The routine may be called by the names g05sef or nagf_rand_dist_dirichlet.
The distribution has PDF (probability density function)
where is a vector of dimension , such that for all and .
g05sef generates a draw from a Dirichlet distribution by first drawing independent samples, , i.e., independent draws from a gamma distribution with parameters and one, and then setting .
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 g05sef.
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
1: – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
2: – IntegerInput
On entry: , the number of dimensions of the distribution.
3: – Real (Kind=nag_wp) arrayInput
On entry: the parameter vector for the distribution.
, for .
4: – 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.
5: – Real (Kind=nag_wp) arrayOutput
Note: the second dimension of the array x
must be at least
On exit: the pseudorandom numbers from the specified Dirichlet distribution, with holding the th dimension for the th variate.
6: – IntegerInput
On entry: the first dimension of the array x as declared in the (sub)program from which g05sef is called.
7: – 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, .
On entry, at least one .
On entry, state vector has been corrupted or not initialized.
On entry, and .
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
Background information to multithreading can be found in the Multithreading documentation.
g05sef 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.
This example prints a set of five pseudorandom numbers from a Dirichlet distribution with parameters and , generated by a single call to g05sef, after initialization by g05kff.