NAG Library Function Document

nag_nearest_correlation (g02aac)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     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:     g[$\mathit{dim}$] – doubleInput/Output

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

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

3:     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:     n – IntegerInput

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

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

5:     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.

6:     maxits – IntegerInput

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 $\mathbf{maxits}\le 0$, $2\times \mathbf{n}$ is used.

7:     maxit – IntegerInput

On entry: specifies the maximum number of Newton iterations.

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

8:     x[$\mathit{dim}$] – doubleOutput

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

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.

9:     pdx – IntegerInput

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

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

10:   iter – Integer *Output

On exit: the number of Newton steps taken.

11:   feval – Integer *Output

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

12:   nrmgrd – double *Output

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

13:   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.

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

Failure to solve intermediate eigenproblem.

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.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g02aace.c)

10.2  Program Data

10.3  Program Results

Program Results (g02aace.r)