# Large Amounts of Massive Arrays (LAMA)¶

Data arrays contained within fields are stored and manipulated in a very memory efficient manner such that large numbers of fields may co-exist and be manipulated regardless of the size of their data arrays. The limiting factor on array size is not the amount of available physical memory, but the amount of disk space available, which is generally far greater.

The basic functionality is:

• Arrays larger than the available physical memory may be created.

Arrays larger than a preset number of bytes are partitioned into smaller sub-arrays which are not kept in memory but stored on disk, either as part of the original file they were read in from or as newly created temporary files, whichever is appropriate. Therefore data arrays larger than a preset size need never wholly exist in memory.

• Large numbers of arrays which are in total larger than the available physical memory may co-exist.

Large numbers of data arrays which are collectively larger than the available physical memory may co-exist, regardless of whether any individual array is in memory or stored on disk.

• Arrays larger than the available physical memory may be operated on.

Array operations (such as subspacing, assignment, arithmetic, comparison, collapses, etc.) are carried out on a partition-by-partition basis. When an operation traverses the partitions, if a partition is stored on disk then it is returned to disk before processing the next partition.

• The memory management does not need to be known at the API level.

As the array’s metadata (such as size, shape, data-type, number of dimensions, etc.) always reflect the data array in its entirety, regardless of how the array is partitioned and whether or not its partitions are in memory, fields and other variables containing data arrays may be used in the API as if they were normal, in-memory objects (like numpy arrays). Partitioning does carry a performance overhead, but this may be minimised for particular applications or hardware configurations.

When a field is read from a file, the data array is not realized in memory, however large or small it may be. Instead each partition refers to part of the original file on disk. Therefore reading even very large fields is initially very fast and uses up only a very small amount of memory.

## Copying¶

When a field is deep copied with its copy method or the copy.deepcopy function, the partitions of its data array are transferred to the new field as object identities and are not deep copied. Therefore copying even very large fields is initially very fast and uses up only a very small amount of memory.

The independence of the copied field is preserved, however, since each partition that is stored in memory (as opposed to on disk) is deep copied if and when the data in the new field is actually accessed, and then only if the partition’s data still exists in the original (or any other) field.

## Aggregation¶

When two fields are aggregated to form one, larger field there is no need for either field’s data array partitions to be accessed, and therefore brought into memory if they were stored on disk. The resulting field recombines the two fields’ array partitions as object identities into the new larger array. Therevy creating an aggregated field that uses up only a very small amount of extra memory.

The independence of the new field is preserved, however, since each partition that is stored in memory (as opposed to on disk) is deep copied when the data in the new field is actually accessed, and then only if the partition’s data still exists in its the original (or any other) field.

## Subspacing¶

When a new field is created by subspacing a field, the new field is actually a LAMA deep copy of the original but with additional instructions on each of its data partitions to only use the part specified by the subspace indices.

As with copying, creating subspaced fields is initially very fast and uses up only a very small amount of memory, with the added advantage that a deep copy of only the requested parts of the data array needs to be carried out at the time of data access, and then only if the partition’s data still exists in the original field.

When subspacing a field that has previously been subspacing but has not yet had its data accessed, the new subspace merely updates the instructions on which parts of the array partitions to use. For example:

>>> f.shape = (12, 73, 96)
>>> g = f[::-2, ...]
>>> h = g[2:5, ...]


is equivalent to

>>> h = f[7:2:-2, ...]


and if all of the partitions of field f are stored on disk then in both cases so are all of the partitions of field h and no data has been read from disk.

## Speed and memory management¶

The creation of temporary files for array partitions of large arrays and the reading of data from files on disk can create significant speed overheads (for example, recent tests show that writing a 100 megabyte array to disk can take O(1) seconds), so it may be desirable to configure the maximum size of array which is kept in memory, and therefore has fast access.

The data array memory management is configurable as follows:

• Data arrays larger than a given size are partitioned into sub-arrays, each of which is smaller than the chunk size. By default this size is set to 1% of the total physical memory and is found and set with the cf.CHUNKSIZE function.
• In-memory sub-arrays may be written to tempoary files on disk when the amount of available physical memory falls below a specified amount. By default this amount is 10% of the total physical memory and is found and set with the cf.MINNCFCM function.

### Temporary files¶

The directory in which temporary files is found and set with the cf.TEMPDIR function:

>>> cf.TEMPDIR()
'/tmp'
>>> cf.TEMPDIR('/home/me/tmp')
>>> cf.TEMPDIR()
'/home/me/tmp'


The removal of temporary files which are no longer required works in the same way as python’s automatic garbage collector. When a partition’s data is stored in a temporary file, that file will only exist for as long as there are partitions referring to it. When no partitions require the file it will be deleted automatically.

When python exits normally, all temporary files are always deleted.

Changing the temporary file directory does not prevent temporary files in the original directory from being garbage collected.

### Partitioning¶

To maximise looping efficiency, array partitioning preserves as much as is possible the faster varying (inner) dimensions’ sizes in each of the sub-arrays.

Examples

If an array with shape (2, 4, 6) is partitioned into 2 partitions then both sub-arrays will have shape (1, 4, 6).

If the same array is partitioned into 4 partitions then all four sub-arrays will have shape (1, 2, 6).

If the same array is partitioned into 8 partitions then all eight sub-arrays will have shape (1, 2, 3).

If the same array is partitioned into 48 partitions then all forty eight sub-arrays will have shape (1, 1, 1).