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computation proceeds Early in the computation, all the rows and columns of the matrix have numerous elements to work with and decompositions based on assigning full rows or columns to UEs are effective Later in the computation, however, rows or columns become sparse, the work per row becomes uneven, and the computational load becomes poorly balanced between UEs The solution is to decompose the problem into many more chunks than there are UEs and to scatter them among the UEs with a cyclic or block cyclic distribution (Cyclic and block cyclic distributions are discussed in the Distributed Array pattern) Then, as chunks become sparse, there are (with high probability) other nonsparse chunks for any given UE to work on, and the load becomes well balanced A rule of thumb is that one needs around ten times as many tasks as UEs for this approach to work well It is also possible to use dynamic load balancing algorithms to periodically redistribute the chunks among the UEs to improve the load balance These incur overhead that must be traded off against the improvement likely to occur from the improved load balance and increased implementation costs In addition, the resulting program is more complex than those that use one of the static methods Generally, one should consider the (static) cyclic allocation strategy first

In addition to queries that match all values in a range, there is a function that lets you match a set of discreet valuesThe IN() function has the same capabilities as a long set of equals operators Instead of writing this:

public class UserAccount implements javaioSerializable { protected String username; protected transient String password; public UserAccount() { } }

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The overall program structure for applications of this pattern will normally use either the Loop Parallelism pattern or the SPMD pattern, with the choice determined largely by the target platform These patterns are described in the Supporting Structures design space Examples We include two examples with this pattern: a mesh computation and matrix multiplication The challenges in working with the Geometric Decomposition pattern are best appreciated in the low level details of the resulting programs Therefore, even though the techniques used in these programs are not fully developed until much later in the book, we provide full programs in this section rather than high level descriptions of the solutions

Other uses for the transient keyword are for fields that are being continuously updated by some means, such as a timer, and hence do not make sense to serialize, or for stopping the serialization of fields that store GUI displays of data The GUI display could be dynamically created, and hence there is no need to serialize it

WHERE id = '1' OR id = '2' OR id = '3' OR id = '4' OR id = '5' OR id = '6'

This problem is described in the Context section of this pattern Fig 411 presents a simple sequential version of a program (some details omitted) that solves the 1D heat diffusion problem The program associated with this problem is straightforward, although one detail might need further explanation: After computing new values in ukp1 at each step, conceptually what we want to do is copy them to uk for the next iteration We avoid a time consuming actual copy by making uk and ukp1 pointers to their respective arrays and simply swapping them at the end of each step This causes uk to point to the newly computed values and ukp1 to point to the area to use for computing new values in the next iteration

The main point of serialization is to write an object out to a stream and to read it back This is accomplished by using the javaioObjectOutputStream and javaioObjectInputStream classes, which can write serializable objects out to an output stream and read them back from an input stream 4541 ObjectInputStream Class The ObjectInputStream class is used to read a serialized object from a byte stream, to allow an object to be reconstituted back to its original form, providing the object's class can be loaded by

The IN() function lets you abbreviate it like this:

the JVM's class loader The ObjectInputStream class implements the ObjectInput interface, which extends the DataInput interface This means that the ObjectInputStream class provides many methods with the same signature as DataInputStream, in addition to extra methods responsible for reading objects Constructors

#define LEFTVAL 10 #define RIGHTVAL 100 #define NSTEPS 10000 void initialize(double uk[], double ukp1[]) { uk[0] = LEFTVAL; uk[NX-1] = RIGHTVAL; for (int i = 1; i < NX-1; ++i) uk[i] = 00; for (int i = 0; i < NX; ++i) ukp1[i] = uk[i]; } void printValues(double uk[], int step) { /* NOT SHOWN */ } int main(void) { /* pointers to arrays for two iterations of algorithm */ double *uk = malloc(sizeof(double) * NX); double *ukp1 = malloc(sizeof(double) * NX); double *temp; double dx = 10/NX; double dt = 05*dx*dx; initialize(uk, ukpl); for (int k = 0; k < NSTEPS; ++k) { /* compute new values */ for (int i = 1; i < NX-1; ++i) { ukp1[i]=uk[i]+ (dt/(dx*dx))*(uk[i+1]-2*uk[i]+uk[i-1]); } /* "copy" ukp1 to uk by swapping pointers */ temp = ukp1; ukp1 = uk; uk = temp; printValues(uk, k); } return 0; }

protected ObjectInputStream() throws javaioIOException javalangSecurityException provides a default constructor for ObjectInputStream subclasses Few developers will want to override the ObjectInputStream class and create a nonstandard implementation ObjectInputStream(InputStream input) throws javaioIOException

This program combines a top level sequential control structure (the time step loop) with an array update operation, which can be parallelized using the Geometric Decomposition pattern We show parallel implementations of this program using OpenMP and MPI

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