g01fb
is the AD Library version of the primal routine
g01fbf.
Based (in the C++ interface) on overload resolution,
g01fb can be used for primal, tangent and adjoint
evaluation. It supports tangents and adjoints of first order.
Corresponding to the overloaded C++ function, the Fortran interface provides five routines with names reflecting the type used for active real arguments. The actual subroutine and type names are formed by replacing AD and ADTYPE in the above as follows:
The function is overloaded on ADTYPE which represents the type of active arguments. ADTYPE may be any of the following types: double, dco::ga1s<double>::type, dco::gt1s<double>::type
Note: this function can be used with AD tools other than dco/c++. For details, please contact NAG.
3Description
g01fb
is the AD Library version of the primal routine
g01fbf.
g01fbf returns the deviate associated with the given tail probability of Student's $t$-distribution with real degrees of freedom.
For further information see Section 3 in the documentation for g01fbf.
4References
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
Hill G W (1970) Student's $t$-distribution Comm. ACM13(10) 617–619
5Arguments
In addition to the arguments present in the interface of the primal routine,
g01fb includes some arguments specific to AD.
A brief summary of the AD specific arguments is given below. For the remainder, links are provided to the corresponding argument from the primal routine.
A tooltip popup for all arguments can be found by hovering over the argument name in Section 2 and in this section.
Note that the primal routine
is a function whereas g01fb_a1w_f,
is a subroutine, where the function value is returned in the additional output parameter, x.
g01fb preserves all error codes from g01fbf and in addition can return:
${\mathbf{ifail}}=-89$
An unexpected AD error has been triggered by this routine. Please
contact NAG.
See Section 4.8.2 in the NAG AD Library Introduction for further information.
${\mathbf{ifail}}=-199$
The routine was called using a mode that has not yet been implemented.
${\mathbf{ifail}}=-443$
On entry: ad_handle is nullptr.
This check is only made if the overloaded C++ interface is used with arguments not of type double.
${\mathbf{ifail}}=-444$
A C++ exception was thrown.
The error message will show the details of the C++ exception text.
${\mathbf{ifail}}=-899$
Dynamic memory allocation failed for AD.
See Section 4.8.1 in the NAG AD Library Introduction for further information.
7Accuracy
Not applicable.
8Parallelism and Performance
g01fb
is not threaded in any implementation.
9Further Comments
None.
10Example
The following examples are variants of the example for
g01fbf,
modified to demonstrate calling the NAG AD Library.
Description of the primal example.
This example reads the probability, the tail that probability represents and the degrees of freedom for a number of Student's $t$-distributions and computes the corresponding deviates.