NAG CL Interface
g02aac (corrmat_​nearest)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or $\mathrm{Nag\_ColMajor}$.

2: $\mathbf{g}\left[\mathit{dim}\right]$ – double Input/Output

Note: the dimension, dim, of the array g must be at least $\mathbf{pdg}\times \mathbf{n}$.

On entry: $G$, the initial matrix.

On exit: a symmetric matrix $\frac{1}{2}\left(G+G^{\mathrm{T}}\right)$ with the diagonal set to $I$.

3: $\mathbf{pdg}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) of the matrix $G$ in the array g.

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

4: $\mathbf{n}$ – Integer Input

On entry: the size of the matrix $G$.

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

5: $\mathbf{errtol}$ – double Input

On entry: the termination tolerance for the Newton iteration. If $\mathbf{errtol}\le 0.0$, $\mathbf{n}\times \sqrt{\mathit{machine precision}}$ is used.

6: $\mathbf{maxits}$ – Integer Input

On entry: maxits specifies the maximum number of iterations used for the iterative scheme used to solve the linear algebraic equations at each Newton step.

If $\mathbf{maxits}\le 0$, $100$ is used.

7: $\mathbf{maxit}$ – Integer Input

On entry: specifies the maximum number of Newton iterations.

If $\mathbf{maxit}\le 0$, $200$ is used.

8: $\mathbf{x}\left[\mathit{dim}\right]$ – double Output

Note: the dimension, dim, of the array x must be at least $\mathbf{pdx}\times \mathbf{n}$.

On exit: contains the nearest correlation matrix.

9: $\mathbf{pdx}$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) of the matrix $X$ in the array x.

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

10: $\mathbf{iter}$ – Integer * Output

On exit: the number of Newton steps taken.

11: $\mathbf{feval}$ – Integer * Output

On exit: the number of function evaluations of the dual problem.

12: $\mathbf{nrmgrd}$ – double * Output

On exit: the norm of the gradient of the last Newton step.

13: $\mathbf{fail}$ – 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_BAD_PARAM

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

NE_CONVERGENCE

Machine precision is limiting convergence.
The array returned in x may still be of interest.

Newton iteration fails to converge in $〈\mathit{\text{value}}〉$ iterations.

NE_EIGENPROBLEM

An intermediate eigenproblem could not be solved. This should not occur. Please contact NAG with details of your call.

NE_INT

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

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

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

NE_INT_2

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

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

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 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.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results