NAG Library Function Document

nag_nearest_correlation_bounded (g02abc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{order}$ – Nag_OrderTypeInput

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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

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

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

Note: the $\left(i,j\right)$th element of the matrix $G$ is stored in

• $\mathbf{g}\left[\left(j-1\right)\times \mathbf{pdg}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{g}\left[\left(i-1\right)\times \mathbf{pdg}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On entry: $G$, the initial matrix.

On exit: $G$ is overwritten.

3:    $\mathbf{pdg}$ – IntegerInput

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

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

4:    $\mathbf{n}$ – IntegerInput

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

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

5:    $\mathbf{opt}$ – Nag_NearCorr_ProbTypeInput

On entry: indicates the problem to be solved.

$\mathbf{opt}=\mathrm{Nag\_LowerBound}$

The lower bound problem is solved.

$\mathbf{opt}=\mathrm{Nag\_WeightedNorm}$

The weighted norm problem is solved.

$\mathbf{opt}=\mathrm{Nag\_Both}$

Both problems are solved.

Constraint: $\mathbf{opt}=\mathrm{Nag\_LowerBound}$, $\mathrm{Nag\_WeightedNorm}$ or $\mathrm{Nag\_Both}$.

6:    $\mathbf{alpha}$ – doubleInput

On entry: the value of $\alpha$.

If $\mathbf{opt}=\mathrm{Nag\_WeightedNorm}$, alpha need not be set.

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

7:    $\mathbf{w}\left[\mathbf{n}\right]$ – doubleInput/Output

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

If $\mathbf{opt}=\mathrm{Nag\_LowerBound}$, w is not referenced and may be NULL.

On exit: if $\mathbf{opt}=\mathrm{Nag\_WeightedNorm}$ or $\mathrm{Nag\_Both}$, the array is scaled so $0<\mathbf{w}\left[\mathit{i}-1\right]\le 1$, for $\mathit{i}=1,2,\dots ,n$.

Constraint: $\mathbf{w}\left[\mathit{i}-1\right]>0.0$, for $\mathit{i}=1,2,\dots ,n$.

8:    $\mathbf{errtol}$ – doubleInput

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.

9:    $\mathbf{maxits}$ – 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.

10:  $\mathbf{maxit}$ – IntegerInput

On entry: specifies the maximum number of Newton iterations.

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

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

Note: the $\left(i,j\right)$th element of the matrix $X$ is stored in

• $\mathbf{x}\left[\left(j-1\right)\times \mathbf{pdx}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{x}\left[\left(i-1\right)\times \mathbf{pdx}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

On exit: contains the nearest correlation matrix.

12:  $\mathbf{pdx}$ – IntegerInput

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

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

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

On exit: the number of Newton steps taken.

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

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

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

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

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

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.

NE_BAD_PARAM

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

NE_CONVERGENCE

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

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

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: $\mathbf{n}>0$.

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

NE_REAL

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

NE_WEIGHTS_NOT_POSITIVE

On entry, all elements of w were not positive.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g02abce.c)

10.2  Program Data

Program Data (g02abce.d)

10.3  Program Results

Program Results (g02abce.r)