write
Write tall array to local and remote locations for checkpointing
Description
write(
uses the file extension from filepattern
,tA
)filepattern
to determine the output
format. filepattern
must include a folder to write the files
into, followed by a file name that includes a wildcard *
. The
wildcard represents incremental numbers for generating unique file names. For
example, write('folder/myfile_*.csv',tA)
.
write(___,
specifies additional options with one or more name-value pair arguments using any of
the previous syntaxes. For example, you can specify the file type with
Name,Value
)'FileType'
and a valid file type ('mat'
,
'seq'
, 'parquet'
,
'text'
, or 'spreadsheet'
), or you can
specify a custom write function to process the data with
'WriteFcn'
and a function handle.
Examples
Write and Reconstruct Tall Array
Write a tall array to disk, and then recover the tall array by creating a new datastore for the written files. This process is useful to save your work or share a tall array with a colleague.
Create a datastore for the airlinesmall.csv
data set. Select only the Year
, Month
, and UniqueCarrier
variables, and treat 'NA'
values as missing data. Convert the datastore into a tall table.
ds = datastore('airlinesmall.csv'); ds.TreatAsMissing = 'NA'; ds.SelectedVariableNames = {'Month','Year','UniqueCarrier'}; tt = tall(ds)
tt = M×3 tall table Month Year UniqueCarrier _____ ____ _____________ 10 1987 {'PS'} 10 1987 {'PS'} 10 1987 {'PS'} 10 1987 {'PS'} 10 1987 {'PS'} 10 1987 {'PS'} 10 1987 {'PS'} 10 1987 {'PS'} : : : : : :
Sort the data in descending order by year and extract the top 25 rows. The resulting tall table is unevaluated.
tt_new = topkrows(tt,25,'Year')
tt_new = M×3 tall table Month Year UniqueCarrier _____ ____ _____________ ? ? ? ? ? ? ? ? ? : : : : : : Preview deferred. Learn more.
Save the results to a new folder named ExampleData
on the C:\
disk. (You can specify a different write location, especially if you are not using a Windows® computer.) The write
function evaluates the tall array prior to writing the files, so there is no need to use the gather
function prior to saving the data.
location = 'C:\ExampleData';
write(location,tt_new)
Writing tall data to folder C:\ExampleData Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.25 sec Evaluation completed in 0.65 sec
Clear tt
and ds
from your working directory. To recover the tall table that was written to disk, first create a new datastore that references the same directory. Then convert the datastore into a tall table. Since the tall table was evaluated before being written to disk, the display now includes a preview of the values.
clear tt ds ds2 = datastore(location); tt2 = tall(ds2)
tt2 = M×3 tall table Month Year UniqueCarrier _____ ____ _____________ 1 2008 {'WN'} 1 2008 {'WN'} 1 2008 {'WN'} 1 2008 {'WN'} 1 2008 {'WN'} 1 2008 {'WN'} 1 2008 {'WN'} 1 2008 {'WN'} : : : : : :
Write Spreadsheet File to Cloud Storage
Create a tall table referencing the tsunamis.xlsx
data file, which contains time-stamped data about the location, magnitude, and cause of tsunamis.
ds = spreadsheetDatastore('tsunamis.xlsx');
T = tall(ds)
T = Mx20 tall table Latitude Longitude Year Month Day Hour Minute Second ValidityCode Validity CauseCode Cause EarthquakeMagnitude Country Location MaxHeight IidaMagnitude Intensity NumDeaths DescDeaths ________ _________ ____ _____ ___ ____ ______ ______ ____________ _________________________ _________ __________________ ___________________ ___________________ __________________________ _________ _____________ _________ _________ __________ -3.8 128.3 1950 10 8 3 23 NaN 2 {'questionable tsunami' } 1 {'Earthquake' } 7.6 {'INDONESIA' } {'JAVA TRENCH, INDONESIA'} 2.8 1.5 1.5 NaN NaN 19.5 -156 1951 8 21 10 57 NaN 4 {'definite tsunami' } 1 {'Earthquake' } 6.9 {'USA' } {'HAWAII' } 3.6 1.8 NaN NaN NaN -9.02 157.95 1951 12 22 NaN NaN NaN 2 {'questionable tsunami' } 6 {'Volcano' } NaN {'SOLOMON ISLANDS'} {'KAVACHI' } 6 2.6 NaN NaN NaN 42.15 143.85 1952 3 4 1 22 41 4 {'definite tsunami' } 1 {'Earthquake' } 8.1 {'JAPAN' } {'SE. HOKKAIDO ISLAND' } 6.5 2.7 2 33 1 19.1 -155 1952 3 17 3 58 NaN 4 {'definite tsunami' } 1 {'Earthquake' } 4.5 {'USA' } {'HAWAII' } 1 NaN NaN NaN NaN 43.1 -82.4 1952 5 6 NaN NaN NaN 1 {'very doubtful tsunami'} 9 {'Meteorological'} NaN {'USA' } {'LAKE HURON, MI' } 1.52 NaN NaN NaN NaN 52.75 159.5 1952 11 4 16 58 NaN 4 {'definite tsunami' } 1 {'Earthquake' } 9 {'RUSSIA' } {'KAMCHATKA' } 18 4.2 4 2236 3 50 156.5 1953 3 18 NaN NaN NaN 3 {'probable tsunami' } 1 {'Earthquake' } 5.8 {'RUSSIA' } {'N. KURIL ISLANDS' } 1.5 0.6 NaN NaN NaN : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
Combine the Year
, Month
, Day
, Hour
, Minute
, and Second
variables into a single datetime variable, and then remove those variables from the table. Remove any rows that contain missing data.
T.DateTime = datetime(T.Year, T.Month, T.Day, T.Hour, T.Minute, T.Second); T(:,3:8) = []; TT = rmmissing(T)
TT = Mx15 tall table Latitude Longitude ValidityCode Validity CauseCode Cause EarthquakeMagnitude Country Location MaxHeight IidaMagnitude Intensity NumDeaths DescDeaths DateTime ________ _________ ____________ ____________________ _________ ____________________________ ___________________ _____________ ____________________________ _________ _____________ _________ _________ __________ ____________________ 42.15 143.85 4 {'definite tsunami'} 1 {'Earthquake' } 8.1 {'JAPAN' } {'SE. HOKKAIDO ISLAND' } 6.5 2.7 2 33 1 04-Mar-1952 01:22:41 58.34 -136.52 4 {'definite tsunami'} 3 {'Earthquake and Landslide'} 8.3 {'USA' } {'SE. ALASKA, AK' } 524.26 4.6 5 5 1 10-Jul-1958 06:15:53 -39.5 -74.5 4 {'definite tsunami'} 1 {'Earthquake' } 9.5 {'CHILE' } {'CENTRAL CHILE' } 25 4.6 4 1260 3 22-May-1960 19:11:17 -6.8 -80.7 4 {'definite tsunami'} 1 {'Earthquake' } 6.8 {'PERU' } {'PERU' } 9 3.2 2.5 66 2 20-Nov-1960 22:01:56 61.1 -147.5 4 {'definite tsunami'} 3 {'Earthquake and Landslide'} 9.2 {'USA' } {'PRINCE WILLIAM SOUND, AK'} 67 6.1 5 221 3 28-Mar-1964 03:36:14 38.65 139.2 4 {'definite tsunami'} 1 {'Earthquake' } 7.5 {'JAPAN' } {'NW. HONSHU ISLAND' } 5.8 2.7 2 26 1 16-Jun-1964 04:01:44 0.2 119.8 4 {'definite tsunami'} 1 {'Earthquake' } 7.8 {'INDONESIA'} {'BANDA SEA' } 10 3.3 3 200 3 14-Aug-1968 22:14:19 -3.1 118.9 4 {'definite tsunami'} 1 {'Earthquake' } 6.9 {'INDONESIA'} {'MAKASSAR STRAIT' } 4 2 2 600 3 23-Feb-1969 00:36:56 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
Write the table as a spreadsheet file to a remote location in Amazon S3™ storage. To read or write data to Amazon S3 you must set the AWS_ACCESS_KEY_ID
and AWS_SECRET_ACCESS_KEY
environment variables using the credentials for your account. For more information, see Work with Remote Data.
setenv('AWS_ACCESS_KEY_ID', 'YOUR_AWS_ACCESS_KEY_ID'); setenv('AWS_SECRET_ACCESS_KEY', 'YOUR_AWS_SECRET_ACCESS_KEY'); location = 's3://bucketname/preprocessedData/'; write(location, TT, 'FileType', 'spreadsheet')
To read the data back, use datastore
to point to the remote location where the data now resides.
ds = datastore(location); tt = tall(ds);
Write Images with Custom Write Function
Create and use a custom writing function to write data in additional formats that are not directly supported by write
, such as image files.
Create an image datastore that references all of the sample images in the toolbox/matlab/demos
folder. The selected images have the extensions .jpg
, .tif
, and .png
. Convert the datastore to a tall cell array.
demoFolder = fullfile(matlabroot,'toolbox','matlab','demos'); ds = imageDatastore(demoFolder,'FileExtensions',{'.jpg' '.tif' '.png'}); T = tall(ds);
Bring one of the images into memory and display it.
I = gather(T(1));
Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 3 sec Evaluation completed in 3.2 sec
imshow(I{1},'InitialMagnification',30)
write
does not support image files directly, so to write the images out in a different format, you must create a new function to handle the file writing. The writing function receives two inputs from write:
info
is a structure containing fields with information about the current block of data. You can use these fields to construct your own unique file name, or simply use theSuggestedFilename
field to use a name suggested bywrite
.data
is the current block of data, obtained by usingread
on the datastore.
The function imageWriter
uses the filename suggested by write
, and uses imwrite
to write the image files to disk as .jpg
files. Save this function in your current working folder.
type imageWriter
function imageWriter(info, data) filename = info.SuggestedFilename; imwrite(data{:}, filename) end
Write the images in the datastore to a new folder named exampleImages
on the C:\
disk. (You can use a different location, especially if you are not using a Windows® computer.) Pass imageWriter
as the custom write function using the 'WriteFcn'
name-value pair argument.
location = 'C:\exampleImages\image_*.jpg'; write(location, T, 'WriteFcn', @imageWriter)
Writing tall data to folder C:\exampleImages Evaluating tall expression using the Local MATLAB Session: - Pass 1 of 1: Completed in 0.71 sec Evaluation completed in 0.98 sec
Display the contents of the folder where the files were written.
dir C:\exampleImages
. image_1_000001.jpg image_3_000001.jpg image_5_000001.jpg .. image_2_000001.jpg image_4_000001.jpg image_6_000001.jpg
To read the images back into MATLAB®, create a datastore that references the same location.
ds = imageDatastore(location); T = tall(ds)
T = 6×1 tall cell array {1024×2048×3 uint8} { 650×600×3 uint8} {1024×2048×3 uint8} { 650×600×3 uint8} { 480×640×3 uint8} { 480×640×3 uint8}
Input Arguments
location
— Folder location to write data
character vector | string
Folder location to write data, specified as a character vector or string.
location
can specify a full or relative path. The
specified folder can be either of these options:
Existing empty folder
New folder that
write
creates
You can write data to local folders on your computer, folders on a shared network, or to remote locations in HDFS™, Azure®, or Amazon S3™. For more information about reading and writing data to remote locations, see Work with Remote Data.
Additional considerations apply for Hadoop® and Apache® Spark™:
If the folder is not available locally, then the full path of the folder must be a uniform resource locator (URL) of the form:
hdfs:///
.path_to_file
Before writing to HDFS, set the
HADOOP_HOME
,HADOOP_PREFIX
, orMATLAB_HADOOP_INSTALL
environment variable to the folder where Hadoop is installed.Before writing to Apache Spark, set the
SPARK_HOME
environment variable to the folder where Apache Spark is installed.
Example: location = 'hdfs:///some/output/folder'
specifies an HDFS URL.
Example: location = '../../dir/data'
specifies a
relative file path.
Example: location = 'C:\Users\MyName\Desktop\data'
specifies an absolute path to a Windows® desktop folder.
Example: location = 'file:///path/to/data'
specifies an
absolute URI path to a folder.
Data Types: char
| string
tA
— Input array
tall array
Input array, specified as a tall array.
filepattern
— File naming pattern
string | character vector
File naming pattern, specified as a string or a character vector. The file
naming pattern must contain a folder to write the files into, followed by a
file name that includes a wildcard *
. The
write
function replaces the wildcard with
sequential numbers to ensure unique file names.
Example: write('folder/data_*.txt',tA)
writes the tall
array tA
as a series of .txt
files in
folder
with the file names
data_1.txt
, data_2.txt
, and so
on.
Data Types: char
| string
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: write('C:\myData', tX, 'FileType', 'text', 'WriteVariableNames',
false)
writes the tall array tX
to
C:\myData
as a collection of text files that do not use
variable names as column headings.
FileType
— Type of file
'auto'
(default) | 'mat'
| 'parquet'
| 'seq'
| 'text'
| 'spreadsheet'
Type of file, specified as the comma-separated pair consisting of
'FileType'
and one of the allowed file types:
'auto'
, 'mat'
,
'parquet'
, 'seq'
,
'text'
, or
'spreadsheet'
.
Use the 'FileType'
name-value pair with the
location
argument to specify what type of files
to write. By default, write
attempts to
automatically detect the proper file type. You do not need to specify
the 'FileType'
name-value pair argument if
write
can determine the file type from an
extension in the location
or
filepattern
arguments. write
can determine the file type from these extensions:
.mat
for MATLAB® data files.parquet
or.parq
for Parquet files.seq
for sequence files.txt
,.dat
, or.csv
for delimited text files.xls
,.xlsx
,.xlsb
,.xlsm
,.xltx
, or.xltm
for spreadsheet files
Example: write('C:\myData', tX, 'FileType',
'text')
WriteFcn
— Custom writing function
function handle
Custom writing function, specified as the comma-separated pair
consisting of 'WriteFcn'
and a function handle. The
specified function receives blocks of data from tA
and is responsible for creating the output files. You can use the
'WriteFcn'
name-value pair argument to write data
in a variety of formats, even if write
does not
directly support the output format.
Functional Signature
The custom writing function must accept two input arguments,
info
and data
:
function myWriter(info, data)
data
contains a block of data fromtA
.info
is a structure with fields that contain information about the block of data. You can use the fields to build a new file name that is globally unique within the final location. The structure fields areField Description RequiredLocation
Fully qualified path to a temporary output folder. Only files written to this folder are copied to the final destination. RequiredFilePattern
The file pattern required for output file names. This field is empty if only a folder name is specified. SuggestedFilename
A fully qualified, globally unique file name that meets the location and naming requirements. PartitionIndex
Index of the tall array partition being written. NumPartitions
Total number of partitions in the tall array. BlockIndexInPartition
Position of current data block within the partition. IsFinalBlock
true
if current block is the final block of the partition.
File Naming
The file name used for the output files determines the order in
which datastore
later reads the files back in.
If the order of the files matters, then the best practice is to use
the SuggestedFilename
field to name the files,
since the suggested name guarantees the file order. If you do not
use the suggested file name, then the custom writing function must
create globally unique, correctly ordered file names. The file names
should follow the naming pattern outlined in
RequiredFilePattern
. When running in parallel
with Parallel Computing Toolbox™, the file names must be unique and correctly ordered
between workers, even though each worker writes to its own local
folder.
Arrays with Multiple Partitions
You can divide a tall array into partitions to facilitate running calculations on the array in parallel with Parallel Computing Toolbox. Each of the partitions is still comprised of smaller blocks that individually fit into memory.
info
contains several fields related to
partitions: PartitionIndex
,
NumPartitions
,
BlockIndexInPartition
, and
IsFinalBlock
. These fields are useful when
you are writing out a single file and appending to it, which is a
common task for arrays with large partitions that have been split
into many blocks. The custom writing function is called once per
block, and the blocks in one partition are always written in order
by the same worker. However, different partitions can be written by
different workers.
Example Function
A simple writing function that writes spreadsheet files is
function dataWriter(info, data) filename = info.SuggestedFilename; writetable(data, filename, 'FileType', 'spreadsheet') end
dataWriter
as the writing function for
some data tt
, use these
commands.tt = tall(array2table(rand(5000,3))); location = '/tmp/MyData/tt_*.xlsx'; write(location, tt, 'WriteFcn', @dataWriter);
dataWriter
function uses the
suggested file name in the info
structure and
calls writetable
to write a spreadsheet file.
The suggested file name takes into account the file naming pattern
that is specified in the location
argument.
Data Types: function_handle
WriteVariableNames
— Indicator for writing variable names as column headings
true
or
1
(default) | false
or 0
Indicator for writing variable names as column headings, specified as
the comma-separated pair consisting of
'WriteVariableNames'
and a numeric or logical
1
(true
) or
0
(false
).
Indicator | Behavior |
---|---|
| Variable names are included as the column headings of the output. (default) |
| Variable names are not included in the output. |
DateLocale
— Locale for writing dates
character vector | string scalar
Locale for writing dates, specified as the comma-separated pair
consisting of 'DateLocale'
and a character vector or
a string scalar. When writing datetime
values to the
file, use DateLocale
to specify the locale in which
write
should write month and day-of-week names
and abbreviations. The character vector or string takes the form
,
where xx
_YY
xx
is a lowercase ISO 639-1 two-letter
code indicating a language, and YY
is an
uppercase ISO 3166-1 alpha-2 code indicating a country. For a list of
common values for the locale, see the Locale
name-value pair argument for the datetime
function.
For Excel® files, write
writes variables
containing datetime
arrays as Excel dates and ignores the 'DateLocale'
parameter value. If the datetime
variables contain
years prior to either 1900 or 1904, then write
writes the variables as text. For more information on Excel dates, see Differences between the 1900 and the 1904 date system in
Excel.
Example: 'DateLocale','ja_JP'
or
'DateLocale',"ja_JP"
Data Types: char
| string
Delimiter
— Field delimiter character
','
or 'comma'
| ' '
or 'space'
| ...
Field delimiter character, specified as the comma-separated pair
consisting of 'Delimiter'
and one of these
specifiers.
Specifier | Field Delimiter |
---|---|
| Comma (default) |
| Space |
| Tab |
| Semicolon |
| Vertical bar |
You can use the 'Delimiter'
name-value pair
argument only for delimited text files.
Example: 'Delimiter','space'
or
'Delimiter',"space"
QuoteStrings
— Indicator for writing quoted text
false
(default) | true
Indicator for writing quoted text, specified as the comma-separated
pair consisting of 'QuoteStrings'
and either
false
or true
. If
'QuoteStrings'
is set to true
,
then write
encloses the text in double quotation
marks and replaces any double-quote characters that appear as part of
that text with two double-quote characters. For an example, see Write Quoted Text to CSV File.
You can use the 'QuoteStrings'
name-value pair
argument only with delimited text files.
Encoding
— Character encoding scheme
'system'
| 'UTF-8'
| 'ISO-8859-1'
| 'windows-1251'
| 'windows-1252'
| ...
Character encoding scheme associated with the file, specified as the
comma-separated pair consisting of 'Encoding'
and
'system'
or a standard character encoding scheme
name like one of the values in this table. When you do not specify any
encoding or specify encoding as 'system'
, the
write
function uses your system default
encoding to write the file.
|
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|
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|
|
|
|
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| |
|
Example: 'Encoding','system'
or
'Encoding',"system"
uses the system default
encoding.
Sheet
— Target worksheet
character vector | string scalar | positive integer
Target worksheet, specified as the comma-separated pair consisting of
'Sheet'
and a character vector or a string scalar
containing the worksheet name or a positive integer indicating the
worksheet index. The worksheet name cannot contain a colon
(:
). To determine the names of sheets in a
spreadsheet file, use sheets = sheetnames(filename)
.
For more information, see sheetnames
.
If the sheet does not exist, then write
adds a
new sheet at the end of the worksheet collection. If the sheet is an
index larger than the number of worksheets, then
write
appends empty sheets until the number of
worksheets in the workbook equals the sheet index. In either case,
write
generates a warning indicating that it
has added a new worksheet.
You can use the 'Sheet'
name-value pair argument
only with spreadsheet files.
Example: 'Sheet'
,2
Example: 'Sheet'
,
'MySheetName'
Data Types: char
| string
| single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
VariableCompression
— Parquet compression algorithm
'snappy'
(default) | 'brotli'
| 'gzip'
| 'uncompressed'
| cell array of character vectors | string vector
Parquet compression algorithm, specified as one of these values.
'snappy'
,'brotli'
,'gzip'
, or'uncompressed'
. If you specify one compression algorithm thenwrite
compresses all variables using the same algorithm.Alternatively, you can specify a cell array of character vectors or a string vector containing the names of the compression algorithms to use for each variable.
In general, 'snappy'
has better performance for
reading and writing, 'gzip'
has a higher compression
ratio at the cost of more CPU processing time, and
'brotli'
typically produces the smallest file
size at the cost of compression speed.
Example: write('C:\myData', tX, 'FileType', 'parquet',
'VariableCompression', 'brotli')
Example: write('C:\myData', tX, 'FileType', 'parquet',
'VariableCompression', {'brotli' 'snappy'
'gzip'})
VariableEncoding
— Encoding scheme names
'auto'
(default) | 'dictionary'
| 'plain'
| cell array of character vectors | string vector
Encoding scheme names, specified as one of these values:
'auto'
—write
uses'plain'
encoding for logical variables, and'dictionary'
encoding for all others.'dictionary'
,'plain'
— If you specify one encoding scheme thenwrite
encodes all variables with that scheme.Alternatively, you can specify a cell array of character vectors or a string vector containing the names of the encoding scheme to use for each variable.
In general, 'dictionary'
encoding results in
smaller file sizes, but 'plain'
encoding can be
faster for variables that do not contain many repeated values. If the
size of the dictionary or number of unique values grows to be too big,
then the encoding automatically reverts to plain encoding. For more
information on Parquet encodings, see Parquet encoding definitions.
Example: write('myData.parquet', T, 'FileType', 'parquet',
'VariableEncoding', 'plain')
Example: write('myData.parquet', T, 'FileType', 'parquet',
'VariableEncoding', {'plain' 'dictionary'
'plain'})
Version
— Parquet version to use
'2.0'
(default) | '1.0'
Parquet version to use, specified as either '1.0'
or '2.0'
. By default, '2.0'
offers
the most efficient storage, but you can select '1.0'
for the broadest compatibility with external applications that support
the Parquet format.
Caution
Parquet version 1.0 has a limitation that it cannot round-trip
variables of type uint32
(they are read back into
MATLAB as int64
).
Limitations
In some cases, write(location, T, 'FileType', type)
creates files
that do not represent the original array T
exactly. If you use
datastore(location)
to read the files, then the result might not
have the same format or contents as the original tall table.
For the
'text'
and'spreadsheet'
file types,write
uses these rules:write
outputs numeric variables usinglongG
format and categorical, character, or string variables as unquoted text.For nontext variables that have more than one column,
write
outputs multiple delimiter-separated fields on each line and constructs suitable column headings for the first line of the file.write
outputs variables with more than two dimensions as two-dimensional variables, with trailing dimensions collapsed.For cell-valued variables with contents that are numeric, logical, character, or categorical,
write
outputs the contents of each cell as a single row, in multiple delimiter-separated fields. If the cells have a different data type,write
outputs a single empty field.
Do not use the
'text'
or'spreadsheet'
file types if you need to write an exact checkpoint of the tall array.For the
'parquet'
file type, there are some cases where the Parquet format cannot fully represent the MATLAB table or timetable data types. If you useparquetread
ordatastore
to read the files, then the result might not have the same format or contents as the original tall table. For more information, see Apache Parquet Data Type Mappings.
Tips
Use the
write
function to create checkpoints or snapshots of your data as you work, especially when working with huge data sets. This practice allows you to reconstruct tall arrays directly from files on disk rather than re-executing all of the commands that produced the tall array.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
Version History
Introduced in R2016b
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