test for trapezoid.f90

Author: Ramy-Badr-Ahmed

tests/maths/numerical_integration/trapezoid.f90

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+!> Test program for the Trapezoidal Rule module
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #32
+!!  https://github.com/TheAlgorithms/Fortran/pull/32
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!!  This program provides test cases to validate the trapezoidal_rule module against known integral values.
+
+
+program test_trapezoidal_rule
+    use trapezoidal_rule
+    implicit none
+
+    real(dp) :: lower_bound, upper_bound, integral_result, expected
+    real(dp), parameter :: pi = 4.d0*DATAN(1.d0)  ! Define Pi. Ensures maximum precision available on any architecture
+
+    integer :: panels_number
+
+    ! Test 1: ∫ x^2 dx from 0 to 1 (Exact result = 1/3 ≈ 0.3333)
+    lower_bound = 0.0_dp
+    upper_bound = 1.0_dp
+    panels_number = 1000000
+    expected = 1.0_dp / 3.0_dp
+    call trapezoid(integral_result, lower_bound, upper_bound, panels_number, f_x_squared)
+    call assert_test(integral_result, expected, "Test 1: ∫ x^2 dx from 0 to 1")
+
+    ! Test 2: ∫ x^2 dx from 0 to 2 (Exact result = 8/3 ≈ 2.6667)
+    lower_bound = 0.0_dp
+    upper_bound = 2.0_dp
+    panels_number = 1000000
+    expected = 8.0_dp / 3.0_dp
+    call trapezoid(integral_result, lower_bound, upper_bound, panels_number, f_x_squared)
+    call assert_test(integral_result, expected, "Test 2: ∫ x^2 dx from 0 to 2")
+
+    ! Test 3: ∫ sin(x) dx from 0 to π (Exact result = 2)
+    lower_bound = 0.0_dp
+    upper_bound = pi
+    panels_number = 1000000
+    expected = 2.0_dp
+    call trapezoid(integral_result, lower_bound, upper_bound, panels_number, sin_function)
+    call assert_test(integral_result, expected, "Test 3: ∫ sin(x) dx from 0 to π")
+
+contains
+
+    ! Function for x^2
+    real(dp) function f_x_squared(x)
+        real(dp), intent(in) :: x
+        f_x_squared = x**2
+    end function f_x_squared
+
+    ! Function for sin(x)
+    real(dp) function sin_function(x)
+        real(dp), intent(in) :: x
+        sin_function = sin(x)
+    end function sin_function
+
+    ! Assertion subroutine
+    subroutine assert_test(result, expected, test_name)
+        real(dp), intent(in) :: result, expected
+        character(len=*), intent(in) :: test_name
+        real(dp), parameter :: tol = 1.0e-5_dp
+
+        if (abs(result - expected) < tol) then
+            print *, test_name, " PASSED"
+        else
+            print *, test_name, " FAILED"
+            print *, " Expected: ", expected
+            print *, " Got:      ", result
+            stop 1
+        end if
+    end subroutine assert_test
+
+end program test_trapezoidal_rule