Logical Variables in Fortran

Fortran, a powerful programming language widely used in scientific and engineering applications, provides a variety of data types to represent different kinds of information. Among these, logical variables play a crucial role in controlling program flow. Logical variables store true or false values and are often used in conditional statements, loops, and logical expressions. Understanding logical variables is essential for writing robust, readable, and efficient Fortran programs.

1. Introduction to Logical Variables

A logical variable in Fortran can take only one of two values:

• .true.
• .false.

Logical variables are commonly used to represent conditions, flags, or binary states within a program. Unlike integers or real numbers, logical variables are specifically designed for decision-making processes in programs.

Declaration of Logical Variables

The syntax for declaring logical variables is straightforward:

logical :: flag

• logical specifies the type.
• flag is the variable name.

Example 1: Basic Logical Variable

program logical_basic
logical :: flag
flag = .true.
if (flag) then
    print *, "The flag is true"
else
    print *, "The flag is false"
end if
end program logical_basic

Explanation:

• flag is assigned the value .true.
• The if statement checks the condition.
• Depending on the value of flag, the corresponding message is printed.

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2. Using Logical Variables in Conditional Statements

Logical variables are commonly used in if statements to control program flow.

Syntax of IF Statements

if (condition) then
! Statements executed if condition is true
else
! Statements executed if condition is false
end if

Example 2: Logical Variable in IF Statement

program check_flag
logical :: is_valid
is_valid = .false.
if (is_valid) then
    print *, "Input is valid"
else
    print *, "Input is not valid"
end if
end program check_flag

Explanation:

• is_valid is assigned .false.
• The else branch executes because the condition is false.

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3. Logical Operators

Logical variables can be combined using logical operators to form complex conditions.

Common Logical Operators

• .and. : Logical AND
• .or. : Logical OR
• .not. : Logical NOT
• .eqv. : Logical equivalence
• .neqv. : Logical non-equivalence

Example 3: Logical Operators

program logical_operators
logical :: a, b, c
a = .true.
b = .false.
c = a .and. b
print *, "a .and. b =", c
c = a .or. b
print *, "a .or. b =", c
c = .not. a
print *, ".not. a =", c
end program logical_operators

Output:

a .and. b = F
a .or. b = T
.not. a = F

Explanation:

• .and. evaluates to true only if both operands are true.
• .or. evaluates to true if at least one operand is true.
• .not. reverses the logical value.

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4. Logical Expressions

Logical expressions combine relational operators with logical variables to produce true or false results.

Relational Operators

• == : equal
• /= : not equal
• > : greater than
• < : less than
• >= : greater than or equal
• <= : less than or equal

Example 4: Logical Expressions

program logical_expression
integer :: x
logical :: result
x = 10
result = (x > 5) .and. (x < 20)
if (result) then
    print *, "x is between 5 and 20"
else
    print *, "x is outside the range"
end if
end program logical_expression

Explanation:

• (x > 5) .and. (x < 20) evaluates to .true.
• The if statement uses the result to control program flow.

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5. Logical Variables in Loops

Logical variables are often used in loops to control iteration, especially in do while loops or conditional exits.

Example 5: Logical Variable in a DO WHILE Loop

program logical_loop
integer :: i
logical :: keep_running
i = 1
keep_running = .true.
do while (keep_running)
    print *, "Iteration", i
    if (i == 5) then
        keep_running = .false.
    end if
    i = i + 1
end do
end program logical_loop

Explanation:

• keep_running controls the loop execution.
• The loop exits when keep_running becomes .false.

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6. Combining Multiple Logical Conditions

Complex logical conditions can be created by combining multiple logical variables and expressions.

Example 6: Combined Conditions

program complex_logical
integer :: age
logical :: has_permission, is_adult
age = 20
has_permission = .true.
is_adult = (age >= 18)
if (is_adult .and. has_permission) then
    print *, "Access granted"
else
    print *, "Access denied"
end if
end program complex_logical

Explanation:

• Both is_adult and has_permission must be true to grant access.
• Logical operators allow flexible decision-making.

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7. Logical Arrays

Fortran allows arrays of logical variables, which are useful in scientific computing, simulations, and data validation.

Example 7: Logical Array

program logical_array
logical, dimension(5) :: flags
integer :: i
flags = [.true., .false., .true., .true., .false.]
do i = 1, 5
    if (flags(i)) then
        print *, "Element", i, "is true"
    else
        print *, "Element", i, "is false"
    end if
end do
end program logical_array

Explanation:

• flags is an array of logical variables.
• Each element is tested in a loop to print its status.

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8. Intrinsic Functions for Logical Variables

Fortran provides intrinsic functions for logical operations and array reductions.

Common Intrinsic Functions

• all(array) : Returns .true. if all elements are true
• any(array) : Returns .true. if any element is true
• lbound(array) and ubound(array) : Work with array indices

Example 8: Using Intrinsic Logical Functions

program logical_intrinsic
logical, dimension(5) :: flags
flags = [.true., .true., .false., .true., .true.]
if (all(flags)) then
    print *, "All flags are true"
else
    print *, "Not all flags are true"
end if
if (any(flags)) then
    print *, "At least one flag is true"
end if
end program logical_intrinsic

Explanation:

• all(flags) checks if every element is true.
• any(flags) checks if at least one element is true.

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9. Logical Variables in Functions and Subroutines

Logical variables can be used as function return types or as parameters in subroutines.

Example 9: Logical Function

program logical_function
logical :: is_even
is_even = check_even(4)
if (is_even) then
    print *, "Number is even"
else
    print *, "Number is odd"
end if
contains
function check_even(n) result(res)
    integer, intent(in) :: n
    logical :: res
    res = mod(n, 2) == 0
end function check_even
end program logical_function

Explanation:

• check_even returns a logical value based on a condition.
• Logical functions simplify conditional checks in programs.

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Example 10: Logical Variable as Subroutine Argument

program logical_subroutine
logical :: flag
flag = .false.
call toggle(flag)
if (flag) then
    print *, "Flag is now true"
else
    print *, "Flag is still false"
end if
contains
subroutine toggle(x)
    logical, intent(inout) :: x
    x = .not. x
end subroutine toggle
end program logical_subroutine

Explanation:

• intent(inout) allows the subroutine to modify the logical variable.
• The toggle subroutine reverses the flag value.

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10. Best Practices for Logical Variables

1. Always use .true. or .false. explicitly: Avoid using integers for logical values.
2. Use descriptive names: Variables like is_valid, flag_active, or has_permission improve readability.
3. Combine logical operators carefully: Parentheses improve clarity in complex conditions.
4. Avoid unnecessary negations: Simplify conditions to reduce cognitive load.
5. Leverage intrinsic functions: Functions like all and any simplify array-based logical operations.
6. Use logical variables in loops and functions to control flow efficiently.

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11. Applications of Logical Variables

Logical variables are essential in numerous applications, including:

• Input validation: Checking user inputs for correctness.
• Control flags: Controlling loops, program modes, and feature toggles.
• Array condition checks: Performing operations based on logical arrays.
• Conditional computations: Selecting algorithms or operations based on conditions.
• Simulation and modeling: Representing states, switches, or binary conditions.

Example 11: Practical Use in Simulation

program simulation
logical :: simulation_running
integer :: timestep
timestep = 0
simulation_running = .true.
do while (simulation_running)
    timestep = timestep + 1
    print *, "Simulation timestep:", timestep
    if (timestep >= 10) simulation_running = .false.
end do
print *, "Simulation completed"
end program simulation

Explanation:

• simulation_running controls the loop for timesteps.
• The simulation stops when the timestep reaches 10.

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12. Summary

• Logical variables store .true. or .false. values.
• They are essential for conditional statements, loops, and functions.
• Logical operators allow complex expressions to control program flow.
• Arrays of logical variables are useful in data processing and scientific computing.
• Intrinsic functions like all and any simplify logical array operations.
• Best practices include descriptive variable names, explicit values, and careful combination of conditions.
• Logical variables are widely used in input validation, control flags, simulations, and decision-making in Fortran programs.