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Tests for gaussin_legendre.f90
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Diff for: ‎tests/maths/numerical_integration/gaussin_legendre.f90

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!> Test program for the Gaussian Legendre Quadrature module
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!!
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!! Created by: Your Name (https://github.com/YourGitHub)
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!! in Pull Request: #32
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!! https://github.com/TheAlgorithms/Fortran/pull/32
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!!
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!! This program provides test cases to validate the gaussian_legendre_quadrature module against known integral values.
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program test_gaussian_legendre_quadrature
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use gaussian_legendre_quadrature
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implicit none
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! Run test cases
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call test_integral_x_squared_0_to_1()
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call test_integral_e_x_0_to_1()
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call test_integral_sin_0_to_pi()
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call test_integral_cos_0_to_pi_over_2()
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call test_integral_1_over_x_1_to_e()
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call test_integral_x_cubed_0_to_1()
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call test_integral_sin_squared_0_to_pi()
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call test_integral_1_over_x_1_to_e()
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print *, "All tests completed."
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contains
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! Test case 1: ∫ x^2 dx from 0 to 1 (Exact result = 1/3 ≈ 0.3333)
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subroutine test_integral_x_squared_0_to_1()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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integer :: panels_number
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lower_bound = 0.0_dp
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upper_bound = 1.0_dp
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panels_number = 5 ! Adjust the number of quadrature points as needed from 1 to 5
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expected = 1.0_dp / 3.0_dp
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, f_x_squared)
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call assert_test(integral_result, expected, "Test 1: ∫ x^2 dx from 0 to 1")
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end subroutine test_integral_x_squared_0_to_1
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! Test case 2: ∫ e^x dx from 0 to 1 (Exact result = e - 1 ≈ 1.7183)
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subroutine test_integral_e_x_0_to_1()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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integer :: panels_number
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lower_bound = 0.0_dp
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upper_bound = 1.0_dp
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panels_number = 3
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expected = exp(1.0_dp) - 1.0_dp
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, exp_function)
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call assert_test(integral_result, expected, "Test 2: ∫ e^x dx from 0 to 1")
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end subroutine test_integral_e_x_0_to_1
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! Test case 3: ∫ sin(x) dx from 0 to π (Exact result = 2)
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subroutine test_integral_sin_0_to_pi()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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integer :: panels_number
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real(dp), parameter :: pi = 4.D0*DATAN(1.D0) ! Define Pi. Ensure maximum precision available on any architecture.
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lower_bound = 0.0_dp
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upper_bound = pi
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panels_number = 5
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expected = 2.0_dp
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, sin_function)
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call assert_test(integral_result, expected, "Test 3: ∫ sin(x) dx from 0 to π")
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end subroutine test_integral_sin_0_to_pi
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! Test case 4: ∫ cos(x) dx from 0 to π/2 (Exact result = 1)
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subroutine test_integral_cos_0_to_pi_over_2()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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real(dp), parameter :: pi = 4.D0*DATAN(1.D0) ! Define Pi. Ensure maximum precision available on any architecture.
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integer :: panels_number
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lower_bound = 0.0_dp
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upper_bound = pi / 2.0_dp
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panels_number = 5
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expected = 1.0_dp
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, cos_function)
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call assert_test(integral_result, expected, "Test 4: ∫ cos(x) dx from 0 to π/2")
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end subroutine test_integral_cos_0_to_pi_over_2
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! Test case 5: ∫ (1/x) dx from 1 to e (Exact result = 1)
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subroutine test_integral_1_over_x_1_to_e()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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integer :: panels_number
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lower_bound = 1.0_dp
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upper_bound = exp(1.0_dp)
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panels_number = 5
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expected = 1.0_dp
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, log_function)
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call assert_test(integral_result, expected, "Test 5: ∫ (1/x) dx from 1 to e")
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end subroutine test_integral_1_over_x_1_to_e
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! Test case 6: ∫ x^3 dx from 0 to 1 (Exact result = 1/4 = 0.25)
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subroutine test_integral_x_cubed_0_to_1()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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integer :: panels_number
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lower_bound = 0.0_dp
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upper_bound = 1.0_dp
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panels_number = 4
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expected = 0.25_dp
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, f_x_cubed)
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call assert_test(integral_result, expected, "Test 6: ∫ x^3 dx from 0 to 1")
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end subroutine test_integral_x_cubed_0_to_1
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! Test case 7: ∫ sin^2(x) dx from 0 to π (Exact result = π/2 ≈ 1.5708)
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subroutine test_integral_sin_squared_0_to_pi()
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real(dp) :: lower_bound, upper_bound, integral_result, expected
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real(dp), parameter :: pi = 4.D0*DATAN(1.D0) ! Define Pi. Ensure maximum precision available on any architecture.
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integer :: panels_number
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lower_bound = 0.0_dp
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upper_bound = pi
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panels_number = 5
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expected = 1.57084_dp ! Approximate value, adjust tolerance as needed
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call gauss_legendre_quadrature(integral_result, lower_bound, upper_bound, panels_number, sin_squared_function)
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call assert_test(integral_result, expected, "Test 7: ∫ sin^2(x) dx from 0 to π")
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end subroutine test_integral_sin_squared_0_to_pi
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! Function for x^2
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real(dp) function f_x_squared(x)
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real(dp), intent(in) :: x
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f_x_squared = x**2
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end function f_x_squared
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! Function for e^x
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real(dp) function exp_function(x)
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real(dp), intent(in) :: x
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exp_function = exp(x)
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end function exp_function
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! Function for 1/x
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real(dp) function log_function(x)
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real(dp), intent(in) :: x
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log_function = 1.0_dp / x
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end function log_function
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! Function for cos(x)
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real(dp) function cos_function(x)
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real(dp), intent(in) :: x
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cos_function = cos(x)
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end function cos_function
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! Function for x^3
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real(dp) function f_x_cubed(x)
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real(dp), intent(in) :: x
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f_x_cubed = x**3
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end function f_x_cubed
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! Function for sin(x)
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real(dp) function sin_function(x)
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real(dp), intent(in) :: x
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sin_function = sin(x)
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end function sin_function
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! Function for sin^2(x)
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real(dp) function sin_squared_function(x)
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real(dp), intent(in) :: x
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sin_squared_function = sin(x)**2
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end function sin_squared_function
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!> Subroutine to assert the test results
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subroutine assert_test(actual, expected, test_name)
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real(dp), intent(in) :: actual, expected
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character(len=*), intent(in) :: test_name
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real(dp), parameter :: tol = 1.0e-5_dp
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if (abs(actual - expected) < tol) then
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print *, test_name, " PASSED"
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else
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print *, test_name, " FAILED"
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print *, " Expected: ", expected
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print *, " Got: ", actual
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stop 1
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end if
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end subroutine assert_test
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end program test_gaussian_legendre_quadrature

Diff for: ‎tests/maths/numerical_integration/midpoint.f90

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!> Test program for the Midpoint Rule module
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!!
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!! Created by: Your Name (https://github.com/YourGitHub)
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!! in Pull Request: #XX
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!! https://github.com/TheAlgorithms/Fortran/pull/XX
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!! in Pull Request: #32
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!! https://github.com/TheAlgorithms/Fortran/pull/32
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!!
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!! This program provides test cases to validate the midpoint_rule module against known integral values.
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@@ -116,8 +116,8 @@ subroutine test_integral_sin_x_squared_0_to_1()
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integer :: panels_number
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lower_bound = 0.0_dp
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upper_bound = 1.0_dp
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panels_number = 1000000 ! Must be a positive integer
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expected = 0.310268_dp ! Approximate value, adjust tolerance as needed
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panels_number = 1000000 ! Must be a positive integer
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expected = 0.310268_dp ! Approximate value, adjust tolerance as needed
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call midpoint(integral_result, lower_bound, upper_bound, panels_number, sin_squared_function)
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call assert_test(integral_result, expected, "Test 8: ∫ sin(x^2) dx from 0 to 1")
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end subroutine test_integral_sin_x_squared_0_to_1

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