NAG C Library Function Document

nag_rand_corr_matrix (g05pyc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the dimension of the correlation matrix to be generated.

Constraint: $\mathbf{n}\ge 1$.

2:    $\mathbf{d}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the $n$ eigenvalues, ${\lambda }_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

Constraints:

• $\mathbf{d}\left[\mathit{i}-1\right]\ge 0.0$, for $\mathit{i}=1,2,\dots ,n$;
• ${\displaystyle \sum _{i=1}^n}\mathbf{d}\left[i-1\right]=n$ to within eps.

3:    $\mathbf{eps}$ – doubleInput

On entry: the maximum acceptable error in the diagonal elements.

Suggested value: $\mathbf{eps}=0.00001$.

Constraint: $\mathbf{eps}\ge \mathbf{n}\times \mathit{machine precision}$ (see Chapter x02).

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:    $\mathbf{c}\left[\mathbf{n}\times \mathbf{pdc}\right]$ – doubleOutput

On exit: a random correlation matrix, $C$, of dimension $n$.

6:    $\mathbf{pdc}$ – IntegerInput

On entry: the stride separating row elements of the matrix $C$ in the array c.

Constraint: $\mathbf{pdc}\ge \mathbf{n}$.

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

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error 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.

NE_BAD_PARAM

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

NE_DIAG_ELEMENTS

The diagonals of the returned matrix are not unity, try increasing the value of eps, or rerun the code using a different seed.

NE_EIGVAL_SUM

On entry, the eigenvalues do not sum to n.

NE_INT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

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

NE_INT_2

On entry, $\mathbf{pdc}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdc}\ge \mathbf{n}$.

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_NEGATIVE_EIGVAL

On entry, an eigenvalue is negative.

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

On entry, $\mathbf{eps}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{eps}\ge \mathbf{n}\times \mathit{machine precision}$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g05pyce.c)

10.2

Program Data

Program Data (g05pyce.d)

10.3

Program Results

Program Results (g05pyce.r)