NAG Library Routine Document

E04NRF

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

E04NRF may be used to supply optional parameters to E04NQF from an external file. The initialization routine E04NPF must have been called before calling E04NRF.

2 Specification

SUBROUTINE E04NRF (

ISPECS, CW, IW, RW, IFAIL)

INTEGER	ISPECS, IW(*), IFAIL
REAL (KIND=nag_wp)	RW(*)
CHARACTER(8)	CW(*)

3 Description

E04NRF may be used to supply values for optional parameters to E04NQF. E04NRF reads an external file and each line of the file defines a single optional parameter. It is only necessary to supply values for those parameters whose values are to be different from their default values.

Each optional parameter is defined by a single character string, of up to

72

characters, consisting of one or more items. The items associated with a given option must be separated by spaces, or equals signs

[=]

. Alphabetic characters may be upper or lower case. The string

Print Level = 1

is an example of a string used to set an optional parameter. For each option the string contains one or more of the following items:

–	a mandatory keyword;
–	a phrase that qualifies the keyword;
–	a number that specifies an integer or real value. Such numbers may be up to $16$ contiguous characters in Fortran's I, F, E or D formats, terminated by a space if this is not the last item on the line.

Blank strings and comments are ignored. A comment begins with an asterisk (*) and all subsequent characters in the string are regarded as part of the comment.

The file containing the options must start with Begin and must finish with End. An example of a valid options file is:

Begin * Example options file 
   Print level = 5 
End

Optional parameter settings are preserved following a call to E04NQF and so the keyword Defaults is provided to allow you to reset all the optional parameters to their default values before a subsequent call to E04NQF.

A complete list of optional parameters, their abbreviations, synonyms and default values is given in Section 12 in E04NQF.

4 References

None.

5 Parameters

1: $ISPECS$ – INTEGERInput: On entry: the unit number of the option file to be read.

Constraint: ISPECS is a valid unit open for reading.
2: $CW (*)$ – CHARACTER(8) arrayCommunication Array: Note: the dimension of the array CW must be at least $LENCW$ (see E04NPF).
3: $IW (*)$ – INTEGER arrayCommunication Array: Note: the dimension of the array IW must be at least $LENIW$ (see E04NPF).
4: $RW (*)$ – REAL (KIND=nag_wp) arrayCommunication Array: Note: the dimension of the array RW must be at least $LENRW$ (see E04NPF).
5: $IFAIL$ – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$: The initialization routine E04NPF has not been called.

$IFAIL = 2$

At least one line of the options file is invalid.

Could not read options file on unit

ISPECS = 〈value〉

Could not read options file on unit ISPECS. This may be due to:

(a)	ISPECS is not a valid unit number;
(b)	a file is not associated with unit ISPECS, or if it is, is unavailable for read access;
(c)	one or more lines of the options file is invalid. Check that all keywords are neither ambiguous nor misspelt;
(d)	Begin was found, but end-of-file was found before End was found;
(e)	end-of-file was found before Begin was found.

$IFAIL = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 3.8 in the Essential Introduction for further information.

$IFAIL = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 3.7 in the Essential Introduction for further information.

$IFAIL = - 999$: Dynamic memory allocation failed.
See Section 3.6 in the Essential Introduction for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

E04NSF, E04NTF or E04NUF may also be used to supply optional parameters to E04NQF.

10 Example

This example minimizes the quadratic function

f (x) = c^{T} x + \frac{1}{2} x^{T} H x

, where

c = {(- 200.0, - 2000.0, - 2000.0, - 2000.0, - 2000.0, 400.0, 400.0)}^{T}

and

H = (\begin{matrix} 2 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 2 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 2 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 & 2 \\ 0 & 0 & 0 & 0 & 0 & 2 & 2 \end{matrix})

subject to the bounds

\begin{matrix} 0 \leq x_{1} \leq 200 \\ 0 \leq x_{2} \leq 2500 \\ 400 \leq x_{3} \leq 800 \\ 100 \leq x_{4} \leq 700 \\ 0 \leq x_{5} \leq 1500 \\ 0 \leq x_{6} \\ 0 \leq x_{7} \end{matrix}

and to the linear constraints

\begin{matrix} x_{1} & + & x_{2} & + & x_{3} & + & x_{4} & + & x_{5} & + & x_{6} & + & x_{7} & = & 2000 \\ 0.15 x_{1} & + & 0.04 x_{2} & + & 0.02 x_{3} & + & 0.04 x_{4} & + & 0.02 x_{5} & + & 0.01 x_{6} & + & 0.03 x_{7} & \leq & 60 \\ 0.03 x_{1} & + & 0.05 x_{2} & + & 0.08 x_{3} & + & 0.02 x_{4} & + & 0.06 x_{5} & + & 0.01 x_{6} & \leq & 100 \\ 0.02 x_{1} & + & 0.04 x_{2} & + & 0.01 x_{3} & + & 0.02 x_{4} & + & 0.02 x_{5} & \leq & 40 \\ 0.02 x_{1} & + & 0.03 x_{2} & + & 0.01 x_{5} & \leq & 30 \\ 1500 & \leq & 0.70 x_{1} & + & 0.75 x_{2} & + & 0.80 x_{3} & + & 0.75 x_{4} & + & 0.80 x_{5} & + & 0.97 x_{6} \\ 250 & \leq & 0.02 x_{1} & + & 0.06 x_{2} & + & 0.08 x_{3} & + & 0.12 x_{4} & + & 0.02 x_{5} & + & 0.01 x_{6} & + & 0.97 x_{7} & \leq & 300 \end{matrix}

The initial point, which is infeasible, is

x_{0} = {(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)}^{T} .

The optimal solution (to five figures) is

x^{*} = {(0.0, 349.40, 648.85, 172.85, 407.52, 271.36, 150.02)}^{T} .

One bound constraint and four linear constraints are active at the solution. Note that the Hessian matrix

H

is positive semidefinite.

NAG Library Routine DocumentE04NRF