tasks a-s

Task/Numerical-integration/Fortran/numerical-integration-1.f

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+elemental function elemf(x)
+   real :: elemf, x
+   elemf = f(x)
+end function elemf

Task/Numerical-integration/Fortran/numerical-integration-2.f

@@ -0,0 +1,75 @@
+module Integration
+  implicit none
+
+contains
+
+  ! function, lower limit, upper limit, steps, method
+  function integrate(f, a, b, in, method)
+    real :: integrate
+    real, intent(in) :: a, b
+    integer, optional, intent(in) :: in
+    character(len=*), intent(in), optional :: method
+    interface
+       elemental function f(ra)
+         real :: f
+         real, intent(in) :: ra
+       end function f
+    end interface
+
+    integer :: n, i, m
+    real :: h
+    real, dimension(:), allocatable :: xpoints
+    real, dimension(:), target, allocatable :: fpoints
+    real, dimension(:), pointer :: fleft, fmid, fright
+
+    if ( present(in) ) then
+       n = in
+    else
+       n = 20
+    end if
+
+    if ( present(method) ) then
+       select case (method)
+       case ('leftrect')
+          m = 1
+       case ('midrect')
+          m = 2
+       case ('rightrect')
+          m = 3
+       case ( 'trapezoid' )
+          m = 4
+       case default
+          m = 0
+       end select
+    else
+       m = 0
+    end if
+
+    h = (b - a) / n
+
+    allocate(xpoints(0:2*n), fpoints(0:2*n))
+
+    xpoints = (/ (a + h*i/2, i = 0,2*n) /)
+
+    fpoints = f(xpoints)
+    fleft  => fpoints(0 : 2*n-2 : 2)
+    fmid   => fpoints(1 : 2*n-1 : 2)
+    fright => fpoints(2 : 2*n   : 2)
+
+    select case (m)
+    case (0) ! simpson
+       integrate = h / 6.0 * sum(fleft + fright + 4.0*fmid)
+    case (1) ! leftrect
+       integrate = h * sum(fleft)
+    case (2) ! midrect
+       integrate = h * sum(fmid)
+    case (3) ! rightrect
+       integrate = h * sum(fright)
+    case (4) ! trapezoid
+       integrate = h * sum(fleft + fright) / 2
+    end select
+
+    deallocate(xpoints, fpoints)
+  end function integrate
+
+end module Integration

Task/Numerical-integration/Fortran/numerical-integration-3.f

@@ -0,0 +1,12 @@
+program IntegrationTest
+  use Integration
+  use FunctionHolder
+  implicit none
+
+  print *, integrate(afun, 0., 3**(1/3.), method='simpson')
+  print *, integrate(afun, 0., 3**(1/3.), method='leftrect')
+  print *, integrate(afun, 0., 3**(1/3.), method='midrect')
+  print *, integrate(afun, 0., 3**(1/3.), method='rightrect')
+  print *, integrate(afun, 0., 3**(1/3.), method='trapezoid')
+
+end program IntegrationTest

Task/Numerical-integration/Fortran/numerical-integration-4.f

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+module FunctionHolder
+  implicit none
+
+contains
+
+  pure function afun(x)
+    real :: afun
+    real, intent(in) :: x
+
+    afun = x**2
+  end function afun
+
+end module FunctionHolder