g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_return_multi_normal (g05ezc)

## 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 #include
 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[${\mathbf{n}}$]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:     rdouble *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).

None.

## 7  Accuracy

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

The time taken by nag_return_multi_normal (g05ezc) is of the order
 $a + b × n + c × n 2$
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
 $1.0 2.0$
and covariance matrix
 $2.0 1.0 1.0 3.0 ,$
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)

None.

### 9.3  Program Results

Program Results (g05ezce.r)