The routine may be called by the names g05kff or nagf_rand_init_repeat.
g05kff selects a base generator through the input value of the arguments genid and subid, and then initializes it based on the values given in the array seed.
A given base generator will yield different sequences of random numbers if initialized with different values of seed. Alternatively, the same sequence of random numbers will be generated if the same value of seed is used. It should be noted that there is no guarantee of statistical properties between sequences, only within sequences.
A definition of some of the terms used in this description, along with details of the various base generators can be found in the G05 Chapter Introduction.
L'Ecuyer P and Simard R (2002) TestU01: a software library in ANSI C for empirical testing of random number generators Departement d'Informatique et de Recherche Operationnelle, Universite de Montreal https://www.iro.umontreal.ca/~lecuyer
Maclaren N M (1989) The generation of multiple independent sequences of pseudorandom numbers Appl. Statist.38 351–359
Matsumoto M and Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudorandom number generator ACM Transactions on Modelling and Computer Simulations
Wichmann B A and Hill I D (2006) Generating good pseudo-random numbers Computational Statistics and Data Analysis51 1614–1622
Wikramaratna R S (1989) ACORN - a new method for generating sequences of uniformly distributed pseudo-random numbers Journal of Computational Physics83 16–31
1: – IntegerInput
On entry: must contain the type of base generator to use.
On entry: if , subid indicates which of the sub-generators to use. In this case, the sub-generator is used.
If , subid indicates the values of and to use, where is the order of the generator, and controls the size of the modulus, , with . If , the default values of and are used, otherwise values for and are calculated from the formula, .
If and the range of the generator is set to , otherwise the range is set to ; in this case the sequence is identical to the implementation of MRG32k3a in TestU01 (see L'Ecuyer and Simard (2002)) for identical seeds.
For all other values of genid, subid is not referenced.
3: – Integer arrayInput
On entry: the initial (seed) values for the selected base generator. The number of initial values required varies with each of the base generators.
If , one seed is required.
If , four seeds are required.
If , seeds are required.
If , four seeds are required.
If , seeds are required, where and are defined by subid. For the ACORN generator it is recommended that an odd value is used for .
If , six seeds are required.
If insufficient seeds are provided then the first values supplied in seed are used and the remaining values are randomly generated using the NAG basic generator. In such cases the NAG basic generator is initialized using the value supplied in .
On exit: contains information on the selected base generator and its current state.
6: – IntegerInput/Output
On entry: the dimension of the state array, or a value . If the Mersenne Twister () is being used and the skip ahead routine g05kjforg05kkf will be called subsequently, then you must ensure that .
On exit: if on entry, then the required length of the state array for the chosen base generator, otherwise lstate is unchanged. When (Mersenne Twister) a value of is returned, allowing for the skip ahead routine to be subsequently called. In all other cases the minimum length, as documented in the constraints below, is returned.
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).