NAG Library Routine Document
G05NDF selects a pseudorandom sample without replacement from an integer vector.
||IPOP(N), N, ISAMPL(M), M, STATE(*), IFAIL
elements from a population vector IPOP
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 1 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: IPOP(N) – INTEGER arrayInput
On entry: the population to be sampled.
- 2: N – INTEGERInput
On entry: the number of elements in the population vector to be sampled.
- 3: ISAMPL(M) – INTEGER arrayOutput
On exit: the selected sample.
- 4: M – INTEGERInput
On entry: the sample size.
- 5: STATE() – INTEGER arrayCommunication Array
the actual argument supplied must be the array STATE
supplied to the initialization routines G05KFF
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: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, 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,||STATE vector was not initialized or has been corrupted.|
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:
||set , for ;
||use G05NDF to take a sample from IPOP and put it into ISAMPL;
||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
9.1 Program Text
Program Text (g05ndfe.f90)
9.2 Program Data
Program Data (g05ndfe.d)
9.3 Program Results
Program Results (g05ndfe.r)