Merge pull request #1 from jchristopherson/Development-v1.1.0

Development v1.1.0

Author: jchristopherson

.gitmodules

@@ -9,6 +9,18 @@ before_install:
 install:
   - sudo apt-get install -qq gfortran-7
   - sudo update-alternatives --install /usr/bin/gfortran gfortran /usr/bin/gfortran-7 90
+  - sudo apt install git
+  - sudo apt install cmake
+  - sudo git clone https://github.com/jchristopherson/ferror.git
+  - pushd ferror
+  - sudo mkdir build
+  - pushd build
+  - sudo cmake -DCMAKE_INSTALL_LIBDIR=$HOME/.local/ferror ..
+  - sudo cmake
+  - sudo make
+  - sudo make install
+  - popd
+  - popd
 
 before_script:
     - mkdir build

.travis.yml

@@ -4,7 +4,7 @@ project(integral C CXX Fortran)
 
 # Define version information
 set(INTEGRAL_MAJOR_VERSION 1)
-set(INTEGRAL_MINOR_VERSION 0)
+set(INTEGRAL_MINOR_VERSION 1)
 set(INTEGRAL_PATCH_VERSION 0)
 set(INTEGRAL_VERSION ${INTEGRAL_MAJOR_VERSION}.${INTEGRAL_MINOR_VERSION}.${INTEGRAL_PATCH_VERSION})
 
@@ -13,11 +13,7 @@ find_package(ferror 1.3.0)
 
 # If FERROR is not installed on the system, build the default implementation
 if (NOT ${ferror_FOUND})
-    message(STATUS "FERROR not found.  The default implementation will be used.")
-    add_subdirectory(src/external/ferror)
-    include_directories(src/external/ferror/include)
-    set(FERROR_LIBRARIES ferror)
-    set(ferror_LibLocation ${ferror_BINARY_DIR})
+    message(STATUS "FERROR not found.")
 else()
     message(STATUS "An acceptable version of FERROR (v" ${ferror_VERSION} ") was found, and will be utilized.")
     include_directories(${ferror_INCLUDE_DIRS})
@@ -34,8 +30,7 @@ if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
   set_property(CACHE CMAKE_BUILD_TYPE PROPERTY STRINGS "Debug" "Release")
 endif()
 
-# By default, shared library
-option(BUILD_SHARED_LIBS "Build shared libraries" ON)
+option(BUILD_SHARED_LIBS "Build shared libraries" OFF)
 
 # Export all symbols on Windows when building shared libraries
 SET(CMAKE_WINDOWS_EXPORT_ALL_SYMBOLS TRUE)

CMakeLists.txt

@@ -48,8 +48,112 @@ end program
 ```text
 The solution is: 789.97089E-03, the integrator computed: 789.97089E-03.
 ```
-
 ## Example 2
+The following example illustrates solution of the Van Der Pol equation comparing two different integrators, an implicit Runge-Kutta integrator (ODE_IRK) and an integrator that automatically switches between an Adams method and a BDF method (ODE_AUTO).
+```fortran
+program example
+    use iso_fortran_env
+    use integral_core
+    use fplot_core
+    implicit none
+
+    ! Local Variables
+    type(ode_helper) :: fcn
+    type(ode_irk) :: integrator1
+    type(ode_auto) :: integrator2
+    procedure(ode_fcn), pointer :: ptr
+    real(real64) :: ic(2), t(2)
+    real(real64), allocatable, dimension(:,:) :: x1, x2
+    type(plot_2d) :: plt
+    type(plot_data_2d) :: d1, d2
+    class(plot_axis), pointer :: xAxis, yAxis
+    class(legend), pointer :: lgnd
+
+    ! Set up the integrator
+    ptr => vdp
+    call fcn%define_equations(2, ptr)
+
+    ! Define the initial conditions
+    t = [0.0d0, 8.0d1]
+    ic = [2.0d0, 0.0d0]
+
+    ! Compute the solution
+    x1 = integrator1%integrate(fcn, t, ic)  ! ODE_IRK integrator
+    x2 = integrator2%integrate(fcn, t, ic)  ! ODE_AUTO integrator
+
+    ! Display the number of solution points in each
+    print '(AI0)', "ODE_IRK Solution Point Count: ", size(x1, 1)
+    print '(AI0)', "ODE_AUTO Solution Point Count: ", size(x2, 1)
+
+    ! ---------------------------- PLOTTING CODE ----------------------------- !
+    ! Plot the solution
+    call plt%initialize()
+    call plt%set_font_size(14)
+
+    xAxis => plt%get_x_axis()
+    call xAxis%set_title("t")
+
+    yAxis => plt%get_y_axis()
+    call yAxis%set_title("x(t)")
+
+    lgnd => plt%get_legend()
+    call lgnd%set_is_visible(.true.)
+    call lgnd%set_draw_border(.false.)
+    call lgnd%set_draw_inside_axes(.false.)
+
+    call d1%set_name("IRK")
+    call d1%set_draw_line(.false.)
+    call d1%set_draw_markers(.true.)
+    call d1%set_marker_style(MARKER_FILLED_TRIANGLE)
+    call d1%set_marker_scaling(1.5)
+    call d1%define_data(x1(:,1), x1(:,2))
+    call plt%push(d1)
+
+    call d2%set_name("AUTO")
+    call d2%set_draw_line(.false.)
+    call d2%set_draw_markers(.true.)
+    call d2%set_marker_style(MARKER_EMPTY_CIRCLE)
+    call d2%set_line_color(CLR_RED)
+    call d2%set_line_style(LINE_DASHED)
+    call d2%define_data(x2(:,1), x2(:,2))
+    call plt%push(d2)
+
+    call plt%draw()
+
+    call plt%clear_all()
+
+    call d1%define_data(x1(:,2), x1(:,3))
+    call d2%define_data(x2(:,2), x2(:,3))
+    call xAxis%set_title("x(t)")
+    call yAxis%set_title("dx/dt")
+    call plt%push(d1)
+    call plt%push(d2)
+    call plt%draw()
+
+contains
+    ! Van Der Pol Equation
+    ! x" + x - mu * (1 - x**2) * x' = 0
+    subroutine vdp(t, x, dxdt)
+        real(real64), intent(in) :: t
+        real(real64), intent(in), dimension(:) :: x
+        real(real64), intent(out), dimension(:) :: dxdt
+
+        real(real64), parameter :: mu = 20.0d0
+
+        dxdt(1) = x(2)
+        dxdt(2) = mu * (1.0d0 - x(1)**2) * x(2) - x(1)
+    end subroutine
+end program
+```
+```text
+ODE_IRK Solution Point Count: 544
+ODE_AUTO Solution Point Count: 1283
+```
+These are the plots resulting from the above program.
+![](images/vanderpol_compare_example.png?raw=true)
+![](images/vanderpol_compare_example_diff.png?raw=true)
+
+## Example 3
 The following example illustrates how to compute the solution to a system of ODEs modeling the bouncing of a ball.  The example also utilizes the [FPLOT](https://github.com/jchristopherson/fplot) library in order to plot the solution.
 ```fortran
 program example