NAG Library Function Document

nag_nearest_correlation_shrinking (g02anc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{g}\left[\mathbf{pdg}\times \mathbf{n}\right]$ – doubleInput/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:    $\mathbf{pdg}$ – IntegerInput

On entry: the stride separating column elements of the matrix $G$ in the array g.

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

3:    $\mathbf{n}$ – IntegerInput

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

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

4:    $\mathbf{k}$ – IntegerInput

On entry: $k$, the order of the leading principal submatrix $A$.

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

5:    $\mathbf{errtol}$ – doubleInput

On entry: the termination tolerance for the iteration.

If $\mathbf{errtol}\le 0$, $\sqrt{\mathit{machine precision}}$ is used. See Section 7 for further details.

6:    $\mathbf{eigtol}$ – doubleInput

On entry: the tolerance used in determining the definiteness of $A$.

If ${\lambda }_{\min }\left(A\right)>\mathbf{n}\times {\lambda }_{\max }\left(A\right)\times \mathbf{eigtol}$, where ${\lambda }_{\min }\left(A\right)$ and ${\lambda }_{\max }\left(A\right)$ denote the minimum and maximum eigenvalues of $A$ respectively, $A$ is positive definite.

If $\mathbf{eigtol}\le 0$, machine precision is used.

7:    $\mathbf{x}\left[\mathbf{pdx}\times \mathbf{n}\right]$ – doubleOutput

On exit: contains the matrix $X$.

8:    $\mathbf{pdx}$ – IntegerInput

On entry: the stride separating column elements of the matrix $X$ in the array x.

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

9:    $\mathbf{alpha}$ – double *Output

On exit: $\alpha$.

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

On exit: the number of iterations taken.

11:  $\mathbf{eigmin}$ – double *Output

On exit: the smallest eigenvalue of the leading principal submatrix $A$.

12:  $\mathbf{norm}$ – double *Output

On exit: the value of ${‖G-X‖}_F$ after the final iteration.

13:  $\mathbf{fail}$ – 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_EIGENPROBLEM

Failure to solve intermediate eigenproblem. This should not occur. Please contact NAG.

NE_INT

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

NE_INT_2

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

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_MAT_NOT_POS_DEF

The $k$ by $k$ principal leading submatrix of the initial matrix $G$ is not positive definite.

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.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g02ance.c)

10.2

Program Data

Program Data (g02ance.d)

10.3

Program Results

Program Results (g02ance.r)