# NAG C Library Function Document

## 1Purpose

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

## 2Specification

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

## 3Description

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).

## 4References

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

## 5Arguments

1:    $\mathbf{n}$IntegerInput
On entry: $n$, the number of pseudorandom numbers to be generated.
Constraint: ${\mathbf{n}}\ge 0$.
2:    $\mathbf{a}$doubleInput
3:    $\mathbf{b}$doubleInput
On entry: the end points $a$ and $b$ of the uniform distribution.
Constraint: ${\mathbf{a}}\le {\mathbf{b}}$.
4:    $\mathbf{state}\left[\mathit{dim}\right]$IntegerCommunication Array
Note: the dimension, $\mathit{dim}$, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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:    $\mathbf{x}\left[{\mathbf{n}}\right]$doubleOutput
On exit: the $n$ pseudorandom numbers from the specified uniform distribution.
6:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_REAL_2
On entry, ${\mathbf{a}}=〈\mathit{\text{value}}〉$ and ${\mathbf{b}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{b}}\ge {\mathbf{a}}$.

Not applicable.

## 8Parallelism and Performance

nag_rand_uniform (g05sqc) 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 function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

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.

## 10Example

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).

### 10.1Program Text

Program Text (g05sqce.c)

None.

### 10.3Program Results

Program Results (g05sqce.r)