NAG C Library Function Document

nag_matop_complex_herm_matrix_fun (f01ffc)

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 3.3.1.3 in How to Use the NAG Library and its Documentation 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_UploTypeInput

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:    $\mathbf{n}$ – IntegerInput

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

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

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

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

On entry: the $n$ by $n$ Hermitian 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:    $\mathbf{pda}$ – IntegerInput

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 userExternal 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 nag_matop_complex_herm_matrix_fun (f01ffc) will terminate the computation, with $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_USER_STOP.

2:    $\mathbf{n}$ – IntegerInput

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

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

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

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

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 nag_matop_complex_herm_matrix_fun (f01ffc) you may allocate memory and initialize these pointers with various quantities for use by f when called from nag_matop_complex_herm_matrix_fun (f01ffc) (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_matop_complex_herm_matrix_fun (f01ffc). If your code inadvertently does return any NaNs or infinities, nag_matop_complex_herm_matrix_fun (f01ffc) is likely to produce unexpected results.

7:    $\mathbf{comm}$ – Nag_Comm *

The NAG communication argument (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

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 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

If $\mathbf{fail}\mathbf{.}\mathbf{code}=i$, the algorithm to compute the spectral factorization failed to converge; $i$ off-diagonal elements of an intermediate tridiagonal form did not converge to zero (see nag_zheev (f08fnc)).

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_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 2.7.6 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_USER_STOP

flag was set to a nonzero value in f.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f01ffce.c)

10.2

Program Data

Program Data (f01ffce.d)

10.3

Program Results

Program Results (f01ffce.r)