Implementing ctest-friendly tests for /maths/numerical_integration. Tests for monte_carlo.f90

Author: Ramy-Badr-Ahmed

tests/maths/numerical_integration/monte_carlo.f90

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+!> Test program for the Monte Carlo Integration 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 monte_carlo_integration module against known integral values.
+
+program test_monte_carlo_integration
+    use monte_carlo_integration
+    implicit none
+
+    ! Run test cases
+    call test_integral_x_squared_0_to_1()
+    call test_integral_e_x_0_to_1()
+    call test_integral_sin_0_to_pi()
+    call test_integral_cos_0_to_pi_over_2()
+    call test_integral_1_over_x_1_to_e()
+    call test_integral_x_cubed_0_to_1()
+    call test_integral_sin_squared_0_to_1()
+
+    print *, "All tests completed."
+
+contains
+
+    ! Test case 1: ∫ x^2 dx from 0 to 1 (Exact result = 1/3 ≈ 0.3333)
+    subroutine test_integral_x_squared_0_to_1()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        integer :: n
+        a = 0.0_dp
+        b = 1.0_dp
+        n = 1000000
+        expected = 1.0_dp / 3.0_dp
+
+        call monte_carlo(integral_result, error_estimate, a, b, n, f_x_squared)
+        call assert_test(integral_result, expected, error_estimate, "Test 1: ∫ x^2 dx from 0 to 1")
+
+    end subroutine test_integral_x_squared_0_to_1
+
+    ! Test case 2: ∫ e^x dx from 0 to 1 (Exact result = e - 1 ≈ 1.7183)
+    subroutine test_integral_e_x_0_to_1()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        integer :: n
+        a = 0.0_dp
+        b = 1.0_dp
+        n = 1000000
+        expected = exp(1.0_dp) - 1.0_dp
+
+        call monte_carlo(integral_result, error_estimate, a, b, n, exp_function)
+        call assert_test(integral_result, expected, error_estimate, "Test 2: ∫ e^x dx from 0 to 1")
+
+    end subroutine test_integral_e_x_0_to_1
+
+    ! Test case 3: ∫ sin(x) dx from 0 to π (Exact result = 2)
+    subroutine test_integral_sin_0_to_pi()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        real(dp), parameter :: pi = 4.D0*DATAN(1.D0)  ! Define Pi. Ensure maximum precision available on any architecture.
+        integer :: n
+        a = 0.0_dp
+        b = pi
+        n = 1000000
+        expected = 2.0_dp
+
+        call monte_carlo(integral_result, error_estimate, a, b, n, sin_function)
+        call assert_test(integral_result, expected, error_estimate, "Test 3: ∫ sin(x) dx from 0 to π")
+
+    end subroutine test_integral_sin_0_to_pi
+
+    ! Test case 4: ∫ cos(x) dx from 0 to π/2 (Exact result = 1)
+    subroutine test_integral_cos_0_to_pi_over_2()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        real(dp), parameter :: pi = 4.D0*DATAN(1.D0)    ! Define Pi. Ensure maximum precision available on any architecture.
+        integer :: n
+        a = 0.0_dp
+        b = pi / 2.0_dp
+        n = 1000000
+        expected = 1.0_dp
+
+        call monte_carlo(integral_result, error_estimate, a, b, n, cos_function)
+        call assert_test(integral_result, expected, error_estimate, "Test 4: ∫ cos(x) dx from 0 to π/2")
+
+    end subroutine test_integral_cos_0_to_pi_over_2
+
+    ! Test case 5: ∫ (1/x) dx from 1 to e (Exact result = 1)
+    subroutine test_integral_1_over_x_1_to_e()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        integer :: n
+        a = 1.0_dp
+        b = exp(1.0_dp)
+        n = 1000000
+        expected = 1.0_dp
+
+        call monte_carlo(integral_result, error_estimate, a, b, n, log_function)
+        call assert_test(integral_result, expected, error_estimate, "Test 5: ∫ (1/x) dx from 1 to e")
+
+    end subroutine test_integral_1_over_x_1_to_e
+
+    ! Test case 6: ∫ x^3 dx from 0 to 1 (Exact result = 1/4 = 0.25)
+    subroutine test_integral_x_cubed_0_to_1()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        integer :: n
+        a = 0.0_dp
+        b = 1.0_dp
+        n = 1000000
+        expected = 0.25_dp
+
+        call monte_carlo(integral_result, error_estimate, a, b, n, f_x_cubed)
+        call assert_test(integral_result, expected, error_estimate, "Test 6: ∫ x^3 dx from 0 to 1")
+
+    end subroutine test_integral_x_cubed_0_to_1
+
+    ! Test case 7: ∫ sin(x^2) dx from 0 to 1 (Approximate value)
+    subroutine test_integral_sin_squared_0_to_1()
+        real(dp) :: a, b, integral_result, error_estimate, expected
+        integer :: n
+        a = 0.0_dp
+        b = 1.0_dp
+        n = 1000000
+        expected = 0.31026_dp       ! Approximate value, adjust tolerance as needed
+        call monte_carlo(integral_result, error_estimate, a, b, n, sin_squared_function)
+        call assert_test(integral_result, expected, error_estimate, "Test 7: ∫ sin(x^2) dx from 0 to 1")
+
+    end subroutine test_integral_sin_squared_0_to_1
+
+    ! 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 e^x
+    real(dp) function exp_function(x)
+        real(dp), intent(in) :: x
+        exp_function = exp(x)
+    end function exp_function
+
+    ! Function for 1/x
+    real(dp) function log_function(x)
+        real(dp), intent(in) :: x
+        log_function = 1.0_dp/x
+    end function log_function
+
+    ! Function for cos(x)
+    real(dp) function cos_function(x)
+        real(dp), intent(in) :: x
+        cos_function = cos(x)
+    end function cos_function
+
+    ! Function for x^3
+    real(dp) function f_x_cubed(x)
+        real(dp), intent(in) :: x
+        f_x_cubed = x**3
+    end function f_x_cubed
+
+    ! Function for sin(x^2)
+    real(dp) function sin_squared_function(x)
+        real(dp), intent(in) :: x
+        sin_squared_function = sin(x**2)
+    end function sin_squared_function
+
+    ! Function for sin(x)
+    real(dp) function sin_function(x)
+        real(dp), intent(in) :: x
+        sin_function = sin(x)
+    end function sin_function
+
+    !> Subroutine to assert the test results
+    subroutine assert_test(actual, expected, error_estimate, test_name)
+        real(dp), intent(in) :: actual, expected, error_estimate
+        character(len=*), intent(in) :: test_name
+        real(dp) :: tol
+
+        ! Set the tolerance based on the error estimate
+        tol = max(1.0e-5_dp, 10.0_dp * error_estimate)      ! Adjust as needed
+
+        if (abs(actual - expected) < tol) then
+            print *, test_name, " PASSED"
+        else
+            print *, test_name, " FAILED"
+            print *, " Expected: ", expected
+            print *, " Got:      ", actual
+            stop 1
+        end if
+    end subroutine assert_test
+
+end program test_monte_carlo_integration