The function may be called by the names: g05nfc or nag_rand_resample.
Given a vector , of integer values, g05nfc selects elements with the probability of selecting proportional to a user-supplied weight, . The sampling is done with replacement, so that each value, , may appear more than once in the sample.
The most common usage case for g05nfc is where was obtained using some other sampling method, for example, importance sampling. In such a case, this function is used to perform resampling.
Several methods of calculating , the number of times appears in the sample, are available:
The vector of counts; is drawn from a multinomial distribution with probabilities given by the normalised weights, .
where are the normalised weights, , , for and is defined to be zero.
In other words, is the number of shifted and scaled uniform variates contained in bins defined by the partial sums of normalised weights.
where (i.e. the integer part of ), and the vector of residual counts, is drawn from a multinomial distribution with probabilities given by .
See g05tgc for more information on the multinomial distribution and Douc et al. (2005) for more details on the resampling methods.
If multiple samples are requested () then the chosen resampling method is performed independently for each sample.
One of the initialization functions g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05nfc.
Cappe O, and
Comparison of resampling schemes for particle filtering
Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis
Bolic M, and
Djuric P M
Resampling Methods for Particle Filtering: Classification, implementation, and strategies
IEEE Signal Processing Magazinevol. 32, no. 3
1: – IntegerInput
On entry: a flag indicating the resampling method to use.
Multinomial resampling will be used.
Systematic resampling will be used.
Residual resampling will be used.
, or .
2: – IntegerInput
On entry: , the size of the population.
3: – const doubleInput
On entry: , the weights. These weights need not sum to .
, for ;
at least one (and preferably more than one) weight must be nonzero.
4: – const IntegerInput
Note: the dimension, dim, of the array ipop
must be at least
, when ;
otherwise is not referenced and may be NULL.
On entry: , the vector to be sampled from. If then the is assumed to be the set of values .
Elements of ipop with the same value are not combined, therefore, if and then there is a nonzero probability that the sample will contain both and , irrespective of their values.
If the values to be returned in isampl are counts, i.e., , then ipop is not referenced.
5: – IntegerInput
On entry: , the size of the sample required.
6: – IntegerInput
On entry: the number of times to resample.
7: – IntegerInput
On entry: a flag indicating what is returned in isampl.
The values returned in isampl are taken from the population.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
11: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, ,
On entry, ,
On entry, argument had an illegal value.
On entry, .
On entry, .
On entry, .
On entry, .
Constraint: or .
On entry, .
Constraint: , or .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
On entry, state vector has been corrupted or not initialized.
On entry, and .
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, all the weights are zero.
Constraint: at least one weight must be nonzero.
There was no random component to the sample. Check the sample size and weights are as expected.
Specifically, check that more than one weight is nonzero.
If , also check the combination of m and weights.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
g05nfc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
It should be noted that whilst a given sample is a random selection from , the ordering of the sample within isampl may not be. For example, when the values returned are likely to be in the same order that the values appear in . If it is important that the returned values represent a random sample from rather than a ordered random sample then each sample should be randomly permuted via a subsequent call to g05ncc. The same applies to the order in which multiple samples are returned. One consequence of this is that if you call g05nfc once with , say, and then again (using the same initial values for state), with the first column of ISAMPL may not be the same in both cases since, on the second call, the sample from the first call may be returned in the second column rather than the first.