NAG Library Routine Document

G02ABF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{G}\left(\mathbf{LDG},\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayInput/Output

On entry: $G$, the initial matrix.

On exit: $G$ is overwritten.

2:     $\mathrm{LDG}$ – INTEGERInput

On entry: the first dimension of the array G as declared in the (sub)program from which G02ABF is called.

Constraint: $\mathbf{LDG}\ge \mathbf{N}$.

3:     $\mathrm{N}$ – INTEGERInput

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

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

4:     $\mathrm{OPT}$ – CHARACTER(1)Input

On entry: indicates the problem to be solved.

$\mathbf{OPT}=\text{'A'}$

The lower bound problem is solved.

$\mathbf{OPT}=\text{'W'}$

The weighted norm problem is solved.

$\mathbf{OPT}=\text{'B'}$

Both problems are solved.

Constraint: $\mathbf{OPT}=\text{'A'}$, $\text{'W'}$ or $\text{'B'}$.

5:     $\mathrm{ALPHA}$ – REAL (KIND=nag_wp)Input

On entry: the value of $\alpha$.

If $\mathbf{OPT}=\text{'W'}$, ALPHA need not be set.

Constraint: $0.0<\mathbf{ALPHA}<1.0$.

6:     $\mathrm{W}\left(\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayInput/Output

On entry: the square roots of the diagonal elements of $W$, that is the diagonal of $W^{\frac{1}{2}}$.

If $\mathbf{OPT}=\text{'A'}$, W is not referenced and need not be set.

On exit: if $\mathbf{OPT}=\text{'W'}$ or $\text{'B'}$, the array is scaled so $0<\mathbf{W}\left(\mathit{i}\right)\le 1$, for $\mathit{i}=1,2,\dots ,n$.

Constraint: $\mathbf{W}\left(\mathit{i}\right)>0.0$, for $\mathit{i}=1,2,\dots ,n$.

7:     $\mathrm{ERRTOL}$ – REAL (KIND=nag_wp)Input

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

8:     $\mathrm{MAXITS}$ – INTEGERInput

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

If $\mathbf{MAXITS}\le 0$, $2\times \mathbf{N}$ is used.

9:     $\mathrm{MAXIT}$ – INTEGERInput

On entry: specifies the maximum number of Newton iterations.

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

10:   $\mathrm{X}\left(\mathbf{LDX},\mathbf{N}\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: contains the nearest correlation matrix.

11:   $\mathrm{LDX}$ – INTEGERInput

On entry: the first dimension of the array X as declared in the (sub)program from which G02ABF is called.

Constraint: $\mathbf{LDX}\ge \mathbf{N}$.

12:   $\mathrm{ITER}$ – INTEGEROutput

On exit: the number of Newton steps taken.

13:   $\mathrm{FEVAL}$ – INTEGEROutput

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

14:   $\mathrm{NRMGRD}$ – REAL (KIND=nag_wp)Output

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

15:   $\mathrm{IFAIL}$ – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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, all elements of W were not positive.

On entry, $\mathbf{ALPHA}=〈\mathit{\text{value}}〉$.
Constraint: $0.0<\mathbf{ALPHA}<1.0$.

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: $\mathbf{N}>0$.

On entry, $\mathbf{OPT}\ne \text{'A'}$, $\text{'W'}$ or $\text{'B'}$.

$\mathbf{IFAIL}=2$

Newton iteration fails to converge in $〈\mathit{\text{value}}〉$ iterations. Increase MAXIT or check the call to the routine.

$\mathbf{IFAIL}=3$

The machine precision is limiting convergence. In this instance the returned value of X may be useful.

$\mathbf{IFAIL}=4$

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 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g02abfe.f90)

10.2  Program Data

Program Data (g02abfe.d)

10.3  Program Results

Program Results (g02abfe.r)