| Distributed
systems offer fantastic gains when it comes to solving large-scale
problems. By sharing the computation load, you can solve problems too
large for a single computer to handle, or solve problems in a fraction
of the time it would take with a single computer. The Grid Computing Toolbox
has been streamlined for Maple 15, making it easy to create and test
parallel distributed programs. New features include a simplified local
grid setup, flexible argument passing, and an extended API. |
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Compatible with Maple 15 Local Grid API
Maple 15 includes the ability to easily set up
multi-process computations on a single computer. The Maple Grid
Computing Toolbox extends this power to multi-machine or cluster
parallelism. The two versions are fully compatible, so that an
algorithm can be created and fully tested using the local implementation
inside Maple, and then deployed to the full cluster using the toolbox,
without changes to the algorithm.
Flexible Argument Passing
The Launch command can now process multi-argument procedures and
automatically pass those parameters to each of the nodes in the grid.
This avoids the need to work with global data referenced by the
'exports' option.
Getting data to each node can be done in two ways using the Launch command.
• Arguments to the called procedure can be passed as arguments to the Launch command.
• Other data can be specified using the 'imports' option to Launch |
Also, once the computation has been started, Send and
Receive can be used for passing chunks of data to each individual node.
Above, the range, 1..10, is passed as an argument to the
execution of randomNumbers on each node. The custom function, f, is not
defined so it returns unevaluated. You can set a value for f, and use
the 'imports' option to pass that value to all of the nodes.
Extended API
A Barrier command has been added to the Grid
package. This is useful as a checkpoint to ensure all grid nodes stop
and sync up before proceeding. A key spot to use Barrier is at the end
of a program that does not use any message passing. Using it forces
node 0 to wait until all working nodes complete their activity before
returning.
Example 1: Monte Carlo Integration
Random values of x can be used to compute an approximation
of a definite integral according to the following formula.
This procedure efficiently calculates a one-variable
integral using the above formula where r is a random input to f.
A sample run using 1000 data points shows how this works:
This can be computed exactly in Maple to show the above
approximation is rough, but close enough for some applications.
A parallel implementation adds the following code to split
the problem over all available nodes and send the partial results back
to node 0. Note that here the head node, 0, is used to accumulate the
results, and does not actually do any computations.
Integrate over the range, lim, using N samples. Use as many nodes as are available in your cluster.
Execution times are summarized as follows. Computations
were executed on a 3-blade cluster with 6 quad-core AMD Opteron
2378/2.4GHz processors and 8GB of memory per pair of CPUs, running
Windows HPC Server 2008.
The compute time in Maple without using MapleGrid is the
first number in the table -- ~6 minutes. The rest of the times were
using MapleGrid with a varying number of cores. The graph shows that
adding cores scales linearly. When 23 cores are dedicated to the same
example, it takes only 15.3 seconds to complete.
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Datasheet
