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Ways to Reduce the Amount of Memory Required Using Appropriate Data Storage |

The source of many "out of memory" problems often involves analyzing
or processing an existing large set of data such as in a file or a
database. This requires bringing all or part of the data set into
the MATLAB^{®} software process. The following techniques deal with
minimizing the required memory during this stage.

Only import into MATLAB as much of a large data set as you need for the problem you are trying to solve. This is not usually a problem when importing from sources such as a database, where you can explicitly search for elements matching a query. But this is a common problem with loading large flat text or binary files. Rather than loading the entire file, use the appropriate MATLAB function to load parts of files.

**MAT-Files. **Load part of a variable by indexing into an object that you
create with the `matfile` function.

**Text Files. **Use the `textscan` function
to access parts of a large text file by reading only the selected
columns and rows. If you specify the number of rows or a repeat format
number with `textscan`, MATLAB calculates
the exact amount of memory required beforehand.

**Binary Files. **You can use low-level binary file I/O functions, such as `fread`, to access parts of any file that
has a known format. For binary files of an unknown format, try using
memory mapping with the `memmapfile` function.

**Image, HDF, Audio, and Video Files. **Many of the MATLAB functions that support loading from
these types of files allow you to select portions of the data to read.
For details, see the function reference pages listed in Supported File Formats for Import and Export.

Consider block processing, that is, processing a large data set one section at a time in a loop. Reducing the size of the largest array in a data set reduces the size of any copies or temporaries needed. You can use this technique in either of two ways:

For a subset of applications that you can break into separate chunks and process independently.

For applications that only rely on the state of a previous block, such as filtering.

Avoid creating large temporary variables, and also make it a
practice to clear those temporary variables you do use when they are
no longer needed. For example, when you create a large array of zeros,
instead of saving to a temporary variable `A`, and
then converting `A` to a single:

A = zeros(1e6,1); As = single(A);

use just the one command to do both operations:

A = zeros(1e6,1,'single');

Using the `repmat` function,
array preallocation and `for` loops
are other ways to work on `nondouble` data without
requiring temporary storage in memory.

When working with large data sets, be aware that MATLAB makes a temporary copy of an input variable if the called function modifies its value. This temporarily doubles the memory required to store the array, which causes MATLAB to generate an error if sufficient memory is not available.

One way to use less memory in this situation is to use nested
functions. A nested function shares the workspace of all outer functions,
giving the nested function access to data outside of its usual scope.
In the example shown here, nested function `setrowval` has
direct access to the workspace of the outer function `myfun`,
making it unnecessary to pass a copy of the variable in the function
call. When `setrowval` modifies the value of `A`,
it modifies it in the workspace of the calling function. There is
no need to use additional memory to hold a separate array for the
function being called, and there also is no need to return the modified
value of `A`:

function myfun A = magic(500); function setrowval(row, value) A(row,:) = value; end setrowval(400, 0); disp('The new value of A(399:401,1:10) is') A(399:401,1:10) end

MATLAB provides you with different sizes of data classes,
such as `double` and `uint8`, so
you do not need to use large classes to store your smaller segments
of data. For example, it takes 7 KB less memory to store 1,000 small
unsigned integer values using the `uint8` class than
it does with `double`.

The numeric class you should use in MATLAB depends on your
intended actions. The default class `double` gives
the best precision, but requires 8 bytes per element of memory to
store. If you intend to perform complicated math such as linear algebra,
you must use a floating-point class such as a `double` or `single`.
The `single` class requires only 4 bytes. There are
some limitations on what you can do with `singles`,
but most MATLAB Math operations are supported.

If you just need to carry out simple arithmetic and you represent the original data as integers, you can use the integer classes in MATLAB. The following is a list of numeric classes, memory requirements (in bytes), and the supported operations.

Class (Data Type) | Bytes | Supported Operations |
---|---|---|

single | 4 | Most math |

double | 8 | All math |

logical | 1 | Logical/conditional operations |

int8, uint8 | 1 | Arithmetic and some simple functions |

int16, uint16 | 2 | Arithmetic and some simple functions |

int32, uint32 | 4 | Arithmetic and some simple functions |

int64, int64 | 8 | Arithmetic and some simple functions |

MATLAB arrays (implemented internally as `mxArrays`)
require room to store meta information about the data in memory, such
as type, dimensions, and attributes. This takes about 80 bytes per
array. This overhead only becomes an issue when you have a large number
(e.g., hundreds or thousands) of small `mxArrays` (e.g.,
scalars). The `whos` command
lists the memory used by variables, but does not include this overhead.

Because simple numeric arrays (comprising one `mxArray`)
have the least overhead, you should use them wherever possible. When
data is too complex to store in a simple array (or matrix), you can
use other data structures.

Cell arrays are comprised of separate `mxArrays` for
each element. As a result, cell arrays with many small elements have
a large overhead.

Structures require a similar amount of overhead per field (see the documentation on Array Headers above). Structures with many fields and small contents have a large overhead and should be avoided. A large array of structures with numeric scalar fields requires much more memory than a structure with fields containing large numeric arrays.

Also note that while MATLAB stores numeric arrays in contiguous memory, this is not the case for structures and cell arrays.

When reading data from a binary file with `fread`, it is a common error to specify
only the class of the data in the file, and not the class of the data MATLAB uses
once it is in the workspace. As a result, the default `double` is
used even if you are reading only 8-bit values. For example,

fid = fopen('large_file_of_uint8s.bin', 'r'); a = fread(fid, 1e3, 'uint8'); % Requires 8k whos a Name Size Bytes Class Attributes a 1000x1 8000 double a = fread(fid, 1e3, 'uint8=>uint8'); % Requires 1k whos a Name Size Bytes Class Attributes a 1000x1 1000 uint8

If your data contains many zeros, consider using sparse arrays, which store only nonzero elements. The example below compares the space required for storage of an array of mainly zeros:

A = diag(1e3,1e3); % Full matrix with ones on the diagonal As = sparse(A) % Sparse matrix with only nonzero elements whos Name Size Bytes Class A 1001x1001 8016008 double array As 1001x1001 4020 double array (sparse)

You can see that this array requires only approximately 4 KB
to be stored as sparse, but approximately 8 MB as a full matrix. In
general, for a sparse double array with `nnz` nonzero
elements and `ncol` columns, the memory required
is

16 *

`nnz`+ 8 *`ncol`+ 8 bytes (on a 64 bit machine)12 *

`nnz`+ 4 *`ncol`+ 4 bytes (on a 32 bit machine)

Note that MATLAB does not support all mathematical operations on sparse arrays.

MATLAB always uses a contiguous segment of memory to store a numeric array. As you manipulate this data, however, the contiguous block can become fragmented. When memory is fragmented, there may be plenty of free space, but not enough contiguous memory to store a new large variable. Increasing fragmentation can use significantly more memory than is necessary.

In the course of a MATLAB session, memory can become fragmented
due to dynamic memory allocation and deallocation. `for` and `while` loops
that incrementally increase, or *grow*, the size
of a data structure each time through the loop can add to this fragmentation
as they have to repeatedly find and allocate larger blocks of memory
to store the data.

To make more efficient use of your memory, preallocate a block of memory large enough to hold the matrix at its final size before entering the loop. When you preallocate memory for an array, MATLAB reserves sufficient contiguous space for the entire full-size array at the beginning of the computation. Once you have this space, you can add elements to the array without having to continually allocate new space for it in memory.

For more information on preallocation, see Preallocating Arrays.

MATLAB uses a heap method of memory management. It requests memory from the operating system when there is not enough memory available in the heap to store the current variables. It reuses memory as long as the size of the memory segment required is available in the heap.

The following statements can require approximately 4.3 MB of RAM. This is because MATLAB may not be able to reuse the space previously occupied by two 1 MB arrays when allocating space for a 2.3 MB array:

a = rand(1e6,1); b = rand(1e6,1); clear c = rand(2.3e6,1);

The simplest way to prevent overallocation of memory is to allocate the largest vectors first. These statements require only about 2.0 MB of RAM:

c = rand(2.3e6,1); clear a = rand(1e6,1); b = rand(1e6,1);

On 32-bit Microsoft^{®} Windows^{®}, the workspace of MATLAB can
fragment over time due to the fact that the Windows memory manager
does not return blocks of certain types and sizes to the operating
system. Clearing the MATLAB workspace does not fix this problem.
You can minimize the problem by allocating the largest variables first.
This cannot address, however, the eventual fragmentation of the workspace
that occurs from continual use of MATLAB over many days and weeks,
for example. The only solution to this is to save your work and restart MATLAB.

The `pack` command, which
saves all variables to disk and loads them back, does not help with
this situation.

One simple way to increase the amount of memory you have available is to clear large arrays that you no longer use.

If your program generates very large amounts of data, consider
writing the data to disk periodically. After saving that portion of
the data, use the `clear` function
to remove the variable from memory and continue with the data generation.

When you are working with a very large data set repeatedly or interactively, clear the old variable first to make space for the new variable. Otherwise, MATLAB requires temporary storage of equal size before overriding the variable. For example,

a = rand(100e6,1) % 800 MB array b = rand(100e6,1) % New 800 MB array Error using rand Out of memory. Type HELP MEMORY for your options. clear a a = rand(100e6,1) % New 800 MB array

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