During the processing of the mesh to create the solver data structures, common tasks arise. These include among others - a unique collection of elements in lists, i.e. without duplicates, - a localization of a stored element, - sorting of a list of records. As Fortran does not intrinsically include dynamically growing data structures, they first have to be introduced manually.
Therefore the modules tem_dyn_array_module and tem_grow_array_module have been introduced. These modules are based on generic CoCo macros stored in arrayMacros.inc.
The definition is depicted in listing lst:tem_dyn_array where macros
are used for the label of a dynamic type ?tname?and the used data type
?tstring?.
What shall be listed in lst:tem_dyn_array ??
The introduction of macros allow for a generic definition for all data types of the container, whereas the compiled source code contains the definitions for each required data type.
The dynamic array is a data structure to store sets of unique elements in a sorted manner. Elements can be added dynamically, and the dynamic array takes care of allocating the space needed to store the elements as well as checking them for uniqueness. Also sorting is done without user interaction.
The initialization is not needed in all cases. Usually, the dynamic array can be
used out of the box. In case you know the total number of elements in advance,
you can provide this information via the init routine. With this hint, the data
structure is able to allocate enough space for the expected number of elements
and thus saves some resizing steps.
When init is called, it simply allocates the container with the given options
and resets the number of records.
type(dyn_intArray_type) :: dynIntArray
call init( me = dynIntArray, length = nTotalElements )
To append an element, simply call append. As a dynamic array only contains
unique elements, the routine checks for the existence of the entry in the
list and, subsequently, the sufficiency of the size of the container to
incorporate another entry. In case the size does not suffice, the array is
expanded. Information about if (wasAdded) and where (pos) the entry was
stored is returned to the caller.
integer :: newPos
logical :: wasAdded
call append( me = dynIntArray, val = 1, length = 5, pos = newPos, wasAdded = wasAdded )
Also appending more than one value is possible using the vectorial append routine:
integer :: newPos(:)
logical :: wasAdded(:)
call append( me = dynIntArray, val = ( 2, 3, 4), length = 5, pos = newPos, wasAdded = wasAdded )
An uninitialized dynamic array starts with the size of 0, but also an
initialized array can become to small over time. If elements should be added,
but the dynamic array doesn't have any free spots left, expand is called to
increase the array's size.
If expand was called and a new length was provided via the length argument,
this length is taken to increase the array. If no length was provided, the array
is simply doubled, but at least increased by minLength.
Another thing influencing the size is the amount of elements that are added. The array is always increased to afterwards contain all new elements.
But the array is only increased up to the maximum value of the index,
which means that an dynamic array can only contain up to huge(me%nVals)
elements, thus elements.
You might want to retrieve the position of an element within a list. In order to achieve this efficiently, the list with entries must be ordered so we can rely on the binary search, which performs with .
Hence we introduce a derived data type which allows an efficient and simple element adding and retrieving process, as well as a sorted order of the entries. tem_dyn_array_module provides the type definitions and all the related procedures to act on this data type. The data type includes the size of the container within, the amount of its actual entries, a flag for uniqueness and the container array itself as well as a conforming array for the sorted retrieval of the entries in the value array.
See Truncating a growing array.
See Destroying a growing array.
A growing array is a data structure to store arbitrary sets of elements. The growing array does not check for uniqueness nor does it sort it's elements. Thus it is similar to the common fortran array except that it can grow dynamically (at least that's how it looks like).
The initialization of the growing array the same applies as it does for the dynamic array; an initialization is only needed, when th ethe total number of elements in known in advance.
type(grw_intArray_type) :: grwIntArray
call init( me = grwIntArray, length = nTotalElements )
Elements can be appended in two different ways. The first one adds a single element to the grwoing array:
call append( me = grwIntArray, val = 1 )
The second routine takes an array of values:
call append( me = grwIntArray, val = ( 2, 3, 4 ) )
After these two calls, the grwoing array contains ( 1, 2, 3, 4 ).
When elements should end up at a speciic position, append is not the routine
of choice, as it appends the new elements to the end of the array. Use placeAt
instead. placeAt needs to be called with the additional argument pos, which
states the position the element should be placed at.
Regarding the example from "Appending elements", the current array looks like
( 1, 2, 3, 4 ). After
call placeAt( me = grwIntArray, val = 5, pos = 3 )
the array wil look like ( 1, 2, 5, 4 ). There is also a vectorial version
available:
call placeAt( me = grwIntArray, val = ( 5, 6, 7 ), pos = 3 )
which results in ( 1, 2, 5, 6, 7 ).
The array starts with a size of 0. When a new element is appended, the array
checks whether the new element fits into it. If not, the array is expanded.
If the caller doesn't explicitly provide a length, the array will be doubled
(whereas the minimum expansion length is minLength).
Regarding the example from the paragraph "Appending elements", the array
contains 4 elements and the array is also 4 elements long. When a fifth element
is added, the array will be resized, so that size(grwIntArray%Val) will return
8, even when grwIntArray%nVals is 5.
In cases where the final size of the array is known or the size of the batch of elements that will be added, this size can be passed along with calls to append or placeAt using the length argument. However, passing the expand length doesn't necessarily mean that it is used. If it is smaller than the position requested by placeAt is even outside the expanded array or the expanded array would exceed it's maximum size, other expand lengths will be used.
Liek the dynamic array, the maximum size for the growing array is also
huge(me%nVals), which denotes to elements.
With the rather involved logic to expand a growing array, it can happen that
the final array has much more element slots available that real elements (which
means: me%nVals << me%ContainerSize). To free the surplus, the truncate
routine shrinks the array to the actually needed size.
Regarding the array ( 1, 2, 5, 6, 7, x, x, x ) with x indicating the available
slots. After
call truncate( me = grwIntArray )
the array will be ( 1, 2, 5, 6, 7 ) and therefore
me%nVals == me%ContainerSize.
If a growing array should be recycled, but it's elements are not needed anymore, the array can be emptied by calling
call empty( me = grwIntArray )
This actually doesn't change the array's container. It will stay untouched,
which means: If it was 8 slots long before calling empty, it is also 8 slots
long after the call. The growing array just forgot that the container contains
anything useful.
In case a growing array is not needed anymore, the memory consumed by the elements with the array and the growing array itself can be freed by calling
call destroy( me = grwIntArray )
There is also a two-dimensional growing array, which actually is an array of growing arrays. The width of the two-dimensional growing array can only be set during initialization of the array, whereas the sizes of each array can be set individually and also after the initialization is already done (or not, as a growing array doesnot necessarily has to be initialized before use).
The following paragraphs do only state the differences to the common, one-dimensional array.
Initialization is similar to the common growing array, with the difference that the width for the first dimension is mandatory (length stays optional):
call init( me = growing2dIntArray, width = 3, length = 3 )
To append an element, the index of the first dimension has to be provided:
call append( me = grw2dIntArray, val = 1, pos1 = 2 )
After initializing an array with 3x3 elements and calling the above example, the array looks like:
( ( _, _, _ ), ( 1, _, _ ), ( _, _, _ ) )
Providing length and retrieving the position where the element was added is also possible for the two-dimensional version:
integer :: addedPos
call append( me = grw2dIntArray, val = 1, pos1 = 2, length = 3, pos2 = addedPos )
Also vectorial access is possible. But in contrast to the one-dimensional version, not all elements are added to one growing array, but to the first free index for all growing arrays. Consider the array from the exmaple above:
( ( _, _, _ ), ( 1, _, _ ), ( _, _, _ ) )
Calling the vectorial append
call append( me = grw2dIntArray, val = ( 4, 5, 6 ) )
will result in
( ( _, 4, _ ), ( 1, 5, _ ), ( _, 6, _ ) )
because the element 1 in the second array blocks the first index, thus the
second index is the first one that is free for all arrays.
When placing elements at a requested position, the scalar approach behaves as expected. The vectorial access is, like for appending values, a little different. Taking the array from the example above:
( ( _, 4, _ ), ( 1, 5, _ ), ( _, 6, _ ) )
calling
call placeAt( me = grw2dIntArray, val = ( 7, 8, 9 ), pos2 = 2 )
will result in
( ( _, 7, _ ), ( 1, 8, _ ), ( _, 9, _ ) )