Structures: derived types

Overview

Teaching: 10 min
Exercises: 15 min

Questions

• How can I group together variables to make more complex structures?

• How are these derived types defined and then initialised?

Objectives

• Understand what a derived type is.

• Learn how to define a derived type.

• Learn the different ways of initialising a derived type variable.

• Get a glimpse of more advanced object oriented methodology.

Derived types

We have seen intrinsic types, such as integer and character. However, in many cases it can be useful to create structured types combining multiple types together in some way of our choosing. We call these derived types.

Type definitions

A derived type with two components would be declared, e.g.,

  type :: my_type
    integer                         :: nmax
    real, dimension(:), allocatable :: data
  end type my_type

Components may be intrinsic data types (all declared in the usual way), or derived types.

A variable of this type is declared

  type (my_type) :: var

and individual components are referenced with the component selector %, e.g.,

  var%nmax = 10
  ...
  print *, "Values are ", var%data(1:3)

The component selector is the same as we have seen earlier for the complex intrinsic type – recall that the real and imaginary components of a complex variable z are accessed with z%re and z%im respectively.

An array of types is defined in the usual way, and the component selector is applied to individual elements, e.g.,

  type (my_type), dimension(10) :: var
  ...
  var(1)%nmax = 100

Dummy arguments to procedures are declared in the same way as for intrinsic types with the appropriate attribute list, including intent.

Put type definitions in a module

If a type definition is placed in the specification part of a module, it can be made available consistently elsewhere via use association.

Some derived type features require that the definition be in a module.

Scope of components

Formally, we have

  type [ [, attribute-list] :: ] type-name
    [private]
    component-part
  [ contains
    procedure-part ]
  end type [ type-name ]

The default situation is for both the type and its components to be public. This may be made explicit by

  type, public :: my_type
    ...
  end type my_type

If one wants a public type with private components (an opaque type), use

  type, public :: my_opaque_type
    private
    ...
  end type my_opaque_type

Externally, other program units will be able to reference this opaque type, but will not be allowed to access the components (a compiler error).

If a type is only for use within the module in which it is defined, then it can be declared private in the attribute list.

Type constructors

For types with public components, it is possible to use a structure constructor to provide initialisation, e.g.,:

  type, public :: my_type
     integer :: ia
     real    :: b
     complex :: z
  end type my_type

  ...
  type (my_type) :: a

  a = my_type(3, 2.0, (0.0, 1.0))

Values or expressions can be used, but must appear in the order specified in the definition of the components. An allocatable or pointer (next episode) component must appear as null() in a constructor expression list.

Default initialisation

A type may be defined with default initial values. One notable exception is that allocatable components do not have an initialisation. E.g.:

  type :: my_type
    integer                            :: nmax = 10
    real                               :: a0 = 1.0
    integer, dimension(:), allocatable :: ndata
  end type

A default initialisation can be applied by using an empty constructor::

  type (my_type) :: a

  a = my_type()

For an allocatable component, the result is a component with a not allocated status.

Warning: some compilers can’t manage an empty constructor for allocatable components. The appropriate expression in the constructor is null().

Exercise (5 minutes)

A type to store a random number generator

The accompanying example (module1.f90 and program1.f90) provides an implementation of a very simple pseudo-random number generator. This is a so-called linear congruential generator.

The module provides a derived type to aggregate the multiplier a, the seed or state s, the increment c and the modulus m. These have some default values. Practical implementations often choose c = 0.

Compile the program, and check the first few numbers returned in the sequence. The key to obtaining acceptable statistics is to identify some appropriate values of a and m (e.g., those given in the default).

Check you can introduce some new values of a and m using the structure constructor (a spectacularly bad choice is suggested in the code).

What happens if you make the components of the type private? What would you then have to provide to allow initialisation?

Solution

Running the code as provided gives the following output:

 Step  1,  45991
 Step  2,  2115172081
 Step  3,  17451818
 Step  4,  1615161307
 Step  5,  1424320507
 Step  6,  1230752996

Changing to use the suggested bad RNG values means doing

type (my_rng) :: rng = my_rng(1, 1, 0, 2147483647)

and this produces the following output (note Cray Fortran being helpful with the first line)

 Step  2*1
 Step  2,  1
 Step  3,  1
 Step  4,  1
 Step  5,  1
 Step  6,  1

Making the RNG type’s components private means doing:

  type, public :: my_rng
    private
    integer (int64) :: a = 45991
    integer (int32) :: s = 1
    integer (int64) :: c = 0
    integer (int64) :: m = 2147483647
  end type my_rng

Trying to compile the program while setting the a etc. values will cause a compiler error; those components are no longer public, and the compiler knows it shouldn’t touch them. If we wanted to change those values while my_rng opaque, we’d need to write another module procedure to do so.

Default input/output for derived types

List-directed output for derived types can be used to provide a default output in which each component appears in order, schematically:

  type (my_type) :: a
  ...
  write (*, fmt = *) a
  write (*, fmt = *) a%component1, a%component2, ...

or one can apply a specific format to correspond to the known type components.

Non-default output

Fortran does have a facility to allow the programmer to override the default behaviour of the formatting when a derived type appears in an io-list.

A special dt editor descriptor exists, of the form:

  dt[iodesc-string][(v-list)]

For example we may have

  dt" my-type: "(2,14)

The iodesc-string and v-list will re-appear as arguments to a special function which must be provided by the programmer. Information on this function is provided as part of the procedure-part of the type definition:

type, public :: my_type
  integer :: n
  complex :: z
contains
  procedure :: my_type_write_formatted
  generic   :: write(formatted) => my_type_write_formatted
end type my_type

The following module subroutine should then be provided:

  subroutine my_type_write_formatted(self, unit, iotype, vlist, iostat, iomsg)

    class (my_type),     intent(in)    :: self
    integer,             intent(in)    :: unit
    character (len = *), intent(in)    :: iotype       ! "DT my-type: "
    integer,             intent(in)    :: vlist(:)     ! (2,14)
    integer,             intent(out)   :: iostat
    character (len = *), intent(inout) :: iomsg

    ! ... process arguments to give required output to unit number ...
    ! iotype is "LISTDIRECTED" for list directed io
    ! iotype is "DTdesc-string" for dt edit descriptor
    ! ...
    ! ... write (unit = unit, fmt = ...)  self%n, self%z

    ! iostat and iomsg should be set if there is an error

  end subroutine my_type_write_formatted

Exercise (15 minutes)

A tri-diagonal structure

In the earlier material on using arrays as dummy arguments we implemented the tri-diagonal solver as a module procedure. Implement a derived type to hold the relevant data for the tri-diagonal matrix, ie., at least the three diagonals.

Define a function which returns a fully initialised matrix type based on arrays holding the three diagonals. Refactor the solver routine to use the new matrix type.

Additional exercise: A very simple tridiagonal matrix may have all diagonal elements the same, and all off-diagonal elements the same. Write an additional function to initialise such a matrix from two scalar values.

A template for the exercise can be found in exercise_program.f90 and exercise_module.f90; or you can use your own version that you have been developing to this point.

Solution

Your new tri-diagonal matrix type should look something like this:

  type, public :: tri_matrix
    integer :: nmax
    real (mykind), dimension(:), allocatable :: a     ! lower (2:nmax)
    real (mykind), dimension(:), allocatable :: b     ! diag (1:nmax)
    real (mykind), dimension(:), allocatable :: c     ! upper (1:nmax-1)
  end type tri_matrix

Implementations of the solution are available in solution_program.f90 and solution_module.f90.

Exercise (optional)

Formats for derived types

Try implementing the generic write(formatted) function for the following type:

  type, public :: my_date
    integer :: day = 1        ! day 1-31
    integer :: month = 1      ! month 1-12
    integer :: year = 1900    ! year
  end type my_date

The format we would like is dd/mm/yyyy e.g, 01/12/1999 for 1st December 1999 for list directed I/O. Then try the dt edit descriptor to allow some more flexibility.

Solution

A suggested implementation of the solution is available in date_program.f90 and date_module.f90.

Key Points

• The ability to aggregate related data in a structure is important.

• Fortran offers the _derived type_ in addition to intrinsic types.

• In its simplest form, one may think of this as the analogue to a C struct.

• Derived types also form the basis of aggregation of data and related operations or procedures (viz. object-oriented programming); however, this introductory course will only touch on this feature.