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NAG[g05ejc] NAG[nag_ran_sample_vec] - Pseudo-random sample without replacement from an integer vector
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Calling Sequence
g05ejc(ia, iz, 'n'=n, 'm'=m, 'fail'=fail)
nag_ran_sample_vec(. . .)
Parameters
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ia - Vector(1..n, datatype=integer[kernelopts('wordsize')/8]);
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On entry: the population to be sampled.
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iz - Vector(1..m, datatype=integer[kernelopts('wordsize')/8]);
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On exit: the selected sample.
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'n'=n - integer; (optional)
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Default value: the first dimension of the array ia.
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On entry: the number of elements in the vector to be sampled.
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Constraint:  . .
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'm'=m - integer; (optional)
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Default value: the first dimension of the array iz.
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On entry: the sample size.
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Constraint:  . .
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_ran_sample_vec (g05ejc) selects a pseudo-random sample without replacement from an integer vector.
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Description
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nag_ran_sample_vec (g05ejc) performs a single pseudo-random selection of  elements from vector ia of length  and then places them in vector iz. Their order in ia will be preserved in iz. Each of the ![[[n],[m]]](/support/helpjp/helpview.aspx?si=9916/file08479/math106.png) possible combinations of elements of ia may be regarded as being equiprobable.
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Error Indicators and Warnings
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"NE_2_INT_ARG_GT"
On entry,  while  . These arguments must satisfy  .
"NE_INT_ARG_LT"
On entry, n must not be less than 1:  .
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Further Comments
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If  is greater than 60 it is theoretically impossible to generate all ![[[n],[m]]](/support/helpjp/helpview.aspx?si=9916/file08479/math146.png) combinations unless  is near 1 or near  . This is because the number of possible combinations exceeds the cycle length of the internal random number generator.
The time taken by nag_ran_sample_vec (g05ejc) is of order  .
In order to sample other kinds of objects (i.e., vectors, or matrices of higher dimensions), the following technique may be used:
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b. Use nag_ran_sample_vec (g05ejc) to take a sample from ia and put it into iz
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c. Use the contents of iz as a set of indices to access the relevant object.
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In order to divide a population into several groups, g05ehc (nag_ran_permut_vec) is more efficient.
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Examples
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n := 8:
m := 1:
ia := Vector([0, 1, 2, 3, 4, 5, 6, 7], datatype=integer[kernelopts('wordsize')/8]):
iz := Vector(1, datatype=integer[kernelopts('wordsize')/8]):
NAG:-g05cbc(0):
NAG:-g05ejc(ia, iz, 'n' = n, 'm' = m):
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