diff --git a/doc/html/annotated.html b/doc/html/annotated.html index 7da6065..8e611cb 100644 --- a/doc/html/annotated.html +++ b/doc/html/annotated.html @@ -3,8 +3,7 @@ - - + integral: Data Types List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
@@ -109,7 +135,7 @@
diff --git a/doc/html/dir_68267d1309a1af8e8297ef4c3efbcdba.html b/doc/html/dir_68267d1309a1af8e8297ef4c3efbcdba.html index 91d359b..64b820a 100644 --- a/doc/html/dir_68267d1309a1af8e8297ef4c3efbcdba.html +++ b/doc/html/dir_68267d1309a1af8e8297ef4c3efbcdba.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src Directory Reference + +integral: D:/users/christopherson/Code/integral/src Directory Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
+ + +

+Files

@@ -93,7 +120,7 @@
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} -p.reference, p.definition { - font: 400 14px/22px Roboto,sans-serif; -} - /* @group Heading Levels */ h1.groupheader { @@ -177,7 +173,7 @@ pre.fragment { } div.fragment { - padding: 0px; + padding: 4px 6px; margin: 4px 8px 4px 2px; background-color: #FBFCFD; border: 1px solid #C4CFE5; @@ -236,15 +232,6 @@ span.lineno a:hover { background-color: #C8C8C8; } -.lineno { - -webkit-touch-callout: none; - -webkit-user-select: none; - -khtml-user-select: none; - -moz-user-select: none; - -ms-user-select: none; - user-select: none; -} - div.ah, span.ah { background-color: black; font-weight: bold; @@ -514,29 +501,6 @@ table.memberdecls { /* Styles for detailed member documentation */ -.memtitle { - padding: 8px; - border-top: 1px solid #A8B8D9; - border-left: 1px solid #A8B8D9; - border-right: 1px solid #A8B8D9; - border-top-right-radius: 4px; - border-top-left-radius: 4px; - margin-bottom: -1px; - background-image: url('nav_f.png'); - background-repeat: repeat-x; - background-color: #E2E8F2; 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    diff --git a/doc/html/functions.html b/doc/html/functions.html index 51d69cb..2c23868 100644 --- a/doc/html/functions.html +++ b/doc/html/functions.html @@ -3,8 +3,7 @@ - - + integral: Data Fields @@ -15,10 +14,14 @@ + @@ -38,19 +41,60 @@
    - + - - - - + + + +
    - + - - - - + + + +
    - + - - - - + + +
    diff --git a/doc/html/hierarchy.html b/doc/html/hierarchy.html index 9831ad2..33fa1b0 100644 --- a/doc/html/hierarchy.html +++ b/doc/html/hierarchy.html @@ -3,8 +3,7 @@ - - + integral: Class Hierarchy @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    diff --git a/doc/html/index.html b/doc/html/index.html index 6c33e48..dd32474 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -3,8 +3,7 @@ - - + integral: Main Page @@ -15,10 +14,14 @@ + @@ -38,19 +41,34 @@
    - + - - - - +
    -
    +

    +Introduction

    +

    INTEGRAL is a Fortran library providing an easy-to-use, object-oriented interface to several integration routines. Integration of functions of one variable are provided by the QUADPACK library. Integration of systems of ordinary differential equations are provided by the ODEPACK library.

    +
    +double_pendulum_example_short_time_no_legend.png +
    +
    diff --git a/doc/html/integral__adaptive__integrator_8f90_source.html b/doc/html/integral__adaptive__integrator_8f90_source.html index 8742d80..8843aa3 100644 --- a/doc/html/integral__adaptive__integrator_8f90_source.html +++ b/doc/html/integral__adaptive__integrator_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_adaptive_integrator.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_adaptive_integrator.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_adaptive_integrator.f90
    2 
    3 submodule(integral_core) integral_adaptive_integrator
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module subroutine ai_init(this, err)
    7  ! Arguments
    8  class(adaptive_integrator), intent(inout) :: this
    9  class(errors), intent(inout), optional, target :: err
    10 
    11  ! Local Variables
    12  class(errors), pointer :: errmgr
    13  type(errors), target :: deferr
    14  integer(int32) :: flag, liwork, lwork, n
    15  logical :: use_breakpoints
    16 
    17  ! Initialization
    18  if (present(err)) then
    19  errmgr => err
    20  else
    21  errmgr => deferr
    22  end if
    23  use_breakpoints = .false.
    24  if (this%get_use_breakpoints()) then
    25  if (allocated(this%m_breakpoints)) use_breakpoints = .true.
    26  end if
    27 
    28  ! Allocate memory
    29  if (use_breakpoints) then
    30  n = size(this%m_breakpoints) + 2
    31  liwork = max(2 * this%get_max_subintervals() + n, 3 * n - 2)
    32  lwork = liwork * 2 - n
    33  else
    34  liwork = this%get_max_subintervals()
    35  lwork = 4 * liwork
    36  end if
    37 
    38  if (.not.allocated(this%m_iwork)) then
    39  allocate(this%m_iwork(liwork), stat = flag)
    40  else
    41  if (size(this%m_iwork) < liwork) then
    42  deallocate(this%m_iwork)
    43  allocate(this%m_iwork(liwork), stat = flag)
    44  end if
    45  end if
    46  if (flag == 0) then
    47  if (.not.allocated(this%m_work)) then
    48  allocate(this%m_work(lwork), stat = flag)
    49  else
    50  if (size(this%m_work) < lwork) then
    51  deallocate(this%m_work)
    52  allocate(this%m_work(lwork), stat = flag)
    53  end if
    54  end if
    55  end if
    56 
    57  ! Report any errors
    58  if (flag /= 0) then
    59  call errmgr%report_error("ai_init", &
    60  "Insufficient memory available.", int_out_of_memory_error)
    61  return
    62  end if
    63  end subroutine
    64 
    65 ! ------------------------------------------------------------------------------
    66  module function ai_integrate(this, fcn, a, b, info, err) result(rst)
    67  ! Arguments
    68  class(adaptive_integrator), intent(inout) :: this
    69  procedure(integrand), intent(in), pointer :: fcn
    70  real(real64), intent(in) :: a, b
    71  type(integration_behavior), intent(out), optional :: info
    72  class(errors), intent(inout), optional, target :: err
    73  real(real64) :: rst
    74 
    75  ! Local Variables
    76  integer(int32) :: ier, neval, limit, lenw, last, leniw, npts, flag
    77  real(real64) :: abserr, epsabs, epsrel
    78  class(errors), pointer :: errmgr
    79  type(errors), target :: deferr
    80  character(len = 256) :: errmsg
    81  logical :: usedqagp
    82  real(real64), allocatable, dimension(:) :: pts
    83 
    84  ! Initialization
    85  if (present(err)) then
    86  errmgr => err
    87  else
    88  errmgr => deferr
    89  end if
    90 
    91  usedqagp = .false.
    92  if (this%get_use_breakpoints()) then
    93  if (allocated(this%m_breakpoints)) then
    94  npts = size(this%m_breakpoints) + 2
    95  allocate(pts(npts), stat = flag)
    96  if (flag /= 0) then
    97  call errmgr%report_error("ai_integrate", &
    98  "Insufficient memory available.", &
    99  int_out_of_memory_error)
    100  return
    101  end if
    102  pts(2:npts-1) = this%m_breakpoints
    103  pts(1) = a
    104  pts(npts) = b
    105  usedqagp = .true.
    106  end if
    107  end if
    108 
    109  call this%initialize(errmgr)
    110  if (errmgr%has_error_occurred()) return
    111 
    112  limit = this%get_max_subintervals()
    113  leniw = size(this%m_iwork)
    114  lenw = size(this%m_work)
    115  epsabs = this%get_abs_tol()
    116  epsrel = this%get_rel_tol()
    117 
    118  ! Compute the integral
    119  if (usedqagp) then
    120  call dqagp(local_fcn, a, b, npts, pts, epsabs, epsrel, &
    121  rst, abserr, neval, ier, leniw, lenw, last, iwork, work)
    122  else
    123  call dqags(local_fcn, a, b, epsabs, epsrel, rst, abserr, neval, &
    124  ier, limit, lenw, last, this%m_iwork, this%m_work)
    125  end if
    126 
    127  ! Collect info regarding the integration process
    128  if (present(info)) then
    129  info%error_estimate = abserr
    130  info%evaluation_count = neval
    131  info%subinterval_count = last
    132  end if
    133 
    134  ! Check for errors
    135  select case (ier)
    136  case (1)
    137  write(errmsg, '(AI0A)') "The maximum number (", limit, &
    138  ") of subdivisions allowed has been achieved."
    139  call errmgr%report_error("ai_integrate", trim(errmsg), &
    140  int_count_exceeded_error)
    141  return
    142  case (2)
    143  call errmgr%report_error("ai_integrate", &
    144  "The occurence of roundoff error has been detected " // &
    145  "thereby preventing the requested tolerance from being " // &
    146  "achieved.", int_round_off_error)
    147  return
    148  case (3)
    149  call errmgr%report_error("ai_integrate", &
    150  "The integrand appears to be behaving too poorly to proceed.", &
    151  int_integrand_behavior_error)
    152  return
    153  case (4)
    154  call errmgr%report_error("ai_integrate", &
    155  "The algorithm cannot converge with the assigned tolerances.", &
    156  int_convergence_error)
    157  return
    158  case (5)
    159  call errmgr%report_error("ai_integrate", &
    160  "The integral is likely divergent", int_divergent_error)
    161  return
    162  case (6)
    163  call errmgr%report_error("ai_integrate", &
    164  "An invalid input has been provided.", int_invalid_input_error)
    165  return
    166  end select
    167 
    168  contains
    169  ! This is required as the F77 code doesn't deal with procedure pointers
    170  function local_fcn(xarg) result(frst)
    171  real(real64), intent(in) :: xarg
    172  real(real64) :: frst
    173  frst = fcn(xarg)
    174  end function
    175  end function
    176 
    177 ! ------------------------------------------------------------------------------
    178  pure module function ai_get_use_brkpnts(this) result(x)
    179  class(adaptive_integrator), intent(in) :: this
    180  logical :: x
    181  x = this%m_userDefinedBreaks
    182  end function
    183 
    184 ! --------------------
    185  module subroutine ai_set_use_brkpnts(this, x)
    186  class(adaptive_integrator), intent(inout) :: this
    187  logical, intent(in) :: x
    188  this%m_userDefinedBreaks = x
    189  end subroutine
    190 
    191 ! ------------------------------------------------------------------------------
    192  module function ai_get_breakpoints(this) result(x)
    193  class(adaptive_integrator), intent(in) :: this
    194  real(real64), allocatable, dimension(:) :: x
    195  if (allocated(this%m_breakpoints)) then
    196  x = this%m_breakpoints
    197  end if
    198  end function
    199 
    200 ! --------------------
    201  module subroutine ai_set_breakpoints(this, x)
    202  class(adaptive_integrator), intent(inout) :: this
    203  real(real64), intent(in), dimension(:) :: x
    204  if (allocated(this%m_breakpoints)) deallocate(this%m_breakpoints)
    205  this%m_breakpoints = x
    206  call this%set_use_breakpoints(.true.)
    207  end subroutine
    208 
    209 ! ------------------------------------------------------------------------------
    210 end submodule
    +
    1 ! integral_adaptive_integrator.f90
    2 
    3 submodule(integral_core) integral_adaptive_integrator
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module subroutine ai_init(this, err)
    7  ! Arguments
    8  class(adaptive_integrator), intent(inout) :: this
    9  class(errors), intent(inout), optional, target :: err
    10 
    11  ! Local Variables
    12  class(errors), pointer :: errmgr
    13  type(errors), target :: deferr
    14  integer(int32) :: flag, liwork, lwork, n
    15  logical :: use_breakpoints
    16 
    17  ! Initialization
    18  if (present(err)) then
    19  errmgr => err
    20  else
    21  errmgr => deferr
    22  end if
    23  use_breakpoints = .false.
    24  if (this%get_use_breakpoints()) then
    25  if (allocated(this%m_breakpoints)) use_breakpoints = .true.
    26  end if
    27 
    28  ! Allocate memory
    29  if (use_breakpoints) then
    30  n = size(this%m_breakpoints) + 2
    31  liwork = max(2 * this%get_max_subintervals() + n, 3 * n - 2)
    32  lwork = liwork * 2 - n
    33  else
    34  liwork = this%get_max_subintervals()
    35  lwork = 4 * liwork
    36  end if
    37 
    38  if (.not.allocated(this%m_iwork)) then
    39  allocate(this%m_iwork(liwork), stat = flag)
    40  else
    41  if (size(this%m_iwork) < liwork) then
    42  deallocate(this%m_iwork)
    43  allocate(this%m_iwork(liwork), stat = flag)
    44  end if
    45  end if
    46  if (flag == 0) then
    47  if (.not.allocated(this%m_work)) then
    48  allocate(this%m_work(lwork), stat = flag)
    49  else
    50  if (size(this%m_work) < lwork) then
    51  deallocate(this%m_work)
    52  allocate(this%m_work(lwork), stat = flag)
    53  end if
    54  end if
    55  end if
    56 
    57  ! Report any errors
    58  if (flag /= 0) then
    59  call errmgr%report_error("ai_init", &
    60  "Insufficient memory available.", int_out_of_memory_error)
    61  return
    62  end if
    63  end subroutine
    64 
    65 ! ------------------------------------------------------------------------------
    66  module function ai_integrate(this, fcn, a, b, info, err) result(rst)
    67  ! Arguments
    68  class(adaptive_integrator), intent(inout) :: this
    69  procedure(integrand), intent(in), pointer :: fcn
    70  real(real64), intent(in) :: a, b
    71  type(integration_behavior), intent(out), optional :: info
    72  class(errors), intent(inout), optional, target :: err
    73  real(real64) :: rst
    74 
    75  ! Local Variables
    76  integer(int32) :: ier, neval, limit, lenw, last, leniw, npts, flag
    77  real(real64) :: abserr, epsabs, epsrel
    78  class(errors), pointer :: errmgr
    79  type(errors), target :: deferr
    80  character(len = 256) :: errmsg
    81  logical :: usedqagp
    82  real(real64), allocatable, dimension(:) :: pts
    83 
    84  ! Initialization
    85  if (present(err)) then
    86  errmgr => err
    87  else
    88  errmgr => deferr
    89  end if
    90 
    91  usedqagp = .false.
    92  if (this%get_use_breakpoints()) then
    93  if (allocated(this%m_breakpoints)) then
    94  npts = size(this%m_breakpoints) + 2
    95  allocate(pts(npts), stat = flag)
    96  if (flag /= 0) then
    97  call errmgr%report_error("ai_integrate", &
    98  "Insufficient memory available.", &
    99  int_out_of_memory_error)
    100  return
    101  end if
    102  pts(2:npts-1) = this%m_breakpoints
    103  pts(1) = a
    104  pts(npts) = b
    105  usedqagp = .true.
    106  end if
    107  end if
    108 
    109  call this%initialize(errmgr)
    110  if (errmgr%has_error_occurred()) return
    111 
    112  limit = this%get_max_subintervals()
    113  leniw = size(this%m_iwork)
    114  lenw = size(this%m_work)
    115  epsabs = this%get_abs_tol()
    116  epsrel = this%get_rel_tol()
    117 
    118  ! Compute the integral
    119  if (usedqagp) then
    120  call dqagp(local_fcn, a, b, npts, pts, epsabs, epsrel, &
    121  rst, abserr, neval, ier, leniw, lenw, last, iwork, work)
    122  else
    123  call dqags(local_fcn, a, b, epsabs, epsrel, rst, abserr, neval, &
    124  ier, limit, lenw, last, this%m_iwork, this%m_work)
    125  end if
    126 
    127  ! Collect info regarding the integration process
    128  if (present(info)) then
    129  info%error_estimate = abserr
    130  info%evaluation_count = neval
    131  info%subinterval_count = last
    132  end if
    133 
    134  ! Check for errors
    135  select case (ier)
    136  case (1)
    137  write(errmsg, '(AI0A)') "The maximum number (", limit, &
    138  ") of subdivisions allowed has been achieved."
    139  call errmgr%report_error("ai_integrate", trim(errmsg), &
    140  int_count_exceeded_error)
    141  return
    142  case (2)
    143  call errmgr%report_error("ai_integrate", &
    144  "The occurence of roundoff error has been detected " // &
    145  "thereby preventing the requested tolerance from being " // &
    146  "achieved.", int_round_off_error)
    147  return
    148  case (3)
    149  call errmgr%report_error("ai_integrate", &
    150  "The integrand appears to be behaving too poorly to proceed.", &
    151  int_integrand_behavior_error)
    152  return
    153  case (4)
    154  call errmgr%report_error("ai_integrate", &
    155  "The algorithm cannot converge with the assigned tolerances.", &
    156  int_convergence_error)
    157  return
    158  case (5)
    159  call errmgr%report_error("ai_integrate", &
    160  "The integral is likely divergent", int_divergent_error)
    161  return
    162  case (6)
    163  call errmgr%report_error("ai_integrate", &
    164  "An invalid input has been provided.", int_invalid_input_error)
    165  return
    166  end select
    167 
    168  contains
    169  ! This is required as the F77 code doesn't deal with procedure pointers
    170  function local_fcn(xarg) result(frst)
    171  real(real64), intent(in) :: xarg
    172  real(real64) :: frst
    173  frst = fcn(xarg)
    174  end function
    175  end function
    176 
    177 ! ------------------------------------------------------------------------------
    178  pure module function ai_get_use_brkpnts(this) result(x)
    179  class(adaptive_integrator), intent(in) :: this
    180  logical :: x
    181  x = this%m_userDefinedBreaks
    182  end function
    183 
    184 ! --------------------
    185  module subroutine ai_set_use_brkpnts(this, x)
    186  class(adaptive_integrator), intent(inout) :: this
    187  logical, intent(in) :: x
    188  this%m_userDefinedBreaks = x
    189  end subroutine
    190 
    191 ! ------------------------------------------------------------------------------
    192  module function ai_get_breakpoints(this) result(x)
    193  class(adaptive_integrator), intent(in) :: this
    194  real(real64), allocatable, dimension(:) :: x
    195  if (allocated(this%m_breakpoints)) then
    196  x = this%m_breakpoints
    197  end if
    198  end function
    199 
    200 ! --------------------
    201  module subroutine ai_set_breakpoints(this, x)
    202  class(adaptive_integrator), intent(inout) :: this
    203  real(real64), intent(in), dimension(:) :: x
    204  if (allocated(this%m_breakpoints)) deallocate(this%m_breakpoints)
    205  this%m_breakpoints = x
    206  call this%set_use_breakpoints(.true.)
    207  end subroutine
    208 
    209 ! ------------------------------------------------------------------------------
    210 end submodule
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    diff --git a/doc/html/integral__core_8f90_source.html b/doc/html/integral__core_8f90_source.html index 75971f3..2014445 100644 --- a/doc/html/integral__core_8f90_source.html +++ b/doc/html/integral__core_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_core.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_core.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_core.f90
    2 
    3 module integral_core
    4  use, intrinsic :: iso_fortran_env, only : int32, real64
    5  use ferror
    6  implicit none
    7  private
    8  public :: int_out_of_memory_error
    9  public :: int_count_exceeded_error
    10  public :: int_round_off_error
    11  public :: int_integrand_behavior_error
    12  public :: int_convergence_error
    13  public :: int_divergent_error
    14  public :: int_invalid_input_error
    15  public :: int_lack_of_definition_error
    16  public :: int_array_size_mismatch_error
    17  public :: int_excessive_work_error
    18  public :: int_impractical_tolerance_error
    19  public :: int_repeated_error_test_failure
    20  public :: int_15_point_rule
    21  public :: int_21_point_rule
    22  public :: int_31_point_rule
    23  public :: int_41_point_rule
    24  public :: int_51_point_rule
    25  public :: int_61_point_rule
    26  public :: integrand
    27  public :: ode_fcn
    28  public :: ode_jacobian
    29  public :: ode_constraint
    30  public :: integration_behavior
    31  public :: integrator_base
    32  public :: finite_interval_integrator
    33  public :: finite_interval_fcn
    34  public :: adaptive_integrator
    35  public :: nonadaptive_integrator
    36  public :: ode_helper
    37  public :: ode_integrator
    38  public :: ode_integrator_interface
    39  public :: ode_integrator_reset
    40  public :: ode_auto
    41 
    42 ! ------------------------------------------------------------------------------
    44  integer(int32), parameter :: int_out_of_memory_error = 1
    47  integer(int32), parameter :: int_count_exceeded_error = 2
    49  integer(int32), parameter :: int_round_off_error = 3
    51  integer(int32), parameter :: int_integrand_behavior_error = 4
    53  integer(int32), parameter :: int_convergence_error = 5
    55  integer(int32), parameter :: int_divergent_error = 6
    57  integer(int32), parameter :: int_invalid_input_error = 7
    59  integer(int32), parameter :: int_lack_of_definition_error = 8
    61  integer(int32), parameter :: int_array_size_mismatch_error = 9
    62  integer(int32), parameter :: int_excessive_work_error = 10
    63  integer(int32), parameter :: int_impractical_tolerance_error = 11
    64  integer(int32), parameter :: int_repeated_error_test_failure = 12
    65 
    66 ! ------------------------------------------------------------------------------
    68  integer(int32), parameter :: int_15_point_rule = 15
    70  integer(int32), parameter :: int_21_point_rule = 21
    72  integer(int32), parameter :: int_31_point_rule = 31
    74  integer(int32), parameter :: int_41_point_rule = 41
    76  integer(int32), parameter :: int_51_point_rule = 51
    78  integer(int32), parameter :: int_61_point_rule = 61
    79 
    80 ! ------------------------------------------------------------------------------
    81  interface
    82 
    87  function integrand(x) result(f)
    88  use, intrinsic :: iso_fortran_env, only : real64
    89  real(real64), intent(in) :: x
    90  real(real64) :: f
    91  end function
    92 
    102  subroutine ode_fcn(x, y, dydx)
    103  use, intrinsic :: iso_fortran_env, only : real64
    104  real(real64), intent(in) :: x
    105  real(real64), intent(in), dimension(:) :: y
    106  real(real64), intent(out), dimension(:) :: dydx
    107  end subroutine
    108 
    117  subroutine ode_jacobian(x, y, jac)
    118  use, intrinsic :: iso_fortran_env, only : real64
    119  real(real64), intent(in) :: x
    120  real(real64), intent(in), dimension(:) :: y
    121  real(real64), intent(out), dimension(:,:) :: jac
    122  end subroutine
    123 
    133  subroutine ode_constraint(x, y, f)
    134  use, intrinsic :: iso_fortran_env, only : real64
    135  real(real64), intent(in) :: x
    136  real(real64), intent(in), dimension(:) :: y
    137  real(real64), intent(out), dimension(:) :: f
    138  end subroutine
    139  end interface
    140 
    141 ! ------------------------------------------------------------------------------
    143  type integration_behavior
    145  real(real64) :: error_estimate
    147  integer(int32) :: evaluation_count
    150  integer(int32) :: subinterval_count
    151  end type
    152 
    153 ! ******************************************************************************
    154 ! INTEGRAL_INTEGRATOR_BASE.F90
    155 ! ------------------------------------------------------------------------------
    157  type integrator_base
    158  private
    160  real(real64) :: m_abstol = 1.0d-8
    162  real(real64) :: m_reltol = 1.0d-8
    164  integer(int32) :: m_maxint = 10
    165  contains
    175  procedure, public :: get_abs_tol => ib_get_abs_tol
    185  procedure, public :: set_abs_tol => ib_set_abs_tol
    195  procedure, public :: get_rel_tol => ib_get_rel_tol
    205  procedure, public :: set_rel_tol => ib_set_rel_tol
    216  procedure, public :: get_max_subintervals => ib_get_max_subintervals
    227  procedure, public :: ib_set_max_subintervals => ib_set_max_subintervals
    228  end type
    229 
    230 ! ------------------------------------------------------------------------------
    231  interface
    232  pure module function ib_get_abs_tol(this) result(x)
    233  class(integrator_base), intent(in) :: this
    234  real(real64) :: x
    235  end function
    236 
    237  module subroutine ib_set_abs_tol(this, x)
    238  class(integrator_base), intent(inout) :: this
    239  real(real64), intent(in) :: x
    240  end subroutine
    241 
    242  pure module function ib_get_rel_tol(this) result(x)
    243  class(integrator_base), intent(in) :: this
    244  real(real64) :: x
    245  end function
    246 
    247  module subroutine ib_set_rel_tol(this, x)
    248  class(integrator_base), intent(inout) :: this
    249  real(real64), intent(in) :: x
    250  end subroutine
    251 
    252  pure module function ib_get_max_subintervals(this) result(x)
    253  class(integrator_base), intent(in) :: this
    254  integer(int32) :: x
    255  end function
    256 
    257  module subroutine ib_set_max_subintervals(this, x)
    258  class(integrator_base), intent(inout) :: this
    259  integer(int32), intent(in) :: x
    260  end subroutine
    261  end interface
    262 
    263 ! ******************************************************************************
    266  type, abstract, extends(integrator_base) :: finite_interval_integrator
    267  contains
    269  procedure(finite_interval_fcn), public, deferred, pass :: integrate
    270  end type
    271 
    272  interface
    273 
    285  function finite_interval_fcn(this, fcn, a, b, info, err) result(rst)
    286  use, intrinsic :: iso_fortran_env, only : real64
    287  use ferror
    288  import finite_interval_integrator
    289  import integrand
    290  import integration_behavior
    291  class(finite_interval_integrator), intent(inout) :: this
    292  procedure(integrand), intent(in), pointer :: fcn
    293  real(real64), intent(in) :: a, b
    294  type(integration_behavior), intent(out), optional :: info
    295  class(errors), intent(inout), optional, target :: err
    296  real(real64) :: rst
    297  end function
    298  end interface
    299 
    300 ! ******************************************************************************
    301 ! INTEGRAL_ADAPTIVE_INTEGRATOR.F90
    302 ! ------------------------------------------------------------------------------
    351  type, extends(finite_interval_integrator) :: adaptive_integrator
    352  private
    354  real(real64), allocatable, dimension(:) :: m_work
    356  integer(int32), allocatable, dimension(:) :: m_iwork
    358  logical :: m_userdefinedbreaks = .false.
    360  real(real64), allocatable, dimension(:) :: m_breakpoints
    361  contains
    376  procedure, public :: initialize => ai_init
    412  procedure, public :: integrate => ai_integrate
    425  procedure, public :: get_use_breakpoints => ai_get_use_brkpnts
    438  procedure, public :: set_use_breakpoints => ai_set_use_brkpnts
    449  procedure, public :: get_breakpoints => ai_get_breakpoints
    462  procedure, public :: set_breakpoints => ai_set_breakpoints
    463  end type
    464 
    465 ! ------------------------------------------------------------------------------
    466  interface
    467  module subroutine ai_init(this, err)
    468  class(adaptive_integrator), intent(inout) :: this
    469  class(errors), intent(inout), optional, target :: err
    470  end subroutine
    471 
    472  module function ai_integrate(this, fcn, a, b, info, err) result(rst)
    473  class(adaptive_integrator), intent(inout) :: this
    474  procedure(integrand), intent(in), pointer :: fcn
    475  real(real64), intent(in) :: a, b
    476  type(integration_behavior), intent(out), optional :: info
    477  class(errors), intent(inout), optional, target :: err
    478  real(real64) :: rst
    479  end function
    480 
    481  pure module function ai_get_use_brkpnts(this) result(x)
    482  class(adaptive_integrator), intent(in) :: this
    483  logical :: x
    484  end function
    485 
    486  module subroutine ai_set_use_brkpnts(this, x)
    487  class(adaptive_integrator), intent(inout) :: this
    488  logical, intent(in) :: x
    489  end subroutine
    490 
    491  module function ai_get_breakpoints(this) result(x)
    492  class(adaptive_integrator), intent(in) :: this
    493  real(real64), allocatable, dimension(:) :: x
    494  end function
    495 
    496  module subroutine ai_set_breakpoints(this, x)
    497  class(adaptive_integrator), intent(inout) :: this
    498  real(real64), intent(in), dimension(:) :: x
    499  end subroutine
    500  end interface
    501 
    502 ! ******************************************************************************
    503 ! INTEGRAL_NONADAPTIVE_INTEGRATOR.F90
    504 ! ------------------------------------------------------------------------------
    508  type, extends(finite_interval_integrator) :: nonadaptive_integrator
    509  private
    511  integer(int32) :: m_rule = int_15_point_rule
    512  contains
    537  procedure, public :: integrate => ni_integrate
    555  procedure, public :: get_rule => ni_get_rule
    578  procedure, public :: set_rule => ni_set_rule
    579  end type
    580 
    581 ! ------------------------------------------------------------------------------
    582  interface
    583  module function ni_integrate(this, fcn, a, b, info, err) result(rst)
    584  class(nonadaptive_integrator), intent(inout) :: this
    585  procedure(integrand), intent(in), pointer :: fcn
    586  real(real64), intent(in) :: a, b
    587  type(integration_behavior), intent(out), optional :: info
    588  class(errors), intent(inout), optional, target :: err
    589  real(real64) :: rst
    590  end function
    591 
    592  pure module function ni_get_rule(this) result(x)
    593  class(nonadaptive_integrator), intent(in) :: this
    594  integer(int32) :: x
    595  end function
    596 
    597  module subroutine ni_set_rule(this, x, err)
    598  class(nonadaptive_integrator), intent(inout) :: this
    599  integer(int32), intent(in) :: x
    600  class(errors), intent(inout), optional, target :: err
    601  end subroutine
    602  end interface
    603 
    604 ! ******************************************************************************
    605 ! INTEGRAL_ODE_HELPER.F90
    606 ! ------------------------------------------------------------------------------
    609  type :: ode_helper
    610  private
    612  procedure(ode_fcn), pointer, nopass :: m_fcn => null()
    614  procedure(ode_jacobian), pointer, nopass :: m_jac => null()
    616  procedure(ode_constraint), pointer, nopass :: m_rts => null()
    618  integer(int32) :: m_count = 0
    620  integer(int32) :: m_constraints = 0
    621  contains
    712  procedure, public :: define_equations => oh_init
    722  procedure, public :: get_equation_count => oh_get_count
    735  procedure, public :: get_equations_defined => oh_is_fcn_defined
    748  procedure, public :: get_jacobian_defined => oh_is_jac_defined
    883  procedure, public :: define_constraints => oh_define_constraints
    893  procedure, public :: get_constraint_count => oh_get_constraint_count
    904  procedure, public :: get_constraints_defined => oh_get_constraints_defined
    905  !! @brief Evaluates the routine containing the system of ODEs.
    906  !!
    907  !! @par Syntax
    908  !! @code{.f90}
    909  !! subroutine evaluate_ode(class(ode_helper) this, real(real64) x, real(real64) y(:), real(real64) dydx(:))
    910  !! @endcode
    911  !!
    912  !! @param[in,out] this The ode_helper object.
    913  !! @param[in] x The value of the independent variable at which to
    914  !! evalaute the ODEs.
    915  !! @param[in] y An N-element array cotnaining the current estimates
    916  !! of the dependent variables as evaluated at @p x.
    917  !! @param[out] dydx An N-element array where the values of the ODEs
    918  !! as evaluated at @p x are to be written.
    919  procedure, public :: evaluate_ode => oh_eval
    933  procedure, public :: evaluate_jacobian => oh_eval_jac
    948  procedure, public :: evaluate_constraints => oh_eval_constraints
    949  end type
    950 
    951  interface
    952  module subroutine oh_init(this, neqn, fcn, jac)
    953  class(ode_helper), intent(inout) :: this
    954  integer(int32), intent(in) :: neqn
    955  procedure(ode_fcn), pointer, intent(in) :: fcn
    956  procedure(ode_jacobian), pointer, intent(in), optional :: jac
    957  end subroutine
    958 
    959  pure module function oh_get_count(this) result(x)
    960  class(ode_helper), intent(in) :: this
    961  integer(int32) :: x
    962  end function
    963 
    964  pure module function oh_is_fcn_defined(this) result(x)
    965  class(ode_helper), intent(in) :: this
    966  logical :: x
    967  end function
    968 
    969  pure module function oh_is_jac_defined(this) result(x)
    970  class(ode_helper), intent(in) :: this
    971  logical :: x
    972  end function
    973 
    974  module subroutine oh_define_constraints(this, n, fcn)
    975  class(ode_helper), intent(inout) :: this
    976  integer(int32), intent(in) :: n
    977  procedure(ode_constraint), intent(in), pointer :: fcn
    978  end subroutine
    979 
    980  pure module function oh_get_constraint_count(this) result(x)
    981  class(ode_helper), intent(in) :: this
    982  integer(int32) :: x
    983  end function
    984 
    985  pure module function oh_get_constraints_defined(this) result(x)
    986  class(ode_helper), intent(in) :: this
    987  logical :: x
    988  end function
    989 
    990  module subroutine oh_eval(this, x, y, dydx)
    991  class(ode_helper), intent(inout) :: this
    992  real(real64), intent(in) :: x
    993  real(real64), intent(in), dimension(:) :: y
    994  real(real64), intent(out), dimension(:) :: dydx
    995  end subroutine
    996 
    997  module subroutine oh_eval_jac(this, x, y, jac)
    998  class(ode_helper), intent(inout) :: this
    999  real(real64), intent(in) :: x
    1000  real(real64), intent(in), dimension(:) :: y
    1001  real(real64), intent(out), dimension(:,:) :: jac
    1002  end subroutine
    1003 
    1004  module subroutine oh_eval_constraints(this, x, y, f)
    1005  class(ode_helper), intent(inout) :: this
    1006  real(real64), intent(in) :: x
    1007  real(real64), intent(in), dimension(:) :: y
    1008  real(real64), intent(out), dimension(:) :: f
    1009  end subroutine
    1010  end interface
    1011 
    1012 ! ******************************************************************************
    1013 ! INTEGRAL_ODE_INTEGRATOR.F90
    1014 ! ------------------------------------------------------------------------------
    1015  type, abstract :: ode_integrator
    1017  real(real64), allocatable, dimension(:) :: m_rtol
    1019  real(real64), allocatable, dimension(:) :: m_atol
    1022  logical :: m_alloutput = .true.
    1026  logical :: m_canovershoot = .true.
    1029  real(real64) :: m_criticalpoint = 0.0d0
    1031  integer(int32) :: m_minbuffersize = 500
    1034  real(real64) :: m_maxstepsize = 1.0d0
    1037  logical :: m_limitstepsize = .false.
    1039  integer(int32) :: m_maxstepcount = 500
    1040  contains
    1075  procedure, public :: integrate => oi_integrate
    1087  procedure, public :: get_provide_all_output => oi_get_use_all_output
    1100  procedure, public :: set_provide_all_output => oi_set_use_all_output
    1112  procedure, public :: get_allow_overshoot => oi_get_allow_overshoot
    1125  procedure, public :: set_allow_overshoot => oi_set_allow_overshoot
    1136  procedure, public :: get_integration_limit => oi_get_critical_point
    1147  procedure, public :: set_integration_limit => oi_set_critical_point
    1157  procedure, public :: get_min_buffer_size => oi_get_min_buffer_size
    1169  procedure, public :: set_min_buffer_size => oi_set_min_buffer_size
    1179  procedure, public :: get_max_step_size => oi_get_max_step_size
    1190  procedure, public :: set_max_step_size => oi_set_max_step_size
    1201  procedure, public :: get_limit_step_size => oi_get_limit_step_size
    1214  procedure, public :: set_limit_step_size => oi_set_limit_step_size
    1225  procedure, public :: get_iteration_limit => oi_get_iteration_limit
    1236  procedure, public :: set_iteration_limit => oi_set_iteration_limit
    1246  procedure, public :: get_relative_tolerances => oi_get_rtol
    1256  procedure, public :: set_relative_tolerances => oi_set_rtol
    1266  procedure, public :: get_absolute_tolerances => oi_get_atol
    1276  procedure, public :: set_absolute_tolerances => oi_set_atol
    1304  procedure(ode_integrator_interface), public, deferred, pass :: step
    1313  procedure(ode_integrator_reset), public, deferred, pass :: reset
    1314  end type
    1315 
    1316 ! ------------------------------------------------------------------------------
    1317  interface
    1318 
    1340  function ode_integrator_interface(this, fcn, x, y, xout, rtol, atol, err) result(brk)
    1341  use, intrinsic :: iso_fortran_env, only : int32, real64
    1342  use ferror
    1343  import ode_integrator
    1344  import ode_helper
    1345  class(ode_integrator), intent(inout) :: this
    1346  class(ode_helper), intent(inout) :: fcn
    1347  real(real64), intent(inout) :: x
    1348  real(real64), intent(inout), dimension(:) :: y
    1349  real(real64), intent(in) :: xout
    1350  real(real64), intent(in), dimension(:) :: rtol, atol
    1351  class(errors), intent(inout), optional, target :: err
    1352  logical :: brk
    1353  end function
    1354 
    1358  subroutine ode_integrator_reset(this)
    1359  import ode_integrator
    1360  class(ode_integrator), intent(inout) :: this
    1361  end subroutine
    1362 
    1363  module function oi_integrate(this, fcnobj, x, y, err) result(rst)
    1364  class(ode_integrator), intent(inout) :: this
    1365  class(ode_helper), intent(inout) :: fcnobj
    1366  real(real64), intent(in), dimension(:) :: x, y
    1367  class(errors), intent(inout), optional, target :: err
    1368  real(real64), allocatable, dimension(:,:) :: rst
    1369  end function
    1370 
    1371  pure module function oi_get_use_all_output(this) result(x)
    1372  class(ode_integrator), intent(in) :: this
    1373  logical :: x
    1374  end function
    1375 
    1376  module subroutine oi_set_use_all_output(this, x)
    1377  class(ode_integrator), intent(inout) :: this
    1378  logical, intent(in) :: x
    1379  end subroutine
    1380 
    1381  pure module function oi_get_allow_overshoot(this) result(x)
    1382  class(ode_integrator), intent(in) :: this
    1383  logical :: x
    1384  end function
    1385 
    1386  module subroutine oi_set_allow_overshoot(this, x)
    1387  class(ode_integrator), intent(inout) :: this
    1388  logical, intent(in) :: x
    1389  end subroutine
    1390 
    1391  pure module function oi_get_critical_point(this) result(x)
    1392  class(ode_integrator), intent(in) :: this
    1393  real(real64) :: x
    1394  end function
    1395 
    1396  module subroutine oi_set_critical_point(this, x)
    1397  class(ode_integrator), intent(inout) :: this
    1398  real(real64), intent(in) :: x
    1399  end subroutine
    1400 
    1401  pure module function oi_get_min_buffer_size(this) result(x)
    1402  class(ode_integrator), intent(in) :: this
    1403  integer(int32) :: x
    1404  end function
    1405 
    1406  module subroutine oi_set_min_buffer_size(this, x)
    1407  class(ode_integrator), intent(inout) :: this
    1408  integer(int32), intent(in) :: x
    1409  end subroutine
    1410 
    1411  pure module function oi_get_max_step_size(this) result(x)
    1412  class(ode_integrator), intent(in) :: this
    1413  real(real64) :: x
    1414  end function
    1415 
    1416  module subroutine oi_set_max_step_size(this, x)
    1417  class(ode_integrator), intent(inout) :: this
    1418  real(real64), intent(in) :: x
    1419  end subroutine
    1420 
    1421  pure module function oi_get_limit_step_size(this) result(x)
    1422  class(ode_integrator), intent(in) :: this
    1423  logical :: x
    1424  end function
    1425 
    1426  module subroutine oi_set_limit_step_size(this, x)
    1427  class(ode_integrator), intent(inout) :: this
    1428  logical, intent(in) :: x
    1429  end subroutine
    1430 
    1431  pure module function oi_get_iteration_limit(this) result(x)
    1432  class(ode_integrator), intent(in) :: this
    1433  integer(int32) :: x
    1434  end function
    1435 
    1436  module subroutine oi_set_iteration_limit(this, x)
    1437  class(ode_integrator), intent(inout) :: this
    1438  integer(int32), intent(in) :: x
    1439  end subroutine
    1440 
    1441  module function oi_get_rtol(this) result(x)
    1442  class(ode_integrator), intent(in) :: this
    1443  real(real64), allocatable, dimension(:) :: x
    1444  end function
    1445 
    1446  module subroutine oi_set_rtol(this, x)
    1447  class(ode_integrator), intent(inout) :: this
    1448  real(real64), intent(in), dimension(:) :: x
    1449  end subroutine
    1450 
    1451  module function oi_get_atol(this) result(x)
    1452  class(ode_integrator), intent(in) :: this
    1453  real(real64), allocatable, dimension(:) :: x
    1454  end function
    1455 
    1456  module subroutine oi_set_atol(this, x)
    1457  class(ode_integrator), intent(inout) :: this
    1458  real(real64), intent(in), dimension(:) :: x
    1459  end subroutine
    1460  end interface
    1461 
    1462 ! ******************************************************************************
    1463 ! INTEGRAL_ODE_AUTO.F90
    1464 ! ------------------------------------------------------------------------------
    1541  type, extends(ode_integrator) :: ode_auto
    1543  real(real64), allocatable, dimension(:) :: m_rwork
    1545  integer(int32), allocatable, dimension(:) :: m_iwork
    1550  integer(int32), allocatable, dimension(:) :: m_rststats
    1552  integer(int32) :: m_istate = 1
    1553  contains
    1594  procedure, public :: step => oa_step
    1603  procedure, public :: reset => oa_reset_integrator
    1615  procedure, public :: get_constraint_status => oa_get_constraint_info
    1616 
    1617  procedure, private :: init_workspace => oa_init_workspace
    1618  end type
    1619 
    1620  interface
    1621  module function oa_step(this, fcn, x, y, xout, rtol, atol, err) result(brk)
    1622  class(ode_auto), intent(inout) :: this
    1623  class(ode_helper), intent(inout) :: fcn
    1624  real(real64), intent(inout) :: x
    1625  real(real64), intent(inout), dimension(:) :: y
    1626  real(real64), intent(in) :: xout
    1627  real(real64), intent(in), dimension(:) :: rtol, atol
    1628  class(errors), intent(inout), optional, target :: err
    1629  logical :: brk
    1630  end function
    1631 
    1632  module subroutine oa_init_workspace(this, liw, lrw, ncnsts, err)
    1633  class(ode_auto), intent(inout) :: this
    1634  integer(int32), intent(in) :: liw, lrw, ncnsts
    1635  class(errors), intent(inout) :: err
    1636  end subroutine
    1637 
    1638  module subroutine oa_reset_integrator(this)
    1639  class(ode_auto), intent(inout) :: this
    1640  end subroutine
    1641 
    1642  module function oa_get_constraint_info(this) result(x)
    1643  class(ode_auto), intent(in) :: this
    1644  logical, allocatable, dimension(:) :: x
    1645  end function
    1646  end interface
    1647 end module
    integral_core::ode_constraint
    Defines a routine capable of describing constraints on a system of ODEs of N variables exposed to M c...
    Definition: integral_core.f90:133
    -
    integral_core::ode_auto
    Defines an integrator for systems of first order ODEs that is capable of switching between an Adams m...
    Definition: integral_core.f90:1541
    -
    integral_core::ode_jacobian
    Defines a routine capable of computing the Jacobian matrix of a system of N first order ODEs of N var...
    Definition: integral_core.f90:117
    -
    integral_core::ode_fcn
    Defines a routine containing a system of first order ODEs.
    Definition: integral_core.f90:102
    -
    integral_core::ode_integrator_reset
    Resets the state of the integrator.
    Definition: integral_core.f90:1358
    -
    integral_core::ode_integrator_interface
    Defines a routine for computing a single integration step in the direction of xout.
    Definition: integral_core.f90:1340
    -
    integral_core::integrator_base
    Defines a base type for integrator types.
    Definition: integral_core.f90:157
    -
    integral_core::finite_interval_fcn
    Defines the signature of a routine used to integrate a function of one variable over a finite interva...
    Definition: integral_core.f90:285
    -
    integral_core::nonadaptive_integrator
    Defines an integrator that uses a non-adaptive Gauss-Kronrod method to compute the integral of a func...
    Definition: integral_core.f90:508
    -
    integral_core::ode_helper
    Defines a type used to pass information regarding the ODEs to the solver.
    Definition: integral_core.f90:609
    -
    integral_core::integrand
    Defines a function of one variable to be integrated.
    Definition: integral_core.f90:87
    -
    integral_core::finite_interval_integrator
    A type that defines an integrator meant to operate on integrands over a finite region.
    Definition: integral_core.f90:266
    -
    integral_core::ode_integrator
    Definition: integral_core.f90:1015
    -
    integral_core::adaptive_integrator
    Defines an integrator that uses an adaptive Gauss-Kronrod method to compute the integral of a functio...
    Definition: integral_core.f90:351
    -
    integral_core::integration_behavior
    Provides information regarding the behavior of an integrator.
    Definition: integral_core.f90:143
    +
    1 ! integral_core.f90
    2 
    12 
    18 module integral_core
    19  use, intrinsic :: iso_fortran_env, only : int32, real64
    20  use ferror
    21  implicit none
    22  private
    23  public :: int_out_of_memory_error
    24  public :: int_count_exceeded_error
    25  public :: int_round_off_error
    26  public :: int_integrand_behavior_error
    27  public :: int_convergence_error
    28  public :: int_divergent_error
    29  public :: int_invalid_input_error
    30  public :: int_lack_of_definition_error
    31  public :: int_array_size_mismatch_error
    32  public :: int_excessive_work_error
    33  public :: int_impractical_tolerance_error
    34  public :: int_repeated_error_test_failure
    35  public :: int_15_point_rule
    36  public :: int_21_point_rule
    37  public :: int_31_point_rule
    38  public :: int_41_point_rule
    39  public :: int_51_point_rule
    40  public :: int_61_point_rule
    41  public :: integrand
    42  public :: ode_fcn
    43  public :: ode_jacobian
    44  public :: ode_constraint
    45  public :: integration_behavior
    46  public :: integrator_base
    47  public :: finite_interval_integrator
    48  public :: finite_interval_fcn
    49  public :: adaptive_integrator
    50  public :: nonadaptive_integrator
    51  public :: ode_helper
    52  public :: ode_integrator
    53  public :: ode_integrator_interface
    54  public :: ode_integrator_reset
    55  public :: ode_auto
    56 
    57 ! ------------------------------------------------------------------------------
    59  integer(int32), parameter :: int_out_of_memory_error = 1
    62  integer(int32), parameter :: int_count_exceeded_error = 2
    64  integer(int32), parameter :: int_round_off_error = 3
    66  integer(int32), parameter :: int_integrand_behavior_error = 4
    68  integer(int32), parameter :: int_convergence_error = 5
    70  integer(int32), parameter :: int_divergent_error = 6
    72  integer(int32), parameter :: int_invalid_input_error = 7
    74  integer(int32), parameter :: int_lack_of_definition_error = 8
    76  integer(int32), parameter :: int_array_size_mismatch_error = 9
    80  integer(int32), parameter :: int_excessive_work_error = 10
    83  integer(int32), parameter :: int_impractical_tolerance_error = 11
    85  integer(int32), parameter :: int_repeated_error_test_failure = 12
    86 
    87 ! ------------------------------------------------------------------------------
    89  integer(int32), parameter :: int_15_point_rule = 15
    91  integer(int32), parameter :: int_21_point_rule = 21
    93  integer(int32), parameter :: int_31_point_rule = 31
    95  integer(int32), parameter :: int_41_point_rule = 41
    97  integer(int32), parameter :: int_51_point_rule = 51
    99  integer(int32), parameter :: int_61_point_rule = 61
    100 
    101 ! ------------------------------------------------------------------------------
    102  interface
    103 
    108  function integrand(x) result(f)
    109  use, intrinsic :: iso_fortran_env, only : real64
    110  real(real64), intent(in) :: x
    111  real(real64) :: f
    112  end function
    113 
    123  subroutine ode_fcn(x, y, dydx)
    124  use, intrinsic :: iso_fortran_env, only : real64
    125  real(real64), intent(in) :: x
    126  real(real64), intent(in), dimension(:) :: y
    127  real(real64), intent(out), dimension(:) :: dydx
    128  end subroutine
    129 
    138  subroutine ode_jacobian(x, y, jac)
    139  use, intrinsic :: iso_fortran_env, only : real64
    140  real(real64), intent(in) :: x
    141  real(real64), intent(in), dimension(:) :: y
    142  real(real64), intent(out), dimension(:,:) :: jac
    143  end subroutine
    144 
    154  subroutine ode_constraint(x, y, f)
    155  use, intrinsic :: iso_fortran_env, only : real64
    156  real(real64), intent(in) :: x
    157  real(real64), intent(in), dimension(:) :: y
    158  real(real64), intent(out), dimension(:) :: f
    159  end subroutine
    160  end interface
    161 
    162 ! ------------------------------------------------------------------------------
    164  type integration_behavior
    166  real(real64) :: error_estimate
    168  integer(int32) :: evaluation_count
    171  integer(int32) :: subinterval_count
    172  end type
    173 
    174 ! ******************************************************************************
    175 ! INTEGRAL_INTEGRATOR_BASE.F90
    176 ! ------------------------------------------------------------------------------
    178  type integrator_base
    179  private
    181  real(real64) :: m_abstol = 1.0d-8
    183  real(real64) :: m_reltol = 1.0d-8
    185  integer(int32) :: m_maxint = 10
    186  contains
    196  procedure, public :: get_abs_tol => ib_get_abs_tol
    206  procedure, public :: set_abs_tol => ib_set_abs_tol
    216  procedure, public :: get_rel_tol => ib_get_rel_tol
    226  procedure, public :: set_rel_tol => ib_set_rel_tol
    237  procedure, public :: get_max_subintervals => ib_get_max_subintervals
    248  procedure, public :: ib_set_max_subintervals => ib_set_max_subintervals
    249  end type
    250 
    251 ! ------------------------------------------------------------------------------
    252  interface
    253  pure module function ib_get_abs_tol(this) result(x)
    254  class(integrator_base), intent(in) :: this
    255  real(real64) :: x
    256  end function
    257 
    258  module subroutine ib_set_abs_tol(this, x)
    259  class(integrator_base), intent(inout) :: this
    260  real(real64), intent(in) :: x
    261  end subroutine
    262 
    263  pure module function ib_get_rel_tol(this) result(x)
    264  class(integrator_base), intent(in) :: this
    265  real(real64) :: x
    266  end function
    267 
    268  module subroutine ib_set_rel_tol(this, x)
    269  class(integrator_base), intent(inout) :: this
    270  real(real64), intent(in) :: x
    271  end subroutine
    272 
    273  pure module function ib_get_max_subintervals(this) result(x)
    274  class(integrator_base), intent(in) :: this
    275  integer(int32) :: x
    276  end function
    277 
    278  module subroutine ib_set_max_subintervals(this, x)
    279  class(integrator_base), intent(inout) :: this
    280  integer(int32), intent(in) :: x
    281  end subroutine
    282  end interface
    283 
    284 ! ******************************************************************************
    287  type, abstract, extends(integrator_base) :: finite_interval_integrator
    288  contains
    290  procedure(finite_interval_fcn), public, deferred, pass :: integrate
    291  end type
    292 
    293  interface
    294 
    306  function finite_interval_fcn(this, fcn, a, b, info, err) result(rst)
    307  use, intrinsic :: iso_fortran_env, only : real64
    308  use ferror
    309  import finite_interval_integrator
    310  import integrand
    311  import integration_behavior
    312  class(finite_interval_integrator), intent(inout) :: this
    313  procedure(integrand), intent(in), pointer :: fcn
    314  real(real64), intent(in) :: a, b
    315  type(integration_behavior), intent(out), optional :: info
    316  class(errors), intent(inout), optional, target :: err
    317  real(real64) :: rst
    318  end function
    319  end interface
    320 
    321 ! ******************************************************************************
    322 ! INTEGRAL_ADAPTIVE_INTEGRATOR.F90
    323 ! ------------------------------------------------------------------------------
    372  type, extends(finite_interval_integrator) :: adaptive_integrator
    373  private
    375  real(real64), allocatable, dimension(:) :: m_work
    377  integer(int32), allocatable, dimension(:) :: m_iwork
    379  logical :: m_userdefinedbreaks = .false.
    381  real(real64), allocatable, dimension(:) :: m_breakpoints
    382  contains
    397  procedure, public :: initialize => ai_init
    433  procedure, public :: integrate => ai_integrate
    446  procedure, public :: get_use_breakpoints => ai_get_use_brkpnts
    459  procedure, public :: set_use_breakpoints => ai_set_use_brkpnts
    470  procedure, public :: get_breakpoints => ai_get_breakpoints
    483  procedure, public :: set_breakpoints => ai_set_breakpoints
    484  end type
    485 
    486 ! ------------------------------------------------------------------------------
    487  interface
    488  module subroutine ai_init(this, err)
    489  class(adaptive_integrator), intent(inout) :: this
    490  class(errors), intent(inout), optional, target :: err
    491  end subroutine
    492 
    493  module function ai_integrate(this, fcn, a, b, info, err) result(rst)
    494  class(adaptive_integrator), intent(inout) :: this
    495  procedure(integrand), intent(in), pointer :: fcn
    496  real(real64), intent(in) :: a, b
    497  type(integration_behavior), intent(out), optional :: info
    498  class(errors), intent(inout), optional, target :: err
    499  real(real64) :: rst
    500  end function
    501 
    502  pure module function ai_get_use_brkpnts(this) result(x)
    503  class(adaptive_integrator), intent(in) :: this
    504  logical :: x
    505  end function
    506 
    507  module subroutine ai_set_use_brkpnts(this, x)
    508  class(adaptive_integrator), intent(inout) :: this
    509  logical, intent(in) :: x
    510  end subroutine
    511 
    512  module function ai_get_breakpoints(this) result(x)
    513  class(adaptive_integrator), intent(in) :: this
    514  real(real64), allocatable, dimension(:) :: x
    515  end function
    516 
    517  module subroutine ai_set_breakpoints(this, x)
    518  class(adaptive_integrator), intent(inout) :: this
    519  real(real64), intent(in), dimension(:) :: x
    520  end subroutine
    521  end interface
    522 
    523 ! ******************************************************************************
    524 ! INTEGRAL_NONADAPTIVE_INTEGRATOR.F90
    525 ! ------------------------------------------------------------------------------
    529  type, extends(finite_interval_integrator) :: nonadaptive_integrator
    530  private
    532  integer(int32) :: m_rule = int_15_point_rule
    533  contains
    558  procedure, public :: integrate => ni_integrate
    576  procedure, public :: get_rule => ni_get_rule
    599  procedure, public :: set_rule => ni_set_rule
    600  end type
    601 
    602 ! ------------------------------------------------------------------------------
    603  interface
    604  module function ni_integrate(this, fcn, a, b, info, err) result(rst)
    605  class(nonadaptive_integrator), intent(inout) :: this
    606  procedure(integrand), intent(in), pointer :: fcn
    607  real(real64), intent(in) :: a, b
    608  type(integration_behavior), intent(out), optional :: info
    609  class(errors), intent(inout), optional, target :: err
    610  real(real64) :: rst
    611  end function
    612 
    613  pure module function ni_get_rule(this) result(x)
    614  class(nonadaptive_integrator), intent(in) :: this
    615  integer(int32) :: x
    616  end function
    617 
    618  module subroutine ni_set_rule(this, x, err)
    619  class(nonadaptive_integrator), intent(inout) :: this
    620  integer(int32), intent(in) :: x
    621  class(errors), intent(inout), optional, target :: err
    622  end subroutine
    623  end interface
    624 
    625 ! ******************************************************************************
    626 ! INTEGRAL_ODE_HELPER.F90
    627 ! ------------------------------------------------------------------------------
    630  type :: ode_helper
    631  private
    633  procedure(ode_fcn), pointer, nopass :: m_fcn => null()
    635  procedure(ode_jacobian), pointer, nopass :: m_jac => null()
    637  procedure(ode_constraint), pointer, nopass :: m_rts => null()
    639  integer(int32) :: m_count = 0
    641  integer(int32) :: m_constraints = 0
    642  contains
    733  procedure, public :: define_equations => oh_init
    743  procedure, public :: get_equation_count => oh_get_count
    756  procedure, public :: get_equations_defined => oh_is_fcn_defined
    769  procedure, public :: get_jacobian_defined => oh_is_jac_defined
    904  procedure, public :: define_constraints => oh_define_constraints
    914  procedure, public :: get_constraint_count => oh_get_constraint_count
    925  procedure, public :: get_constraints_defined => oh_get_constraints_defined
    926  !! @brief Evaluates the routine containing the system of ODEs.
    927  !!
    928  !! @par Syntax
    929  !! @code{.f90}
    930  !! subroutine evaluate_ode(class(ode_helper) this, real(real64) x, real(real64) y(:), real(real64) dydx(:))
    931  !! @endcode
    932  !!
    933  !! @param[in,out] this The ode_helper object.
    934  !! @param[in] x The value of the independent variable at which to
    935  !! evalaute the ODEs.
    936  !! @param[in] y An N-element array cotnaining the current estimates
    937  !! of the dependent variables as evaluated at @p x.
    938  !! @param[out] dydx An N-element array where the values of the ODEs
    939  !! as evaluated at @p x are to be written.
    940  procedure, public :: evaluate_ode => oh_eval
    954  procedure, public :: evaluate_jacobian => oh_eval_jac
    969  procedure, public :: evaluate_constraints => oh_eval_constraints
    970  end type
    971 
    972  interface
    973  module subroutine oh_init(this, neqn, fcn, jac)
    974  class(ode_helper), intent(inout) :: this
    975  integer(int32), intent(in) :: neqn
    976  procedure(ode_fcn), pointer, intent(in) :: fcn
    977  procedure(ode_jacobian), pointer, intent(in), optional :: jac
    978  end subroutine
    979 
    980  pure module function oh_get_count(this) result(x)
    981  class(ode_helper), intent(in) :: this
    982  integer(int32) :: x
    983  end function
    984 
    985  pure module function oh_is_fcn_defined(this) result(x)
    986  class(ode_helper), intent(in) :: this
    987  logical :: x
    988  end function
    989 
    990  pure module function oh_is_jac_defined(this) result(x)
    991  class(ode_helper), intent(in) :: this
    992  logical :: x
    993  end function
    994 
    995  module subroutine oh_define_constraints(this, n, fcn)
    996  class(ode_helper), intent(inout) :: this
    997  integer(int32), intent(in) :: n
    998  procedure(ode_constraint), intent(in), pointer :: fcn
    999  end subroutine
    1000 
    1001  pure module function oh_get_constraint_count(this) result(x)
    1002  class(ode_helper), intent(in) :: this
    1003  integer(int32) :: x
    1004  end function
    1005 
    1006  pure module function oh_get_constraints_defined(this) result(x)
    1007  class(ode_helper), intent(in) :: this
    1008  logical :: x
    1009  end function
    1010 
    1011  module subroutine oh_eval(this, x, y, dydx)
    1012  class(ode_helper), intent(inout) :: this
    1013  real(real64), intent(in) :: x
    1014  real(real64), intent(in), dimension(:) :: y
    1015  real(real64), intent(out), dimension(:) :: dydx
    1016  end subroutine
    1017 
    1018  module subroutine oh_eval_jac(this, x, y, jac)
    1019  class(ode_helper), intent(inout) :: this
    1020  real(real64), intent(in) :: x
    1021  real(real64), intent(in), dimension(:) :: y
    1022  real(real64), intent(out), dimension(:,:) :: jac
    1023  end subroutine
    1024 
    1025  module subroutine oh_eval_constraints(this, x, y, f)
    1026  class(ode_helper), intent(inout) :: this
    1027  real(real64), intent(in) :: x
    1028  real(real64), intent(in), dimension(:) :: y
    1029  real(real64), intent(out), dimension(:) :: f
    1030  end subroutine
    1031  end interface
    1032 
    1033 ! ******************************************************************************
    1034 ! INTEGRAL_ODE_INTEGRATOR.F90
    1035 ! ------------------------------------------------------------------------------
    1036  type, abstract :: ode_integrator
    1038  real(real64), allocatable, dimension(:) :: m_rtol
    1040  real(real64), allocatable, dimension(:) :: m_atol
    1043  logical :: m_alloutput = .true.
    1047  logical :: m_canovershoot = .true.
    1050  real(real64) :: m_criticalpoint = 0.0d0
    1052  integer(int32) :: m_minbuffersize = 500
    1055  real(real64) :: m_maxstepsize = 1.0d0
    1058  logical :: m_limitstepsize = .false.
    1060  integer(int32) :: m_maxstepcount = 500
    1061  contains
    1096  procedure, public :: integrate => oi_integrate
    1108  procedure, public :: get_provide_all_output => oi_get_use_all_output
    1121  procedure, public :: set_provide_all_output => oi_set_use_all_output
    1133  procedure, public :: get_allow_overshoot => oi_get_allow_overshoot
    1146  procedure, public :: set_allow_overshoot => oi_set_allow_overshoot
    1157  procedure, public :: get_integration_limit => oi_get_critical_point
    1168  procedure, public :: set_integration_limit => oi_set_critical_point
    1178  procedure, public :: get_min_buffer_size => oi_get_min_buffer_size
    1190  procedure, public :: set_min_buffer_size => oi_set_min_buffer_size
    1200  procedure, public :: get_max_step_size => oi_get_max_step_size
    1211  procedure, public :: set_max_step_size => oi_set_max_step_size
    1222  procedure, public :: get_limit_step_size => oi_get_limit_step_size
    1235  procedure, public :: set_limit_step_size => oi_set_limit_step_size
    1246  procedure, public :: get_iteration_limit => oi_get_iteration_limit
    1257  procedure, public :: set_iteration_limit => oi_set_iteration_limit
    1267  procedure, public :: get_relative_tolerances => oi_get_rtol
    1277  procedure, public :: set_relative_tolerances => oi_set_rtol
    1287  procedure, public :: get_absolute_tolerances => oi_get_atol
    1297  procedure, public :: set_absolute_tolerances => oi_set_atol
    1325  procedure(ode_integrator_interface), public, deferred, pass :: step
    1334  procedure(ode_integrator_reset), public, deferred, pass :: reset
    1335  end type
    1336 
    1337 ! ------------------------------------------------------------------------------
    1338  interface
    1339 
    1361  function ode_integrator_interface(this, fcn, x, y, xout, rtol, atol, err) result(brk)
    1362  use, intrinsic :: iso_fortran_env, only : int32, real64
    1363  use ferror
    1364  import ode_integrator
    1365  import ode_helper
    1366  class(ode_integrator), intent(inout) :: this
    1367  class(ode_helper), intent(inout) :: fcn
    1368  real(real64), intent(inout) :: x
    1369  real(real64), intent(inout), dimension(:) :: y
    1370  real(real64), intent(in) :: xout
    1371  real(real64), intent(in), dimension(:) :: rtol, atol
    1372  class(errors), intent(inout), optional, target :: err
    1373  logical :: brk
    1374  end function
    1375 
    1379  subroutine ode_integrator_reset(this)
    1380  import ode_integrator
    1381  class(ode_integrator), intent(inout) :: this
    1382  end subroutine
    1383 
    1384  module function oi_integrate(this, fcnobj, x, y, err) result(rst)
    1385  class(ode_integrator), intent(inout) :: this
    1386  class(ode_helper), intent(inout) :: fcnobj
    1387  real(real64), intent(in), dimension(:) :: x, y
    1388  class(errors), intent(inout), optional, target :: err
    1389  real(real64), allocatable, dimension(:,:) :: rst
    1390  end function
    1391 
    1392  pure module function oi_get_use_all_output(this) result(x)
    1393  class(ode_integrator), intent(in) :: this
    1394  logical :: x
    1395  end function
    1396 
    1397  module subroutine oi_set_use_all_output(this, x)
    1398  class(ode_integrator), intent(inout) :: this
    1399  logical, intent(in) :: x
    1400  end subroutine
    1401 
    1402  pure module function oi_get_allow_overshoot(this) result(x)
    1403  class(ode_integrator), intent(in) :: this
    1404  logical :: x
    1405  end function
    1406 
    1407  module subroutine oi_set_allow_overshoot(this, x)
    1408  class(ode_integrator), intent(inout) :: this
    1409  logical, intent(in) :: x
    1410  end subroutine
    1411 
    1412  pure module function oi_get_critical_point(this) result(x)
    1413  class(ode_integrator), intent(in) :: this
    1414  real(real64) :: x
    1415  end function
    1416 
    1417  module subroutine oi_set_critical_point(this, x)
    1418  class(ode_integrator), intent(inout) :: this
    1419  real(real64), intent(in) :: x
    1420  end subroutine
    1421 
    1422  pure module function oi_get_min_buffer_size(this) result(x)
    1423  class(ode_integrator), intent(in) :: this
    1424  integer(int32) :: x
    1425  end function
    1426 
    1427  module subroutine oi_set_min_buffer_size(this, x)
    1428  class(ode_integrator), intent(inout) :: this
    1429  integer(int32), intent(in) :: x
    1430  end subroutine
    1431 
    1432  pure module function oi_get_max_step_size(this) result(x)
    1433  class(ode_integrator), intent(in) :: this
    1434  real(real64) :: x
    1435  end function
    1436 
    1437  module subroutine oi_set_max_step_size(this, x)
    1438  class(ode_integrator), intent(inout) :: this
    1439  real(real64), intent(in) :: x
    1440  end subroutine
    1441 
    1442  pure module function oi_get_limit_step_size(this) result(x)
    1443  class(ode_integrator), intent(in) :: this
    1444  logical :: x
    1445  end function
    1446 
    1447  module subroutine oi_set_limit_step_size(this, x)
    1448  class(ode_integrator), intent(inout) :: this
    1449  logical, intent(in) :: x
    1450  end subroutine
    1451 
    1452  pure module function oi_get_iteration_limit(this) result(x)
    1453  class(ode_integrator), intent(in) :: this
    1454  integer(int32) :: x
    1455  end function
    1456 
    1457  module subroutine oi_set_iteration_limit(this, x)
    1458  class(ode_integrator), intent(inout) :: this
    1459  integer(int32), intent(in) :: x
    1460  end subroutine
    1461 
    1462  module function oi_get_rtol(this) result(x)
    1463  class(ode_integrator), intent(in) :: this
    1464  real(real64), allocatable, dimension(:) :: x
    1465  end function
    1466 
    1467  module subroutine oi_set_rtol(this, x)
    1468  class(ode_integrator), intent(inout) :: this
    1469  real(real64), intent(in), dimension(:) :: x
    1470  end subroutine
    1471 
    1472  module function oi_get_atol(this) result(x)
    1473  class(ode_integrator), intent(in) :: this
    1474  real(real64), allocatable, dimension(:) :: x
    1475  end function
    1476 
    1477  module subroutine oi_set_atol(this, x)
    1478  class(ode_integrator), intent(inout) :: this
    1479  real(real64), intent(in), dimension(:) :: x
    1480  end subroutine
    1481  end interface
    1482 
    1483 ! ******************************************************************************
    1484 ! INTEGRAL_ODE_AUTO.F90
    1485 ! ------------------------------------------------------------------------------
    1562  type, extends(ode_integrator) :: ode_auto
    1564  real(real64), allocatable, dimension(:) :: m_rwork
    1566  integer(int32), allocatable, dimension(:) :: m_iwork
    1571  integer(int32), allocatable, dimension(:) :: m_rststats
    1573  integer(int32) :: m_istate = 1
    1574  contains
    1615  procedure, public :: step => oa_step
    1624  procedure, public :: reset => oa_reset_integrator
    1636  procedure, public :: get_constraint_status => oa_get_constraint_info
    1637 
    1638  procedure, private :: init_workspace => oa_init_workspace
    1639  end type
    1640 
    1641  interface
    1642  module function oa_step(this, fcn, x, y, xout, rtol, atol, err) result(brk)
    1643  class(ode_auto), intent(inout) :: this
    1644  class(ode_helper), intent(inout) :: fcn
    1645  real(real64), intent(inout) :: x
    1646  real(real64), intent(inout), dimension(:) :: y
    1647  real(real64), intent(in) :: xout
    1648  real(real64), intent(in), dimension(:) :: rtol, atol
    1649  class(errors), intent(inout), optional, target :: err
    1650  logical :: brk
    1651  end function
    1652 
    1653  module subroutine oa_init_workspace(this, liw, lrw, ncnsts, err)
    1654  class(ode_auto), intent(inout) :: this
    1655  integer(int32), intent(in) :: liw, lrw, ncnsts
    1656  class(errors), intent(inout) :: err
    1657  end subroutine
    1658 
    1659  module subroutine oa_reset_integrator(this)
    1660  class(ode_auto), intent(inout) :: this
    1661  end subroutine
    1662 
    1663  module function oa_get_constraint_info(this) result(x)
    1664  class(ode_auto), intent(in) :: this
    1665  logical, allocatable, dimension(:) :: x
    1666  end function
    1667  end interface
    1668 end module
    integral_core::ode_constraint
    Defines a routine capable of describing constraints on a system of ODEs of N variables exposed to M c...
    Definition: integral_core.f90:154
    +
    integral_core::ode_auto
    Defines an integrator for systems of first order ODEs that is capable of switching between an Adams m...
    Definition: integral_core.f90:1562
    +
    integral_core::ode_jacobian
    Defines a routine capable of computing the Jacobian matrix of a system of N first order ODEs of N var...
    Definition: integral_core.f90:138
    +
    integral_core::ode_fcn
    Defines a routine containing a system of first order ODEs.
    Definition: integral_core.f90:123
    +
    integral_core::ode_integrator_reset
    Resets the state of the integrator.
    Definition: integral_core.f90:1379
    +
    integral_core::ode_integrator_interface
    Defines a routine for computing a single integration step in the direction of xout.
    Definition: integral_core.f90:1361
    +
    integral_core::integrator_base
    Defines a base type for integrator types.
    Definition: integral_core.f90:178
    +
    integral_core::finite_interval_fcn
    Defines the signature of a routine used to integrate a function of one variable over a finite interva...
    Definition: integral_core.f90:306
    +
    integral_core::nonadaptive_integrator
    Defines an integrator that uses a non-adaptive Gauss-Kronrod method to compute the integral of a func...
    Definition: integral_core.f90:529
    +
    integral_core::ode_helper
    Defines a type used to pass information regarding the ODEs to the solver.
    Definition: integral_core.f90:630
    +
    integral_core::integrand
    Defines a function of one variable to be integrated.
    Definition: integral_core.f90:108
    +
    integral_core::finite_interval_integrator
    A type that defines an integrator meant to operate on integrands over a finite region.
    Definition: integral_core.f90:287
    +
    integral_core::ode_integrator
    Definition: integral_core.f90:1036
    +
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    integral_core::adaptive_integrator
    Defines an integrator that uses an adaptive Gauss-Kronrod method to compute the integral of a functio...
    Definition: integral_core.f90:372
    +
    integral_core::integration_behavior
    Provides information regarding the behavior of an integrator.
    Definition: integral_core.f90:164
    @@ -108,7 +132,7 @@
  • src
  • integral_core.f90
  • Generated by - doxygen 1.8.13
    • + doxygen 1.8.11 diff --git a/doc/html/integral__integrator__base_8f90_source.html b/doc/html/integral__integrator__base_8f90_source.html index 4ab8a31..074cf31 100644 --- a/doc/html/integral__integrator__base_8f90_source.html +++ b/doc/html/integral__integrator__base_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_integrator_base.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_integrator_base.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_integrator_base.f90
    2 
    3 submodule(integral_core) integral_integrator_base
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  pure module function ib_get_abs_tol(this) result(x)
    7  class(integrator_base), intent(in) :: this
    8  real(real64) :: x
    9  x = this%m_absTol
    10  end function
    11 
    12  module subroutine ib_set_abs_tol(this, x)
    13  class(integrator_base), intent(inout) :: this
    14  real(real64), intent(in) :: x
    15  this%m_absTol = x
    16  end subroutine
    17 
    18 ! ------------------------------------------------------------------------------
    19  pure module function ib_get_rel_tol(this) result(x)
    20  class(integrator_base), intent(in) :: this
    21  real(real64) :: x
    22  x = this%m_relTol
    23  end function
    24 
    25  module subroutine ib_set_rel_tol(this, x)
    26  class(integrator_base), intent(inout) :: this
    27  real(real64), intent(in) :: x
    28  this%m_relTol = x
    29  end subroutine
    30 
    31 ! ------------------------------------------------------------------------------
    32  pure module function ib_get_max_subintervals(this) result(x)
    33  class(integrator_base), intent(in) :: this
    34  integer(int32) :: x
    35  x = this%m_maxInt
    36  end function
    37 
    38  module subroutine ib_set_max_subintervals(this, x)
    39  class(integrator_base), intent(inout) :: this
    40  integer(int32), intent(in) :: x
    41  this%m_maxInt = x
    42  end subroutine
    43 
    44 ! ------------------------------------------------------------------------------
    45 end submodule
    +
    1 ! integral_integrator_base.f90
    2 
    3 submodule(integral_core) integral_integrator_base
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  pure module function ib_get_abs_tol(this) result(x)
    7  class(integrator_base), intent(in) :: this
    8  real(real64) :: x
    9  x = this%m_absTol
    10  end function
    11 
    12  module subroutine ib_set_abs_tol(this, x)
    13  class(integrator_base), intent(inout) :: this
    14  real(real64), intent(in) :: x
    15  this%m_absTol = x
    16  end subroutine
    17 
    18 ! ------------------------------------------------------------------------------
    19  pure module function ib_get_rel_tol(this) result(x)
    20  class(integrator_base), intent(in) :: this
    21  real(real64) :: x
    22  x = this%m_relTol
    23  end function
    24 
    25  module subroutine ib_set_rel_tol(this, x)
    26  class(integrator_base), intent(inout) :: this
    27  real(real64), intent(in) :: x
    28  this%m_relTol = x
    29  end subroutine
    30 
    31 ! ------------------------------------------------------------------------------
    32  pure module function ib_get_max_subintervals(this) result(x)
    33  class(integrator_base), intent(in) :: this
    34  integer(int32) :: x
    35  x = this%m_maxInt
    36  end function
    37 
    38  module subroutine ib_set_max_subintervals(this, x)
    39  class(integrator_base), intent(inout) :: this
    40  integer(int32), intent(in) :: x
    41  this%m_maxInt = x
    42  end subroutine
    43 
    44 ! ------------------------------------------------------------------------------
    45 end submodule
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    diff --git a/doc/html/integral__nonadaptive__integrator_8f90_source.html b/doc/html/integral__nonadaptive__integrator_8f90_source.html index bdffaef..4914fcc 100644 --- a/doc/html/integral__nonadaptive__integrator_8f90_source.html +++ b/doc/html/integral__nonadaptive__integrator_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_nonadaptive_integrator.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_nonadaptive_integrator.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_nonadaptive_integrator.f90
    2 
    3 submodule(integral_core) integral_nonadaptive_integrator
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module function ni_integrate(this, fcn, a, b, info, err) result(rst)
    7  ! Arguments
    8  class(nonadaptive_integrator), intent(inout) :: this
    9  procedure(integrand), intent(in), pointer :: fcn
    10  real(real64), intent(in) :: a, b
    11  type(integration_behavior), intent(out), optional :: info
    12  class(errors), intent(inout), optional, target :: err
    13  real(real64) :: rst
    14 
    15  ! Local Variables
    16  real(real64) :: abserr, resabs, resasc
    17  integer(int32) :: n
    18 
    19  ! Determine the correct rule, and perform the integration
    20  select case (this%get_rule())
    21  case (int_15_point_rule)
    22  n = 15
    23  call dqk15(local_fcn, a, b, rst, abserr, resabs, resasc)
    24  case (int_21_point_rule)
    25  n = 21
    26  call dqk21(local_fcn, a, b, rst, abserr, resabs, resasc)
    27  case (int_31_point_rule)
    28  n = 31
    29  call dqk31(local_fcn, a, b, rst, abserr, resabs, resasc)
    30  case (int_41_point_rule)
    31  n = 41
    32  call dqk41(local_fcn, a, b, rst, abserr, resabs, resasc)
    33  case (int_51_point_rule)
    34  n = 51
    35  call dqk51(local_fcn, a, b, rst, abserr, resabs, resasc)
    36  case (int_61_point_rule)
    37  n = 61
    38  call dqk61(local_fcn, a, b, rst, abserr, resabs, resasc)
    39  end select
    40 
    41  ! Report out the integration statistics
    42  if (present(info)) then
    43  info%error_estimate = abserr
    44  info%evaluation_count = n
    45  info%subinterval_count = 0
    46  end if
    47  contains
    48  ! This is required as the F77 code doesn't deal with procedure pointers
    49  function local_fcn(xarg) result(frst)
    50  real(real64), intent(in) :: xarg
    51  real(real64) :: frst
    52  frst = fcn(xarg)
    53  end function
    54  end function
    55 
    56 ! ------------------------------------------------------------------------------
    57  pure module function ni_get_rule(this) result(x)
    58  class(nonadaptive_integrator), intent(in) :: this
    59  integer(int32) :: x
    60  x = this%m_rule
    61  end function
    62 
    63 ! ------------------------------------------------------------------------------
    64  module subroutine ni_set_rule(this, x, err)
    65  class(nonadaptive_integrator), intent(inout) :: this
    66  integer(int32), intent(in) :: x
    67  class(errors), intent(inout), optional, target :: err
    68  class(errors), pointer :: errmgr
    69  type(errors), target :: deferr
    70  if (present(err)) then
    71  errmgr => err
    72  else
    73  errmgr => deferr
    74  end if
    75  if (x /= int_15_point_rule .and. x /= int_21_point_rule .and. &
    76  x /= int_31_point_rule .and. x /= int_41_point_rule .and. &
    77  x /= int_51_point_rule .and. x /= int_61_point_rule) then
    78  call errmgr%report_error("ni_set_rule", &
    79  "Unknown integration rule requested.", &
    80  int_invalid_input_error)
    81  return
    82  end if
    83  this%m_rule = x
    84  end subroutine
    85 
    86 ! ------------------------------------------------------------------------------
    87 end submodule
    +
    1 ! integral_nonadaptive_integrator.f90
    2 
    3 submodule(integral_core) integral_nonadaptive_integrator
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module function ni_integrate(this, fcn, a, b, info, err) result(rst)
    7  ! Arguments
    8  class(nonadaptive_integrator), intent(inout) :: this
    9  procedure(integrand), intent(in), pointer :: fcn
    10  real(real64), intent(in) :: a, b
    11  type(integration_behavior), intent(out), optional :: info
    12  class(errors), intent(inout), optional, target :: err
    13  real(real64) :: rst
    14 
    15  ! Local Variables
    16  real(real64) :: abserr, resabs, resasc
    17  integer(int32) :: n
    18 
    19  ! Determine the correct rule, and perform the integration
    20  select case (this%get_rule())
    21  case (int_15_point_rule)
    22  n = 15
    23  call dqk15(local_fcn, a, b, rst, abserr, resabs, resasc)
    24  case (int_21_point_rule)
    25  n = 21
    26  call dqk21(local_fcn, a, b, rst, abserr, resabs, resasc)
    27  case (int_31_point_rule)
    28  n = 31
    29  call dqk31(local_fcn, a, b, rst, abserr, resabs, resasc)
    30  case (int_41_point_rule)
    31  n = 41
    32  call dqk41(local_fcn, a, b, rst, abserr, resabs, resasc)
    33  case (int_51_point_rule)
    34  n = 51
    35  call dqk51(local_fcn, a, b, rst, abserr, resabs, resasc)
    36  case (int_61_point_rule)
    37  n = 61
    38  call dqk61(local_fcn, a, b, rst, abserr, resabs, resasc)
    39  end select
    40 
    41  ! Report out the integration statistics
    42  if (present(info)) then
    43  info%error_estimate = abserr
    44  info%evaluation_count = n
    45  info%subinterval_count = 0
    46  end if
    47  contains
    48  ! This is required as the F77 code doesn't deal with procedure pointers
    49  function local_fcn(xarg) result(frst)
    50  real(real64), intent(in) :: xarg
    51  real(real64) :: frst
    52  frst = fcn(xarg)
    53  end function
    54  end function
    55 
    56 ! ------------------------------------------------------------------------------
    57  pure module function ni_get_rule(this) result(x)
    58  class(nonadaptive_integrator), intent(in) :: this
    59  integer(int32) :: x
    60  x = this%m_rule
    61  end function
    62 
    63 ! ------------------------------------------------------------------------------
    64  module subroutine ni_set_rule(this, x, err)
    65  class(nonadaptive_integrator), intent(inout) :: this
    66  integer(int32), intent(in) :: x
    67  class(errors), intent(inout), optional, target :: err
    68  class(errors), pointer :: errmgr
    69  type(errors), target :: deferr
    70  if (present(err)) then
    71  errmgr => err
    72  else
    73  errmgr => deferr
    74  end if
    75  if (x /= int_15_point_rule .and. x /= int_21_point_rule .and. &
    76  x /= int_31_point_rule .and. x /= int_41_point_rule .and. &
    77  x /= int_51_point_rule .and. x /= int_61_point_rule) then
    78  call errmgr%report_error("ni_set_rule", &
    79  "Unknown integration rule requested.", &
    80  int_invalid_input_error)
    81  return
    82  end if
    83  this%m_rule = x
    84  end subroutine
    85 
    86 ! ------------------------------------------------------------------------------
    87 end submodule
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    diff --git a/doc/html/integral__ode__auto_8f90_source.html b/doc/html/integral__ode__auto_8f90_source.html index 1588ff7..101cddd 100644 --- a/doc/html/integral__ode__auto_8f90_source.html +++ b/doc/html/integral__ode__auto_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_ode_auto.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_ode_auto.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_ode_auto.f90
    2 
    3 submodule(integral_core) integral_ode_auto
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module function oa_step(this, fcn, x, y, xout, rtol, atol, err) result(brk)
    7  ! Arguments
    8  class(ode_auto), intent(inout) :: this
    9  class(ode_helper), intent(inout) :: fcn
    10  real(real64), intent(inout) :: x
    11  real(real64), intent(inout), dimension(:) :: y
    12  real(real64), intent(in) :: xout
    13  real(real64), intent(in), dimension(:) :: rtol, atol
    14  class(errors), intent(inout), optional, target :: err
    15  logical :: brk
    16 
    17  ! Local Variables
    18  integer(int32) :: neq, itask, iopt, lrw, liw, jt, ncnst, lrn, lrs, itol
    19  logical :: useconstraints
    20  class(errors), pointer :: errmgr
    21  type(errors), target :: deferr
    22 
    23  ! Initialization
    24  brk = .false.
    25  neq = fcn%get_equation_count()
    26  ncnst = fcn%get_constraint_count()
    27  useconstraints = fcn%get_constraints_defined()
    28  if (present(err)) then
    29  errmgr => err
    30  else
    31  errmgr => deferr
    32  end if
    33 
    34  ! Ensure workspace arrays are sized appropriately
    35  lrn = 20 + 16 * neq + 3 * ncnst
    36  lrs = 22 + 9 * neq + neq**2 + 3 * ncnst
    37  lrw = max(lrn, lrs)
    38  liw = 20 + neq
    39 
    40  ! Define workspace arrays
    41  call this%init_workspace(liw, lrw, ncnst, errmgr)
    42  if (errmgr%has_error_occurred()) return
    43 
    44  ! Additional Initialization
    45  iopt = 0
    46  if (this%get_allow_overshoot()) then
    47  itask = 1
    48  if (this%get_provide_all_output()) itask = 2
    49  else
    50  itask = 4
    51  iopt = 1
    52  this%m_rwork(1) = this%get_integration_limit()
    53  if (this%get_provide_all_output()) itask = 5
    54  end if
    55  if (fcn%get_jacobian_defined()) then
    56  jt = 1
    57  else
    58  jt = 2
    59  end if
    60  itol = 4
    61 
    62  if (this%get_limit_step_size()) then
    63  iopt = 1
    64  this%m_rwork(6) = this%get_max_step_size()
    65  end if
    66 
    67  if (this%get_iteration_limit() /= 500) then
    68  iopt = 1
    69  this%m_iwork(6) = this%get_iteration_limit()
    70  end if
    71 
    72  ! Determine if we are to call DLSODA or DLSODAR
    73  if (useconstraints .and. ncnst > 0) then
    74  call dlsodar(odepackfcn, neq, y, x, xout, itol, rtol, atol, itask, &
    75  this%m_istate, iopt, this%m_rwork, lrw, this%m_iwork, liw, &
    76  odepackjac, jt, odepackconstraints, ncnst, this%m_rststats)
    77 
    78  ! Check output condition
    79  select case (this%m_istate)
    80  case (3)
    81  ! Root Found
    82  brk = .true.
    83  case (-1)
    84  call errmgr%report_error("oa_step", &
    85  "Excessive work has been done during this " // &
    86  "integration step.", int_excessive_work_error)
    87  case (-2)
    88  call errmgr%report_error("oa_step", &
    89  "Unachievable tolerances have been requested.", &
    90  int_impractical_tolerance_error)
    91  case (-3)
    92  call errmgr%report_error("oa_step", &
    93  "An invalid input was encountered.", &
    94  int_invalid_input_error)
    95  case (-4)
    96  call errmgr%report_error("oa_step", &
    97  "Error testing has failed repeatadly. " // &
    98  "Ensure inputs are valid.", int_repeated_error_test_failure)
    99  case (-5)
    100  call errmgr%report_error("oa_step", "Repeated convergence " // &
    101  "failures have been encountered.", int_convergence_error)
    102  case (-6)
    103  call errmgr%report_error("oa_step", "A solution component " // &
    104  "has effectively vanished.", int_integrand_behavior_error)
    105  case (-7)
    106  call errmgr%report_error("oa_step", "An insufficiently " // &
    107  "sized workspace array was provided.", &
    108  int_invalid_input_error)
    109  end select
    110  else
    111  call dlsoda(odepackfcn, neq, y, x, xout, itol, rtol, atol, itask, &
    112  this%m_istate, iopt, this%m_rwork, lrw, this%m_iwork, liw, &
    113  odepackjac, jt)
    114 
    115  ! Check output condition
    116  select case (this%m_istate)
    117  case (-1)
    118  call errmgr%report_error("oa_step", &
    119  "Excessive work has been done during this " // &
    120  "integration step.", int_excessive_work_error)
    121  case (-2)
    122  call errmgr%report_error("oa_step", &
    123  "Unachievable tolerances have been requested.", &
    124  int_impractical_tolerance_error)
    125  case (-3)
    126  call errmgr%report_error("oa_step", &
    127  "An invalid input was encountered.", &
    128  int_invalid_input_error)
    129  case (-4)
    130  call errmgr%report_error("oa_step", &
    131  "Error testing has failed repeatadly. " // &
    132  "Ensure inputs are valid.", int_repeated_error_test_failure)
    133  case (-5)
    134  call errmgr%report_error("oa_step", "Repeated convergence " // &
    135  "failures have been encountered.", int_convergence_error)
    136  case (-6)
    137  call errmgr%report_error("oa_step", "A solution component " // &
    138  "has effectively vanished.", int_integrand_behavior_error)
    139  case (-7)
    140  call errmgr%report_error("oa_step", "An insufficiently " // &
    141  "sized workspace array was provided.", &
    142  int_invalid_input_error)
    143  end select
    144  end if
    145 
    146  contains
    147  subroutine odepackfcn(n, x, y, dydx)
    148  integer(int32), intent(in) :: n
    149  real(real64), intent(in) :: x, y(n)
    150  real(real64), intent(out) :: dydx(n)
    151  call fcn%evaluate_ode(x, y, dydx)
    152  end subroutine
    153 
    154  subroutine odepackjac(n, x, y, ml, mu, pd, nrowpd)
    155  integer(int32), intent(in) :: n, ml, mu, nrowpd
    156  real(real64), intent(in) :: x, y(n)
    157  real(real64), intent(out) :: pd(nrowpd, n)
    158  call fcn%evaluate_jacobian(x, y, pd)
    159  end subroutine
    160 
    161  subroutine odepackconstraints(neq, x, y, ng, gout)
    162  integer(int32), intent(in) :: neq, ng
    163  real(real64), intent(in) :: x, y(neq)
    164  real(real64), intent(out) :: gout(ng)
    165  call fcn%evaluate_constraints(x, y, gout)
    166  end subroutine
    167  end function
    168 
    169 ! ------------------------------------------------------------------------------
    170  module subroutine oa_reset_integrator(this)
    171  class(ode_auto), intent(inout) :: this
    172  this%m_istate = 1
    173  end subroutine
    174 
    175 ! ------------------------------------------------------------------------------
    176  module subroutine oa_init_workspace(this, liw, lrw, ncnsts, err)
    177  ! Arguments
    178  class(ode_auto), intent(inout) :: this
    179  integer(int32), intent(in) :: liw, lrw, ncnsts
    180  class(errors), intent(inout) :: err
    181 
    182  ! Local Variables
    183  integer(int32) :: flag
    184 
    185  ! Process
    186  flag = 0
    187  if (allocated(this%m_iwork)) then
    188  if (size(this%m_iwork) < liw) then
    189  deallocate(this%m_iwork)
    190  allocate(this%m_iwork(liw), stat = flag)
    191  end if
    192  else
    193  allocate(this%m_iwork(liw), stat = flag)
    194  end if
    195 
    196  if (flag == 0) then
    197  if (allocated(this%m_rwork)) then
    198  if (size(this%m_rwork) < lrw) then
    199  deallocate(this%m_rwork)
    200  allocate(this%m_rwork(lrw), stat = flag)
    201  end if
    202  else
    203  allocate(this%m_rwork(lrw), stat = flag)
    204  end if
    205  end if
    206 
    207  if (flag == 0 .and. ncnsts > 0) then
    208  if (allocated(this%m_rststats)) then
    209  if (size(this%m_rststats) /= ncnsts) then
    210  deallocate(this%m_rststats)
    211  allocate(this%m_rststats(ncnsts), stat = flag)
    212  end if
    213  else
    214  allocate(this%m_rststats(ncnsts), stat = flag)
    215  end if
    216  end if
    217 
    218  ! Error Checking
    219  if (flag /= 0) then
    220  call err%report_error("oa_init_workspace", &
    221  "Insufficient memory available.", int_out_of_memory_error)
    222  return
    223  end if
    224  end subroutine
    225 
    226 ! ------------------------------------------------------------------------------
    227  module function oa_get_constraint_info(this) result(x)
    228  ! Arguments
    229  class(ode_auto), intent(in) :: this
    230  logical, allocatable, dimension(:) :: x
    231 
    232  ! Local Variables
    233  integer(int32) :: i, n
    234 
    235  ! Process
    236  if (.not.allocated(this%m_rststats)) return
    237  n = size(this%m_rststats)
    238  allocate(x(n))
    239  do i = 1, n
    240  x(i) = this%m_rststats(i) == 1
    241  end do
    242  end function
    243 
    244 ! ------------------------------------------------------------------------------
    245 end submodule
    +
    1 ! integral_ode_auto.f90
    2 
    3 submodule(integral_core) integral_ode_auto
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module function oa_step(this, fcn, x, y, xout, rtol, atol, err) result(brk)
    7  ! Arguments
    8  class(ode_auto), intent(inout) :: this
    9  class(ode_helper), intent(inout) :: fcn
    10  real(real64), intent(inout) :: x
    11  real(real64), intent(inout), dimension(:) :: y
    12  real(real64), intent(in) :: xout
    13  real(real64), intent(in), dimension(:) :: rtol, atol
    14  class(errors), intent(inout), optional, target :: err
    15  logical :: brk
    16 
    17  ! Local Variables
    18  integer(int32) :: neq, itask, iopt, lrw, liw, jt, ncnst, lrn, lrs, itol
    19  logical :: useconstraints
    20  class(errors), pointer :: errmgr
    21  type(errors), target :: deferr
    22 
    23  ! Initialization
    24  brk = .false.
    25  neq = fcn%get_equation_count()
    26  ncnst = fcn%get_constraint_count()
    27  useconstraints = fcn%get_constraints_defined()
    28  if (present(err)) then
    29  errmgr => err
    30  else
    31  errmgr => deferr
    32  end if
    33 
    34  ! Ensure workspace arrays are sized appropriately
    35  lrn = 20 + 16 * neq + 3 * ncnst
    36  lrs = 22 + 9 * neq + neq**2 + 3 * ncnst
    37  lrw = max(lrn, lrs)
    38  liw = 20 + neq
    39 
    40  ! Define workspace arrays
    41  call this%init_workspace(liw, lrw, ncnst, errmgr)
    42  if (errmgr%has_error_occurred()) return
    43 
    44  ! Additional Initialization
    45  iopt = 0
    46  if (this%get_allow_overshoot()) then
    47  itask = 1
    48  if (this%get_provide_all_output()) itask = 2
    49  else
    50  itask = 4
    51  iopt = 1
    52  this%m_rwork(1) = this%get_integration_limit()
    53  if (this%get_provide_all_output()) itask = 5
    54  end if
    55  if (fcn%get_jacobian_defined()) then
    56  jt = 1
    57  else
    58  jt = 2
    59  end if
    60  itol = 4
    61 
    62  if (this%get_limit_step_size()) then
    63  iopt = 1
    64  this%m_rwork(6) = this%get_max_step_size()
    65  end if
    66 
    67  if (this%get_iteration_limit() /= 500) then
    68  iopt = 1
    69  this%m_iwork(6) = this%get_iteration_limit()
    70  end if
    71 
    72  ! Determine if we are to call DLSODA or DLSODAR
    73  if (useconstraints .and. ncnst > 0) then
    74  call dlsodar(odepackfcn, neq, y, x, xout, itol, rtol, atol, itask, &
    75  this%m_istate, iopt, this%m_rwork, lrw, this%m_iwork, liw, &
    76  odepackjac, jt, odepackconstraints, ncnst, this%m_rststats)
    77 
    78  ! Check output condition
    79  select case (this%m_istate)
    80  case (3)
    81  ! Root Found
    82  brk = .true.
    83  case (-1)
    84  call errmgr%report_error("oa_step", &
    85  "Excessive work has been done during this " // &
    86  "integration step.", int_excessive_work_error)
    87  case (-2)
    88  call errmgr%report_error("oa_step", &
    89  "Unachievable tolerances have been requested.", &
    90  int_impractical_tolerance_error)
    91  case (-3)
    92  call errmgr%report_error("oa_step", &
    93  "An invalid input was encountered.", &
    94  int_invalid_input_error)
    95  case (-4)
    96  call errmgr%report_error("oa_step", &
    97  "Error testing has failed repeatadly. " // &
    98  "Ensure inputs are valid.", int_repeated_error_test_failure)
    99  case (-5)
    100  call errmgr%report_error("oa_step", "Repeated convergence " // &
    101  "failures have been encountered.", int_convergence_error)
    102  case (-6)
    103  call errmgr%report_error("oa_step", "A solution component " // &
    104  "has effectively vanished.", int_integrand_behavior_error)
    105  case (-7)
    106  call errmgr%report_error("oa_step", "An insufficiently " // &
    107  "sized workspace array was provided.", &
    108  int_invalid_input_error)
    109  end select
    110  else
    111  call dlsoda(odepackfcn, neq, y, x, xout, itol, rtol, atol, itask, &
    112  this%m_istate, iopt, this%m_rwork, lrw, this%m_iwork, liw, &
    113  odepackjac, jt)
    114 
    115  ! Check output condition
    116  select case (this%m_istate)
    117  case (-1)
    118  call errmgr%report_error("oa_step", &
    119  "Excessive work has been done during this " // &
    120  "integration step.", int_excessive_work_error)
    121  case (-2)
    122  call errmgr%report_error("oa_step", &
    123  "Unachievable tolerances have been requested.", &
    124  int_impractical_tolerance_error)
    125  case (-3)
    126  call errmgr%report_error("oa_step", &
    127  "An invalid input was encountered.", &
    128  int_invalid_input_error)
    129  case (-4)
    130  call errmgr%report_error("oa_step", &
    131  "Error testing has failed repeatadly. " // &
    132  "Ensure inputs are valid.", int_repeated_error_test_failure)
    133  case (-5)
    134  call errmgr%report_error("oa_step", "Repeated convergence " // &
    135  "failures have been encountered.", int_convergence_error)
    136  case (-6)
    137  call errmgr%report_error("oa_step", "A solution component " // &
    138  "has effectively vanished.", int_integrand_behavior_error)
    139  case (-7)
    140  call errmgr%report_error("oa_step", "An insufficiently " // &
    141  "sized workspace array was provided.", &
    142  int_invalid_input_error)
    143  end select
    144  end if
    145 
    146  contains
    147  subroutine odepackfcn(n, x, y, dydx)
    148  integer(int32), intent(in) :: n
    149  real(real64), intent(in) :: x, y(n)
    150  real(real64), intent(out) :: dydx(n)
    151  call fcn%evaluate_ode(x, y, dydx)
    152  end subroutine
    153 
    154  subroutine odepackjac(n, x, y, ml, mu, pd, nrowpd)
    155  integer(int32), intent(in) :: n, ml, mu, nrowpd
    156  real(real64), intent(in) :: x, y(n)
    157  real(real64), intent(out) :: pd(nrowpd, n)
    158  call fcn%evaluate_jacobian(x, y, pd)
    159  end subroutine
    160 
    161  subroutine odepackconstraints(neq, x, y, ng, gout)
    162  integer(int32), intent(in) :: neq, ng
    163  real(real64), intent(in) :: x, y(neq)
    164  real(real64), intent(out) :: gout(ng)
    165  call fcn%evaluate_constraints(x, y, gout)
    166  end subroutine
    167  end function
    168 
    169 ! ------------------------------------------------------------------------------
    170  module subroutine oa_reset_integrator(this)
    171  class(ode_auto), intent(inout) :: this
    172  this%m_istate = 1
    173  end subroutine
    174 
    175 ! ------------------------------------------------------------------------------
    176  module subroutine oa_init_workspace(this, liw, lrw, ncnsts, err)
    177  ! Arguments
    178  class(ode_auto), intent(inout) :: this
    179  integer(int32), intent(in) :: liw, lrw, ncnsts
    180  class(errors), intent(inout) :: err
    181 
    182  ! Local Variables
    183  integer(int32) :: flag
    184 
    185  ! Process
    186  flag = 0
    187  if (allocated(this%m_iwork)) then
    188  if (size(this%m_iwork) < liw) then
    189  deallocate(this%m_iwork)
    190  allocate(this%m_iwork(liw), stat = flag)
    191  end if
    192  else
    193  allocate(this%m_iwork(liw), stat = flag)
    194  end if
    195 
    196  if (flag == 0) then
    197  if (allocated(this%m_rwork)) then
    198  if (size(this%m_rwork) < lrw) then
    199  deallocate(this%m_rwork)
    200  allocate(this%m_rwork(lrw), stat = flag)
    201  end if
    202  else
    203  allocate(this%m_rwork(lrw), stat = flag)
    204  end if
    205  end if
    206 
    207  if (flag == 0 .and. ncnsts > 0) then
    208  if (allocated(this%m_rststats)) then
    209  if (size(this%m_rststats) /= ncnsts) then
    210  deallocate(this%m_rststats)
    211  allocate(this%m_rststats(ncnsts), stat = flag)
    212  end if
    213  else
    214  allocate(this%m_rststats(ncnsts), stat = flag)
    215  end if
    216  end if
    217 
    218  ! Error Checking
    219  if (flag /= 0) then
    220  call err%report_error("oa_init_workspace", &
    221  "Insufficient memory available.", int_out_of_memory_error)
    222  return
    223  end if
    224  end subroutine
    225 
    226 ! ------------------------------------------------------------------------------
    227  module function oa_get_constraint_info(this) result(x)
    228  ! Arguments
    229  class(ode_auto), intent(in) :: this
    230  logical, allocatable, dimension(:) :: x
    231 
    232  ! Local Variables
    233  integer(int32) :: i, n
    234 
    235  ! Process
    236  if (.not.allocated(this%m_rststats)) return
    237  n = size(this%m_rststats)
    238  allocate(x(n))
    239  do i = 1, n
    240  x(i) = this%m_rststats(i) == 1
    241  end do
    242  end function
    243 
    244 ! ------------------------------------------------------------------------------
    245 end submodule
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    diff --git a/doc/html/integral__ode__helper_8f90_source.html b/doc/html/integral__ode__helper_8f90_source.html index a1ee055..e923319 100644 --- a/doc/html/integral__ode__helper_8f90_source.html +++ b/doc/html/integral__ode__helper_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_ode_helper.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_ode_helper.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_ode_helper.f90
    2 
    3 submodule(integral_core) integral_ode_helper
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module subroutine oh_init(this, neqn, fcn, jac)
    7  class(ode_helper), intent(inout) :: this
    8  integer(int32), intent(in) :: neqn
    9  procedure(ode_fcn), pointer, intent(in) :: fcn
    10  procedure(ode_jacobian), pointer, intent(in), optional :: jac
    11  nullify(this%m_fcn)
    12  nullify(this%m_jac)
    13  this%m_count = neqn
    14  this%m_fcn => fcn
    15  if (present(jac)) this%m_jac => jac
    16  end subroutine
    17 
    18 ! ------------------------------------------------------------------------------
    19  pure module function oh_get_count(this) result(x)
    20  class(ode_helper), intent(in) :: this
    21  integer(int32) :: x
    22  x = this%m_count
    23  end function
    24 
    25 ! ------------------------------------------------------------------------------
    26  pure module function oh_is_fcn_defined(this) result(x)
    27  class(ode_helper), intent(in) :: this
    28  logical :: x
    29  x = associated(this%m_fcn)
    30  end function
    31 
    32 ! ------------------------------------------------------------------------------
    33  pure module function oh_is_jac_defined(this) result(x)
    34  class(ode_helper), intent(in) :: this
    35  logical :: x
    36  x = associated(this%m_jac)
    37  end function
    38 
    39 ! ------------------------------------------------------------------------------
    40  module subroutine oh_define_constraints(this, n, fcn)
    41  class(ode_helper), intent(inout) :: this
    42  integer(int32), intent(in) :: n
    43  procedure(ode_constraint), intent(in), pointer :: fcn
    44  this%m_constraints = n
    45  this%m_rts => fcn
    46  end subroutine
    47 
    48 ! ------------------------------------------------------------------------------
    49  pure module function oh_get_constraint_count(this) result(x)
    50  class(ode_helper), intent(in) :: this
    51  integer(int32) :: x
    52  x = this%m_constraints
    53  end function
    54 
    55 ! ------------------------------------------------------------------------------
    56  pure module function oh_get_constraints_defined(this) result(x)
    57  class(ode_helper), intent(in) :: this
    58  logical :: x
    59  x = associated(this%m_rts)
    60  end function
    61 
    62 ! ------------------------------------------------------------------------------
    63  module subroutine oh_eval(this, x, y, dydx)
    64  class(ode_helper), intent(inout) :: this
    65  real(real64), intent(in) :: x
    66  real(real64), intent(in), dimension(:) :: y
    67  real(real64), intent(out), dimension(:) :: dydx
    68  call this%m_fcn(x, y, dydx)
    69  end subroutine
    70 
    71 ! ------------------------------------------------------------------------------
    72  module subroutine oh_eval_jac(this, x, y, jac)
    73  class(ode_helper), intent(inout) :: this
    74  real(real64), intent(in) :: x
    75  real(real64), intent(in), dimension(:) :: y
    76  real(real64), intent(out), dimension(:,:) :: jac
    77  call this%m_jac(x, y, jac)
    78  end subroutine
    79 
    80 ! ------------------------------------------------------------------------------
    81  module subroutine oh_eval_constraints(this, x, y, f)
    82  class(ode_helper), intent(inout) :: this
    83  real(real64), intent(in) :: x
    84  real(real64), intent(in), dimension(:) :: y
    85  real(real64), intent(out), dimension(:) :: f
    86  call this%m_rts(x, y, f)
    87  end subroutine
    88 
    89 ! ------------------------------------------------------------------------------
    90 end submodule
    +
    1 ! integral_ode_helper.f90
    2 
    3 submodule(integral_core) integral_ode_helper
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module subroutine oh_init(this, neqn, fcn, jac)
    7  class(ode_helper), intent(inout) :: this
    8  integer(int32), intent(in) :: neqn
    9  procedure(ode_fcn), pointer, intent(in) :: fcn
    10  procedure(ode_jacobian), pointer, intent(in), optional :: jac
    11  nullify(this%m_fcn)
    12  nullify(this%m_jac)
    13  this%m_count = neqn
    14  this%m_fcn => fcn
    15  if (present(jac)) this%m_jac => jac
    16  end subroutine
    17 
    18 ! ------------------------------------------------------------------------------
    19  pure module function oh_get_count(this) result(x)
    20  class(ode_helper), intent(in) :: this
    21  integer(int32) :: x
    22  x = this%m_count
    23  end function
    24 
    25 ! ------------------------------------------------------------------------------
    26  pure module function oh_is_fcn_defined(this) result(x)
    27  class(ode_helper), intent(in) :: this
    28  logical :: x
    29  x = associated(this%m_fcn)
    30  end function
    31 
    32 ! ------------------------------------------------------------------------------
    33  pure module function oh_is_jac_defined(this) result(x)
    34  class(ode_helper), intent(in) :: this
    35  logical :: x
    36  x = associated(this%m_jac)
    37  end function
    38 
    39 ! ------------------------------------------------------------------------------
    40  module subroutine oh_define_constraints(this, n, fcn)
    41  class(ode_helper), intent(inout) :: this
    42  integer(int32), intent(in) :: n
    43  procedure(ode_constraint), intent(in), pointer :: fcn
    44  this%m_constraints = n
    45  this%m_rts => fcn
    46  end subroutine
    47 
    48 ! ------------------------------------------------------------------------------
    49  pure module function oh_get_constraint_count(this) result(x)
    50  class(ode_helper), intent(in) :: this
    51  integer(int32) :: x
    52  x = this%m_constraints
    53  end function
    54 
    55 ! ------------------------------------------------------------------------------
    56  pure module function oh_get_constraints_defined(this) result(x)
    57  class(ode_helper), intent(in) :: this
    58  logical :: x
    59  x = associated(this%m_rts)
    60  end function
    61 
    62 ! ------------------------------------------------------------------------------
    63  module subroutine oh_eval(this, x, y, dydx)
    64  class(ode_helper), intent(inout) :: this
    65  real(real64), intent(in) :: x
    66  real(real64), intent(in), dimension(:) :: y
    67  real(real64), intent(out), dimension(:) :: dydx
    68  call this%m_fcn(x, y, dydx)
    69  end subroutine
    70 
    71 ! ------------------------------------------------------------------------------
    72  module subroutine oh_eval_jac(this, x, y, jac)
    73  class(ode_helper), intent(inout) :: this
    74  real(real64), intent(in) :: x
    75  real(real64), intent(in), dimension(:) :: y
    76  real(real64), intent(out), dimension(:,:) :: jac
    77  call this%m_jac(x, y, jac)
    78  end subroutine
    79 
    80 ! ------------------------------------------------------------------------------
    81  module subroutine oh_eval_constraints(this, x, y, f)
    82  class(ode_helper), intent(inout) :: this
    83  real(real64), intent(in) :: x
    84  real(real64), intent(in), dimension(:) :: y
    85  real(real64), intent(out), dimension(:) :: f
    86  call this%m_rts(x, y, f)
    87  end subroutine
    88 
    89 ! ------------------------------------------------------------------------------
    90 end submodule
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    diff --git a/doc/html/integral__ode__integrator_8f90_source.html b/doc/html/integral__ode__integrator_8f90_source.html index 20737ce..9fed4aa 100644 --- a/doc/html/integral__ode__integrator_8f90_source.html +++ b/doc/html/integral__ode__integrator_8f90_source.html @@ -3,9 +3,8 @@ - - -integral: /home/jason/github/integral/src/integral_ode_integrator.f90 Source File + +integral: D:/users/christopherson/Code/integral/src/integral_ode_integrator.f90 Source File @@ -15,10 +14,14 @@ + @@ -38,19 +41,39 @@ - + - - - - + +
    -
    1 ! integral_ode_integrator.f90
    2 
    3 submodule(integral_core) integral_ode_integrator
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module function oi_integrate(this, fcnobj, x, y, err) result(rst)
    7  ! Arguments
    8  class(ode_integrator), intent(inout) :: this
    9  class(ode_helper), intent(inout) :: fcnobj
    10  real(real64), intent(in), dimension(:) :: x, y
    11  class(errors), intent(inout), optional, target :: err
    12  real(real64), allocatable, dimension(:,:) :: rst
    13 
    14  ! Local Variables
    15  integer(int32) :: neqn, ncols, flag, i, n, nbuffer
    16  real(real64), allocatable, dimension(:,:) :: buffer
    17  real(real64), allocatable, dimension(:) :: ytemp
    18  real(real64) :: xout, xi
    19  class(errors), pointer :: errmgr
    20  type(errors), target :: deferr
    21  character(len = 256) :: errmsg
    22  logical :: brk, ascending
    23 
    24  ! Initialization
    25  if (present(err)) then
    26  errmgr => err
    27  else
    28  errmgr => deferr
    29  end if
    30  neqn = fcnobj%get_equation_count()
    31  ncols = neqn + 1
    32  n = size(x)
    33  if (this%get_provide_all_output()) then
    34  nbuffer = this%get_min_buffer_size()
    35  else
    36  nbuffer = n
    37  end if
    38  allocate(ytemp(neqn), stat = flag)
    39  if (flag /= 0) then
    40  call errmgr%report_error("oi_integrate", &
    41  "Insufficient memory available.", int_out_of_memory_error)
    42  return
    43  end if
    44 
    45  ! Quick Return
    46  if (neqn <= 0) return
    47 
    48  ! Input Checking
    49  if (.not.fcnobj%get_equations_defined()) then
    50  ! ERROR: Equations undefined
    51  call errmgr%report_error("oi_integrate", &
    52  "The routine expected to hold the ODEs is undefined.", &
    53  int_lack_of_definition_error)
    54  return
    55  end if
    56  if (neqn /= size(y)) then
    57  ! ERROR: # of equations does not match initial condition vector size
    58  write(errmsg, '(AI0AI0A)') "Expected an array of size ", neqn, &
    59  ", but found an array of size ", size(y), "."
    60  call errmgr%report_error("oi_integrate", trim(errmsg), &
    61  int_array_size_mismatch_error)
    62  return
    63  end if
    64  if (n < 2) then
    65  ! ERROR: There must be at least a starting and ending point for the
    66  ! integration routine
    67  end if
    68  if (x(n) == x(1)) then
    69  ! ERROR: No integration range
    70  call errmgr%report_error("oi_integrate", &
    71  "The starting and ending integration points are the same.", &
    72  int_invalid_input_error)
    73  return
    74  end if
    75 
    76  ! Ensure tolerances are defined. If not, utilize defaults
    77  if (allocated(this%m_rtol)) then
    78  if (size(this%m_rtol) /= neqn) then
    79  ! WARNING: Size mismatch in tolerance array - using defaults
    80  call errmgr%report_warning("oi_integrate", &
    81  "The relative tolerance array is not correctly " // &
    82  "sized for the problem. Using a default tolerance " // &
    83  "instead.", int_array_size_mismatch_error)
    84  deallocate(this%m_rtol)
    85  this%m_rtol = alloc_default_rtol(neqn)
    86  end if
    87  else
    88  this%m_rtol = alloc_default_rtol(neqn)
    89  end if
    90 
    91  if (allocated(this%m_atol)) then
    92  if (size(this%m_rtol) /= neqn) then
    93  ! WARNING: Size mismatch in tolerance array - using defaults
    94  call errmgr%report_warning("oi_integrate", &
    95  "The absolute tolerance array is not correctly " // &
    96  "sized for the problem. Using a default tolerance " // &
    97  "instead.", int_array_size_mismatch_error)
    98  deallocate(this%m_atol)
    99  this%m_atol = alloc_default_atol(neqn)
    100  end if
    101  else
    102  this%m_atol = alloc_default_atol(neqn)
    103  end if
    104 
    105  ! Additional Initialization
    106  allocate(buffer(nbuffer, ncols), stat = flag)
    107  if (flag /= 0) then
    108  call errmgr%report_error("oi_integrate", &
    109  "Insufficient memory available.", int_out_of_memory_error)
    110  return
    111  end if
    112  ascending = x(n) > x(1)
    113 
    114  ! Store the initial conditions
    115  buffer(1,1) = x(1)
    116  buffer(1,2:ncols) = y
    117 
    118  ! Integrate
    119  i = 1
    120  if (this%get_provide_all_output()) then
    121  xout = x(n)
    122  call this%set_integration_limit(x(n))
    123  call this%set_allow_overshoot(.false.)
    124  end if
    125  do
    126  ! Copy the previous step's output
    127  xi = buffer(i,1)
    128  ytemp = buffer(i,2:ncols)
    129 
    130  ! Increment i
    131  i = i + 1
    132 
    133  ! Ensure the buffer is sufficiently sized
    134  if (i > size(buffer, 1)) then
    135  call realloc_buffer(buffer, &
    136  size(buffer, 1) + nbuffer, errmgr)
    137  if (errmgr%has_error_occurred()) return
    138  end if
    139 
    140  ! Take the next integration step
    141  if (.not.this%get_provide_all_output()) xout = x(i)
    142  brk = this%step(fcnobj, xi, ytemp, xout, this%m_rtol, this%m_atol, &
    143  errmgr)
    144  if (brk) then
    145  ! Store the output, and then exit
    146  buffer(i,1) = xi
    147  buffer(i,2:ncols) = ytemp
    148  exit
    149  end if
    150  if (errmgr%has_error_occurred()) return
    151 
    152  ! Store the output
    153  buffer(i,1) = xi
    154  buffer(i,2:ncols) = ytemp
    155 
    156  ! Break if X exceeds XOUT
    157  if (ascending .and. xi >= x(n)) then
    158  exit
    159  else if (.not.ascending .and. xi <= x(n)) then
    160  exit
    161  end if
    162  end do
    163 
    164  ! Resize the buffer to tightly fit the data, if necessary
    165  rst = buffer(1:i,:)
    166  end function
    167 
    168 ! ------------------------------------------------------------------------------
    169  pure module function oi_get_use_all_output(this) result(x)
    170  class(ode_integrator), intent(in) :: this
    171  logical :: x
    172  x = this%m_allOutput
    173  end function
    174 
    175 ! --------------------
    176  module subroutine oi_set_use_all_output(this, x)
    177  class(ode_integrator), intent(inout) :: this
    178  logical, intent(in) :: x
    179  this%m_allOutput = x
    180  end subroutine
    181 
    182 ! ------------------------------------------------------------------------------
    183  pure module function oi_get_allow_overshoot(this) result(x)
    184  class(ode_integrator), intent(in) :: this
    185  logical :: x
    186  x = this%m_canOvershoot
    187  end function
    188 
    189 ! --------------------
    190  module subroutine oi_set_allow_overshoot(this, x)
    191  class(ode_integrator), intent(inout) :: this
    192  logical, intent(in) :: x
    193  this%m_canOvershoot = x
    194  end subroutine
    195 
    196 ! ------------------------------------------------------------------------------
    197  pure module function oi_get_critical_point(this) result(x)
    198  class(ode_integrator), intent(in) :: this
    199  real(real64) :: x
    200  x = this%m_criticalPoint
    201  end function
    202 
    203 ! --------------------
    204  module subroutine oi_set_critical_point(this, x)
    205  class(ode_integrator), intent(inout) :: this
    206  real(real64), intent(in) :: x
    207  this%m_criticalPoint = x
    208  end subroutine
    209 
    210 ! ------------------------------------------------------------------------------
    211  pure module function oi_get_min_buffer_size(this) result(x)
    212  class(ode_integrator), intent(in) :: this
    213  integer(int32) :: x
    214  x = this%m_minBufferSize
    215  end function
    216 
    217 ! --------------------
    218  module subroutine oi_set_min_buffer_size(this, x)
    219  class(ode_integrator), intent(inout) :: this
    220  integer(int32), intent(in) :: x
    221  this%m_minBufferSize = x
    222  end subroutine
    223 
    224 ! ------------------------------------------------------------------------------
    225  pure module function oi_get_max_step_size(this) result(x)
    226  class(ode_integrator), intent(in) :: this
    227  real(real64) :: x
    228  x = this%m_maxStepSize
    229  end function
    230 
    231 ! --------------------
    232  module subroutine oi_set_max_step_size(this, x)
    233  class(ode_integrator), intent(inout) :: this
    234  real(real64), intent(in) :: x
    235  this%m_maxStepSize = x
    236  end subroutine
    237 
    238 ! ------------------------------------------------------------------------------
    239  pure module function oi_get_limit_step_size(this) result(x)
    240  class(ode_integrator), intent(in) :: this
    241  logical :: x
    242  x = this%m_limitStepSize
    243  end function
    244 
    245 ! --------------------
    246  module subroutine oi_set_limit_step_size(this, x)
    247  class(ode_integrator), intent(inout) :: this
    248  logical, intent(in) :: x
    249  this%m_limitStepSize = x
    250  end subroutine
    251 
    252 ! ------------------------------------------------------------------------------
    253  pure module function oi_get_iteration_limit(this) result(x)
    254  class(ode_integrator), intent(in) :: this
    255  integer(int32) :: x
    256  x = this%m_maxStepCount
    257  end function
    258 
    259 ! --------------------
    260  module subroutine oi_set_iteration_limit(this, x)
    261  class(ode_integrator), intent(inout) :: this
    262  integer(int32), intent(in) :: x
    263  this%m_maxStepCount = x
    264  end subroutine
    265 
    266 ! ------------------------------------------------------------------------------
    267  module function oi_get_rtol(this) result(x)
    268  class(ode_integrator), intent(in) :: this
    269  real(real64), allocatable, dimension(:) :: x
    270  x = this%m_rtol
    271  end function
    272 
    273 ! --------------------
    274  module subroutine oi_set_rtol(this, x)
    275  class(ode_integrator), intent(inout) :: this
    276  real(real64), intent(in), dimension(:) :: x
    277  this%m_rtol = x
    278  end subroutine
    279 
    280 ! ------------------------------------------------------------------------------
    281  module function oi_get_atol(this) result(x)
    282  class(ode_integrator), intent(in) :: this
    283  real(real64), allocatable, dimension(:) :: x
    284  x = this%m_atol
    285  end function
    286 
    287 ! --------------------
    288  module subroutine oi_set_atol(this, x)
    289  class(ode_integrator), intent(inout) :: this
    290  real(real64), intent(in), dimension(:) :: x
    291  this%m_atol = x
    292  end subroutine
    293 
    294 ! ******************************************************************************
    295 ! PRIVATE SUBMODULE ROUTINES
    296 ! ------------------------------------------------------------------------------
    297  ! Establishes a default relative tolerance array.
    298  function alloc_default_rtol(n) result(x)
    299  integer(int32), intent(in) :: n
    300  real(real64), dimension(n) :: x
    301  x = 1.0d-6
    302  end function
    303 
    304 ! ------------------------------------------------------------------------------
    305  ! Establishes a default absolute tolerance array.
    306  function alloc_default_atol(n) result(x)
    307  integer(int32), intent(in) :: n
    308  real(real64), dimension(n) :: x
    309  x = 1.0d-8
    310  end function
    311 
    312 ! ------------------------------------------------------------------------------
    313  subroutine realloc_buffer(x, new_row_count, err)
    314  ! Arguments
    315  real(real64), intent(inout), allocatable, dimension(:,:) :: x
    316  integer(int32), intent(in) :: new_row_count
    317  class(errors), intent(inout) :: err
    318 
    319  ! Local Variables
    320  integer(int32) :: oldm, n, flag
    321  real(real64), allocatable, dimension(:,:) :: temp
    322 
    323  ! Initialization
    324  oldm = size(x, 1)
    325  n = size(x, 2)
    326 
    327  ! If oldm == new_row_count, do nothing
    328  if (oldm == new_row_count) return
    329 
    330  ! Allocate space for a temporary array that allows for resizing of X
    331  allocate(temp(oldm, n), stat = flag)
    332  if (flag /= 0) then
    333  call err%report_error("realloc_buffer", &
    334  "Insufficient memory available.", int_out_of_memory_error)
    335  return
    336  end if
    337  temp = x
    338 
    339  ! Deallocate X, and resize
    340  deallocate(x)
    341  allocate(x(new_row_count, n), stat = flag)
    342  if (flag /= 0) then
    343  call err%report_error("realloc_buffer", &
    344  "Insufficient memory available.", int_out_of_memory_error)
    345  return
    346  end if
    347 
    348  ! Copy temp back into X
    349  if (new_row_count > oldm) then
    350  x(1:oldm,:) = temp
    351  else
    352  x = temp(1:new_row_count,:)
    353  end if
    354  end subroutine
    355 
    356 ! ------------------------------------------------------------------------------
    357 end submodule
    +
    1 ! integral_ode_integrator.f90
    2 
    3 submodule(integral_core) integral_ode_integrator
    4 contains
    5 ! ------------------------------------------------------------------------------
    6  module function oi_integrate(this, fcnobj, x, y, err) result(rst)
    7  ! Arguments
    8  class(ode_integrator), intent(inout) :: this
    9  class(ode_helper), intent(inout) :: fcnobj
    10  real(real64), intent(in), dimension(:) :: x, y
    11  class(errors), intent(inout), optional, target :: err
    12  real(real64), allocatable, dimension(:,:) :: rst
    13 
    14  ! Local Variables
    15  integer(int32) :: neqn, ncols, flag, i, n, nbuffer
    16  real(real64), allocatable, dimension(:,:) :: buffer
    17  real(real64), allocatable, dimension(:) :: ytemp
    18  real(real64) :: xout, xi
    19  class(errors), pointer :: errmgr
    20  type(errors), target :: deferr
    21  character(len = 256) :: errmsg
    22  logical :: brk, ascending
    23 
    24  ! Initialization
    25  if (present(err)) then
    26  errmgr => err
    27  else
    28  errmgr => deferr
    29  end if
    30  neqn = fcnobj%get_equation_count()
    31  ncols = neqn + 1
    32  n = size(x)
    33  if (this%get_provide_all_output()) then
    34  nbuffer = this%get_min_buffer_size()
    35  else
    36  nbuffer = n
    37  end if
    38  allocate(ytemp(neqn), stat = flag)
    39  if (flag /= 0) then
    40  call errmgr%report_error("oi_integrate", &
    41  "Insufficient memory available.", int_out_of_memory_error)
    42  return
    43  end if
    44 
    45  ! Quick Return
    46  if (neqn <= 0) return
    47 
    48  ! Input Checking
    49  if (.not.fcnobj%get_equations_defined()) then
    50  ! ERROR: Equations undefined
    51  call errmgr%report_error("oi_integrate", &
    52  "The routine expected to hold the ODEs is undefined.", &
    53  int_lack_of_definition_error)
    54  return
    55  end if
    56  if (neqn /= size(y)) then
    57  ! ERROR: # of equations does not match initial condition vector size
    58  write(errmsg, '(AI0AI0A)') "Expected an array of size ", neqn, &
    59  ", but found an array of size ", size(y), "."
    60  call errmgr%report_error("oi_integrate", trim(errmsg), &
    61  int_array_size_mismatch_error)
    62  return
    63  end if
    64  if (n < 2) then
    65  ! ERROR: There must be at least a starting and ending point for the
    66  ! integration routine
    67  end if
    68  if (x(n) == x(1)) then
    69  ! ERROR: No integration range
    70  call errmgr%report_error("oi_integrate", &
    71  "The starting and ending integration points are the same.", &
    72  int_invalid_input_error)
    73  return
    74  end if
    75 
    76  ! Ensure tolerances are defined. If not, utilize defaults
    77  if (allocated(this%m_rtol)) then
    78  if (size(this%m_rtol) /= neqn) then
    79  ! WARNING: Size mismatch in tolerance array - using defaults
    80  call errmgr%report_warning("oi_integrate", &
    81  "The relative tolerance array is not correctly " // &
    82  "sized for the problem. Using a default tolerance " // &
    83  "instead.", int_array_size_mismatch_error)
    84  deallocate(this%m_rtol)
    85  this%m_rtol = alloc_default_rtol(neqn)
    86  end if
    87  else
    88  this%m_rtol = alloc_default_rtol(neqn)
    89  end if
    90 
    91  if (allocated(this%m_atol)) then
    92  if (size(this%m_rtol) /= neqn) then
    93  ! WARNING: Size mismatch in tolerance array - using defaults
    94  call errmgr%report_warning("oi_integrate", &
    95  "The absolute tolerance array is not correctly " // &
    96  "sized for the problem. Using a default tolerance " // &
    97  "instead.", int_array_size_mismatch_error)
    98  deallocate(this%m_atol)
    99  this%m_atol = alloc_default_atol(neqn)
    100  end if
    101  else
    102  this%m_atol = alloc_default_atol(neqn)
    103  end if
    104 
    105  ! Additional Initialization
    106  allocate(buffer(nbuffer, ncols), stat = flag)
    107  if (flag /= 0) then
    108  call errmgr%report_error("oi_integrate", &
    109  "Insufficient memory available.", int_out_of_memory_error)
    110  return
    111  end if
    112  ascending = x(n) > x(1)
    113 
    114  ! Store the initial conditions
    115  buffer(1,1) = x(1)
    116  buffer(1,2:ncols) = y
    117 
    118  ! Integrate
    119  i = 1
    120  if (this%get_provide_all_output()) then
    121  xout = x(n)
    122  call this%set_integration_limit(x(n))
    123  call this%set_allow_overshoot(.false.)
    124  end if
    125  do
    126  ! Copy the previous step's output
    127  xi = buffer(i,1)
    128  ytemp = buffer(i,2:ncols)
    129 
    130  ! Increment i
    131  i = i + 1
    132 
    133  ! Ensure the buffer is sufficiently sized
    134  if (i > size(buffer, 1)) then
    135  call realloc_buffer(buffer, &
    136  size(buffer, 1) + nbuffer, errmgr)
    137  if (errmgr%has_error_occurred()) return
    138  end if
    139 
    140  ! Take the next integration step
    141  if (.not.this%get_provide_all_output()) xout = x(i)
    142  brk = this%step(fcnobj, xi, ytemp, xout, this%m_rtol, this%m_atol, &
    143  errmgr)
    144  if (brk) then
    145  ! Store the output, and then exit
    146  buffer(i,1) = xi
    147  buffer(i,2:ncols) = ytemp
    148  exit
    149  end if
    150  if (errmgr%has_error_occurred()) return
    151 
    152  ! Store the output
    153  buffer(i,1) = xi
    154  buffer(i,2:ncols) = ytemp
    155 
    156  ! Break if X exceeds XOUT
    157  if (ascending .and. xi >= x(n)) then
    158  exit
    159  else if (.not.ascending .and. xi <= x(n)) then
    160  exit
    161  end if
    162  end do
    163 
    164  ! Resize the buffer to tightly fit the data, if necessary
    165  rst = buffer(1:i,:)
    166  end function
    167 
    168 ! ------------------------------------------------------------------------------
    169  pure module function oi_get_use_all_output(this) result(x)
    170  class(ode_integrator), intent(in) :: this
    171  logical :: x
    172  x = this%m_allOutput
    173  end function
    174 
    175 ! --------------------
    176  module subroutine oi_set_use_all_output(this, x)
    177  class(ode_integrator), intent(inout) :: this
    178  logical, intent(in) :: x
    179  this%m_allOutput = x
    180  end subroutine
    181 
    182 ! ------------------------------------------------------------------------------
    183  pure module function oi_get_allow_overshoot(this) result(x)
    184  class(ode_integrator), intent(in) :: this
    185  logical :: x
    186  x = this%m_canOvershoot
    187  end function
    188 
    189 ! --------------------
    190  module subroutine oi_set_allow_overshoot(this, x)
    191  class(ode_integrator), intent(inout) :: this
    192  logical, intent(in) :: x
    193  this%m_canOvershoot = x
    194  end subroutine
    195 
    196 ! ------------------------------------------------------------------------------
    197  pure module function oi_get_critical_point(this) result(x)
    198  class(ode_integrator), intent(in) :: this
    199  real(real64) :: x
    200  x = this%m_criticalPoint
    201  end function
    202 
    203 ! --------------------
    204  module subroutine oi_set_critical_point(this, x)
    205  class(ode_integrator), intent(inout) :: this
    206  real(real64), intent(in) :: x
    207  this%m_criticalPoint = x
    208  end subroutine
    209 
    210 ! ------------------------------------------------------------------------------
    211  pure module function oi_get_min_buffer_size(this) result(x)
    212  class(ode_integrator), intent(in) :: this
    213  integer(int32) :: x
    214  x = this%m_minBufferSize
    215  end function
    216 
    217 ! --------------------
    218  module subroutine oi_set_min_buffer_size(this, x)
    219  class(ode_integrator), intent(inout) :: this
    220  integer(int32), intent(in) :: x
    221  this%m_minBufferSize = x
    222  end subroutine
    223 
    224 ! ------------------------------------------------------------------------------
    225  pure module function oi_get_max_step_size(this) result(x)
    226  class(ode_integrator), intent(in) :: this
    227  real(real64) :: x
    228  x = this%m_maxStepSize
    229  end function
    230 
    231 ! --------------------
    232  module subroutine oi_set_max_step_size(this, x)
    233  class(ode_integrator), intent(inout) :: this
    234  real(real64), intent(in) :: x
    235  this%m_maxStepSize = x
    236  end subroutine
    237 
    238 ! ------------------------------------------------------------------------------
    239  pure module function oi_get_limit_step_size(this) result(x)
    240  class(ode_integrator), intent(in) :: this
    241  logical :: x
    242  x = this%m_limitStepSize
    243  end function
    244 
    245 ! --------------------
    246  module subroutine oi_set_limit_step_size(this, x)
    247  class(ode_integrator), intent(inout) :: this
    248  logical, intent(in) :: x
    249  this%m_limitStepSize = x
    250  end subroutine
    251 
    252 ! ------------------------------------------------------------------------------
    253  pure module function oi_get_iteration_limit(this) result(x)
    254  class(ode_integrator), intent(in) :: this
    255  integer(int32) :: x
    256  x = this%m_maxStepCount
    257  end function
    258 
    259 ! --------------------
    260  module subroutine oi_set_iteration_limit(this, x)
    261  class(ode_integrator), intent(inout) :: this
    262  integer(int32), intent(in) :: x
    263  this%m_maxStepCount = x
    264  end subroutine
    265 
    266 ! ------------------------------------------------------------------------------
    267  module function oi_get_rtol(this) result(x)
    268  class(ode_integrator), intent(in) :: this
    269  real(real64), allocatable, dimension(:) :: x
    270  x = this%m_rtol
    271  end function
    272 
    273 ! --------------------
    274  module subroutine oi_set_rtol(this, x)
    275  class(ode_integrator), intent(inout) :: this
    276  real(real64), intent(in), dimension(:) :: x
    277  this%m_rtol = x
    278  end subroutine
    279 
    280 ! ------------------------------------------------------------------------------
    281  module function oi_get_atol(this) result(x)
    282  class(ode_integrator), intent(in) :: this
    283  real(real64), allocatable, dimension(:) :: x
    284  x = this%m_atol
    285  end function
    286 
    287 ! --------------------
    288  module subroutine oi_set_atol(this, x)
    289  class(ode_integrator), intent(inout) :: this
    290  real(real64), intent(in), dimension(:) :: x
    291  this%m_atol = x
    292  end subroutine
    293 
    294 ! ******************************************************************************
    295 ! PRIVATE SUBMODULE ROUTINES
    296 ! ------------------------------------------------------------------------------
    297  ! Establishes a default relative tolerance array.
    298  function alloc_default_rtol(n) result(x)
    299  integer(int32), intent(in) :: n
    300  real(real64), dimension(n) :: x
    301  x = 1.0d-6
    302  end function
    303 
    304 ! ------------------------------------------------------------------------------
    305  ! Establishes a default absolute tolerance array.
    306  function alloc_default_atol(n) result(x)
    307  integer(int32), intent(in) :: n
    308  real(real64), dimension(n) :: x
    309  x = 1.0d-8
    310  end function
    311 
    312 ! ------------------------------------------------------------------------------
    313  subroutine realloc_buffer(x, new_row_count, err)
    314  ! Arguments
    315  real(real64), intent(inout), allocatable, dimension(:,:) :: x
    316  integer(int32), intent(in) :: new_row_count
    317  class(errors), intent(inout) :: err
    318 
    319  ! Local Variables
    320  integer(int32) :: oldm, n, flag
    321  real(real64), allocatable, dimension(:,:) :: temp
    322 
    323  ! Initialization
    324  oldm = size(x, 1)
    325  n = size(x, 2)
    326 
    327  ! If oldm == new_row_count, do nothing
    328  if (oldm == new_row_count) return
    329 
    330  ! Allocate space for a temporary array that allows for resizing of X
    331  allocate(temp(oldm, n), stat = flag)
    332  if (flag /= 0) then
    333  call err%report_error("realloc_buffer", &
    334  "Insufficient memory available.", int_out_of_memory_error)
    335  return
    336  end if
    337  temp = x
    338 
    339  ! Deallocate X, and resize
    340  deallocate(x)
    341  allocate(x(new_row_count, n), stat = flag)
    342  if (flag /= 0) then
    343  call err%report_error("realloc_buffer", &
    344  "Insufficient memory available.", int_out_of_memory_error)
    345  return
    346  end if
    347 
    348  ! Copy temp back into X
    349  if (new_row_count > oldm) then
    350  x(1:oldm,:) = temp
    351  else
    352  x = temp(1:new_row_count,:)
    353  end if
    354  end subroutine
    355 
    356 ! ------------------------------------------------------------------------------
    357 end submodule
    integral_core
    integral_core
    Definition: integral_core.f90:18
    +
    diff --git a/doc/html/interfaceintegral__core_1_1finite__interval__fcn-members.html b/doc/html/interfaceintegral__core_1_1finite__interval__fcn-members.html index 5ad0468..3227220 100644 --- a/doc/html/interfaceintegral__core_1_1finite__interval__fcn-members.html +++ b/doc/html/interfaceintegral__core_1_1finite__interval__fcn-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1finite__interval__fcn.html b/doc/html/interfaceintegral__core_1_1finite__interval__fcn.html index 9d12943..407fc39 100644 --- a/doc/html/interfaceintegral__core_1_1finite__interval__fcn.html +++ b/doc/html/interfaceintegral__core_1_1finite__interval__fcn.html @@ -3,8 +3,7 @@ - - + integral: integral_core::finite_interval_fcn Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
    diff --git a/doc/html/interfaceintegral__core_1_1integrand-members.html b/doc/html/interfaceintegral__core_1_1integrand-members.html index 4f1bee3..169b778 100644 --- a/doc/html/interfaceintegral__core_1_1integrand-members.html +++ b/doc/html/interfaceintegral__core_1_1integrand-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1integrand.html b/doc/html/interfaceintegral__core_1_1integrand.html index 5bb7e74..2052964 100644 --- a/doc/html/interfaceintegral__core_1_1integrand.html +++ b/doc/html/interfaceintegral__core_1_1integrand.html @@ -3,8 +3,7 @@ - - + integral: integral_core::integrand Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
    diff --git a/doc/html/interfaceintegral__core_1_1ode__constraint-members.html b/doc/html/interfaceintegral__core_1_1ode__constraint-members.html index 067014b..5abde51 100644 --- a/doc/html/interfaceintegral__core_1_1ode__constraint-members.html +++ b/doc/html/interfaceintegral__core_1_1ode__constraint-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1ode__constraint.html b/doc/html/interfaceintegral__core_1_1ode__constraint.html index f1beb39..a76b6b1 100644 --- a/doc/html/interfaceintegral__core_1_1ode__constraint.html +++ b/doc/html/interfaceintegral__core_1_1ode__constraint.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_constraint Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
    diff --git a/doc/html/interfaceintegral__core_1_1ode__fcn-members.html b/doc/html/interfaceintegral__core_1_1ode__fcn-members.html index f957777..6e0652b 100644 --- a/doc/html/interfaceintegral__core_1_1ode__fcn-members.html +++ b/doc/html/interfaceintegral__core_1_1ode__fcn-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1ode__fcn.html b/doc/html/interfaceintegral__core_1_1ode__fcn.html index fea564f..92fc373 100644 --- a/doc/html/interfaceintegral__core_1_1ode__fcn.html +++ b/doc/html/interfaceintegral__core_1_1ode__fcn.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_fcn Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
    diff --git a/doc/html/interfaceintegral__core_1_1ode__integrator__interface-members.html b/doc/html/interfaceintegral__core_1_1ode__integrator__interface-members.html index 5cdc832..09ac0f2 100644 --- a/doc/html/interfaceintegral__core_1_1ode__integrator__interface-members.html +++ b/doc/html/interfaceintegral__core_1_1ode__integrator__interface-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1ode__integrator__interface.html b/doc/html/interfaceintegral__core_1_1ode__integrator__interface.html index 31aa3e7..ac8a42d 100644 --- a/doc/html/interfaceintegral__core_1_1ode__integrator__interface.html +++ b/doc/html/interfaceintegral__core_1_1ode__integrator__interface.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_integrator_interface Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
    diff --git a/doc/html/interfaceintegral__core_1_1ode__integrator__reset-members.html b/doc/html/interfaceintegral__core_1_1ode__integrator__reset-members.html index 49f60d5..b53ba3d 100644 --- a/doc/html/interfaceintegral__core_1_1ode__integrator__reset-members.html +++ b/doc/html/interfaceintegral__core_1_1ode__integrator__reset-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1ode__integrator__reset.html b/doc/html/interfaceintegral__core_1_1ode__integrator__reset.html index e93f162..e5b2be8 100644 --- a/doc/html/interfaceintegral__core_1_1ode__integrator__reset.html +++ b/doc/html/interfaceintegral__core_1_1ode__integrator__reset.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_integrator_reset Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
    diff --git a/doc/html/interfaceintegral__core_1_1ode__jacobian-members.html b/doc/html/interfaceintegral__core_1_1ode__jacobian-members.html index daf4637..ef3c124 100644 --- a/doc/html/interfaceintegral__core_1_1ode__jacobian-members.html +++ b/doc/html/interfaceintegral__core_1_1ode__jacobian-members.html @@ -3,8 +3,7 @@ - - + integral: Member List @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    diff --git a/doc/html/interfaceintegral__core_1_1ode__jacobian.html b/doc/html/interfaceintegral__core_1_1ode__jacobian.html index 5ef282d..bcfbabe 100644 --- a/doc/html/interfaceintegral__core_1_1ode__jacobian.html +++ b/doc/html/interfaceintegral__core_1_1ode__jacobian.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_jacobian Interface Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    The documentation for this interface was generated from the following file:
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m=this.activatedItems[l].dataSM("sub");if(m){this.menuHide(m)}}},menuIframeShim:function(l){if(e&&this.opts.overlapControlsInIE&&!l.dataSM("ie-shim")){l.dataSM("ie-shim",a(" +
    + +
    +
    +Data Types | +Variables
    +
    +
    integral_core Module Reference
    +
    +
    + +

    integral_core +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Data Types

    type  adaptive_integrator
     Defines an integrator that uses an adaptive Gauss-Kronrod method to compute the integral of a function of one variable over a finite interval. More...
     
    interface  finite_interval_fcn
     Defines the signature of a routine used to integrate a function of one variable over a finite interval. More...
     
    type  finite_interval_integrator
     A type that defines an integrator meant to operate on integrands over a finite region. More...
     
    interface  integrand
     Defines a function of one variable to be integrated. More...
     
    type  integration_behavior
     Provides information regarding the behavior of an integrator. More...
     
    type  integrator_base
     Defines a base type for integrator types. More...
     
    type  nonadaptive_integrator
     Defines an integrator that uses a non-adaptive Gauss-Kronrod method to compute the integral of a function of one variable over a finite interval. More...
     
    type  ode_auto
     Defines an integrator for systems of first order ODEs that is capable of switching between an Adams method and a BDF method automatically. This integrator is able to handle both stiff and non-stiff systems of equations. More...
     
    interface  ode_constraint
     Defines a routine capable of describing constraints on a system of ODEs of N variables exposed to M constraints. More...
     
    interface  ode_fcn
     Defines a routine containing a system of first order ODEs. More...
     
    type  ode_helper
     Defines a type used to pass information regarding the ODEs to the solver. More...
     
    type  ode_integrator
     
    interface  ode_integrator_interface
     Defines a routine for computing a single integration step in the direction of xout. More...
     
    interface  ode_integrator_reset
     Resets the state of the integrator. More...
     
    interface  ode_jacobian
     Defines a routine capable of computing the Jacobian matrix of a system of N first order ODEs of N variables. More...
     
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Variables

    +integer(int32), parameter, public int_out_of_memory_error = 1
     An error flag indicating insufficient memory.
     
    +integer(int32), parameter, public int_count_exceeded_error = 2
     An error flag indicates a specific parameter count has been exceeded.
     
    +integer(int32), parameter, public int_round_off_error = 3
     An error flag indicating round off error has become an issue.
     
    +integer(int32), parameter, public int_integrand_behavior_error = 4
     An error flag indicating difficult integrand behavior.
     
    +integer(int32), parameter, public int_convergence_error = 5
     An error flag indicating convergence issues.
     
    +integer(int32), parameter, public int_divergent_error = 6
     An error flag indicating divergent behavior.
     
    +integer(int32), parameter, public int_invalid_input_error = 7
     An error flag indicating an invalid input.
     
    +integer(int32), parameter, public int_lack_of_definition_error = 8
     An error flag denoting a lack of definition.
     
    +integer(int32), parameter, public int_array_size_mismatch_error = 9
     An error indicating an inappropriately sized array.
     
    +integer(int32), parameter, public int_excessive_work_error = 10
     An error indicating the too many iterations have been performed suggesting that excessive amounts of work are required to continue the solution process.
     
    +integer(int32), parameter, public int_impractical_tolerance_error = 11
     An error indicating that the user-defined tolerances are too stringent to be practical for the problem at hand.
     
    +integer(int32), parameter, public int_repeated_error_test_failure = 12
     An error that occurs if integrator error tests fail repeatadly.
     
    +integer(int32), parameter, public int_15_point_rule = 15
     Defines a 15-point Gauss-Kronrod integration rule.
     
    +integer(int32), parameter, public int_21_point_rule = 21
     Defines a 21-point Gauss-Kronrod integration rule.
     
    +integer(int32), parameter, public int_31_point_rule = 31
     Defines a 31-point Gauss-Kronrod integration rule.
     
    +integer(int32), parameter, public int_41_point_rule = 41
     Defines a 41-point Gauss-Kronrod integration rule.
     
    +integer(int32), parameter, public int_51_point_rule = 51
     Defines a 51-point Gauss-Kronrod integration rule.
     
    +integer(int32), parameter, public int_61_point_rule = 61
     Defines a 61-point Gauss-Kronrod integration rule.
     
    +

    Detailed Description

    +

    integral_core

    +
    Purpose
    Provides types and routines allowing for the integration of functions and systems of ordinary differential equations.
    +
    + + + + + diff --git a/doc/html/namespaceintegral__core.js b/doc/html/namespaceintegral__core.js new file mode 100644 index 0000000..3bd0d97 --- /dev/null +++ b/doc/html/namespaceintegral__core.js @@ -0,0 +1,18 @@ +var namespaceintegral__core = +[ + [ "adaptive_integrator", "structintegral__core_1_1adaptive__integrator.html", "structintegral__core_1_1adaptive__integrator" ], + [ "finite_interval_fcn", "interfaceintegral__core_1_1finite__interval__fcn.html", "interfaceintegral__core_1_1finite__interval__fcn" ], + [ "finite_interval_integrator", "structintegral__core_1_1finite__interval__integrator.html", "structintegral__core_1_1finite__interval__integrator" ], + [ "integrand", "interfaceintegral__core_1_1integrand.html", "interfaceintegral__core_1_1integrand" ], + [ "integration_behavior", "structintegral__core_1_1integration__behavior.html", "structintegral__core_1_1integration__behavior" ], + [ "integrator_base", "structintegral__core_1_1integrator__base.html", "structintegral__core_1_1integrator__base" ], + [ "nonadaptive_integrator", "structintegral__core_1_1nonadaptive__integrator.html", "structintegral__core_1_1nonadaptive__integrator" ], + [ "ode_auto", "structintegral__core_1_1ode__auto.html", "structintegral__core_1_1ode__auto" ], + [ "ode_constraint", "interfaceintegral__core_1_1ode__constraint.html", "interfaceintegral__core_1_1ode__constraint" ], + [ "ode_fcn", "interfaceintegral__core_1_1ode__fcn.html", "interfaceintegral__core_1_1ode__fcn" ], + [ "ode_helper", "structintegral__core_1_1ode__helper.html", "structintegral__core_1_1ode__helper" ], + [ "ode_integrator", "structintegral__core_1_1ode__integrator.html", "structintegral__core_1_1ode__integrator" ], + [ "ode_integrator_interface", "interfaceintegral__core_1_1ode__integrator__interface.html", "interfaceintegral__core_1_1ode__integrator__interface" ], + [ "ode_integrator_reset", "interfaceintegral__core_1_1ode__integrator__reset.html", "interfaceintegral__core_1_1ode__integrator__reset" ], + [ "ode_jacobian", "interfaceintegral__core_1_1ode__jacobian.html", "interfaceintegral__core_1_1ode__jacobian" ] +]; \ No newline at end of file diff --git a/doc/html/namespacemembers.html b/doc/html/namespacemembers.html new file mode 100644 index 0000000..c8dfef4 --- /dev/null +++ b/doc/html/namespacemembers.html @@ -0,0 +1,181 @@ + + + + + + +integral: Module Members + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    Here is a list of all documented module members with links to the modules they belong to:
    +
    +
    + + + + diff --git a/doc/html/namespacemembers_vars.html b/doc/html/namespacemembers_vars.html new file mode 100644 index 0000000..61742c2 --- /dev/null +++ b/doc/html/namespacemembers_vars.html @@ -0,0 +1,181 @@ + + + + + + +integral: Module Members + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +  +
    +
    + + + + diff --git a/doc/html/namespaces.html b/doc/html/namespaces.html new file mode 100644 index 0000000..68b9906 --- /dev/null +++ b/doc/html/namespaces.html @@ -0,0 +1,128 @@ + + + + + + +integral: Modules List + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Modules List
    +
    +
    +
    Here is a list of all documented modules with brief descriptions:
    + + +
     Nintegral_coreintegral_core
    +
    +
    +
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document.createElement("span"); - imgNode.className = 'arrow'; + var imgNode = document.createElement("img"); imgNode.style.paddingLeft=(16*level).toString()+'px'; - imgNode.innerHTML=arrowRight; + imgNode.width = 16; + imgNode.height = 22; + imgNode.border = 0; node.plus_img = imgNode; node.expandToggle = document.createElement("a"); node.expandToggle.href = "javascript:void(0)"; node.expandToggle.onclick = function() { if (node.expanded) { $(node.getChildrenUL()).slideUp("fast"); - node.plus_img.innerHTML=arrowRight; + node.plus_img.src = node.relpath+"arrowright.png"; node.expanded = false; } else { expandNode(o, node, false, false); @@ -114,13 +113,15 @@ function createIndent(o,domNode,node,level) } node.expandToggle.appendChild(imgNode); domNode.appendChild(node.expandToggle); + imgNode.src = node.relpath+"arrowright.png"; } else { var span = document.createElement("span"); - span.className = 'arrow'; + span.style.display = 'inline-block'; span.style.width = 16*(level+1)+'px'; + 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    +
    Loading...
    +
    + +
    Searching...
    +
    No Matches
    + +
    + + diff --git a/doc/html/search/variables_3.js b/doc/html/search/variables_3.js new file mode 100644 index 0000000..9f63964 --- /dev/null +++ b/doc/html/search/variables_3.js @@ -0,0 +1,4 @@ +var searchData= +[ + ['subinterval_5fcount',['subinterval_count',['../structintegral__core_1_1integration__behavior.html#af119d968518a0f9d11c5ce1b6a30b31f',1,'integral_core::integration_behavior']]] +]; diff --git a/doc/html/structintegral__core_1_1adaptive__integrator.html b/doc/html/structintegral__core_1_1adaptive__integrator.html index f1dc4a9..08d92c1 100644 --- a/doc/html/structintegral__core_1_1adaptive__integrator.html +++ b/doc/html/structintegral__core_1_1adaptive__integrator.html @@ -3,8 +3,7 @@ - - + integral: integral_core::adaptive_integrator Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@ - + - - - - + +
    integral_core::adaptive_integrator Type Reference
    @@ -97,7 +123,7 @@
    - + integral_core::finite_interval_integrator integral_core::integrator_base @@ -124,58 +150,56 @@  Sets an array of user-defined breakpoints. Additionally, this array call set_use_breakpoints with an argument of true such that the integrator will use the breakpoints defined by this routine. More...
      - Public Member Functions inherited from integral_core::finite_interval_integrator - + procedure(finite_interval_fcn), deferred, pass, public integrate  Performs the actual integration.
      - Public Member Functions inherited from integral_core::integrator_base procedure, public get_abs_tol => ib_get_abs_tol - Gets the absolute tolerance value. More...
    + Gets the absolute tolerance value. More...
      procedure, public set_abs_tol => ib_set_abs_tol - Sets the absolute tolerance value. More...
    + Sets the absolute tolerance value. More...
      procedure, public get_rel_tol => ib_get_rel_tol - Gets the relative tolerance value. More...
    + Gets the relative tolerance value. More...
      procedure, public set_rel_tol => ib_set_rel_tol - Sets the relative tolerance value. More...
    + Sets the relative tolerance value. More...
      procedure, public get_max_subintervals => ib_get_max_subintervals - Gets the maximum number of subintervals into which the integrator may divide the problem region. More...
    + Gets the maximum number of subintervals into which the integrator may divide the problem region. More...
      procedure, public ib_set_max_subintervals => ib_set_max_subintervals - Sets the maximum number of subintervals into which the integrator may divide the problem region. More...
    + Sets the maximum number of subintervals into which the integrator may divide the problem region. More...
      - - - -

    Private Attributes

    +
    real(real64), dimension(:), allocatable m_work
     A workspace array.
     
    +
    integer(int32), dimension(:), allocatable m_iwork
     A workspace array.
     
    +
    logical m_userdefinedbreaks = .false.
     True for user defined breakpoints; else, false.
     
    +
    real(real64), dimension(:), allocatable m_breakpoints
     A list of user-defined breakpoints.
     

    Detailed Description

    Defines an integrator that uses an adaptive Gauss-Kronrod method to compute the integral of a function of one variable over a finite interval.

    -
    Example
    The following example illustrates how to use the adaptive_integrator to compute the integral of a function over a finite interval.
    program example
    use iso_fortran_env
    use integral_core
    implicit none
    ! Variables
    real(real64) :: ans, y, pi, a, b
    procedure(integrand), pointer :: fcn
    type(adaptive_integrator) :: integrator
    ! Define the integration limits
    pi = 2.0d0 * acos(0.0d0)
    a = pi / 6.0d0
    b = pi / 4.0d0
    ! Evaluate the integral
    fcn => int_fcn
    y = integrator%integrate(fcn, a, b)
    ! Display the results
    ans = 5.0d0 * pi / 12.0d0 - 2.0d0 * sqrt(2.0d0) + 4.0d0 / sqrt(3.0d0)
    print '(AEN13.5AEN13.5A)', "The solution is: ", ans, &
    ", the integrator computed: ", y, "."
    contains
    ! This example is from http://tutorial.math.lamar.edu/Classes/CalcI/ComputingDefiniteIntegrals.aspx#Int_CompDef_Ex3a
    ! The integrand is: f(x) = 5 - 2 sec(x) tan(x).
    ! If the integral is considered over the range [pi/6, pi/4], the solution
    ! is 5 pi / 12 - 2 sqrt(2) + 4 / sqrt(3).
    function int_fcn(x) result(f)
    real(real64), intent(in) :: x
    real(real64) :: f
    f = 5.0d0 - 2.0d0 * tan(x) / cos(x) ! Remember, sec(x) = 1 / cos(x)
    end function
    end program
    The above program produces the following output.
    The solution is: 789.97089E-03, the integrator computed: 789.97089E-03.
    +
    Example
    The following example illustrates how to use the adaptive_integrator to compute the integral of a function over a finite interval.
    program example
    use iso_fortran_env
    use integral_core
    implicit none
    ! Variables
    real(real64) :: ans, y, pi, a, b
    procedure(integrand), pointer :: fcn
    type(adaptive_integrator) :: integrator
    ! Define the integration limits
    pi = 2.0d0 * acos(0.0d0)
    a = pi / 6.0d0
    b = pi / 4.0d0
    ! Evaluate the integral
    fcn => int_fcn
    y = integrator%integrate(fcn, a, b)
    ! Display the results
    ans = 5.0d0 * pi / 12.0d0 - 2.0d0 * sqrt(2.0d0) + 4.0d0 / sqrt(3.0d0)
    print '(AEN13.5AEN13.5A)', "The solution is: ", ans, &
    ", the integrator computed: ", y, "."
    contains
    ! This example is from http://tutorial.math.lamar.edu/Classes/CalcI/ComputingDefiniteIntegrals.aspx#Int_CompDef_Ex3a
    ! The integrand is: f(x) = 5 - 2 sec(x) tan(x).
    ! If the integral is considered over the range [pi/6, pi/4], the solution
    ! is 5 pi / 12 - 2 sqrt(2) + 4 / sqrt(3).
    function int_fcn(x) result(f)
    real(real64), intent(in) :: x
    real(real64) :: f
    f = 5.0d0 - 2.0d0 * tan(x) / cos(x) ! Remember, sec(x) = 1 / cos(x)
    end function
    end program
    The above program produces the following output.
    The solution is: 789.97089E-03, the integrator computed: 789.97089E-03.
    -

    Definition at line 351 of file integral_core.f90.

    +

    Definition at line 372 of file integral_core.f90.

    Member Function/Subroutine Documentation

    - -

    ◆ get_breakpoints()

    - +
    @@ -198,13 +222,11 @@

    Returns
    The array of points. This array will not be allocated if no points have been defined.
    -

    Definition at line 449 of file integral_core.f90.

    +

    Definition at line 470 of file integral_core.f90.

    - -

    ◆ get_use_breakpoints()

    - +

    @@ -227,13 +249,11 @@

    Returns
    Returns true if the user-defined breakpoints should be used; else, false.
    -

    Definition at line 425 of file integral_core.f90.

    +

    Definition at line 446 of file integral_core.f90.

    - -

    ◆ initialize()

    - +

    @@ -259,13 +279,11 @@

    Definition at line 376 of file integral_core.f90.

    +

    Definition at line 397 of file integral_core.f90.

    - -

    ◆ integrate()

    - +

    @@ -303,13 +321,11 @@

    Returns
    The value of the integral over the specified range.
    Remarks
    This routine utilizes the QUADPACK routine QAGS. For more information on this routine see http://www.netlib.org/quadpack/.
    -

    Definition at line 412 of file integral_core.f90.

    +

    Definition at line 433 of file integral_core.f90.

    - -

    ◆ set_breakpoints()

    - +

    @@ -332,13 +348,11 @@

    Definition at line 462 of file integral_core.f90.

    +

    Definition at line 483 of file integral_core.f90.

    - -

    ◆ set_use_breakpoints()

    - +

    @@ -361,22 +375,22 @@

    Definition at line 438 of file integral_core.f90.

    +

    Definition at line 459 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/structintegral__core_1_1finite__interval__integrator.html b/doc/html/structintegral__core_1_1finite__interval__integrator.html index 0a49058..7424657 100644 --- a/doc/html/structintegral__core_1_1finite__interval__integrator.html +++ b/doc/html/structintegral__core_1_1finite__interval__integrator.html @@ -3,8 +3,7 @@ - - + integral: integral_core::finite_interval_integrator Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@

    - + - - - - + +
    @@ -96,7 +122,7 @@
    - + integral_core::integrator_base integral_core::adaptive_integrator integral_core::nonadaptive_integrator @@ -105,46 +131,46 @@ - - + - + - + - + - + - +

    Public Member Functions

    +
    procedure(finite_interval_fcn), deferred, pass, public integrate
     Performs the actual integration.
     
    - Public Member Functions inherited from integral_core::integrator_base
    procedure, public get_abs_tol => ib_get_abs_tol
     Gets the absolute tolerance value. More...
     Gets the absolute tolerance value. More...
     
    procedure, public set_abs_tol => ib_set_abs_tol
     Sets the absolute tolerance value. More...
     Sets the absolute tolerance value. More...
     
    procedure, public get_rel_tol => ib_get_rel_tol
     Gets the relative tolerance value. More...
     Gets the relative tolerance value. More...
     
    procedure, public set_rel_tol => ib_set_rel_tol
     Sets the relative tolerance value. More...
     Sets the relative tolerance value. More...
     
    procedure, public get_max_subintervals => ib_get_max_subintervals
     Gets the maximum number of subintervals into which the integrator may divide the problem region. More...
     Gets the maximum number of subintervals into which the integrator may divide the problem region. More...
     
    procedure, public ib_set_max_subintervals => ib_set_max_subintervals
     Sets the maximum number of subintervals into which the integrator may divide the problem region. More...
     Sets the maximum number of subintervals into which the integrator may divide the problem region. More...
     

    Detailed Description

    A type that defines an integrator meant to operate on integrands over a finite region.

    -

    Definition at line 266 of file integral_core.f90.

    +

    Definition at line 287 of file integral_core.f90.

    The documentation for this type was generated from the following file:
    diff --git a/doc/html/structintegral__core_1_1integration__behavior.html b/doc/html/structintegral__core_1_1integration__behavior.html index 6c934ef..36c6ab3 100644 --- a/doc/html/structintegral__core_1_1integration__behavior.html +++ b/doc/html/structintegral__core_1_1integration__behavior.html @@ -3,8 +3,7 @@ - - + integral: integral_core::integration_behavior Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@
    - + - - - - + +
    @@ -94,15 +120,15 @@ - - - @@ -110,19 +136,19 @@

    Detailed Description

    Provides information regarding the behavior of an integrator.

    -

    Definition at line 143 of file integral_core.f90.

    +

    Definition at line 164 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/structintegral__core_1_1integrator__base.html b/doc/html/structintegral__core_1_1integrator__base.html index d82cec7..c7c4d0d 100644 --- a/doc/html/structintegral__core_1_1integrator__base.html +++ b/doc/html/structintegral__core_1_1integrator__base.html @@ -3,8 +3,7 @@ - - +integral: integral_core::integrator_base Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@

    Private Attributes

    +
    real(real64) error_estimate
     An estimate of the absolute error of the integration process.
     
    +
    integer(int32) evaluation_count
     The number of integrand evaluations.
     
    +
    integer(int32) subinterval_count
     The number of subintervals into which the integration region was divided.
     
    - + - - - - + +
    integral_core::integrator_base Type Reference
    @@ -97,7 +123,7 @@
    - + integral_core::finite_interval_integrator integral_core::adaptive_integrator integral_core::nonadaptive_integrator @@ -127,15 +153,15 @@ - - - @@ -143,11 +169,9 @@

    Detailed Description

    Defines a base type for integrator types.

    -

    Definition at line 157 of file integral_core.f90.

    +

    Definition at line 178 of file integral_core.f90.

    Member Function/Subroutine Documentation

    - -

    ◆ get_abs_tol()

    - +

    Private Attributes

    +
    real(real64) m_abstol = 1.0d-8
     The absolute tolerance.
     
    +
    real(real64) m_reltol = 1.0d-8
     The relative tolerance.
     
    +
    integer(int32) m_maxint = 10
     The maximum number of subintervals.
     
    @@ -170,13 +194,11 @@

    Returns
    The tolerance value.
    -

    Definition at line 175 of file integral_core.f90.

    +

    Definition at line 196 of file integral_core.f90.

    - -

    ◆ get_max_subintervals()

    - +

    @@ -199,13 +221,11 @@

    Returns
    The number of intervals.
    -

    Definition at line 216 of file integral_core.f90.

    +

    Definition at line 237 of file integral_core.f90.

    - -

    ◆ get_rel_tol()

    - +

    @@ -228,13 +248,11 @@

    Returns
    The tolerance value.
    -

    Definition at line 195 of file integral_core.f90.

    +

    Definition at line 216 of file integral_core.f90.

    - -

    ◆ ib_set_max_subintervals()

    - +

    @@ -257,13 +275,11 @@

    Definition at line 227 of file integral_core.f90.

    +

    Definition at line 248 of file integral_core.f90.

    - -

    ◆ set_abs_tol()

    - +

    @@ -286,13 +302,11 @@

    Definition at line 185 of file integral_core.f90.

    +

    Definition at line 206 of file integral_core.f90.

    - -

    ◆ set_rel_tol()

    - +

    @@ -315,22 +329,22 @@

    Definition at line 205 of file integral_core.f90.

    +

    Definition at line 226 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/structintegral__core_1_1nonadaptive__integrator.html b/doc/html/structintegral__core_1_1nonadaptive__integrator.html index 16dd222..116a0fc 100644 --- a/doc/html/structintegral__core_1_1nonadaptive__integrator.html +++ b/doc/html/structintegral__core_1_1nonadaptive__integrator.html @@ -3,8 +3,7 @@ - - + integral: integral_core::nonadaptive_integrator Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@

    - + - - - - + +
    integral_core::nonadaptive_integrator Type Reference
    @@ -97,7 +123,7 @@
    - + integral_core::finite_interval_integrator integral_core::integrator_base @@ -115,33 +141,33 @@  Sets the integration rule being utilized. The default integration rule is given by INT_15_POINT_RULE. More...
      - Public Member Functions inherited from integral_core::finite_interval_integrator - + procedure(finite_interval_fcn), deferred, pass, public integrate  Performs the actual integration.
      - Public Member Functions inherited from integral_core::integrator_base procedure, public get_abs_tol => ib_get_abs_tol - Gets the absolute tolerance value. More...
    + Gets the absolute tolerance value. More...
      procedure, public set_abs_tol => ib_set_abs_tol - Sets the absolute tolerance value. More...
    + Sets the absolute tolerance value. More...
      procedure, public get_rel_tol => ib_get_rel_tol - Gets the relative tolerance value. More...
    + Gets the relative tolerance value. More...
      procedure, public set_rel_tol => ib_set_rel_tol - Sets the relative tolerance value. More...
    + Sets the relative tolerance value. More...
      procedure, public get_max_subintervals => ib_get_max_subintervals - Gets the maximum number of subintervals into which the integrator may divide the problem region. More...
    + Gets the maximum number of subintervals into which the integrator may divide the problem region. More...
      procedure, public ib_set_max_subintervals => ib_set_max_subintervals - Sets the maximum number of subintervals into which the integrator may divide the problem region. More...
    + Sets the maximum number of subintervals into which the integrator may divide the problem region. More...
      - @@ -149,11 +175,9 @@

    Detailed Description

    Defines an integrator that uses a non-adaptive Gauss-Kronrod method to compute the integral of a function of one variable over a finite interval.

    -

    Definition at line 508 of file integral_core.f90.

    +

    Definition at line 529 of file integral_core.f90.

    Member Function/Subroutine Documentation

    - -

    ◆ get_rule()

    - +

    Private Attributes

    +
    integer(int32) m_rule = INT_15_POINT_RULE
     The integration rule to use.
     
    @@ -184,13 +208,11 @@

    Definition at line 555 of file integral_core.f90.

    +

    Definition at line 576 of file integral_core.f90.

    - -

    ◆ integrate()

    - +

    @@ -222,13 +244,11 @@

    Returns
    The value of the integral over the specified range.
    Remarks
    This routine utilizes the QUADPACK routine QAGS. For more information on this routine see http://www.netlib.org/quadpack/.
    -

    Definition at line 537 of file integral_core.f90.

    +

    Definition at line 558 of file integral_core.f90.

    - -

    ◆ set_rule()

    - +

    @@ -263,22 +283,22 @@

    Definition at line 578 of file integral_core.f90.

    +

    Definition at line 599 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/structintegral__core_1_1ode__auto.html b/doc/html/structintegral__core_1_1ode__auto.html index de73036..8f29569 100644 --- a/doc/html/structintegral__core_1_1ode__auto.html +++ b/doc/html/structintegral__core_1_1ode__auto.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_auto Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@

    - + - - - - + +
    integral_core::ode_auto Type Reference
    @@ -98,7 +124,7 @@
    - + integral_core::ode_integrator
    @@ -116,106 +142,104 @@   - Public Member Functions inherited from integral_core::ode_integrator procedure, public integrate => oi_integrate - Performs the integration. More...
    + Performs the integration. More...
      procedure, public get_provide_all_output => oi_get_use_all_output - Gets a value determining if all integrator output should be reported. More...
    + Gets a value determining if all integrator output should be reported. More...
      procedure, public set_provide_all_output => oi_set_use_all_output - Sets a value determining if all integrator output should be reported. More...
    + Sets a value determining if all integrator output should be reported. More...
      procedure, public get_allow_overshoot => oi_get_allow_overshoot - Gets a value determining if the integrator can overshoot the integration limits and interpolate back to achieve the desired solution point. More...
    + Gets a value determining if the integrator can overshoot the integration limits and interpolate back to achieve the desired solution point. More...
      procedure, public set_allow_overshoot => oi_set_allow_overshoot - Sets a value determining if the integrator can overshoot the integration limits and interpolate back to achieve the desired solution point. More...
    + Sets a value determining if the integrator can overshoot the integration limits and interpolate back to achieve the desired solution point. More...
      procedure, public get_integration_limit => oi_get_critical_point - Gets a critical integration limit that the integrator is not allowed to step beyond. More...
    + Gets a critical integration limit that the integrator is not allowed to step beyond. More...
      procedure, public set_integration_limit => oi_set_critical_point - Sets a critical integration limit that the integrator is not allowed to step beyond. More...
    + Sets a critical integration limit that the integrator is not allowed to step beyond. More...
      procedure, public get_min_buffer_size => oi_get_min_buffer_size - Gets the minimum internal storage buffer size. More...
    + Gets the minimum internal storage buffer size. More...
      procedure, public set_min_buffer_size => oi_set_min_buffer_size - Sets the minimum internal storage buffer size. Properly sizing the buffer has the potential of improving the performance of the integrator. More...
    + Sets the minimum internal storage buffer size. Properly sizing the buffer has the potential of improving the performance of the integrator. More...
      procedure, public get_max_step_size => oi_get_max_step_size - Gets the maximum allowed step size. More...
    + Gets the maximum allowed step size. More...
      procedure, public set_max_step_size => oi_set_max_step_size - Sets the maximum allowed step size. This value is only honored if get_limit_step_size is set to true. More...
    + Sets the maximum allowed step size. This value is only honored if get_limit_step_size is set to true. More...
      procedure, public get_limit_step_size => oi_get_limit_step_size - Gets a value determining if the step size should be limited. More...
    + Gets a value determining if the step size should be limited. More...
      procedure, public set_limit_step_size => oi_set_limit_step_size - Sets a value determining if the step size should be limited. This value must be set to true to use the value defined by set_max_step_size. More...
    + Sets a value determining if the step size should be limited. This value must be set to true to use the value defined by set_max_step_size. More...
      procedure, public get_iteration_limit => oi_get_iteration_limit - Gets the limit on the number of iterations allowed per integration step. More...
    + Gets the limit on the number of iterations allowed per integration step. More...
      procedure, public set_iteration_limit => oi_set_iteration_limit - Sets the limit on the number of iterations allowed per integration step. More...
    + Sets the limit on the number of iterations allowed per integration step. More...
      procedure, public get_relative_tolerances => oi_get_rtol - Gets the relative tolerances for each ODE. More...
    + Gets the relative tolerances for each ODE. More...
      procedure, public set_relative_tolerances => oi_set_rtol - Sets the relative tolerances for each ODE. More...
    + Sets the relative tolerances for each ODE. More...
      procedure, public get_absolute_tolerances => oi_get_atol - Gets the absolute tolerances for each ODE. More...
    + Gets the absolute tolerances for each ODE. More...
      procedure, public set_absolute_tolerances => oi_set_atol - Sets the absolute tolerances for each ODE. More...
    + Sets the absolute tolerances for each ODE. More...
      procedure(ode_integrator_interface), deferred, pass, public step - Takes a single integration step towards the desired point. More...
    + Takes a single integration step towards the desired point. More...
      procedure(ode_integrator_reset), deferred, pass, public reset - Resets the state of the integrator. More...
    + Resets the state of the integrator. More...
      -

    Private Member Functions

    +
    procedure, private init_workspace => oa_init_workspace
     
    - - - -

    Private Attributes

    +
    real(real64), dimension(:), allocatable m_rwork
     A workspace array.
     
    +
    integer(int32), dimension(:), allocatable m_iwork
     An integer workspace array.
     
    +
    integer(int32), dimension(:), allocatable m_rststats
     An array used to contain information regarding constraint status. A value of 1 indicates the constraint was satisfied; else, a value of 0 indicates the constraint wasn't satisfied. There is one entry in the array for each constraint.
     
    +
    integer(int32) m_istate = 1
     This flag is used directly by ODEPACK. Set to 1 for initial call.
     

    Detailed Description

    Defines an integrator for systems of first order ODEs that is capable of switching between an Adams method and a BDF method automatically. This integrator is able to handle both stiff and non-stiff systems of equations.

    -
    Example
    The following example illustrates the use of this integrator to solve the Van Der Pol equation, which is a second-order ODE that does exhibit difficult and stiff behavior.
    program example
    use iso_fortran_env
    use integral_core
    use fplot_core
    implicit none
    ! Local Variables
    type(ode_helper) :: fcn
    type(ode_auto) :: integrator
    procedure(ode_fcn), pointer :: ptr
    real(real64) :: ic(2), t(2)
    real(real64), allocatable, dimension(:,:) :: x
    type(plot_2d) :: plt
    type(plot_data_2d) :: d1
    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
    x = integrator%integrate(fcn, t, ic)
    ! Plot the solution
    call plt%initialize()
    call plt%set_font_size(14)
    lgnd => plt%get_legend()
    call lgnd%set_is_visible(.false.)
    xaxis => plt%get_x_axis()
    call xaxis%set_title("t")
    yaxis => plt%get_y_axis()
    call yaxis%set_title("x(t)")
    call d1%set_name("x(t)")
    call d1%set_line_width(2.0)
    call d1%set_line_color(clr_blue)
    call d1%define_data(x(:,1), x(:,2))
    call plt%push(d1)
    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
    The above program produces the following output.
    +
    Example
    The following example illustrates the use of this integrator to solve the Van Der Pol equation, which is a second-order ODE that does exhibit difficult and stiff behavior.
    program example
    use iso_fortran_env
    use integral_core
    use fplot_core
    implicit none
    ! Local Variables
    type(ode_helper) :: fcn
    type(ode_auto) :: integrator
    procedure(ode_fcn), pointer :: ptr
    real(real64) :: ic(2), t(2)
    real(real64), allocatable, dimension(:,:) :: x
    type(plot_2d) :: plt
    type(plot_data_2d) :: d1
    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
    x = integrator%integrate(fcn, t, ic)
    ! Plot the solution
    call plt%initialize()
    call plt%set_font_size(14)
    lgnd => plt%get_legend()
    call lgnd%set_is_visible(.false.)
    xaxis => plt%get_x_axis()
    call xaxis%set_title("t")
    yaxis => plt%get_y_axis()
    call yaxis%set_title("x(t)")
    call d1%set_name("x(t)")
    call d1%set_line_width(2.0)
    call d1%set_line_color(clr_blue)
    call d1%define_data(x(:,1), x(:,2))
    call plt%push(d1)
    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
    The above program produces the following output.
    vanderpol_example.png
    -

    Definition at line 1541 of file integral_core.f90.

    +

    Definition at line 1562 of file integral_core.f90.

    Member Function/Subroutine Documentation

    - -

    ◆ get_constraint_status()

    - +
    @@ -238,13 +262,11 @@

    Returns
    An array containing the status of each constraint equation. A value of true indicates that the constraint was satisfied; else, a value of false indicates the constraint was not satisfied.
    -

    Definition at line 1615 of file integral_core.f90.

    +

    Definition at line 1636 of file integral_core.f90.

    - -

    ◆ reset()

    - +

    @@ -266,13 +288,11 @@

    Definition at line 1603 of file integral_core.f90.

    +

    Definition at line 1624 of file integral_core.f90.

    - -

    ◆ step()

    - +

    @@ -310,22 +330,22 @@

    Returns
    Returns true if the integrator requests a stop; else, false, to continue as normal. A possible sitaution resulting in a true value is in the event a constraint has been satisfied.
    -

    Definition at line 1594 of file integral_core.f90.

    +

    Definition at line 1615 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/structintegral__core_1_1ode__helper.html b/doc/html/structintegral__core_1_1ode__helper.html index cbde4c8..1fd3212 100644 --- a/doc/html/structintegral__core_1_1ode__helper.html +++ b/doc/html/structintegral__core_1_1ode__helper.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_helper Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@

    - + - - - - + +
    integral_core::ode_helper Type Reference
    @@ -116,7 +142,7 @@ procedure, public get_constraints_defined => oh_get_constraints_defined  Determines if any constraints have been defined. More...
      - + procedure, public evaluate_ode => oh_eval   procedure, public evaluate_jacobian => oh_eval_jac @@ -128,23 +154,23 @@ - - - - - @@ -152,11 +178,9 @@

    Detailed Description

    Defines a type used to pass information regarding the ODEs to the solver.

    -

    Definition at line 609 of file integral_core.f90.

    +

    Definition at line 630 of file integral_core.f90.

    Member Function/Subroutine Documentation

    - -

    ◆ define_constraints()

    - +

    Private Attributes

    +
    procedure(ode_fcn), pointer, nopass m_fcn => null()
     A pointer to the routine containing the ODEs to integrate.
     
    +
    procedure(ode_jacobian), pointer, nopass m_jac => null()
     A pointer to the routine containing the Jacobian.
     
    +
    procedure(ode_constraint), pointer, nopass m_rts => null()
     A pointer to a routine containing any constraint equations.
     
    +
    integer(int32) m_count = 0
     The number of first order ODEs to integrate.
     
    +
    integer(int32) m_constraints = 0
     The number of constraint equations.
     
    @@ -179,18 +203,16 @@

    Example
    The following example illustrates how to employ constraints by modeling a bouncing ball.
    program example
    use iso_fortran_env
    use integral_core
    use fplot_core
    implicit none
    ! Parameters
    real(real64), parameter :: g = 9.81d0 ! Gravitational acceleration
    real(real64), parameter :: k = -0.8d0 ! Coefficient of restitution
    ! Local Variables
    procedure(ode_fcn), pointer :: ptr
    procedure(ode_constraint), pointer :: cptr
    type(ode_helper) :: fcn
    type(ode_auto) :: integrator
    integer(int32) :: n
    real(real64) :: ic(2), t(2)
    real(real64), allocatable, dimension(:,:) :: x1, x2, x3, x4
    type(plot_2d) :: plt
    type(plot_data_2d) :: d1, d2, d3, d4
    class(plot_axis), pointer :: xaxis, yaxis
    type(legend), pointer :: lgnd
    ! Set up the integrator
    ptr => ball
    cptr => ground_constraint
    call fcn%define_equations(2, ptr)
    call fcn%define_constraints(1, cptr)
    call integrator%set_max_step_size(1.0d-3)
    call integrator%set_limit_step_size(.true.)
    ! Compute the solution
    t = [0.0d0, 1.0d1]
    ic = [1.0d1, 5.0d0]
    x1 = integrator%integrate(fcn, t, ic)
    ! The integrator stops when the ball first makes contact. As a result, lets
    ! reset the time limits and initial conditions to continue the integration
    n = size(x1, 1)
    t(1) = x1(n,1)
    ic = [abs(x1(n,2)), k * x1(n,3)]
    call integrator%reset()
    x2 = integrator%integrate(fcn, t, ic)
    ! Again
    n = size(x2, 1)
    t(1) = x2(n,1)
    ic = [abs(x2(n,2)), k * x2(n,3)]
    call integrator%reset()
    x3 = integrator%integrate(fcn, t, ic)
    ! Again
    n = size(x3, 1)
    t(1) = x3(n,1)
    ic = [abs(x3(n,2)), k * x3(n,3)]
    call integrator%reset()
    x4 = integrator%integrate(fcn, t, ic)
    ! Plot the solution
    call plt%initialize()
    call plt%set_font_size(14)
    lgnd => plt%get_legend()
    call lgnd%set_is_visible(.false.)
    xaxis => plt%get_x_axis()
    call xaxis%set_title("t")
    yaxis => plt%get_y_axis()
    call yaxis%set_title("x(t)")
    call d1%set_line_color(clr_blue)
    call d1%set_line_width(2.0)
    call d1%define_data(x1(:,1), x1(:,2))
    call d2%set_line_color(clr_blue)
    call d2%set_line_width(2.0)
    call d2%define_data(x2(:,1), x2(:,2))
    call d3%set_line_color(clr_blue)
    call d3%set_line_width(2.0)
    call d3%define_data(x3(:,1), x3(:,2))
    call d4%set_line_color(clr_blue)
    call d4%set_line_width(2.0)
    call d4%define_data(x4(:,1), x4(:,2))
    call plt%push(d1)
    call plt%push(d2)
    call plt%push(d3)
    call plt%push(d4)
    call plt%draw()
    contains
    ! A bouncing ball can be described by the following equation:
    ! x" = -g
    !
    ! Where g = gravitational acceleration
    subroutine ball(t, x, dxdt)
    real(real64), intent(in) :: t
    real(real64), intent(in), dimension(:) :: x
    real(real64), intent(out), dimension(:) :: dxdt
    dxdt(1) = x(2)
    dxdt(2) = -g
    end subroutine
    ! The constraint function
    subroutine ground_constraint(t, x, f)
    real(real64), intent(in) :: t
    real(real64), intent(in), dimension(:) :: x
    real(real64), intent(out), dimension(:) :: f
    f(1) = x(1) ! Find when x == 0
    end subroutine
    end program
    The above program produces the following output.
    +
    Example
    The following example illustrates how to employ constraints by modeling a bouncing ball.
    program example
    use iso_fortran_env
    use integral_core
    use fplot_core
    implicit none
    ! Parameters
    real(real64), parameter :: g = 9.81d0 ! Gravitational acceleration
    real(real64), parameter :: k = -0.8d0 ! Coefficient of restitution
    ! Local Variables
    procedure(ode_fcn), pointer :: ptr
    procedure(ode_constraint), pointer :: cptr
    type(ode_helper) :: fcn
    type(ode_auto) :: integrator
    integer(int32) :: n
    real(real64) :: ic(2), t(2)
    real(real64), allocatable, dimension(:,:) :: x1, x2, x3, x4
    type(plot_2d) :: plt
    type(plot_data_2d) :: d1, d2, d3, d4
    class(plot_axis), pointer :: xaxis, yaxis
    type(legend), pointer :: lgnd
    ! Set up the integrator
    ptr => ball
    cptr => ground_constraint
    call fcn%define_equations(2, ptr)
    call fcn%define_constraints(1, cptr)
    call integrator%set_max_step_size(1.0d-3)
    call integrator%set_limit_step_size(.true.)
    ! Compute the solution
    t = [0.0d0, 1.0d1]
    ic = [1.0d1, 5.0d0]
    x1 = integrator%integrate(fcn, t, ic)
    ! The integrator stops when the ball first makes contact. As a result, lets
    ! reset the time limits and initial conditions to continue the integration
    n = size(x1, 1)
    t(1) = x1(n,1)
    ic = [abs(x1(n,2)), k * x1(n,3)]
    call integrator%reset()
    x2 = integrator%integrate(fcn, t, ic)
    ! Again
    n = size(x2, 1)
    t(1) = x2(n,1)
    ic = [abs(x2(n,2)), k * x2(n,3)]
    call integrator%reset()
    x3 = integrator%integrate(fcn, t, ic)
    ! Again
    n = size(x3, 1)
    t(1) = x3(n,1)
    ic = [abs(x3(n,2)), k * x3(n,3)]
    call integrator%reset()
    x4 = integrator%integrate(fcn, t, ic)
    ! Plot the solution
    call plt%initialize()
    call plt%set_font_size(14)
    lgnd => plt%get_legend()
    call lgnd%set_is_visible(.false.)
    xaxis => plt%get_x_axis()
    call xaxis%set_title("t")
    yaxis => plt%get_y_axis()
    call yaxis%set_title("x(t)")
    call d1%set_line_color(clr_blue)
    call d1%set_line_width(2.0)
    call d1%define_data(x1(:,1), x1(:,2))
    call d2%set_line_color(clr_blue)
    call d2%set_line_width(2.0)
    call d2%define_data(x2(:,1), x2(:,2))
    call d3%set_line_color(clr_blue)
    call d3%set_line_width(2.0)
    call d3%define_data(x3(:,1), x3(:,2))
    call d4%set_line_color(clr_blue)
    call d4%set_line_width(2.0)
    call d4%define_data(x4(:,1), x4(:,2))
    call plt%push(d1)
    call plt%push(d2)
    call plt%push(d3)
    call plt%push(d4)
    call plt%draw()
    contains
    ! A bouncing ball can be described by the following equation:
    ! x" = -g
    !
    ! Where g = gravitational acceleration
    subroutine ball(t, x, dxdt)
    real(real64), intent(in) :: t
    real(real64), intent(in), dimension(:) :: x
    real(real64), intent(out), dimension(:) :: dxdt
    dxdt(1) = x(2)
    dxdt(2) = -g
    end subroutine
    ! The constraint function
    subroutine ground_constraint(t, x, f)
    real(real64), intent(in) :: t
    real(real64), intent(in), dimension(:) :: x
    real(real64), intent(out), dimension(:) :: f
    f(1) = x(1) ! Find when x == 0
    end subroutine
    end program
    The above program produces the following output.
    bouncing_ball_example.png
    -

    Definition at line 883 of file integral_core.f90.

    +

    Definition at line 904 of file integral_core.f90.

    - -

    ◆ define_equations()

    - +

    @@ -214,18 +236,16 @@

    Example
    The following example illustrates how to define and solve a system of differential equations. The Lorenz system is illustrated.
    program example
    use iso_fortran_env
    use integral_core
    use fplot_core
    implicit none
    ! Local Variables
    type(ode_helper) :: fcn
    type(ode_auto) :: integrator
    procedure(ode_fcn), pointer :: ptr
    real(real64) :: ic(3), t(2)
    real(real64), allocatable, dimension(:,:) :: x
    type(plot_3d) :: plt
    type(plot_data_3d) :: d1
    class(plot_axis), pointer :: xaxis, yaxis, zaxis
    ! Set up the integrator
    ptr => lorenz
    call fcn%define_equations(3, ptr)
    ic = [1.0d0, 1.0d0, 1.0d0]
    t = [0.0d0, 1.0d2]
    ! Integrate
    x = integrator%integrate(fcn, t, ic)
    ! Plot
    call plt%initialize()
    call plt%set_font_size(14)
    xaxis => plt%get_x_axis()
    call xaxis%set_title("x(t)")
    yaxis => plt%get_y_axis()
    call yaxis%set_title("y(t)")
    zaxis => plt%get_z_axis()
    call zaxis%set_title("z(t)")
    call d1%set_line_color(clr_blue)
    call d1%define_data(x(:,2), x(:,3), x(:,4))
    call plt%push(d1)
    call plt%draw()
    contains
    ! The Lorenz system of equations:
    ! REF: https://en.wikipedia.org/wiki/Lorenz_system
    !
    ! x' = s * (y - x)
    ! y' = x * (r - z) - y
    ! z' = x * y - b * z
    subroutine lorenz(t, x, dxdt)
    real(real64), intent(in) :: t
    real(real64), intent(in), dimension(:) :: x
    real(real64), intent(out), dimension(:) :: dxdt
    ! Parameters
    real(real64), parameter :: r = 28.0d0
    real(real64), parameter :: s = 10.0d0
    real(real64), parameter :: b = 8.0d0 / 3.0d0
    ! Equations
    dxdt(1) = s * (x(2) - x(1))
    dxdt(2) = x(1) * (r - x(3)) - x(2)
    dxdt(3) = x(1) * x(2) - b * x(3)
    end subroutine
    end program
    The above program produces the following output.
    +
    Example
    The following example illustrates how to define and solve a system of differential equations. The Lorenz system is illustrated.
    program example
    use iso_fortran_env
    use integral_core
    use fplot_core
    implicit none
    ! Local Variables
    type(ode_helper) :: fcn
    type(ode_auto) :: integrator
    procedure(ode_fcn), pointer :: ptr
    real(real64) :: ic(3), t(2)
    real(real64), allocatable, dimension(:,:) :: x
    type(plot_3d) :: plt
    type(plot_data_3d) :: d1
    class(plot_axis), pointer :: xaxis, yaxis, zaxis
    ! Set up the integrator
    ptr => lorenz
    call fcn%define_equations(3, ptr)
    ic = [1.0d0, 1.0d0, 1.0d0]
    t = [0.0d0, 1.0d2]
    ! Integrate
    x = integrator%integrate(fcn, t, ic)
    ! Plot
    call plt%initialize()
    call plt%set_font_size(14)
    xaxis => plt%get_x_axis()
    call xaxis%set_title("x(t)")
    yaxis => plt%get_y_axis()
    call yaxis%set_title("y(t)")
    zaxis => plt%get_z_axis()
    call zaxis%set_title("z(t)")
    call d1%set_line_color(clr_blue)
    call d1%define_data(x(:,2), x(:,3), x(:,4))
    call plt%push(d1)
    call plt%draw()
    contains
    ! The Lorenz system of equations:
    ! REF: https://en.wikipedia.org/wiki/Lorenz_system
    !
    ! x' = s * (y - x)
    ! y' = x * (r - z) - y
    ! z' = x * y - b * z
    subroutine lorenz(t, x, dxdt)
    real(real64), intent(in) :: t
    real(real64), intent(in), dimension(:) :: x
    real(real64), intent(out), dimension(:) :: dxdt
    ! Parameters
    real(real64), parameter :: r = 28.0d0
    real(real64), parameter :: s = 10.0d0
    real(real64), parameter :: b = 8.0d0 / 3.0d0
    ! Equations
    dxdt(1) = s * (x(2) - x(1))
    dxdt(2) = x(1) * (r - x(3)) - x(2)
    dxdt(3) = x(1) * x(2) - b * x(3)
    end subroutine
    end program
    The above program produces the following output.
    lorenz_example.png
    -

    Definition at line 712 of file integral_core.f90.

    +

    Definition at line 733 of file integral_core.f90.

    - -

    ◆ evaluate_constraints()

    - +

    @@ -250,13 +270,11 @@

    Definition at line 948 of file integral_core.f90.

    +

    Definition at line 969 of file integral_core.f90.

    - -

    ◆ evaluate_jacobian()

    - +

    @@ -281,13 +299,11 @@

    Definition at line 933 of file integral_core.f90.

    +

    Definition at line 954 of file integral_core.f90.

    - -

    ◆ get_constraint_count()

    - +

    @@ -310,13 +326,11 @@

    Returns
    The number of constraint equations.
    -

    Definition at line 893 of file integral_core.f90.

    +

    Definition at line 914 of file integral_core.f90.

    - -

    ◆ get_constraints_defined()

    - +

    @@ -339,13 +353,11 @@

    Returns
    True if the constraint equation routine is defined; else, false.
    -

    Definition at line 904 of file integral_core.f90.

    +

    Definition at line 925 of file integral_core.f90.

    - -

    ◆ get_equation_count()

    - +

    @@ -368,13 +380,11 @@

    Returns
    The number of ODEs.
    -

    Definition at line 722 of file integral_core.f90.

    +

    Definition at line 743 of file integral_core.f90.

    - -

    ◆ get_equations_defined()

    - +

    @@ -397,13 +407,11 @@

    Returns
    Returns true if the equations have been defined (by calling define_equations); else, false if they have not yet been defined.
    -

    Definition at line 735 of file integral_core.f90.

    +

    Definition at line 756 of file integral_core.f90.

    - -

    ◆ get_jacobian_defined()

    - +

    @@ -426,22 +434,22 @@

    Returns
    Returns true if the routine for computing the Jacobian has been defined (by calling define_equations); else, false if it has not.
    -

    Definition at line 748 of file integral_core.f90.

    +

    Definition at line 769 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/structintegral__core_1_1ode__integrator.html b/doc/html/structintegral__core_1_1ode__integrator.html index fbcd964..54ed575 100644 --- a/doc/html/structintegral__core_1_1ode__integrator.html +++ b/doc/html/structintegral__core_1_1ode__integrator.html @@ -3,8 +3,7 @@ - - + integral: integral_core::ode_integrator Type Reference @@ -15,10 +14,14 @@ + @@ -38,19 +41,42 @@

    - + - - - - + +
    integral_core::ode_integrator Type Reference
    @@ -94,7 +120,7 @@
    - + integral_core::ode_auto
    @@ -167,50 +193,48 @@ - - - - - - - - -

    Private Attributes

    +
    real(real64), dimension(:), allocatable m_rtol
     An array of relative error tolerance values for each ODE.
     
    +
    real(real64), dimension(:), allocatable m_atol
     An array of absolute error tolerance values for each ODE.
     
    +
    logical m_alloutput = .true.
     Determines if output should be provided wherever the integrator computes the solution as well as at user-specified points.
     
    +
    logical m_canovershoot = .true.
     Determines if the integrator is allowed to overshoot a critical point and interpolate back to achieve output at the correct location.
     
    +
    real(real64) m_criticalpoint = 0.0d0
     The critical point that cannot be overshot. This is only utilized in the event that m_canOvershoot is set to true.
     
    +
    integer(int32) m_minbuffersize = 500
     Defines the minimum buffer size.
     
    +
    real(real64) m_maxstepsize = 1.0d0
     The maximum allowable step size. This is only used if m_limitStepSize is set to true.
     
    +
    logical m_limitstepsize = .false.
     Determines if limits should be imposed upon maximum step size.
     
    +
    integer(int32) m_maxstepcount = 500
     Determines the iteration step limit per integration step.
     

    Detailed Description

    -

    Definition at line 1015 of file integral_core.f90.

    +

    Definition at line 1036 of file integral_core.f90.

    Member Function/Subroutine Documentation

    - -

    ◆ get_absolute_tolerances()

    - +
    @@ -233,13 +257,11 @@

    Returns
    An array containing the tolerance value for each ODE.
    -

    Definition at line 1266 of file integral_core.f90.

    +

    Definition at line 1287 of file integral_core.f90.

    - -

    ◆ get_allow_overshoot()

    - +

    @@ -262,13 +284,11 @@

    Returns
    Returns true if the integrator can overshoot; else, false.
    -

    Definition at line 1112 of file integral_core.f90.

    +

    Definition at line 1133 of file integral_core.f90.

    - -

    ◆ get_integration_limit()

    - +

    @@ -291,13 +311,11 @@

    Returns
    The integration limit.
    -

    Definition at line 1136 of file integral_core.f90.

    +

    Definition at line 1157 of file integral_core.f90.

    - -

    ◆ get_iteration_limit()

    - +

    @@ -320,13 +338,11 @@

    Returns
    The iteration limit.
    -

    Definition at line 1225 of file integral_core.f90.

    +

    Definition at line 1246 of file integral_core.f90.

    - -

    ◆ get_limit_step_size()

    - +

    @@ -349,13 +365,11 @@

    Returns
    Returns true if the integrator's step size should be limited; else, false.
    -

    Definition at line 1201 of file integral_core.f90.

    +

    Definition at line 1222 of file integral_core.f90.

    - -

    ◆ get_max_step_size()

    - +

    @@ -378,13 +392,11 @@

    Returns
    The maximum step size.
    -

    Definition at line 1179 of file integral_core.f90.

    +

    Definition at line 1200 of file integral_core.f90.

    - -

    ◆ get_min_buffer_size()

    - +

    @@ -407,13 +419,11 @@

    Returns
    The minimum buffer size.
    -

    Definition at line 1157 of file integral_core.f90.

    +

    Definition at line 1178 of file integral_core.f90.

    - -

    ◆ get_provide_all_output()

    - +

    @@ -436,13 +446,11 @@

    Returns
    Returns true if all integrator output should be reported; else, returns false.
    -

    Definition at line 1087 of file integral_core.f90.

    +

    Definition at line 1108 of file integral_core.f90.

    - -

    ◆ get_relative_tolerances()

    - +

    @@ -465,13 +473,11 @@

    Returns
    An array containing the tolerance value for each ODE.
    -

    Definition at line 1246 of file integral_core.f90.

    +

    Definition at line 1267 of file integral_core.f90.

    - -

    ◆ integrate()

    - +

    @@ -504,13 +510,11 @@

    Returns
    Returns the solution in a matrix of N+1 columns. The first column contains the values of the independent variable at which the solution was computed. The remaining columns contain the solution points for each ODE.
    -

    Definition at line 1075 of file integral_core.f90.

    +

    Definition at line 1096 of file integral_core.f90.

    - -

    ◆ reset()

    - +

    @@ -532,13 +536,11 @@

    Definition at line 1313 of file integral_core.f90.

    +

    Definition at line 1334 of file integral_core.f90.

    - -

    ◆ set_absolute_tolerances()

    - +

    @@ -561,13 +563,11 @@

    Definition at line 1276 of file integral_core.f90.

    +

    Definition at line 1297 of file integral_core.f90.

    - -

    ◆ set_allow_overshoot()

    - +

    @@ -590,13 +590,11 @@

    Definition at line 1125 of file integral_core.f90.

    +

    Definition at line 1146 of file integral_core.f90.

    - -

    ◆ set_integration_limit()

    - +

    @@ -619,13 +617,11 @@

    Definition at line 1147 of file integral_core.f90.

    +

    Definition at line 1168 of file integral_core.f90.

    - -

    ◆ set_iteration_limit()

    - +

    @@ -648,13 +644,11 @@

    Definition at line 1236 of file integral_core.f90.

    +

    Definition at line 1257 of file integral_core.f90.

    - -

    ◆ set_limit_step_size()

    - +

    @@ -677,13 +671,11 @@

    Definition at line 1214 of file integral_core.f90.

    +

    Definition at line 1235 of file integral_core.f90.

    - -

    ◆ set_max_step_size()

    - +

    @@ -706,13 +698,11 @@

    Definition at line 1190 of file integral_core.f90.

    +

    Definition at line 1211 of file integral_core.f90.

    - -

    ◆ set_min_buffer_size()

    - +

    @@ -735,13 +725,11 @@

    Definition at line 1169 of file integral_core.f90.

    +

    Definition at line 1190 of file integral_core.f90.

    - -

    ◆ set_provide_all_output()

    - +

    @@ -764,13 +752,11 @@

    Definition at line 1100 of file integral_core.f90.

    +

    Definition at line 1121 of file integral_core.f90.

    - -

    ◆ set_relative_tolerances()

    - +

    @@ -793,13 +779,11 @@

    Definition at line 1256 of file integral_core.f90.

    +

    Definition at line 1277 of file integral_core.f90.

    - -

    ◆ step()

    - +

    @@ -829,22 +813,22 @@

    Returns
    Returns true if the integrator requests a stop; else, false, to continue as normal. A possible sitaution resulting in a true value is in the event a constraint has been satisfied.
    -

    Definition at line 1304 of file integral_core.f90.

    +

    Definition at line 1325 of file integral_core.f90.

    The documentation for this type was generated from the following file: diff --git a/doc/html/tabs.css b/doc/html/tabs.css index bbde11e..9cf578f 100644 --- a/doc/html/tabs.css +++ b/doc/html/tabs.css @@ -1 +1,60 @@ -.sm{position:relative;z-index:9999}.sm,.sm ul,.sm li{display:block;list-style:none;margin:0;padding:0;line-height:normal;direction:ltr;text-align:left;-webkit-tap-highlight-color:transparent}.sm-rtl,.sm-rtl ul,.sm-rtl li{direction:rtl;text-align:right}.sm>li>h1,.sm>li>h2,.sm>li>h3,.sm>li>h4,.sm>li>h5,.sm>li>h6{margin:0;padding:0}.sm ul{display:none}.sm li,.sm a{position:relative}.sm a{display:block}.sm a.disabled{cursor:not-allowed}.sm:after{content:"\00a0";display:block;height:0;font:0px/0 serif;clear:both;visibility:hidden;overflow:hidden}.sm,.sm *,.sm *:before,.sm *:after{-moz-box-sizing:border-box;-webkit-box-sizing:border-box;box-sizing:border-box}.sm-dox{background-image:url("tab_b.png")}.sm-dox a,.sm-dox a:focus,.sm-dox a:hover,.sm-dox a:active{padding:0px 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    +
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    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
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    integral_core::adaptive_integrator Member List
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    This is the complete list of members for integral_core::adaptive_integrator, including all inherited members.

    + + + + + + + + + + + + + + + + + +
    get_abs_tol=> ib_get_abs_tolintegral_core::integrator_base
    get_breakpoints=> ai_get_breakpointsintegral_core::adaptive_integrator
    get_max_subintervals=> ib_get_max_subintervalsintegral_core::integrator_base
    get_rel_tol=> ib_get_rel_tolintegral_core::integrator_base
    get_use_breakpoints=> ai_get_use_brkpntsintegral_core::adaptive_integrator
    ib_set_max_subintervals=> ib_set_max_subintervalsintegral_core::integrator_base
    initialize=> ai_initintegral_core::adaptive_integrator
    integrate=> ai_integrateintegral_core::adaptive_integrator
    m_breakpointsintegral_core::adaptive_integratorprivate
    m_iworkintegral_core::adaptive_integratorprivate
    m_userdefinedbreaksintegral_core::adaptive_integratorprivate
    m_workintegral_core::adaptive_integratorprivate
    set_abs_tol=> ib_set_abs_tolintegral_core::integrator_base
    set_breakpoints=> ai_set_breakpointsintegral_core::adaptive_integrator
    set_rel_tol=> ib_set_rel_tolintegral_core::integrator_base
    set_use_breakpoints=> ai_set_use_brkpntsintegral_core::adaptive_integrator
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1finite__interval__integrator-members.html b/doc/html/typeintegral__core_1_1finite__interval__integrator-members.html new file mode 100644 index 0000000..57b7755 --- /dev/null +++ b/doc/html/typeintegral__core_1_1finite__interval__integrator-members.html @@ -0,0 +1,135 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
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    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
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    integral_core::finite_interval_integrator Member List
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    This is the complete list of members for integral_core::finite_interval_integrator, including all inherited members.

    + + + + + + + + +
    get_abs_tol=> ib_get_abs_tolintegral_core::integrator_base
    get_max_subintervals=> ib_get_max_subintervalsintegral_core::integrator_base
    get_rel_tol=> ib_get_rel_tolintegral_core::integrator_base
    ib_set_max_subintervals=> ib_set_max_subintervalsintegral_core::integrator_base
    integrateintegral_core::finite_interval_integrator
    set_abs_tol=> ib_set_abs_tolintegral_core::integrator_base
    set_rel_tol=> ib_set_rel_tolintegral_core::integrator_base
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1integration__behavior-members.html b/doc/html/typeintegral__core_1_1integration__behavior-members.html new file mode 100644 index 0000000..60debb6 --- /dev/null +++ b/doc/html/typeintegral__core_1_1integration__behavior-members.html @@ -0,0 +1,131 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
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    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
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    integral_core::integration_behavior Member List
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    This is the complete list of members for integral_core::integration_behavior, including all inherited members.

    + + + + +
    error_estimateintegral_core::integration_behaviorprivate
    evaluation_countintegral_core::integration_behaviorprivate
    subinterval_countintegral_core::integration_behaviorprivate
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1integrator__base-members.html b/doc/html/typeintegral__core_1_1integrator__base-members.html new file mode 100644 index 0000000..dae847e --- /dev/null +++ b/doc/html/typeintegral__core_1_1integrator__base-members.html @@ -0,0 +1,137 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
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    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + +
    +
    + +
    +
    +
    + +
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    integral_core::integrator_base Member List
    +
    +
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    This is the complete list of members for integral_core::integrator_base, including all inherited members.

    + + + + + + + + + + +
    get_abs_tol=> ib_get_abs_tolintegral_core::integrator_base
    get_max_subintervals=> ib_get_max_subintervalsintegral_core::integrator_base
    get_rel_tol=> ib_get_rel_tolintegral_core::integrator_base
    ib_set_max_subintervals=> ib_set_max_subintervalsintegral_core::integrator_base
    m_abstolintegral_core::integrator_baseprivate
    m_maxintintegral_core::integrator_baseprivate
    m_reltolintegral_core::integrator_baseprivate
    set_abs_tol=> ib_set_abs_tolintegral_core::integrator_base
    set_rel_tol=> ib_set_rel_tolintegral_core::integrator_base
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1nonadaptive__integrator-members.html b/doc/html/typeintegral__core_1_1nonadaptive__integrator-members.html new file mode 100644 index 0000000..4fe4a58 --- /dev/null +++ b/doc/html/typeintegral__core_1_1nonadaptive__integrator-members.html @@ -0,0 +1,138 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    integral_core::nonadaptive_integrator Member List
    +
    +
    + +

    This is the complete list of members for integral_core::nonadaptive_integrator, including all inherited members.

    + + + + + + + + + + + +
    get_abs_tol=> ib_get_abs_tolintegral_core::integrator_base
    get_max_subintervals=> ib_get_max_subintervalsintegral_core::integrator_base
    get_rel_tol=> ib_get_rel_tolintegral_core::integrator_base
    get_rule=> ni_get_ruleintegral_core::nonadaptive_integrator
    ib_set_max_subintervals=> ib_set_max_subintervalsintegral_core::integrator_base
    integrate=> ni_integrateintegral_core::nonadaptive_integrator
    m_ruleintegral_core::nonadaptive_integratorprivate
    set_abs_tol=> ib_set_abs_tolintegral_core::integrator_base
    set_rel_tol=> ib_set_rel_tolintegral_core::integrator_base
    set_rule=> ni_set_ruleintegral_core::nonadaptive_integrator
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1ode__auto-members.html b/doc/html/typeintegral__core_1_1ode__auto-members.html new file mode 100644 index 0000000..c306363 --- /dev/null +++ b/doc/html/typeintegral__core_1_1ode__auto-members.html @@ -0,0 +1,155 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
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    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    integral_core::ode_auto Member List
    +
    +
    + +

    This is the complete list of members for integral_core::ode_auto, including all inherited members.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    get_absolute_tolerances=> oi_get_atolintegral_core::ode_integrator
    get_allow_overshoot=> oi_get_allow_overshootintegral_core::ode_integrator
    get_constraint_status=> oa_get_constraint_infointegral_core::ode_auto
    get_integration_limit=> oi_get_critical_pointintegral_core::ode_integrator
    get_iteration_limit=> oi_get_iteration_limitintegral_core::ode_integrator
    get_limit_step_size=> oi_get_limit_step_sizeintegral_core::ode_integrator
    get_max_step_size=> oi_get_max_step_sizeintegral_core::ode_integrator
    get_min_buffer_size=> oi_get_min_buffer_sizeintegral_core::ode_integrator
    get_provide_all_output=> oi_get_use_all_outputintegral_core::ode_integrator
    get_relative_tolerances=> oi_get_rtolintegral_core::ode_integrator
    init_workspace=> oa_init_workspace (defined in integral_core::ode_auto)integral_core::ode_autoprivate
    integrate=> oi_integrateintegral_core::ode_integrator
    m_istateintegral_core::ode_autoprivate
    m_iworkintegral_core::ode_autoprivate
    m_rststatsintegral_core::ode_autoprivate
    m_rworkintegral_core::ode_autoprivate
    reset=> oa_reset_integratorintegral_core::ode_auto
    set_absolute_tolerances=> oi_set_atolintegral_core::ode_integrator
    set_allow_overshoot=> oi_set_allow_overshootintegral_core::ode_integrator
    set_integration_limit=> oi_set_critical_pointintegral_core::ode_integrator
    set_iteration_limit=> oi_set_iteration_limitintegral_core::ode_integrator
    set_limit_step_size=> oi_set_limit_step_sizeintegral_core::ode_integrator
    set_max_step_size=> oi_set_max_step_sizeintegral_core::ode_integrator
    set_min_buffer_size=> oi_set_min_buffer_sizeintegral_core::ode_integrator
    set_provide_all_output=> oi_set_use_all_outputintegral_core::ode_integrator
    set_relative_tolerances=> oi_set_rtolintegral_core::ode_integrator
    step=> oa_stepintegral_core::ode_auto
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1ode__helper-members.html b/doc/html/typeintegral__core_1_1ode__helper-members.html new file mode 100644 index 0000000..6318eb4 --- /dev/null +++ b/doc/html/typeintegral__core_1_1ode__helper-members.html @@ -0,0 +1,143 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + +
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    integral_core::ode_helper Member List
    +
    +
    + +

    This is the complete list of members for integral_core::ode_helper, including all inherited members.

    + + + + + + + + + + + + + + + + +
    define_constraints=> oh_define_constraintsintegral_core::ode_helper
    define_equations=> oh_initintegral_core::ode_helper
    evaluate_constraints=> oh_eval_constraintsintegral_core::ode_helper
    evaluate_jacobian=> oh_eval_jacintegral_core::ode_helper
    evaluate_ode=> oh_eval (defined in integral_core::ode_helper)integral_core::ode_helper
    get_constraint_count=> oh_get_constraint_countintegral_core::ode_helper
    get_constraints_defined=> oh_get_constraints_definedintegral_core::ode_helper
    get_equation_count=> oh_get_countintegral_core::ode_helper
    get_equations_defined=> oh_is_fcn_definedintegral_core::ode_helper
    get_jacobian_defined=> oh_is_jac_definedintegral_core::ode_helper
    m_constraintsintegral_core::ode_helperprivate
    m_countintegral_core::ode_helperprivate
    m_fcnintegral_core::ode_helperprivate
    m_jacintegral_core::ode_helperprivate
    m_rtsintegral_core::ode_helperprivate
    +
    + + + + diff --git a/doc/html/typeintegral__core_1_1ode__integrator-members.html b/doc/html/typeintegral__core_1_1ode__integrator-members.html new file mode 100644 index 0000000..5a9e834 --- /dev/null +++ b/doc/html/typeintegral__core_1_1ode__integrator-members.html @@ -0,0 +1,158 @@ + + + + + + +integral: Member List + + + + + + + + + + + + + + + +
    +
    + + + + + + +
    +
    integral +  1.0.0 +
    +
    A Fortran library providing integration routines for functions and differential equations.
    +
    +
    + + + + + +
    +
    + +
    +
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    + +
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    +
    integral_core::ode_integrator Member List
    +
    +
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    This is the complete list of members for integral_core::ode_integrator, including all inherited members.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    get_absolute_tolerances=> oi_get_atolintegral_core::ode_integrator
    get_allow_overshoot=> oi_get_allow_overshootintegral_core::ode_integrator
    get_integration_limit=> oi_get_critical_pointintegral_core::ode_integrator
    get_iteration_limit=> oi_get_iteration_limitintegral_core::ode_integrator
    get_limit_step_size=> oi_get_limit_step_sizeintegral_core::ode_integrator
    get_max_step_size=> oi_get_max_step_sizeintegral_core::ode_integrator
    get_min_buffer_size=> oi_get_min_buffer_sizeintegral_core::ode_integrator
    get_provide_all_output=> oi_get_use_all_outputintegral_core::ode_integrator
    get_relative_tolerances=> oi_get_rtolintegral_core::ode_integrator
    integrate=> oi_integrateintegral_core::ode_integrator
    m_alloutputintegral_core::ode_integratorprivate
    m_atolintegral_core::ode_integratorprivate
    m_canovershootintegral_core::ode_integratorprivate
    m_criticalpointintegral_core::ode_integratorprivate
    m_limitstepsizeintegral_core::ode_integratorprivate
    m_maxstepcountintegral_core::ode_integratorprivate
    m_maxstepsizeintegral_core::ode_integratorprivate
    m_minbuffersizeintegral_core::ode_integratorprivate
    m_rtolintegral_core::ode_integratorprivate
    resetintegral_core::ode_integrator
    set_absolute_tolerances=> oi_set_atolintegral_core::ode_integrator
    set_allow_overshoot=> oi_set_allow_overshootintegral_core::ode_integrator
    set_integration_limit=> oi_set_critical_pointintegral_core::ode_integrator
    set_iteration_limit=> oi_set_iteration_limitintegral_core::ode_integrator
    set_limit_step_size=> oi_set_limit_step_sizeintegral_core::ode_integrator
    set_max_step_size=> oi_set_max_step_sizeintegral_core::ode_integrator
    set_min_buffer_size=> oi_set_min_buffer_sizeintegral_core::ode_integrator
    set_provide_all_output=> oi_set_use_all_outputintegral_core::ode_integrator
    set_relative_tolerances=> oi_set_rtolintegral_core::ode_integrator
    stepintegral_core::ode_integrator
    +
    + + + + diff --git a/examples/pendulum.f90 b/examples/pendulum.f90 index 3a527e4..a28e4d2 100644 --- a/examples/pendulum.f90 +++ b/examples/pendulum.f90 @@ -13,6 +13,7 @@ program example type(plot_2d) :: plt type(plot_data_2d) :: d1, d2 class(plot_axis), pointer :: xAxis, yAxis + type(legend), pointer :: lgnd real(real64) :: t(2), ic(4) real(real64), allocatable, dimension(:,:) :: s real(real64), allocatable, dimension(:) :: x1, y1, x2, y2 @@ -29,7 +30,7 @@ program example call fcn%define_equations(4, ptr) ! Compute the solution - t = [0.0d0, 60.0d0] + t = [0.0d0, 40.0d0] ic = [0.2d0, 0.0d0, 0.8d0, 0.0d0] s = integrator%integrate(fcn, t, ic) @@ -44,6 +45,10 @@ program example call plt%initialize() call plt%set_font_size(14) + lgnd => plt%get_legend() + call lgnd%set_horizontal_position(LEGEND_LEFT) + call lgnd%set_vertical_position(LEGEND_BOTTOM) + xAxis => plt%get_x_axis() call xAxis%set_title("t") @@ -64,6 +69,10 @@ program example ! ---------- call plt%clear_all() + call lgnd%set_horizontal_position(LEGEND_RIGHT) + call lgnd%set_vertical_position(LEGEND_TOP) + call lgnd%set_draw_inside_axes(.false.) + call lgnd%set_draw_border(.false.) call xAxis%set_title("") call yAxis%set_title("") diff --git a/images/double_pendulum_example.png b/images/double_pendulum_example.png new file mode 100644 index 0000000..11ad25b Binary files /dev/null and b/images/double_pendulum_example.png differ diff --git a/images/double_pendulum_example_no_legend.png b/images/double_pendulum_example_no_legend.png new file mode 100644 index 0000000..d3f5dfe Binary files /dev/null and b/images/double_pendulum_example_no_legend.png differ diff --git a/images/double_pendulum_example_short_time.png b/images/double_pendulum_example_short_time.png new file mode 100644 index 0000000..9f9e332 Binary files /dev/null and b/images/double_pendulum_example_short_time.png differ diff --git a/images/double_pendulum_example_short_time_no_legend.png b/images/double_pendulum_example_short_time_no_legend.png new file mode 100644 index 0000000..55f8b8a Binary files /dev/null and b/images/double_pendulum_example_short_time_no_legend.png differ diff --git a/images/double_pendulum_time_history_short.png b/images/double_pendulum_time_history_short.png new file mode 100644 index 0000000..891b3da Binary files /dev/null and b/images/double_pendulum_time_history_short.png differ diff --git a/src/integral_core.f90 b/src/integral_core.f90 index 5468ba6..a00f269 100644 --- a/src/integral_core.f90 +++ b/src/integral_core.f90 @@ -1,5 +1,20 @@ ! integral_core.f90 +!> @mainpage +!! +!! @section intro_sec Introduction +!! INTEGRAL is a Fortran library providing an easy-to-use, object-oriented +!! interface to several integration routines. Integration of functions of one +!! variable are provided by the QUADPACK library. Integration of systems of +!! ordinary differential equations are provided by the ODEPACK library. +!! +!! @image html double_pendulum_example_short_time_no_legend.png + +!> @brief \b integral_core +!! +!! @par Purpose +!! Provides types and routines allowing for the integration of functions and +!! systems of ordinary differential equations. module integral_core use, intrinsic :: iso_fortran_env, only : int32, real64 use ferror @@ -59,8 +74,14 @@ module integral_core integer(int32), parameter :: INT_LACK_OF_DEFINITION_ERROR = 8 !> @brief An error indicating an inappropriately sized array. integer(int32), parameter :: INT_ARRAY_SIZE_MISMATCH_ERROR = 9 + !> @brief An error indicating the too many iterations have been performed + !! suggesting that excessive amounts of work are required to continue the + !! solution process. integer(int32), parameter :: INT_EXCESSIVE_WORK_ERROR = 10 + !> @brief An error indicating that the user-defined tolerances are too + !! stringent to be practical for the problem at hand. integer(int32), parameter :: INT_IMPRACTICAL_TOLERANCE_ERROR = 11 + !> @brief An error that occurs if integrator error tests fail repeatadly. integer(int32), parameter :: INT_REPEATED_ERROR_TEST_FAILURE = 12 ! ------------------------------------------------------------------------------