NAG CL Interface
f01efc (real_​symm_​matrix_​fun)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{order}$ – Nag_OrderType Input

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 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.

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

2: $\mathbf{uplo}$ – Nag_UploType Input

On entry: if $\mathbf{uplo}=\mathrm{Nag\_Upper}$, the upper triangle of the matrix $A$ is stored.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, the lower triangle of the matrix $A$ is stored.

Constraint: $\mathbf{uplo}=\mathrm{Nag\_Upper}$ or $\mathrm{Nag\_Lower}$.

3: $\mathbf{n}$ – Integer Input

On entry: $n$, the order of the matrix $A$.

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

4: $\mathbf{a}\left[\mathit{dim}\right]$ – double Input/Output

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

On entry: the $n$ by $n$ symmetric matrix $A$.

If $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(j-1\right)\times \mathbf{pda}+i-1\right]$.

If $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $A_{ij}$ is stored in $\mathbf{a}\left[\left(i-1\right)\times \mathbf{pda}+j-1\right]$.

If $\mathbf{uplo}=\mathrm{Nag\_Upper}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.

If $\mathbf{uplo}=\mathrm{Nag\_Lower}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: if $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_NOERROR, the upper or lower triangular part of the $n$ by $n$ matrix function, $f\left(A\right)$.

5: $\mathbf{pda}$ – Integer Input

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

Constraint: $\mathbf{pda}\ge \max \left(1,\mathbf{n}\right)$.

6: $\mathbf{f}$ – function, supplied by the user External Function

The function f evaluates $f\left(z_i\right)$ at a number of points $z_i$.

The specification of f is:

void  f (Integer *flag, Integer n, const double x[], double fx[], Nag_Comm *comm)

1: $\mathbf{flag}$ – Integer * Input/Output

On entry: flag will be zero.

On exit: flag should either be unchanged from its entry value of zero, or may be set nonzero to indicate that there is a problem in evaluating the function $f\left(x\right)$; for instance $f\left(x\right)$ may not be defined, or may be complex. If flag is returned as nonzero then f01efc will terminate the computation, with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

2: $\mathbf{n}$ – Integer Input

On entry: $n$, the number of function values required.

3: $\mathbf{x}\left[\mathbf{n}\right]$ – const double Input

On entry: the $n$ points $x_1,x_2,\dots ,x_n$ at which the function $f$ is to be evaluated.

4: $\mathbf{fx}\left[\mathbf{n}\right]$ – double Output

On exit: the $n$ function values. $\mathbf{fx}\left[\mathit{i}-1\right]$ should return the value $f\left(x_{\mathit{i}}\right)$, for $\mathit{i}=1,2,\dots ,n$.

5: $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to f.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void *. Before calling f01efc you may allocate memory and initialize these pointers with various quantities for use by f when called from f01efc (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by f01efc. If your code inadvertently does return any NaNs or infinities, f01efc is likely to produce unexpected results.

7: $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.1.1 in the Introduction to the NAG Library CL Interface).

8: $\mathbf{flag}$ – Integer * Output

On exit: $\mathbf{flag}=0$, unless you have set flag nonzero inside f, in which case flag will be the value you set and fail will be set to $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

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

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

The value of fail gives the number of off-diagonal elements of an intermediate tridiagonal form that did not converge to zero (see f08fac).

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

NE_BAD_PARAM

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

NE_CONVERGENCE

The computation of the spectral factorization failed to converge.

NE_INT

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

NE_INT_2

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

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 7.5 in the Introduction to the NAG Library CL Interface for further information.

An internal error occurred when computing the spectral factorization. Please contact NAG.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

NE_USER_STOP

Termination requested in f.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results