NAG FL Interface
f01kcf (complex_​gen_​matrix_​cond_​usd)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

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

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

2: $\mathbf{a}\left(\mathbf{lda},*\right)$ – Complex (Kind=nag_wp) array Input/Output

Note: the second dimension of the array a must be at least $\mathbf{n}$.

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

On exit: the $n$ by $n$ matrix, $f\left(A\right)$.

3: $\mathbf{lda}$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f01kcf is called.

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

4: $\mathbf{f}$ – Subroutine, supplied by the user. External Procedure

Given an integer $m$, the subroutine f evaluates $f^{\left(m\right)}\left(z_i\right)$ at a number of points $z_i$.

The specification of f is:

Fortran Interface

Subroutine f ( m, iflag, nz, z, fz, iuser, ruser) Integer, Intent (In) :: m, nz Integer, Intent (Inout) :: iflag, iuser(*) Real (Kind=nag_wp), Intent (Inout) :: ruser(*) Complex (Kind=nag_wp), Intent (In) :: z(nz) Complex (Kind=nag_wp), Intent (Out) :: fz(nz)

C Header Interface

void  f_ (const Integer *m, Integer *iflag, const Integer *nz, const Complex z[], Complex fz[], Integer iuser[], double ruser[])

C++ Header Interface

#include <nag.h> extern "C" { void  f_ (const Integer &m, Integer &iflag, const Integer &nz, const Complex z[], Complex fz[], Integer iuser[], double ruser[]) }

1: $\mathbf{m}$ – Integer Input

On entry: the order, $m$, of the derivative required.

If $\mathbf{m}=0$, $f\left(z_i\right)$ should be returned. For $\mathbf{m}>0$, $f^{\left(m\right)}\left(z_i\right)$ should be returned.

2: $\mathbf{iflag}$ – Integer Input/Output

On entry: iflag will be zero.

On exit: iflag 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 $f\left(z\right)$; for instance $f\left(z\right)$ may not be defined. If iflag is returned as nonzero then f01kcf will terminate the computation, with $\mathbf{ifail}=\mathbf{3}$.

3: $\mathbf{nz}$ – Integer Input

On entry: $n_z$, the number of function or derivative values required.

4: $\mathbf{z}\left(\mathbf{nz}\right)$ – Complex (Kind=nag_wp) array Input

On entry: the $n_z$ points $z_1,z_2,\dots ,z_{n_z}$ at which the function $f$ is to be evaluated.

5: $\mathbf{fz}\left(\mathbf{nz}\right)$ – Complex (Kind=nag_wp) array Output

On exit: the $n_z$ function or derivative values. $\mathbf{fz}\left(\mathit{i}\right)$ should return the value $f^{\left(m\right)}\left(z_{\mathit{i}}\right)$, for $\mathit{i}=1,2,\dots ,n_z$.

6: $\mathbf{iuser}\left(*\right)$ – Integer array User Workspace

7: $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) array User Workspace

f is called with the arguments iuser and ruser as supplied to f01kcf. You should use the arrays iuser and ruser to supply information to f.

f must either be a module subprogram USEd by, or declared as EXTERNAL in, the (sub)program from which f01kcf is called. Arguments denoted as Input must not be changed by this procedure.

Note: f should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by f01kcf. If your code inadvertently does return any NaNs or infinities, f01kcf is likely to produce unexpected results.

5: $\mathbf{iuser}\left(*\right)$ – Integer array User Workspace

6: $\mathbf{ruser}\left(*\right)$ – Real (Kind=nag_wp) array User Workspace

iuser and ruser are not used by f01kcf, but are passed directly to f and may be used to pass information to this routine.

7: $\mathbf{iflag}$ – Integer Output

On exit: $\mathbf{iflag}=0$, unless iflag has been set nonzero inside f, in which case iflag will be the value set and ifail will be set to $\mathbf{ifail}=\mathbf{3}$.

8: $\mathbf{conda}$ – Real (Kind=nag_wp) Output

On exit: an estimate of the absolute condition number of $f$ at $A$.

9: $\mathbf{norma}$ – Real (Kind=nag_wp) Output

On exit: the $1$-norm of $A$.

10: $\mathbf{normfa}$ – Real (Kind=nag_wp) Output

On exit: the $1$-norm of $f\left(A\right)$.

11: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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

$\mathbf{ifail}=1$

An internal error occurred when estimating the norm of the Fréchet derivative of $f$ at $A$. Please contact NAG.

$\mathbf{ifail}=2$

An internal error occurred when evaluating the matrix function $f\left(A\right)$. You can investigate further by calling f01fmf with the matrix $A$ and the function $f$.

$\mathbf{ifail}=3$

Termination requested in f.

$\mathbf{ifail}=-1$

On entry, $\mathbf{n}<0$.

$\mathbf{ifail}=-3$

On entry, argument lda is invalid.
Constraint: $\mathbf{lda}\ge \mathbf{n}$.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results