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2 Parallel for-Loops (parfor)
2-36
parfor statement might produce values of X with different round-off errors. This is an
unavoidable cost of parallelism.
For example, the statement on the left yields 1, while the statement on the right returns
1 + eps:
(1 + eps/2) + eps/2 1 + (eps/2 + eps/2)
With the exception of the minus operator (-), all the special cases listed in the table in
“Reduction Variables” on page 2-32 have a corresponding (perhaps approximately)
associative function. MATLAB calculates the assignment X = X - expr by using X =
X + (-expr). (So, technically, the function for calculating this reduction assignment is
plus, not minus.) However, the assignment X = expr - X cannot be written using an
associative function, which explains its exclusion from the table.
Commutativity in Reduction Assignments. Some associative functions, including +, .*,
min, and max, intersect, and union, are also commutative. That is, they satisfy the
following for all a and b:
f(a,b) = f(b,a)
Examples of noncommutative functions are * (because matrix multiplication is not
commutative for matrices in which both dimensions have size greater than one), [,],
[;], {,}, and {;}. Noncommutativity is the reason that consistency in the order
of arguments to these functions is required. As a practical matter, a more efficient
algorithm is possible when a function is commutative as well as associative, and parfor
is optimized to exploit commutativity.
Recommended: Except in the cases of *, [,], [;], {,}, and {;}, the function f of
a reduction assignment should be commutative. If f is not commutative, different
executions of the loop might result in different answers.
Violating the restriction on commutativity in a function used for reduction, could result
in unexpected behavior, even if it does not generate an error.
Unless f is a known noncommutative built-in, it is assumed to be commutative. There is
currently no way to specify a user-defined, noncommutative function in parfor.
Overloading in Reduction Assignments. Most associative functions f have an identity
element e, so that for any a, the following holds true:
- Parallel Computing Toolbox™ 1
- User's Guide 1
- How to Contact MathWorks 2
- Revision History 3
- Contents 5
- Program Independent Jobs 11
- Program Communicating Jobs 12
- GPU Computing 12
- Objects — Alphabetical List 14
- Functions — Alphabetical List 14
- Glossary 14
- Getting Started 15
- 1 Getting Started 16
- Partition Large Data Sets 19
- Run a Batch Job 22
- Run a Batch Parallel Loop 23
- Parallel for-Loops (parfor) 29
- Introduction to parfor 30
- Create a parfor-Loop 32
- Create a parfor-Loop 33
- 2 Parallel for-Loops (parfor) 34
- parfor Limitations 39
- Using Objects in parfor-Loops 41
- Handle Classes 41
- Nested Functions 43
- Nested Loops 43
- Nested spmd Statements 45
- Break and Return Statements 45
- P-Code Scripts 45
- Unambiguous Variable Names 47
- Transparency 47
- Loop Variable 53
- Sliced Variables 55
- Broadcast Variables 59
- Reduction Variables 60
- Reduction Variables 65
- Temporary Variables 67
- Temporary Variables 69
- Improving parfor Performance 70
- Improving parfor Performance 71
- Parallel Pools 72
- Parallel Pools 73
- Start a Parallel Pool 73
- When to Use spmd 80
- Define an spmd Statement 81
- Display Output 83
- Introduction to Composites 84
- Distribute Arrays 88
- Create Codistributed Arrays 89
- P>> help magic 97
- P>> x = pi 97
- P>> x = labindex 98
- P>> all = numlabs 98
- P>> getLocalPart(I) 102
- P>> pmode exit 103
- Parallel Command Window 104
- Click tiling icon 105
- Select layout 105
- Select vertical 106
- Drag to adjust 106
- Click tabbed output 107
- Select only two tabs 107
- Multiple labs 108
- Using Graphics in pmode 112
- Connectivity Testing 113
- Hostname Resolution 113
- Socket Connections 113
- Introduction 116
- Nondistributed Arrays 116
- Codistributed Arrays 118
- A = zeros(80, 1000); 119
- D = codistributed(A) 119
- Local Arrays 124
- Restoring the Full Array 127
- 2-Dimensional Distribution 130
- Parallelizing a for-Loop 134
- plot(1:numDataSets, res); 135
- Programming Overview 141
- 6 Programming Overview 142
- Toolbox and Server Components 143
- Life Cycle of a Job 147
- Parallel Preferences 152
- Parallel Preferences 153
- Clusters and Cluster Profiles 154
- Job Monitor 169
- Job Monitor 171
- Programming Tips 172
- Programming Tips 173
- Using the pause Function 175
- Interrupting a Job 175
- Speeding Up a Job 175
- Control Random Number Streams 177
- Client and GPU 179
- Worker CPU and Worker GPU 181
- Profiling Parallel Code 182
- Viewing Parallel Profile Data 183
- Profiling Parallel Code 185
- Benchmarking Performance 191
- Troubleshooting and Debugging 192
- Caused by: 195
- Start Parallel Pool 197
- Compare Parallel mapreduce 197
- See Also 199
- Cluster Preparation 201
- Output Format and Order 201
- Calculate Mean Delay 201
- Related Examples 203
- More About 203
- 7 Program Independent Jobs 212
- MJS Cluster 217
- Properties 217
- Share Code with the Workers 224
- Share Code with the Workers 227
- Overview 229
- Client node 231
- MATLAB client 231
- Scheduler 231
- MATLAB Worker Decode Function 235
- Program Communicating Jobs 249
- 8 Program Communicating Jobs 250
- Code in the Client 251
- 9 GPU Computing 260
- Establish Arrays on a GPU 261
- Establish Arrays on a GPU 265
- 100 100 265
- Supported MATLAB Code 273
- Run CUDA or PTX Code on GPU 278
- Create a CUDAKernel Object 279
- Run CUDA or PTX Code on GPU 281
- Compile a GPU MEX-File 291
- Comparison to a CUDA Kernel 291
- Constructor 302
- Description 302
- codistributed 303
- Properties 304
- Composite 306
- CUDAKernel 307
- distributed 311
- GPUDevice 314
- Constructors 319
- Container Hierarchy 319
- parallel.Cluster 321
- HPC Server 322
- PBS Pro and TORQUE 322
- MJS Jobs 332
- CJS Jobs 332
- RemoteClusterAccess 341
- Examples 344
- Input Arguments 346
- arrayfun 349
- Arguments 352
- Create gpuArray False Matrix 430
- Create gpuArray Inf Matrix 484
- Output Arguments 513
- mpiprofile 519
- C Syntax 524
- Create gpuArray NaN Matrix 549
- Create gpuArray Rand Matrix 605
- Create gpuArray True Matrix 641
- Glossary 653
- Glossary-5 655
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