z = D.uminus().times(((A.times(5)).plus(B.inverse()))).times(

C.transpose()).times(E.getMatrix(0,0,0,E.getRowDimension()));

Note that if you write code like A=B, you only let A refer to the same matrix object that B does. If you change matrix B, A changes too, and otherwise. To avoid this dependency you must assign matrix A a copy of matrix B. To make a copy of a matrix, type

A=B.copy();

If you need checking the matrix content at some moment, you can print it out to the global log. Just type in the appropriate place of the event handler the following:

A.print(Engine.log, <number of characters in column>, <number of digits after the decimal>);

To solve a linear equation, write:

Matrix x = A.solve(B)

To get the eigenvalues of a matrix, write:

EigenvalueDecomposition e = A.eig();

double[] eigRe = e.getRealEigenvalues(); // vector of real parts double[] eigIm = e.getImagEigenvalues(); // vector of image parts Matrix V = e.getV(); // matrix of eigenvectors

AnyLogic V User’s Manual

6.2.1Enumerations

Sometimes you need a parameter representing an attribute which can take a finite set of values. For example, you work with colors. You can create an integer parameter representing a color and, e.g., assign number 1 to red color, 2 to green color, 3 to blue one. However, you see only integer numbers in code, but not the names of colors. To increase the readability of code, you should use enumerations. Each enumeration has named elements, each of them having an integer counterpart that is hidden from you. For example, you can define Color enumeration with Red, Green, and Blue elements and use these self-descriptive names instead of integer numbers in code.

Color myColor = Red;

...

myColor = Green;

...

if (myColor == Green) traceln(“I’m green”);

...

6.2.1.1 Defining an enumeration

►To define an enumeration

1.Click the New Enumeration toolbar button, or Choose Insert|New Enumeration… from the main menu. The New Enumeration dialog box is displayed.

Specify the name of the new enumeration, choose the package, which will contain the enumeration, and click OK.

2.Alternatively, in the Project window, right-click the package, which will contain the enumeration, and choose New Enumeration… from the popup menu.

The New Enumeration dialog box is displayed.

Specify the name of the new enumeration and click OK.

An enumeration has the following set of properties:

AnyLogic V User’s Manual

2.Initialize the hyper-array in the Default value combo box.

For example, you can initialize the hyper-array with another one, defined and initialized in the Additional class code code section of the active object class.

►To define a hyper-array variable

1.Select the variable on a structure diagram.

2.In the Properties window, choose the variable type Array.

3.Specify as much dimensions as you need in the table on the right of the Array option. Each row of the table defines one dimension.

To define a new dimension, go to the last row of the table and click the Dimension field. In the combo box, choose an enumeration to be a hyper-array’s subscript.

A hyper-array cannot have a single enumeration as two or more dimensions.

The order of dimensions is also important. You can reorder the dimensions pressing Ctrl+Up and Ctrl+Down.

6.2.3Setting an initial value for a hyper-array

►To set the initial value for a hyper-array

1.Select the variable on the structure diagram.

2.In the Equations section of the Properties window, choose No equation from the Form drop-down list.

3.Specify the Initial Value expression.

There are two different notations for hyper-array constants. We illustrate both notations by hyper-array constants used as initial values of some variables. The subscripts are listed before each constant in the order of dimension declarations in these variables.

Suppose you create a model of a nation’s health, describing some social or health processes in respect to different groups of population. Separate people by three characteristics: gender,