g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_uniform (g05sqc)

## 1  Purpose

nag_rand_uniform (g05sqc) generates a vector of pseudorandom numbers uniformly distributed over the interval $\left[a,b\right]$.

## 2  Specification

 #include #include
 void nag_rand_uniform (Integer n, double a, double b, Integer state[], double x[], NagError *fail)

## 3  Description

If $a=0$ and $b=1$, nag_rand_uniform (g05sqc) returns the next $n$ values ${y}_{i}$ from a uniform $\left(0,1\right]$ generator (see nag_rand_basic (g05sac) for details).
For other values of $a$ and $b$, nag_rand_uniform (g05sqc) applies the transformation
 $xi=a+b-ayi.$
The function ensures that the values ${x}_{i}$ lie in the closed interval $\left[a,b\right]$.
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_uniform (g05sqc).

## 4  References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

## 5  Arguments

1:     nIntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
3:     bdoubleInput
On entry: the end points $a$ and $b$ of the uniform distribution.
Constraint: ${\mathbf{a}}\le {\mathbf{b}}$.
4:     state[$\mathit{dim}$]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
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:     x[n]doubleOutput
On exit: the $n$ pseudorandom numbers from the specified uniform distribution.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_REAL_2
On entry, ${\mathbf{a}}=〈\mathit{\text{value}}〉$ and ${\mathbf{b}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{b}}\ge {\mathbf{a}}$.

## 7  Accuracy

Not applicable.

Although ${y}_{i}$ takes a value from the half closed interval $\left(0,1\right]$ and ${x}_{i}=a+\left(b-a\right){y}_{i}$, ${x}_{i}$ is documented as taking values from the closed interval $\left[a,b\right]$. This is because for some values of $a$ and $b$, nag_rand_uniform (g05sqc) may return a value of $a$ due to numerical rounding.

## 9  Example

This example prints five pseudorandom numbers from a uniform distribution between $-1.0$ and $1.0$, generated by a single call to nag_rand_uniform (g05sqc), after initialization by nag_rand_init_repeatable (g05kfc).

### 9.1  Program Text

Program Text (g05sqce.c)

None.

### 9.3  Program Results

Program Results (g05sqce.r)