The routine may be called by the names g05ndf or nagf_rand_sample.
g05ndf selects elements from a population vector ipop of length and places them in a sample vector isampl. Their order in ipop will be preserved in isampl. Each of the possible combinations of elements of isampl may be regarded as being equally probable.
For moderate or large values of it is theoretically impossible that all combinations of size may occur, unless is near or near . This is because exceeds the cycle length of any of the base generators. For practical purposes this is irrelevant, as the time taken to generate all possible combinations is many millenia.
One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05ndf.
Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley
1: – Integer arrayInput
On entry: the population to be sampled.
2: – IntegerInput
On entry: the number of elements in the population to be sampled.
3: – Integer arrayOutput
On exit: the selected sample.
4: – IntegerInput
On entry: the sample size.
5: – Integer arrayCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
6: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, .
On entry, and .
On entry, state vector has been corrupted or not initialized.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
8Parallelism and Performance
g05ndf 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 routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The time taken by g05ndf is of order .
In order to sample other kinds of vectors, or matrices of higher dimension, the following technique may be used:
(a)set , for ;
(b)use g05ndf to take a sample from ipop and put it into isampl;
(c)use the contents of isampl as a set of indices to access the relevant vector or matrix.
In order to divide a population into several groups, g05ncf is more efficient.
In the example program random samples of size are selected from a vector containing the first eight positive integers in ascending order. The samples are generated and printed for each sample size by a call to g05ndf after initialization by g05kff.