Checking Array Size with size in Fortran

Arrays are one of the most commonly used data structures in programming, especially in scientific computing and numerical simulations. In Fortran, arrays are crucial for storing collections of data, whether it’s a series of numbers, a matrix, or higher-dimensional datasets. Understanding the size of an array is often necessary for various operations, such as loops, memory management, or data manipulation.

The size function in Fortran is a powerful tool used to return the total number of elements in an array. This post will delve into the use of the size function in Fortran, explaining its syntax, usage, and real-world applications.

Understanding the size Function in Fortran

In Fortran, the size function is used to return the number of elements in an array along a specified dimension or for the entire array if no dimension is specified.

Syntax:

result = size(array, dimension)

• array: The array whose size you want to determine. It can be a one-dimensional, two-dimensional, or multi-dimensional array.
• dimension (optional): The dimension along which you want to find the size. If not provided, the function returns the total number of elements in the entire array.

Return Value:

• If the dimension argument is provided, the size function returns the size along that specific dimension.
• If the dimension argument is omitted, it returns the total number of elements in the array.

For example:

• If array is a 1D array of size n, size(array) will return n.
• If array is a 2D array of size m x n, size(array) will return m * n, unless you specify one dimension.

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Basic Usage of size in Fortran

Example 1: Getting the Size of a One-Dimensional Array

program array_size_example
integer :: arr(5)
integer :: arr_size
! Assign values to the array elements
arr = [1, 2, 3, 4, 5]
! Use the size function to get the total number of elements
arr_size = size(arr)
! Print the result
print *, "Array size: ", arr_size
end program array_size_example

Explanation:

• In this program, an integer array arr of size 5 is declared and initialized with the values [1, 2, 3, 4, 5].
• The size function is used to get the total number of elements in the array. Since arr contains 5 elements, the size(arr) function returns 5.
• The result is printed out, which shows the array’s size.

Output:

Array size:            5

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Getting the Size of Multi-Dimensional Arrays

Fortran also supports multi-dimensional arrays. The size function can be used to determine the size along specific dimensions of a multi-dimensional array. By default, if no dimension is specified, size will return the total number of elements in the entire array.

Example 2: Getting the Size of a Two-Dimensional Array

program array_size_2d
integer :: arr(3, 4)
integer :: arr_size
! Assign values to the 3x4 matrix
arr = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], shape(arr))
! Get the total number of elements in the array
arr_size = size(arr)
! Print the result
print *, "Total number of elements in the 2D array: ", arr_size
end program array_size_2d

Explanation:

• The array arr is a 2D array with dimensions 3 x 4 (3 rows and 4 columns). We use the reshape function to initialize the array with the values from 1 to 12.
• The size function returns the total number of elements in the array. Since the array is 3 x 4, the total number of elements is 12, and size(arr) will return 12.

Output:

Total number of elements in the 2D array:        12

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Getting the Size Along Specific Dimensions

You can also use the size function to determine the size of an array along a specific dimension. For a 2D array, this could be the number of rows (dimension 1) or the number of columns (dimension 2).

Example 3: Getting the Size Along Specific Dimensions

program array_size_dimensions
integer :: arr(3, 4)
integer :: rows, cols
! Initialize the 2D array
arr = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], shape(arr))
! Get the number of rows (size along the first dimension)
rows = size(arr, 1)
! Get the number of columns (size along the second dimension)
cols = size(arr, 2)
! Print the results
print *, "Number of rows: ", rows
print *, "Number of columns: ", cols
end program array_size_dimensions

Explanation:

• In this example, arr is a 2D array of size 3 x 4.
• The size(arr, 1) function returns the number of rows, which is 3.
• The size(arr, 2) function returns the number of columns, which is 4.
• The results are printed out, showing the number of rows and columns separately.

Output:

Number of rows:            3
Number of columns:        4

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Using size with Multi-Dimensional Arrays

The size function can be applied to arrays with more than two dimensions as well. The same logic applies: you can get the size along a specific dimension or the total number of elements in the entire array.

Example 4: Using size with a Three-Dimensional Array

program array_size_3d
integer :: arr(2, 3, 4)
integer :: arr_size, dim1, dim2, dim3
! Initialize a 3D array
arr = reshape([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], shape(arr))
! Get the total number of elements in the 3D array
arr_size = size(arr)
! Get the size along each dimension
dim1 = size(arr, 1)
dim2 = size(arr, 2)
dim3 = size(arr, 3)
! Print the results
print *, "Total number of elements: ", arr_size
print *, "Size along dimension 1: ", dim1
print *, "Size along dimension 2: ", dim2
print *, "Size along dimension 3: ", dim3
end program array_size_3d

Explanation:

• arr is a 3D array with dimensions 2 x 3 x 4, which has a total of 2 * 3 * 4 = 24 elements.
• The size(arr) function returns the total number of elements in the array.
• The size(arr, 1) function returns 2, the size along the first dimension (the number of “layers”).
• The size(arr, 2) function returns 3, the size along the second dimension (the number of rows per layer).
• The size(arr, 3) function returns 4, the size along the third dimension (the number of columns per row).

Output:

Total number of elements:           24
Size along dimension 1:            2
Size along dimension 2:            3
Size along dimension 3:            4

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Real-World Applications of size

The size function is commonly used in many real-world scenarios, such as:

1. Matrix Operations:

In matrix operations, you often need to know the size of matrices to perform tasks like matrix multiplication or solving systems of linear equations. The size function can be used to check if the matrices have compatible dimensions before performing the operation.

2. Memory Allocation:

In large-scale scientific simulations, you might need to dynamically allocate memory for arrays. The size function can help check the dimensions of arrays and ensure that sufficient memory is allocated.

3. Iterative Algorithms:

In algorithms that involve looping through array elements, such as numerical methods or data processing, the size function helps in determining the bounds of loops based on the array size.