NAG Library Function Document

nag_return_multi_normal (g05ezc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

+− 9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

1 Purpose

nag_return_multi_normal (g05ezc) generates a pseudorandom multivariate Normal vector taken from a distribution described by a reference vector set up by nag_ref_vec_multi_normal (g05eac).

2 Specification

#include <nag.h>

#include <nagg05.h>

void	nag_return_multi_normal (double z[], double *r)

3 Description

nag_return_multi_normal (g05ezc) is designed for use in conjunction with nag_ref_vec_multi_normal (g05eac). The description of nag_ref_vec_multi_normal (g05eac) should be referred to for a specification of the operation of these two functions.

4 References

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

5 Arguments

1: z[ $n$ ] – doubleOutput: where $n$ is the number of dimensions of the distribution as supplied to nag_ref_vec_multi_normal (g05eac).
On exit: the pseudorandom multivariate Normal vector.
2: r – double *Input: On entry: the reference vector to which memory has been allocated as set up by nag_ref_vec_multi_normal (g05eac). To free this memory the macro NAG_FREE should be added in your program after the final call to nag_return_multi_normal (g05ezc).

6 Error Indicators and Warnings

None.

7 Accuracy

The accuracy is discussed in the document for nag_ref_vec_multi_normal (g05eac).

8 Further Comments

The time taken by nag_return_multi_normal (g05ezc) is of the order

a + b \times n + c \times n^{2}

where

a

and

b

are appreciably (say 10-20 times) larger than

c

9 Example

The example program prints five pseudorandom observations from a bivariate Normal distribution with means vector

[\begin{matrix} 1.0 & 2.0 \end{matrix}]

and covariance matrix

[\begin{matrix} 2.0 & 1.0 & 1.0 & 3.0 \end{matrix}],

generated by nag_ref_vec_multi_normal (g05eac) and nag_return_multi_normal (g05ezc) after initialization by nag_random_init_repeatable (g05cbc).

9.1 Program Text

Program Text (g05ezce.c)

9.2 Program Data

None.

9.3 Program Results

Program Results (g05ezce.r)

nag_return_multi_normal (g05ezc) (PDF version)

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NAG C Library Manual

NAG Library Function Documentnag_return_multi_normal (g05ezc)