NAG FL Interface
g02aaf (corrmat_​nearest)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{g}\left(\mathbf{ldg},\mathbf{n}\right)$ – Real (Kind=nag_wp) array Input/Output

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 $I$.

2: $\mathbf{ldg}$ – Integer Input

On entry: the first dimension of the array g as declared in the (sub)program from which g02aaf is called.

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

3: $\mathbf{n}$ – Integer Input

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

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

4: $\mathbf{errtol}$ – Real (Kind=nag_wp) 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.

5: $\mathbf{maxits}$ – 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.

6: $\mathbf{maxit}$ – Integer Input

On entry: specifies the maximum number of Newton iterations.

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

7: $\mathbf{x}\left(\mathbf{ldx},\mathbf{n}\right)$ – Real (Kind=nag_wp) array Output

On exit: contains the nearest correlation matrix.

8: $\mathbf{ldx}$ – Integer Input

On entry: the first dimension of the array x as declared in the (sub)program from which g02aaf is called.

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

9: $\mathbf{iter}$ – Integer Output

On exit: the number of Newton steps taken.

10: $\mathbf{feval}$ – Integer Output

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

11: $\mathbf{nrmgrd}$ – Real (Kind=nag_wp) Output

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

12: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

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

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

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

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL 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