NAG CL Interface
g01scc (prob_​chisq_​vector)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{ltail}$ – Integer Input

On entry: the length of the array tail.

Constraint: $\mathbf{ltail}>0$.

2: $\mathbf{tail}\left[\mathbf{ltail}\right]$ – const Nag_TailProbability Input

On entry: indicates whether the lower or upper tail probabilities are required. For $j=\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{ltail}$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{ltail},\mathbf{lx},\mathbf{ldf}\right)$:

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_LowerTail}$

The lower tail probability is returned, i.e., $p_i=P\left(X_i\le x_i:{\nu }_i\right)$.

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_UpperTail}$

The upper tail probability is returned, i.e., $p_i=P\left(X_i\ge x_i:{\nu }_i\right)$.

Constraint: $\mathbf{tail}\left[\mathit{j}-1\right]=\mathrm{Nag\_LowerTail}$ or $\mathrm{Nag\_UpperTail}$, for $\mathit{j}=1,2,\dots ,\mathbf{ltail}$.

3: $\mathbf{lx}$ – Integer Input

On entry: the length of the array x.

Constraint: $\mathbf{lx}>0$.

4: $\mathbf{x}\left[\mathbf{lx}\right]$ – const double Input

On entry: $x_i$, the values of the ${\chi }^2$ variates with ${\nu }_i$ degrees of freedom with $x_i=\mathbf{x}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lx}$.

Constraint: $\mathbf{x}\left[\mathit{j}-1\right]\ge 0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{lx}$.

5: $\mathbf{ldf}$ – Integer Input

On entry: the length of the array df.

Constraint: $\mathbf{ldf}>0$.

6: $\mathbf{df}\left[\mathbf{ldf}\right]$ – const double Input

On entry: ${\nu }_i$, the degrees of freedom of the ${\chi }^2$-distribution with ${\nu }_i=\mathbf{df}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{ldf}$.

Constraint: $\mathbf{df}\left[\mathit{j}-1\right]>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{ldf}$.

7: $\mathbf{p}\left[\mathit{dim}\right]$ – double Output

Note: the dimension, dim, of the array p must be at least $\max \left(\mathbf{ltail},\mathbf{ldf},\mathbf{lx}\right)$.

On exit: $p_i$, the probabilities for the ${\chi }^2$ distribution.

8: $\mathbf{ivalid}\left[\mathit{dim}\right]$ – Integer Output

Note: the dimension, dim, of the array ivalid must be at least $\max \left(\mathbf{ltail},\mathbf{ldf},\mathbf{lx}\right)$.

On exit: $\mathbf{ivalid}\left[i-1\right]$ indicates any errors with the input arguments, with

$\mathbf{ivalid}\left[i-1\right]=0$

No error.

$\mathbf{ivalid}\left[i-1\right]=1$

On entry, invalid value supplied in tail when calculating $p_i$.

$\mathbf{ivalid}\left[i-1\right]=2$

On entry, $x_i<0.0$.

$\mathbf{ivalid}\left[i-1\right]=3$

On entry, ${\nu }_i\le 0.0$.

$\mathbf{ivalid}\left[i-1\right]=4$

The solution has failed to converge while calculating the gamma variate. The result returned should represent an approximation to the solution.

9: $\mathbf{fail}$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_ARRAY_SIZE

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldf}>0$.

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ltail}>0$.

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lx}>0$.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

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 7.5 in the Introduction to the NAG Library CL Interface for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NW_IVALID

On entry, at least one value of x, df or tail was invalid, or the solution failed to converge.
Check ivalid for more information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results