NAG C Library, Mark 7 : Essential Introduction

Exceptionally, Chapters h and s have one-character names. (The chapters and their names are based on the ACM modified SHARE classification index (see ACM (1960–1976)).)

All documented functions have two names. One is based on the SHARE index classification and consists of a six-character name which begins with the characters of the chapter/subchapter name, for example

c06ebc

The letters of this type of function name are always lower case, the second and third characters being digits and the last letter being c. This function name is referred to as the short name. Each function (except the Linear Algebra Support Functions in Chapter f16) also has a more meaningful and longer name, for example

nag_fft_hermitian

which we refer to as the long name. The long name may be used as an alternative to the short name when calling the function. See Section 2.3 for further details.

1.2 Structure of the Documentation

The NAG C Library Manual is the principal printed form of documentation for the NAG C Library. It has the same chapter structure as the Library: each chapter of functions in the Library has a corresponding chapter (of the same name) in the Manual. The chapters occur in alphanumeric order. General introductory documents are placed in Volume 1 of the Manual.

Each chapter consists of the following documents:

Chapter Contents, e.g., Contents – d01;
Chapter Introduction, e.g., Introduction – d01;
Function Documents, one for each documented function in the chapter.

A function document has the same short name as the function which it describes. Within each chapter, function documents occur in alphanumeric order. Exceptionally, some chapters (Chapters f16, x01 and x02) do not have individual function documents; instead, all the functions are described together in the Chapter Introduction.

In addition to the full printed Manual, NAG also produces a printed Introductory Guide, which contains all the introductory material from the Manual, together with all the Chapter Contents and Chapter Introductions.

1.3 Alternative Forms of Documentation

NAG also provides machine-based documentation. Currently NAG provides online documentation in the form of unlinked PDF files accompanied by an HTML index. Introductory material is provided in both PDF and HTML but the Keywords in Context and GAMS Classification Index are provided in HTML only. It is anticipated that future releases will provide HTML files (taking advantage of technology that is currently being developed, e.g., MathML) for the full manual and fully linked PDF files for all but the Keywords in Context and GAMS Classification Index. The most up-to-date version of the online documentation is accessible via the NAG Web site (see Section 4).

2 Using the Library

2.1 General Advice

A NAG C Library function cannot be guaranteed to return meaningful results irrespective of the data supplied to it. Care and thought must be exercised in:

formulating the problem;
programming the use of library functions;
assessing the significance of the results.

The Foreword to the Manual provides some further discussion of points (a) and (c); the remainder of Section 2 is concerned with (b).

2.2 Programming Advice

The NAG C Library and its documentation are designed on the assumption that you know how to write a calling program in C.

When a suitable NAG function has been selected, the function must be called from the C Library via a suitable user-written C program, the calling program. This Manual assumes that the user has sufficient knowledge of the C programming language to be able to write such a program. Each C Library function document contains an example of a suitable calling program (see Section 3.2).

When writing a calling program, a number of environmental features common to all such NAG programs must be observed in addition to specific features which are relevant to the particular NAG function being called. These features are discussed below; the user should refer to the above example calling program while studying the description of these features. Users are also recommended to pay particular attention to the specification of the function parameters, array sizes and array indices.

2.2.1 The NAG C environment

The environment for the NAG C Library is defined in a number of include files; a list is given in Section 2.2.1.6. The most important of the header files is <nag.h>, which must be included in any program that calls a NAG C Library function and must precede any other NAG header file.

These include files are normally located in the standard directory for C include files. The exact location is installation dependent; please see the Users' Note or other local documentation.

The file nag.h defines data types and error codes used in the NAG C Library together with a number of macros used in example programs. File nag.h also contains the definitions for the input/output and string handling functions Vscanf, Vprintf, Vfprintf, Vsprintf, Vstrcpy which are the C functions scanf, printf, etc., cast to void.

The user may also need to include the header file nag_stdlib.h in the calling program; see Section 2.2.1.6.

2.2.1.1 NAG data types

Integer

This data type is used for almost all integer parameters to NAG C Library functions. It is normally defined to be long.

Boolean

This data type is used for all parameters that take a true or false value. If TRUE and FALSE have not previously been defined, then the following definitions are used:

#define TRUE 1#define FALSE 0

Complex

This data type is a structure defined for use with complex numbers:

 typedef struct {double re, im;} Complex;

Pointer

This data type represents a generic pointer and is defined as void *.

Nag_User

This data type is a structure containing a generic pointer used for communicating information between a user defined function and the user's calling program, where the user defined function is supplied as an argument to the NAG function. This avoids the necessity of using global variables for such communication. A brief example of use (taken from Chapter d02) is given below:

Brief example of use

Enumeration Types

A number of enumerated types are defined in <nag_types.h> for use in calls to various NAG C Library functions. Users must use these enumerated types in their calling programs.

Other structure types

A number of structures have been defined to facilitate calls to NAG functions. The components of a structure that are relevant to a call to a NAG function are described in the corresponding function document. A complete specification of a NAG defined structure can be found in the NAG C Library header file nag_types.h included in the distribution materials. For futher details please contact NAG.

2.2.1.2 Memory management in the Library

Memory is frequently dynamically allocated within NAG C Library functions. All requests for memory are checked for success or failure. In the unlikely event of failure occurring the Library function returns or terminates with the error state NE_ALLOC_FAIL (details of error handling in the Library are given in Section 2.6).

The macros NAG_ALLOC and NAG_FREE are defined to select suitable memory management functions for the NAG C Library. NAG_ALLOC has two arguments; the first specifies the number of elements to be allocated while the second specifies the type of element. The statement

p = NAG_ALLOC(n, double);

allocates n elements of memory of type double to p, a pointer to double.

NAG_FREE frees memory allocated by NAG_ALLOC; its single argument is the pointer which specifies the memory to be deallocated. The statement

NAG_FREE(p);

deallocates memory pointed to by p.

These macros are defined in the header file nag_stdlib.h which must be included if these macros are used in the calling program. NAG_FREE must be used to free memory allocated and returned from a NAG function. If memory is allocated using NAG_ALLOC for whatever reason, it must be freed using NAG_FREE. For an illustration of its use, see Section 9.1 of the document for nag_1d_quad_inf_wt_trig (d01asc).

2.2.1.3 The Nag_Order parameter

Different programming languages lay out two-dimensional data in memory in different ways. The C language treats a two-dimensional array as a single block of memory arranged in rows, the so called ‘row-major’ ordering. Some other languages, notably Fortran 77, arrange two-dimensional arrays by column (‘column-major’ ordering). Commencing at Mark 7, those functions in the C Library that deal with two-dimensional arrays and where it is sensible to do so, have an extra parameter, called order, which allows the user to specify that their data is arranged in rows (by setting order to Nag_RowMajor) or in columns (by setting order to Nag_ColMajor). This is particularly useful if the NAG C Library is being called from a language which uses the column-major ordering or if you wish to call a function from a language which supports column-major ordering.

2.2.1.4 Array references

In C it is possible to declare a two-dimensional variable using notation of the form:

 double a[dim1][dim2];

When this variable is a parameter to a function, it is effectively treated by the compiler as a pointer, *a, of type double with an allocated memory of dim1*dim2 on the stack. The address of an element of this array, say a[3][5] is then an explicit address computed to be *(a+3*dim2+5), since C stores data in row-major order. The C pre-processor allows a succinct notation for computing this explicit address by using a macro definition:

#define A(I,J) A[I*dim2+J]

[1]

Alternatively it is possible for a user to allocate memory explicitly (on the heap) to a pointer of type double *, using the form:

a=(double *)malloc((size_t)(dim1*dim2*sizeof(double));

[2]

The

i j

th element of this array is then indexed using the pointer notation *(a+i*dim2+j) or by using the array notation a[i*dim2+j]; or by using A(I,J) assuming the macro [1] is already defined.

If the data is to be stored using column-major ordering and we have declared an array variable as

 double a[dim1][dim2];

then the

i j

th element is effectively transposed. That is, the element a[i][j] under row-major ordering is the element a[j][i] under column-major ordering.

As another alternative the user may choose to malloc the required memory as in [2] above. In this case, the

i j

th element of this array is indexed using the pointer notation *(a+j*dim1+i); or by using the array notation a[j*dim1+i]; or by using A(I,J) if the macro is defined as

#define A(I,J) A[J*dim1+I]

[3]

Note the difference in definition between [1] and [3] above.

In order to simplify the documentation, we refer to array elements using the macro definitions above. Further, we note that in the pre-processor directive [1] and [3], the critical dimension is either dim2 if the row-major ordering is used or dim1 if column-major ordering is used. We designate either dim2 or dim1 as the principal dimension depending on the storage ordering scheme. The principal dimension can be thought of as a stride which must be taken to traverse either a row or a column depending on the order parameter.

We illustrate these concepts using two examples. In the first example, memory is allocated while in the second example memory is declared. In both examples, row or column modes are demarcated using the pre-processor macro NAG_ROW_MAJOR.

Example 1

Example 1

Example 2

Example 2

2.2.1.5 Internal data structures in the NAG C Library

For efficiency, and wherever possible, the NAG C Library is designed to make use of the Basic Linear Algebra Subprograms (BLAS), a suite of low-level functions tuned by many computer manufacturers for their particular hardware. Since the BLAS are specified in Fortran, and therefore use the column-major storage order, the NAG C Library also uses this scheme internally, for new functions introduced at Mark 7 wherever it is practical. Thus any two-dimensional arrays provided by the user may be re-ordered on entry and/or on exit from the NAG functions, as appropriate. It is therefore slightly more efficient to use the column-major ordering; however, except for very large data sets, the effect is negligible in practice.

2.2.1.6 Chapter header files

Chapter header files contain the function declarations for the NAG C Library with ANSI function prototyping. The appropriate chapter header file must be included for each NAG function called by your program. For example, to call the function nag_fft_complex (c06ecc) the chapter header file nagc06.h must be included as

 #include <nagc06.h>

The naming convention is to prefix the first three characters of the function name in lower case by nag and use .h as the postfix as in normal C practice, except that all functions in Chapter s use the header file nags.h.

(a) Header files intended for inclusion by the user within calling programs to the NAG C Library

<nag.h> defines the basic environment for use of the NAG C Library. This header file must be included in each calling program to the NAG C Library and must precede all other header files that are included. This must be followed by one or more of the following chapter header files.

<naga00.h>	<naga02.h>	<nagc02.h>	<nagc05.h>	<nagc06.h>	<nagd01.h>
<nagd02.h>	<nagd03.h>	<nagd06.h>	<nage01.h>	<nage02.h>	<nage04.h>
<nagf01.h>	<nagf02.h>	<nagf03.h>	<nagf04.h>	<nagf06.h>	<nagf07.h>
<nagf08.h>	<nagf11.h>	<nagg01.h>	<nagg02.h>	<nagg03.h>	<nagg04.h>
<nagg05.h>	<nagg07.h>	<nagg08.h>	<nagg10.h>	<nagg11.h>	<nagg12.h>
<nagg13.h>	<nagh02.h>	<nagh03.h>	<nagm01.h>	<nags.h>	<nagx01.h>
<nagx02.h>	<nagx04.h>

<nag_stdlib.h> defines EXIT_SUCCESS and EXIT_FAILURE and the memory allocation macro
NAG_ALLOC and NAG_FREE. This header file must be included by the user if the NAG definitions of EXIT_SUCCESS, EXIT_FAILURE, NAG_ALLOC and NAG_FREE, as used in the example programs, are required.

(b) The following three header files are included by nag.h (the user does not need to supply a specific statement to include them)

<nag_types.h> defines the NAG types used in the Library.

<nag_errlist.h> defines the NAG error codes and messages used in the Library.

<nag_names.h> maps the NAG long names to short names.

2.3 Use of NAG Long Names

The long names defined in the header file nag_names.h are #defines. Users should note that the short function names given in upper case in this file are also #defines and therefore their corresponding long names will not require a terminating pair of brackets. These declarations are to be found in nagx01.h and nagx02.h. As the header file nag_names.h is already included via nag.h, users need not include nag_names.h in their calling programs.

2.4 Input/Output

NAG C Library functions output all error and warning messages to the C standard error stream stderr. Chapters e04, g02 and g13 will optionally output results to the C standard output stream stdout or to an alternative user-specified file. A number of functions in the Minimizing or Maximizing a Function (e04) and Operations Research (Chapter h) areas read input from external files.

2.5 Auxiliary Functions

In addition to the documented functions available to the user, the NAG C Library contains a much larger number of auxiliary functions. Users do not normally need to concern themselves with these functions, as they will automatically be called as required by the user-callable function selected by the user. The function declarations of these auxiliary functions can be found in the relevant chapter header files together with the user-callable function declarations.

2.6 NAG Error Handling and the fail Parameter

All functions that have error exits have a parameter that allows the user control over the printing of error messages when an error is detected. There is a further option which allows users either to continue running their program, having returned from the NAG function, or to stop with either an exit statement or an abort within the NAG function. The different ways of using these error handling facilities are described below.

Note that in some implementations, the Library is linked with the vendor library containing LAPACK functions and the f07 and f08 function interfaces, where appropriate, act as wrappers to the corresponding vendor LAPACK functions. In this case, the fail parameter passed through the f07 and f08 interfaces does not have full control over the printing of error messages; nor does it determine whether or not control is returned to the calling program when an error is detected.

2.6.1 Use of NAGERR_DEFAULT

The simplest method of using the error handling facility is to put NAGERR_DEFAULT in place of the fail parameter in calls to the NAG C functions. If an error is detected the appropriate NAG error message is output on stderr and the program is stopped by the use of abort (in some implementations the program may be stopped with exit rather than abort). This method of use is illustrated in the above example program for nag_real_eigensystem (f02agc). NAGERR_DEFAULT is defined in <nag.h> as (NagError *)0.

2.6.2 Use of the fail parameter

The two remaining ways of using the NAG error handling facility both involve defining the fail parameter in the calling program. The fail parameter is of type NagError which is a structure defined in
<nag_types.h> as:

Components in the NagError Structure

where the symbol NAG_ERROR_BUF_LEN is normally defined to be 512.

This structure will contain the NAG error code and message on return from a call to a NAG C Library function. The NAG error codes and associated NAG error messages are defined in <nag_errlist.h>. A detailed description of the individual members of this structure is given below (see Section 2.6.3).

The NAG error parameter fail is declared in the calling program as:

 NagError fail;

The address of the parameter is then passed to the NAG C function being called. All members of the structure must be initialised before passing the parameter to the called function, even though a member may not actually be required by the user. It is recommended that the NAG defined macro INIT_FAIL be used for this purpose. The SET_FAIL macros is also available. This sets fail.print to TRUE.

(a) Use of the fail parameter with the print member set to TRUE

If the user requires that the NAG error message be printed when an error is found, but that the called function should return control to the calling program, then the fail parameter must be declared with all members initialised and the print member set to TRUE. Use of the NAG-defined macro SET_FAIL with the statement SET_FAIL(fail); performs the appropriate assignments. Alternatively the initialisation could be done by declaring the fail parameter with static (see the example declaration above) and then setting fail.print to TRUE.

If no error occurs, fail.code will contain the error code NE_NOERROR on return from the called function. However, if an error is found, the appropriate NAG error message will be output on stderr before returning control to the calling program; fail.code will contain the relevant NAG error code. The user must ensure that the calling program tests the code member of the fail parameter on return from the NAG C function; the user may then choose whether to exit the calling program or continue. See the example program for nag_real_svd (f02wec) for such a case. The option of continuing may be advantageous if the results being returned are of some value even when an error has been detected. In the case of nag_real_svd (f02wec) the code could be altered to allow the program to continue if the specific error code of NE_QR_NOT_CONV occurs, as in such a case useful partial results are returned (see the routine document for nag_real_svd (f02wec)).

(b) Use of the fail parameter with the print member set to FALSE

If the user does not wish the NAG error messages to be printed automatically when an error is found then the fail parameter must be declared with all members initialised and the print member set to FALSE. Use of static in the declaration of fail will automatically leave the print member as FALSE as will the use of INIT_FAIL(fail).

This method is suitable for users who wish to produce their own error messages rather than use the NAG C Library versions. Alternative error messages may be coded directly into the calling program or be produced via a user-written error-handling function which is assigned to the handler member of the fail parameter (see the description of the handler member below).

2.6.3 The NagError structure

The individual members of the NagError structure are described in full below.

code

On successful exit, code contains the NAG error code NE_NOERROR; if an error or warning has been detected, then code contains the specific error or warning code. Error codes are prefixed with NE_ whereas warning codes have the prefix NW_.

print must be set before calling any NAG C Library function with a fail parameter. It should be set to TRUE if the NAG error message is to be printed, otherwise FALSE. It is not changed by the NAG C Library function.

message

On successful exit the array message contains the character string "NE_NOERROR:\n No error". If an error has been detected, then message contains the error message text, whether or not this is printed.

errnum

On successful exit, errnum is unchanged. For certain error or warning exits errnum will contain a value specifying additional information concerning the error. For example if a vector is supplied incorrectly, then errnum may specify which component of the vector is wrong. Cases where errnum returns information are described in the relevant function documents.

handler

handler must be set to 0 if control is to be returned to the calling function after an error has been detected. Otherwise it must point to a user-supplied error-handling function. An example of the ANSI C declaration of a user-supplied error function (here called errhan) is:

 void errhan(const char *string, int code, const char *name)

where string contains the NAG error message on input, code is the NAG error code and name is the short name of the NAG C Library function which detected the error. If print (see above) is TRUE, then the NAG error message is printed before the user-supplied error handler is called. If the user-supplied error handler returns control, then the NAG error handler will return control to the calling program; otherwise the user-supplied error handler may abort, exit or longjmp.

An elementary example of where this feature might be used is if it is preferred to print error messages on stdout rather than the default stderr. In this case errhan could be defined as:

errhan

2.7 Thread Safety

The NAG C Library is thread safe by design; all communication between functions is via argument lists, and, with the exception of Chapter g05 (Random Number Generators), no use of read and write static storage is made.

In Chapter g05, for efficiency, functions in the range g05c–g05h use global variables internally for communication. Simultaneous access to these global variables by multiple threads has been guarded against using thread mutexes. For UNIX machines, these mutexes come from the POSIX standard thread library (ANSI/IEEE POSIX (1995)), also known as pthreads. For PC implementations of the NAG C Library, the mutexes are those implemented by the Microsoft thread package.

The NAG C Library is therefore thread safe with respect to the thread package against which it was built, either pthreads or Microsoft threads. Some older UNIX architectures did not have implementations of pthreads available, and implementations of the NAG C Library on such architectures could not therefore be made thread safe - though of course on such machines it would not be possible to write a POSIX multi-threaded program anyway. Current implementations of the NAG C Library that are NOT thread safe are:

CLSG506DA

Although the NAG C Library is thread safe, sometimes care must be taken to use it in a thread-safe way. In particular, this is the case with Chapter c05 (Roots of One or More Transcendental Equations), and
Chapter d01 (Quadrature). In these chapters, the solution of a problem usually involves a user-supplied function being passed to the NAG Library function, the user-supplied C function being called to evaluate the mathematical function which is the object of the problem. It is sometimes the case that the user would like the evaluation function to communicate with the main program, to pass relevant information involved in the function evaluation. The simplest way to do this is to use global variables for communication, but these global variables render the resulting code unsuitable for use by multiple threads simultaneously.

Using pthread or Microsoft thread package functionality, it is perfectly possible for the user to avoid this problem by writing code which passes thread-specific data between main program and evaluation function. As an alternative to this method, however, where relevant we have provided alternative versions of the NAG Library functions. These alternative functions have an extra argument which can be used for safe communication of additional data if it is required. Please see documentation for nag_1d_quad_gen (d01ajc) and nag_1d_quad_gen_1 (d01sjc) for examples.

Finally we recommend that when using the C Library error mechanism, the output is switched off (by setting

fail.print = FALSE

Note that in some implementations, the Library is linked with one or more vendor libraries to provide, for example, efficient BLAS routines. NAG cannot guarantee that any such vendor library is thread safe.

2.8 Calling the Library from Other Languages

In general the NAG C Library can be called from other computer languages (such as C++, Java and Visual Basic) provided that appropriate mappings exist between their data types.

3 Using the Documentation

3.1 Using the Manual

The Manual is designed to serve the following functions:

to give background information about different areas of numerical and statistical computation;
to advise on the choice of the most suitable NAG Library function or functions to solve a particular problem;
to give all the information needed to call a NAG Library function correctly from a C program, and to assess the results.

At the beginning of the Manual are some general introductory documents which provide some background and additional information. The Library Contents (a structured list of functions in the Library, by chapter) may help you to find the chapter, and possibly the function, which you need to solve your problem. Online documentation provides you with a fully linked HTML Keywords in Context (a keyword index to chapters and functions) and GAMS Classification Index (a list of NAG functions classified according to the GAMS scheme).

Having found a likely chapter or function, you should read the corresponding Chapter Introduction, which gives background information about that area of numerical computation, and recommendations on the choice of a function, including indexes, tables or decision trees.

When you have chosen a function, you must consult the function document. Each function document is essentially self-contained (it may, however, contain references to related documents). It includes a description of the method, detailed specifications of each parameter, explanations of each error exit, remarks on accuracy, and (in most cases) an example program to illustrate the use of the function.

3.2 Structure of Function Documents

Note that at Mark 7 a new typesetting scheme was used to generate documentation. If you have a Manual which contains pre-Mark 7 function documents, you will find that it contains older documents which differ in style, although they contain essentially the same information.

All function documents have the same structure, consisting of nine numbered sections:

1.	Purpose
2.	Specification
3.	Description
4.	References
5.	Parameters (see Section 3.3 below)
6.	Error Indicators and Warnings
7.	Accuracy
8.	Further Comments
9.	Example (see Section 3.4 below)

In a few documents (notably Chapter e04) there are a further three sections:

10.	Algorithmic Details
11.	Optional Parameters
12.	Description of Monitoring Information

3.3 Specification of Parameters

Section 5 of each function document contains the specification of the parameters, in the order of their appearance in the parameter list.

3.3.1 Classification of parameters

Parameters are classified as follows.

Input: you must assign values to these parameters on or before entry to the function, and these values are unchanged on exit from the function.

Output: you need not assign values to these parameters on or before entry to the function; the function may assign values to them.

Input/Output: you must assign values to these parameters on or before entry to the function, and the function may then change these values.

External Procedure: a subfunction or function which must be supplied (e.g., to evaluate an integrand or to print intermediate output). Usually it must be supplied as part of your calling program, in which case its specification includes full details of its parameter list and specifications of its parameters (all enclosed in a box). Its parameters are classified in the same way as those of the Library function, but because you must write the procedure rather than call it, the significance of the classification is different.

Input: values may be supplied on entry.
Output: you may or must assign values to these parameters before exit from your procedure.
Input/Output: values may be supplied on entry, and you may or must assign values to them before exit from your procedure.

3.3.2 Constraints and suggested values

The word ‘Constraint:’ or ‘Constraints:’ in the specification of an Input parameter introduces a statement of the range of valid values for that parameter, e.g.,

Constraint: $n > 0$ .

If the function is called with an invalid value for the parameter (e.g.,

n = 0

), the function will usually take an error exit.

The phrase ‘Suggested Value:’ introduces a suggestion for a reasonable initial setting for an Input parameter (e.g., accuracy or maximum number of iterations) in case you are unsure what value to use; you should be prepared to use a different setting if the suggested value turns out to be unsuitable for your problem.

3.4 Example Programs and Results

The example program in Section 9 of each function document illustrates a simple call of the function. The programs are designed so that they can fairly easily be modified, and so serve as the basis for a simple program to solve your problem.

For each implementation of the Library, NAG distributes the example programs in machine-readable form, with all necessary modifications already applied. Many sites make the programs accessible to you in this form. They may also be obtained directly from the NAG Web site.

Note that the results from running the example programs may not be identical in all implementations, and may not agree exactly with the results which are printed in the Manual and which were obtained from a double precision implementation (with approximately 16 digits of precision).

The Users' Note for your implementation will mention any special changes which need to be made to the example programs, and any significant differences in the results.

3.5 Summary for New Users

If you are unfamiliar with this Library and are thinking of using a function from it, please follow these instructions:

read the whole of this Essential Introduction;

consult the Library Contents list to select an appropriate chapter or function;
or search through the Keywords in Context, GAMS Classification Index;
read the relevant Chapter Introduction;
choose a function, and read the function document. If the function does not after all meet your needs, return to step (b), (c) or (d);
read the Users' Note for your implementation;
consult local documentation, which should be provided by your local support staff, about access to the this Library on your computing system;
obtain an online copy of the example program for the particular function of interest and experiment with it.

You should now be in a position to include a call to the function in a program, and to attempt to compile and run it. You may of course need to refer back to the relevant documentation in the case of difficulties, for advice on assessment of results, and so on.

As you become familiar with the Library, some of steps (a) to (h) can be omitted, but it is always essential to:

be familiar with the Chapter Introduction;
read the function document;
be aware of the Users' Note for your implementation.

4 Support from NAG

(a) Contact with NAG

Queries concerning this library should be directed initially to your local Advisory Service. If you have difficulty in making contact locally, you can contact NAG directly.

(b) NAG Response Centres

The NAG Response Centres are available for general enquiries from all users and also for technical queries from users with Support.

The Response Centres are open during office hours, but contact is possible by fax, email and telephone (answering machine) at all times. Please see the Users' Note or the NAG web sites for contact details.

When contacting one of our Response Centres it helps us to deal with you query quickly if you can quote your NAG user reference and NAG product code.

(c) NAG Web Site

The NAG web site is an information service providing items of interest to users and prospective users of NAG products and services. The information is regularly updated and reviewed, and includes implementation availability, descriptions of products, down-loadable software and technical reports. NAG web sites can be accessed at