In this section, we will delve into multi-dimensional arrays in COBOL. Multi-dimensional arrays are a powerful feature that allows you to handle complex data structures efficiently. By the end of this section, you will understand how to declare, initialize, and manipulate multi-dimensional arrays in COBOL.

1. Definition: Multi-dimensional arrays are arrays of arrays, allowing for more complex data structures.
2. Declaration: How to declare multi-dimensional arrays in COBOL.
3. Initialization: Methods to initialize multi-dimensional arrays.
4. Accessing Elements: Techniques to access and manipulate elements within multi-dimensional arrays.
5. Practical Examples: Real-world scenarios where multi-dimensional arrays are useful.

In COBOL, multi-dimensional arrays are declared using the OCCURS clause. Here is the syntax for declaring a two-dimensional array:

• MULTI-DIM-ARRAY: The name of the array.
• FIRST-DIMENSION OCCURS 10 TIMES: The first dimension of the array, which can hold 10 elements.
• SECOND-DIMENSION OCCURS 5 TIMES: The second dimension of the array, nested within the first dimension, which can hold 5 elements.
• ELEMENT PIC 9(2): The data type and size of each element in the array.

Initialization of multi-dimensional arrays can be done using the VALUE clause or through procedural code. Here is an example of initializing a two-dimensional array:

• PERFORM VARYING I FROM 1 BY 1 UNTIL I > 2: Outer loop to iterate over the first dimension.
• PERFORM VARYING J FROM 1 BY 1 UNTIL J > 3: Inner loop to iterate over the second dimension.
• MOVE 0 TO ELEMENT (I, J): Initializes each element to zero.

Accessing elements in a multi-dimensional array involves specifying the indices for each dimension. Here is an example:

• MOVE 25 TO ELEMENT (1, 1): Assigns the value 25 to the element at the first row and first column.
• DISPLAY ELEMENT (1, 1): Displays the value of the element at the first row and first column.

Let's consider a practical example where we use a two-dimensional array to store and display a multiplication table.

• Data Division: Declares a two-dimensional array MULTI-DIM-ARRAY with 10 rows and 10 columns.
• Procedure Division:
  • First Loop: Fills the array with the product of the row and column indices.
  • Second Loop: Displays the multiplication table.

Task: Write a COBOL program to initialize a 3x3 identity matrix and display it.

Solution:

• Data Division: Declares a 3x3 matrix initialized to zero.
• Procedure Division:
  • First Loop: Sets the diagonal elements to 1.
  • Second Loop: Displays the matrix.

In this section, we covered the following key points about multi-dimensional arrays in COBOL:

• How to declare multi-dimensional arrays using the OCCURS clause.
• Methods to initialize multi-dimensional arrays both declaratively and procedurally.
• Techniques to access and manipulate elements within multi-dimensional arrays.
• Practical examples and exercises to reinforce the concepts.

Understanding multi-dimensional arrays is crucial for handling complex data structures in COBOL, and mastering these concepts will significantly enhance your programming skills.