Implemented Several Numerical Integration Algorithms in maths/

.github/workflows/ci.yml

@@ -0,0 +1,49 @@
+---
+name: ci
+
+'on':
+  workflow_dispatch:
+  push:
+    branches:
+      - main
+  pull_request:
+
+env:
+  build_path: ${{github.workspace}}/build
+
+jobs:
+  build_and_test:
+    runs-on: ${{matrix.os}}
+    strategy:
+      fail-fast: false
+      matrix:
+        os: [ubuntu-22.04, ubuntu-24.04]
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Display versions
+        run: |
+          gfortran --version
+          cmake --version
+
+      - name: Create Build Directory
+        run: cmake -E make_directory ${{env.build_path}}
+
+      - name: Configure CMake
+        working-directory: ${{env.build_path}}
+        run: cmake ../
+
+      - name: Build
+        working-directory: ${{env.build_path}}
+        run: cmake --build .
+
+      - name: Test
+        working-directory: ${{env.build_path}}
+        run: ctest
+
+      - name: Run examples
+        working-directory: ${{env.build_path}}
+        run: make run_all_examples
+...

.gitignore

@@ -33,3 +33,4 @@
 
 .idea/
 
+/build/

CMakeLists.txt

@@ -0,0 +1,50 @@
+cmake_minimum_required(VERSION 3.16)
+project(FortranProject LANGUAGES Fortran)
+
+add_compile_options(-Wall -Wextra -Wpedantic)
+
+function(add_fortran_sources DIR SOURCES)
+    file(GLOB_RECURSE NEW_SOURCES "${DIR}/*.f90")
+    list(APPEND ${SOURCES} ${NEW_SOURCES})
+    set(${SOURCES} ${${SOURCES}} PARENT_SCOPE)
+endfunction()
+
+set(MODULE_SOURCES)
+add_fortran_sources(${CMAKE_SOURCE_DIR}/modules MODULE_SOURCES)
+
+add_library(modules STATIC ${MODULE_SOURCES})
+
+function(create_unique_name FILE_NAME OUTPUT_NAME)
+    file(RELATIVE_PATH REL_PATH "${CMAKE_SOURCE_DIR}" "${FILE_NAME}")
+    get_filename_component(CUR_EXT "${REL_PATH}" LAST_EXT)
+    string(REPLACE "/" "_" UNIQUE_NAME "${REL_PATH}")
+    string(REPLACE "${CUR_EXT}" "" UNIQUE_NAME "${UNIQUE_NAME}")
+    set(${OUTPUT_NAME} ${UNIQUE_NAME} PARENT_SCOPE)
+endfunction()
+
+
+file(GLOB_RECURSE TEST_FILES "${CMAKE_SOURCE_DIR}/tests/*.f90")
+
+foreach(TEST_FILE ${TEST_FILES})
+    create_unique_name(${TEST_FILE} TEST_NAME)
+    add_executable(${TEST_NAME} ${TEST_FILE})
+    target_link_libraries(${TEST_NAME} modules)
+    add_test(NAME ${TEST_NAME} COMMAND ${TEST_NAME})
+endforeach()
+
+file(GLOB_RECURSE EXAMPLE_FILES "${CMAKE_SOURCE_DIR}/examples/*.f90")
+
+foreach(EXAMPLE_FILE ${EXAMPLE_FILES})
+    create_unique_name(${EXAMPLE_FILE} EXAMPLE_NAME)
+    add_executable(${EXAMPLE_NAME} ${EXAMPLE_FILE})
+    target_link_libraries(${EXAMPLE_NAME} modules)
+    list(APPEND EXAMPLE_NAME_LIST run_${EXAMPLE_NAME})
+    add_custom_target(run_${EXAMPLE_NAME}
+        COMMAND ${EXAMPLE_NAME}
+        DEPENDS ${EXAMPLE_NAME}
+        COMMENT "Running example: ${EXAMPLE_NAME}")
+endforeach()
+
+enable_testing()
+
+add_custom_target(run_all_examples DEPENDS ${EXAMPLE_NAME_LIST})

DIRECTORY.md

@@ -1,5 +1,11 @@
 # The Algorithms - Directory of Fortran
 ## Maths
+* numerical_integration
+  * [trapezoidal_rule](/modules/maths/numerical_integration/trapezoid.f90)
+  * [simpson_rule](/modules/maths/numerical_integration/simpson.f90)
+  * [midpoint_rule](/modules/maths/numerical_integration/midpoint.f90)
+  * [monte_carlo](/modules/maths/numerical_integration/monte_carlo.f90)
+  * [gauss_legendre](/modules/maths/numerical_integration/gaussian_legendre.f90)
 * [euclid_gcd](/modules/maths/euclid_gcd.f90)
 * [factorial](/modules/maths/factorial.f90)
 * [fibonacci](/modules/maths/fibonacci.f90)

examples/maths/euclid_gcd.f90

@@ -4,17 +4,11 @@ program euclid_gcd_program
     use gcd_module
     implicit none
     integer :: a, b, val
-    character(len=1024) :: msg
-    integer :: istat
 
-    print *, "Enter the two numbers (+ve integers): "
-    read(*, *, iostat=istat, iomsg=msg) a, b
-    if (istat /= 0) then
-        write(*, fmt='(2A)') 'error: ', trim(msg)
-        stop 1
-    end if
+    a = 56
+    b = 98
 
     val = gcd(a, b)
-    print *, 'The greatest common divisor is: ', val
+    print *, 'The greatest common divisor of ', a, ' and ', b, ' is: ', val
 
 end program euclid_gcd_program

examples/maths/factorial.f90

@@ -7,7 +7,7 @@ program factorial_program
     use factorial_module
     implicit none
 
-    Print*, factorial(5)
-    Print*, recursive_factorial(5)
+    Print *, factorial(5)
+    Print *, recursive_factorial(5)
 
 end program factorial_program

examples/maths/fibonacci.f90

@@ -6,14 +6,9 @@ program example_fibonacci
     implicit none
     integer :: n
 
-    print *, 'Enter a number: '
-    read *, n
-    if (n <= 0) then
-        print *, 'Number must be a positive integer.'
-        stop 1
-    end if
+    n = 7
 
-    print *, 'The Fibonacci number for the specified position is:'
+    print *, 'The Fibonacci number for the position', n, ' is:'
     print *, 'Recursive solution: ', fib_rec(n)
     print *, 'Iterative solution: ', fib_itr(n)
 

examples/maths/numerical_integration/gaussian_legendre.f90

@@ -0,0 +1,45 @@
+!> Example Program for Gaussian-Legendre Quadrature Module
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #25
+!!  https://github.com/TheAlgorithms/Fortran/pull/25
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!! This program demonstrates the use of Gaussian-Legendre Quadrature Module for numerical integration.
+!!
+!! It sets the integration limits and the number of quadrature points (n), and calls the
+!! gauss_legendre_quadrature subroutine to compute the approximate value of the definite integral
+!! of the specified function.
+!!
+!! Example function: f(x) = exp(-x^2) * cos(2.0_dp * x)
+
+program example_gaussian_quadrature
+    use gaussian_legendre_quadrature
+    implicit none
+
+    real(dp) :: a, b, integral_result
+    integer :: n
+
+    ! Set the integration limits and number of quadrature points
+    a = -1.0_dp
+    b = 1.0_dp
+    n = 5       !! Number of quadrature points
+
+    ! Call Gaussian quadrature to compute the integral
+    call gauss_legendre_quadrature(integral_result, a, b, n, func)
+
+    write (*, '(A, F12.6)') "Gaussian Quadrature result: ", integral_result          !! ≈ 0.858574
+
+contains
+
+    function func(x) result(fx)
+        implicit none
+        real(dp), intent(in) :: x
+        real(dp) :: fx
+
+        fx = exp(-x**2)*cos(2.0_dp*x)       !! Example function to integrate
+    end function func
+
+end program example_gaussian_quadrature

examples/maths/numerical_integration/midpoint.f90

@@ -0,0 +1,44 @@
+!> Example Program for Midpoint Rule
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #25
+!!  https://github.com/TheAlgorithms/Fortran/pull/25
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!! This program demonstrates the use of Midpoint Rule for numerical integration.
+!!
+!! It sets the integration limits and number of subintervals (panels), and calls the
+!! midpoint subroutine to compute the approximate value of the definite integral
+!! of the specified function.
+!!
+!! Example function: f(x) = exp(-x^2) * cos(2.0_dp * x)
+
+program example_midpoint
+    use midpoint_rule
+    implicit none
+    real(dp) :: a, b, integral_result
+    integer :: n
+
+    ! Set the integration limits and number of panels
+    a = -1.0_dp
+    b = 1.0_dp
+    n = 400     !! Number of subdivisions
+
+    ! Call the midpoint rule subroutine with the function passed as an argument
+    call midpoint(integral_result, a, b, n, func)
+
+    write (*, '(A, F12.6)') "Midpoint rule yields: ", integral_result  !! ≈ 0.858196
+
+contains
+
+    function func(x) result(fx)
+        implicit none
+        real(dp), intent(in) :: x
+        real(dp) :: fx
+
+        fx = exp(-x**2)*cos(2.0_dp*x)       !! Example function to integrate
+    end function func
+
+end program example_midpoint

examples/maths/numerical_integration/monte_carlo.f90

@@ -0,0 +1,45 @@
+!> Example Program for Monte Carlo Integration
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #25
+!!  https://github.com/TheAlgorithms/Fortran/pull/25
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!! This program demonstrates the use of Monte Carlo module for numerical integration.
+!!
+!! It sets the integration limits and number of random samples, and calls the
+!! monte_carlo subroutine to compute the approximate value of the definite integral
+!! of the specified function.
+!!
+!! Example function: f(x) = exp(-x^2) * cos(2.0_dp * x)
+
+program example_monte_carlo
+    use monte_carlo_integration
+    implicit none
+
+    real(dp) :: a, b, integral_result, error_estimate
+    integer :: n
+
+    ! Set the integration limits and number of random samples
+    a = -1.0_dp
+    b = 1.0_dp
+    n = 1000000     !! 1E6 Number of random samples
+
+    ! Call Monte Carlo integration
+    call monte_carlo(integral_result, error_estimate, a, b, n, func)
+
+    write (*, '(A, F12.6, A, F12.6)') "Monte Carlo result: ", integral_result, " +- ", error_estimate     !! ≈ 0.858421
+
+contains
+
+    function func(x) result(fx)
+        implicit none
+        real(dp), intent(in) :: x
+        real(dp) :: fx
+
+        fx = exp(-x**2)*cos(2.0_dp*x)       !! Example function to integrate
+    end function func
+
+end program example_monte_carlo

examples/maths/numerical_integration/simpson.f90

@@ -0,0 +1,45 @@
+!> Example Program for Simpson's Rule
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #25
+!!  https://github.com/TheAlgorithms/Fortran/pull/25
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!! This program demonstrates the use of Simpson's rule for numerical integration.
+!!
+!! It sets the integration limits and number of panels, and calls the
+!! simpson subroutine to compute the approximate value of the definite integral
+!! of the specified function.
+!!
+!! Example function: f(x) = exp(-x^2) * cos(2.0_dp * x)
+
+program example_simpson
+    use simpson_rule
+    implicit none
+
+    real(dp) :: a, b, integral_result
+    integer :: n
+
+    ! Set the integration limits and number of panels
+    a = -1.0_dp
+    b = 1.0_dp
+    n = 100     !! Number of subdivisions (must be even)
+
+    ! Call Simpson's rule with the function passed as an argument
+    call simpson(integral_result, a, b, n, func)
+
+    write (*, '(A, F12.8)') "Simpson's rule yields: ", integral_result       !! ≈ 0.85819555
+
+contains
+
+    function func(x) result(fx)
+        implicit none
+        real(dp), intent(in) :: x
+        real(dp) :: fx
+
+        fx = exp(-x**2)*cos(2.0_dp*x)       !! Example function to integrate
+    end function func
+
+end program example_simpson

examples/maths/numerical_integration/trapezoid.f90

@@ -0,0 +1,45 @@
+!> Example Program for Trapezoidal Rule
+!!
+!!  Created by: Ramy-Badr-Ahmed (https://github.com/Ramy-Badr-Ahmed)
+!!  in Pull Request: #25
+!!  https://github.com/TheAlgorithms/Fortran/pull/25
+!!
+!!  Please mention me (@Ramy-Badr-Ahmed) in any issue or pull request
+!!  addressing bugs/corrections to this file. Thank you!
+!!
+!! This program demonstrates the use of the Trapezoidal rule for numerical integration.
+!!
+!! It sets the integration limits and number of panels, and calls the
+!! trapezoid subroutine to compute the approximate value of the definite integral
+!! of the specified function.
+!!
+!! Example function: f(x) = exp(-x^2) * cos(2.0_dp * x)
+
+program example_tapezoid
+    use trapezoidal_rule
+    implicit none
+
+    real(dp) :: a, b, integral_result
+    integer :: n
+
+    ! Set the integration limits and number of panels
+    a = -1.0_dp
+    b = 1.0_dp
+    n = 1000000     !! 1E6 Number of subdivisions
+
+    ! Call the trapezoidal rule with the function passed as an argument
+    call trapezoid(integral_result, a, b, n, func)
+
+    write (*, '(A, F12.6)') 'Trapezoidal rule yields: ', integral_result     !! ≈ 0.858195
+
+contains
+
+    function func(x) result(fx)
+        implicit none
+        real(dp), intent(in) :: x
+        real(dp) :: fx
+
+        fx = exp(-x**2)*cos(2.0_dp*x)       !! Example function to integrate
+    end function func
+
+end program example_tapezoid