/** @mainpage WCSLIB 5.17 and PGSBOX 5.17

@image html Bonne.gif "Bonne's projection"

@section contents Contents

- @subpage intro
- @subpage software
- @subpage overview
- @subpage structs
- @subpage memory
- @subpage diagnostics
- @subpage vector
- @subpage threads
- @subpage testing
- @subpage fortran
- @subpage pgsbox
- @subpage versioning

@section copyright Copyright

@verbatim
  WCSLIB 5.17 - an implementation of the FITS WCS standard.
  Copyright (C) 1995-2017, Mark Calabretta

  WCSLIB is free software: you can redistribute it and/or modify it under the
  terms of the GNU Lesser General Public License as published by the Free
  Software Foundation, either version 3 of the License, or (at your option)
  any later version.

  WCSLIB is distributed in the hope that it will be useful, but WITHOUT ANY
  WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public License for
  more details.

  You should have received a copy of the GNU Lesser General Public License
  along with WCSLIB.  If not, see http://www.gnu.org/licenses.

  Direct correspondence concerning WCSLIB to mark@calabretta.id.au

  Author: Mark Calabretta, Australia Telescope National Facility, CSIRO.
  http://www.atnf.csiro.au/people/Mark.Calabretta
  $Id: mainpage.dox,v 5.17 2017/09/18 08:44:25 mcalabre Exp $
@endverbatim
*/

/** @page intro Introduction

WCSLIB is a C library, supplied with a full set of Fortran wrappers, that
implements the "World Coordinate System" (WCS) standard in FITS (Flexible
Image Transport System).  It also includes a @ref software "PGPLOT"-based
routine, @ref pgsbox "PGSBOX", for drawing general curvilinear coordinate
graticules and a number of utility programs.

The FITS data format is widely used within the international astronomical
community, from the radio to gamma-ray regimes, for data interchange and
archive, and also increasingly as an online format.  It is described in

- "Definition of The Flexible Image Transport System (FITS)",
   FITS Standard, Version 3.0, 2008 July 10.

available from the FITS Support Office at http://fits.gsfc.nasa.gov.

The FITS WCS standard is described in

- "Representations of world coordinates in FITS" (Paper I),
   Greisen, E.W., & Calabretta, M.R. 2002, A&A, 395, 1061-1075

- "Representations of celestial coordinates in FITS" (Paper II),
   Calabretta, M.R., & Greisen, E.W. 2002, A&A, 395, 1077-1122

- "Representations of spectral coordinates in FITS" (Paper III),
   Greisen, E.W., Calabretta, M.R., Valdes, F.G., & Allen, S.L.
   2006, A&A, 446, 747

- "Mapping on the HEALPix Grid" (HPX),
   Calabretta, M.R., & Roukema, B.F. 2007, MNRAS, 381, 865

- "Representing the 'Butterfly' Projection in FITS: Projection Code XPH"
   (XPH), Calabretta, M.R., & Lowe, S.R. 2013, PASA, 30, e050

- "Representations of time coordinates in FITS: Time and relative dimension in
   space", Rots, A.H., Bunclark, P.S., Calabretta, M.R., Allen, S.L.,
   Manchester R.N., & Thompson, W.T. 2015, A&A, 574, A36

Reprints of all published papers may be obtained from NASA's Astrophysics
Data System (ADS), http://adsabs.harvard.edu/.  Reprints of Papers I, II
(including HPX & XPH), and III are available from
http://www.atnf.csiro.au/people/Mark.Calabretta.  This site also includes
errata and supplementary material for Papers I, II and III.

Additional information on all aspects of FITS and its various software
implementations may be found at the FITS Support Office
http://fits.gsfc.nasa.gov.
*/


/** @page software FITS-WCS and related software

Several implementations of the FITS WCS standards are available:

  - The @ref overview "WCSLIB" software distribution (i.e. this library) may
    be obtained from
    http://www.atnf.csiro.au/people/Mark.Calabretta/WCS/<I></I>.  The
    remainder of this manual describes its use.

  - @b wcstools, developed by Jessica Mink, may be obtained from
    http://tdc-www.harvard.edu/software/wcstools/<I></I>.

  - @b AST, developed by David Berry within the U.K. Starlink project,
    http://www.starlink.ac.uk/ast/ and now supported by JAC, Hawaii
    http://starlink.jach.hawaii.edu/starlink/<I></I>.  A useful utility for
    experimenting with FITS WCS descriptions (similar to @a wcsgrid) is also
    provided; go to the above site and then look at the section entitled
    "FITS-WCS Plotting Demo".

  - @b SolarSoft, http://sohowww.nascom.nasa.gov/solarsoft/<I></I>, primarily
    an IDL-based system for analysis of Solar physics data, contains a module
    written by Bill Thompson oriented towards Solar coordinate systems,
    including spectral,
    http://sohowww.nascom.nasa.gov/solarsoft/gen/idl/wcs/<I></I>.

  - The IDL Astronomy Library, http://idlastro.gsfc.nasa.gov/<I></I>, contains
    an independent implementation of FITS-WCS in IDL by Rick Balsano,
    Wayne Landsman and others.  See
    http://idlastro.gsfc.nasa.gov/contents.html#C5<I></I>.

Python wrappers to @ref overview "WCSLIB" are provided by

  - The <B>Kapteyn Package</B> http://www.astro.rug.nl/software/kapteyn/ by
    Hans Terlouw and Martin Vogelaar.

  - <B>pywcs</B>, http://stsdas.stsci.edu/astrolib/pywcs/ by
    Michael Droettboom.

Java is supported via

  - CADC/CCDA Java Native Interface (JNI) bindings to @ref overview "WCSLIB"
    4.2 http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/cadc/source/ by
    Patrick Dowler.

and Javascript by

  -  <B>wcsjs</B>, https://github.com/astrojs/wcsjs, a port created by Amit
     Kapadia using Emscripten, an LLVM to Javascript compiler.  wcsjs provides
     a code base for running @ref overview "WCSLIB" on web browsers.

Recommended WCS-aware FITS image viewers:

  - Bill Joye's <B>DS9</B>, http://hea-www.harvard.edu/RD/ds9/<I></I>, and

  - <B>Fv</B> by Pan Chai, http://heasarc.gsfc.nasa.gov/ftools/fv/<I></I>.

both handle 2-D images.

Currently (2013/01/29) I know of no image viewers that handle 1-D spectra
properly nor multi-dimensional data, not even multi-dimensional data with
only two non-degenerate image axes (please inform me if you know otherwise).

Pre-built @ref overview "WCSLIB" packages are available, generally a little
behind the main release (this list will probably be stale by the time you read
it, best do a web search):

  - archlinux (tgz),
    https://www.archlinux.org/packages/extra/i686/wcslib<I></I>.

  - Debian (deb),
    http://packages.debian.org/search?keywords=wcslib<I></I>.

  - Fedora (RPM),
    https://admin.fedoraproject.org/pkgdb/package/wcslib<I></I>.

  - Fresh Ports (RPM), http://www.freshports.org/astro/wcslib<I></I>.

  - Gentoo, http://packages.gentoo.org/package/sci-astronomy/wcslib<I></I>.

  - Homebrew (MacOSX),
    https://github.com/Homebrew/homebrew-science<I></I>.

  - RPM (general)
    http://rpmfind.net/linux/rpm2html/search.php?query=wcslib<I></I>,
    http://www.rpmseek.com/rpm-pl/wcslib.html<I></I>.

  - Ubuntu (deb),
    https://launchpad.net/ubuntu/+source/wcslib<I></I>.

Bill Pence's general FITS IO library, <B>CFITSIO</B> is available from
http://heasarc.gsfc.nasa.gov/fitsio/<I></I>.  It is used optionally by some of
the high-level WCSLIB test programs and is required by two of the utility
programs.

<B>PGPLOT</B>, Tim Pearson's Fortran plotting package on which @ref pgsbox
"PGSBOX" is based, also used by some of the WCSLIB self-test suite and a
utility program, is available from
http://astro.caltech.edu/~tjp/pgplot/<I></I>.
*/


/** @page overview Overview of WCSLIB

WCSLIB is documented in the prologues of its header files which provide a
detailed description of the purpose of each function and its interface (this
material is, of course, used to generate the doxygen manual).  Here we explain
how the library as a whole is structured.  We will normally refer to WCSLIB
'routines', meaning C functions or Fortran 'subroutines', though the latter
are actually wrappers implemented in C.

WCSLIB is layered software, each layer depends only on those beneath;
understanding WCSLIB first means understanding its stratigraphy.  There are
essentially three levels, though some intermediate levels exist within these:

- The <B>top layer</B> consists of routines that provide the connection
  between FITS files and the high-level WCSLIB data structures, the main
  function being to parse a FITS header, extract WCS information, and copy it
  into a wcsprm struct.  The lexical parsers among these are implemented as
  Flex descriptions (source files with .l suffix) and the C code generated
  from these by Flex is included in the source distribution.
  - wcshdr.h,c    -- Routines for constructing wcsprm data structures from
                     information in a FITS header and conversely for writing a
                     wcsprm struct out as a FITS header.
  - wcspih.l      -- Flex implementation of wcspih(), a lexical parser for WCS
                     "keyrecords" in an image header.  A @b @e keyrecord
                     (formerly called "card image") consists of a
                     @b @e keyword, its value - the @b @e keyvalue - and an
                     optional comment, the @b @e keycomment.
  - wcsbth.l      -- Flex implementation of wcsbth() which parses binary table
                     image array and pixel list headers in addition to image
                     array headers.
  - getwcstab.h,c -- Implementation of a -TAB binary table reader in @ref
                     software "CFITSIO".
  .
  @n
  A generic FITS header parser is also provided to handle non-WCS keyrecords
  that are ignored by wcspih():
  - fitshdr.h,l   -- Generic FITS header parser (not WCS-specific).
  .
  @n
  The philosophy adopted for dealing with non-standard WCS usage is to
  translate it at this level so that the middle- and low-level routines need
  only deal with standard constructs:
  - wcsfix.h,c    -- Translator for non-standard FITS WCS constructs (uses
                     wcsutrne()).
  - wcsutrn.l     -- Lexical translator for non-standard units specifications.
  .
  @n
  As a concrete example, within this layer the @c CTYPEia keyvalues would be
  extracted from a FITS header and copied into the @a ctype[] array within a
  wcsprm struct.  None of the header keyrecords are interpreted.

- The <B>middle layer</B> analyses the WCS information obtained from the FITS
  header by the top-level routines, identifying the separate steps of the WCS
  algorithm chain for each of the coordinate axes in the image.  It constructs
  the various data structures on which the low-level routines are based and
  invokes them in the correct sequence.  Thus the wcsprm struct is essentially
  the glue that binds together the low-level routines into a complete
  coordinate description.
  - wcs.h,c       -- Driver routines for the low-level routines.
  - wcsunits.h,c  -- Unit conversions (uses wcsulexe()).
  - wcsulex.l     -- Lexical parser for units specifications.
  .
  @n
  To continue the above example, within this layer the @a ctype[] keyvalues in
  a wcsprm struct are analysed to determine the nature of the coordinate axes
  in the image.

- Applications programmers who use the top- and middle-level routines
  generally need know nothing about the <B>low-level routines</B>.  These are
  essentially mathematical in nature and largely independent of FITS itself.
  The mathematical formulae and algorithms cited in the WCS Papers, for
  example the spherical projection equations of Paper II and the lookup-table
  methods of Paper III, are implemented by the routines in this layer, some of
  which serve to aggregate others:
  - cel.h,c       -- Celestial coordinate transformations, combines prj.h,c
                     and sph.h,c.
  - spc.h,c       -- Spectral coordinate transformations, combines
                     transformations from spx.h,c.
  .
  @n
  The remainder of the routines in this level are independent of everything
  other than the grass-roots mathematical functions:
  - lin.h,c       -- Linear transformation matrix.
  - log.h,c       -- Logarithmic coordinates.
  - prj.h,c       -- Spherical projection equations.
  - sph.h,c       -- Spherical coordinate transformations.
  - spx.h,c       -- Basic spectral transformations.
  - tab.h,c       -- Coordinate lookup tables.
  .
  @n
  As the routines within this layer are quite generic, some, principally the
  implementation of the spherical projection equations, have been used in
  other packages (AST, wcstools) that provide their own implementations of the
  functionality of the top and middle-level routines.

- At the <B>grass-roots level</B> there are a number of mathematical and
  utility routines.
  @n@n
  When dealing with celestial coordinate systems it is often desirable to use
  an angular measure that provides an exact representation of the latitude of
  the north or south pole.  The WCSLIB routines use the following
  trigonometric functions that take or return angles in degrees:
  - cosd(), sind(), sincosd(), tand(), acosd(), asind(), atand(), atan2d()
  .
  @n
  These "trigd" routines are expected to handle angles that are a multiple of
  @f$90^\circ@f$ returning an exact result.  Some C implementations provide
  these as part of a system library and in such cases it may (or may not!) be
  preferable to use them.  wcstrig.c provides wrappers on the standard trig
  functions based on radian measure, adding tests for multiples of
  @f$90^\circ@f$.
  @n@n
  However, wcstrig.h also provides the choice of using preprocessor macro
  implementations of the trigd functions that don't test for multiples of
  @f$90^\circ@f$ (compile with @c -DWCSTRIG_MACRO).  These are typically 20%
  faster but may lead to problems near the poles.
  - wcsmath.h     -- Defines mathematical and other constants.
  - wcstrig.h,c   -- Various implementations of trigd functions.
  - wcsutil.h,c   -- Simple utility functions for string manipulation, etc.
                     used by WCSLIB.

Complementary to the C library, a set of wrappers are provided that allow all
WCSLIB C functions to be called by Fortran programs, see below.

Plotting of coordinate graticules is one of the more important requirements of
a world coordinate system.  WCSLIB provides a @ref software "PGPLOT"-based
subroutine, @ref pgsbox "PGSBOX" (Fortran), which handles general curvilinear
coordinates via a user-supplied function - @c PGWCSL provides the interface
to WCSLIB.  A C wrapper, @a cpgsbox(), is also provided, see below.

Several utility programs are distributed with WCSLIB:

- @a wcsgrid extracts the WCS keywords for an image from the specified FITS
  file and uses @a cpgsbox() to plot a 2-D coordinate graticule for it.  It
  requires WCSLIB, @ref pgsbox "PGSBOX" and @ref software "CFITSIO".

- @a wcsware extracts the WCS keywords for an image from the specified FITS
  file and constructs wcsprm structs for each coordinate representation found.
  The structs may then be printed or used to transform pixel coordinates to
  world coordinates.  It requires WCSLIB and @ref software "CFITSIO".

- @a HPXcvt reorganises HEALPix data into a 2-D FITS image with HPX coordinate
  system.  The input data may be stored in a FITS file as a primary image or
  image extension, or as a binary table extension.  Both NESTED and RING pixel
  indices are supported.  It uses @ref software "CFITSIO".

- @a fitshdr lists headers from a FITS file specified on the command line, or
  else on stdin, printing them as 80-character keyrecords without trailing
  blanks.  It is independent of WCSLIB.
*/


/** @page structs WCSLIB data structures

The WCSLIB routines are based on data structures specific to them: wcsprm for
the wcs.h,c routines, celprm for cel.h,c, and likewise spcprm, linprm,
prjprm and tabprm, with struct definitions contained in the corresponding
header files: wcs.h, cel.h, etc.  The structs store the parameters that define
a coordinate transformation and also intermediate values derived from those
parameters.  As a high-level object, the wcsprm struct contains linprm,
tabprm, spcprm, and celprm structs, and in turn the celprm struct contains a
prjprm struct.  Hence the wcsprm struct contains everything needed for a
complete coordinate description.

Applications programmers who use the top- and middle-level routines generally
only need to pass wcsprm structs from one routine that fills them to another
that uses them.  However, since these structs are fundamental to WCSLIB it is
worthwhile knowing something about the way they work.

Three basic operations apply to all WCSLIB structs:

- Initialize.  Each struct has a specific initialization routine, e.g.
  wcsini(), celini(), spcini(), etc.  These allocate memory (if required) and
  set all struct members to default values.

- Fill in the required values.  Each struct has members whose values must be
  provided.  For example, for wcsprm these values correspond to FITS WCS
  header keyvalues as are provided by the top-level header parsing routine,
  wcspih().

- Compute intermediate values.  Specific setup routines, e.g. wcsset(),
  celset(), spcset(), etc., compute intermediate values from the values
  provided.  In particular, wcsset() analyses the FITS WCS keyvalues provided,
  fills the required values in the lower-level structs contained in wcsprm,
  and invokes the setup routine for each of them.

Each struct contains a @a flag member that records its setup state.  This is
cleared by the initialization routine and checked by the routines that use the
struct; they will invoke the setup routine automatically if necessary, hence
it need not be invoked specifically by the application programmer.  However,
if any of the required values in a struct are changed then either the setup
routine must be invoked on it, or else the @a flag must be zeroed to signal
that the struct needs to be reset.

The initialization routine may be invoked repeatedly on a struct if it is
desired to reuse it.  However, the @a flag member of structs that contain
allocated memory (wcsprm, linprm and tabprm) must be set to -1 before the
first initialization to initialize memory management, but not subsequently or
else memory leaks will result.

Each struct has one or more service routines: to do deep copies from one to
another, to print its contents, and to free allocated memory.  Refer to the
header files for a detailed description.
*/


/** @page memory Memory management

The initialization routines for certain of the WCSLIB data structures allocate
memory for some of their members:

- wcsini() optionally allocates memory for the @a crpix, @a pc, @a cdelt,
    @a crval, @a cunit, @a ctype, @a pv, @a ps, @a cd, @a crota, @a colax,
    @a cname, @a crder, and @a csyer arrays in the wcsprm struct (using
    linini() for certain of these).  Note that wcsini() does not allocate
    memory for the @a tab array - refer to the usage notes for wcstab() in
    wcshdr.h.  If the @a pc matrix is not unity, wcsset() (via linset()) also
    allocates memory for the @a piximg and @a imgpix arrays.

- linini(): optionally allocates memory for the @a crpix, @a pc, and @a cdelt
    arrays in the linprm struct.  If the @a pc matrix is not unity, linset()
    also allocates memory for the @a piximg and @a imgpix arrays.  Typically
    these would be used by wcsini() and wcsset().

- tabini(): optionally allocates memory for the @a K, @a map, @a crval,
    @a index, and @a coord arrays (including the arrays referenced by
    @a index[]) in the tabprm struct.  tabmem() takes control of any of these
    arrays that may have been allocated by the user, specifically in that
    tabfree() will then free it.  tabset() also allocates memory for the
    @a sense, @a p0, @a delta and @a extrema arrays.

The caller may load data into these arrays but must not modify the struct
members (i.e. the pointers) themselves or else memory leaks will result.

wcsini() maintains a record of memory it has allocated and this is used by
wcsfree() which wcsini() uses to free any memory that it may have allocated
on a previous invokation.  Thus it is not necessary for the caller to invoke
wcsfree() separately if wcsini() is invoked repeatedly on the same wcsprm
struct.  Likewise, wcsset() deallocates memory that it may have allocated on
a previous invokation.  The same comments apply to linini(), linfree(), and
linset() and to tabini(), tabfree(), and tabset().

A memory leak will result if a wcsprm, linprm or tabprm struct goes out of
scope before the memory has been @a free'd, either by the relevant routine,
wcsfree(), linfree() or tabfree(), or otherwise.  Likewise, if one of these
structs itself has been @a malloc'd and the allocated memory is not @a free'd
when the memory for the struct is @a free'd.  A leak may also arise if the
caller interferes with the array pointers in the "private" part of these
structs.

Beware of making a shallow copy of a wcsprm, linprm or tabprm struct by
assignment; any changes made to allocated memory in one would be reflected in
the other, and if the memory allocated for one was @a free'd the other would
reference unallocated memory.  Use the relevant routine instead to make a deep
copy: wcssub(), lincpy() or tabcpy().
*/


/** @page diagnostics Diagnostic output

All @ref overview "WCSLIB" functions return a status value, each of which is
associated with a fixed error message which may be used for diagnostic output.
For example
@verbatim
  int status;
  struct wcsprm wcs;

  ...

  if ((status = wcsset(&wcs)) {
    fprintf(stderr, "ERROR %d from wcsset(): %s.\n", status, wcs_errmsg[status]);
    return status;
  }
@endverbatim
This might produce output like
@verbatim
ERROR 5 from wcsset(): Invalid parameter value.
@endverbatim
The error messages are provided as global variables with names of the form
@a cel_errmsg, @a prj_errmsg, etc. by including the relevant header file.

As of version 4.8, courtesy of Michael Droettboom @ref software "(pywcs)",
WCSLIB has a second error messaging system which provides more detailed
information about errors, including the function, source file, and line number
where the error occurred.  For example,
@verbatim
  struct wcsprm wcs;

  /* Enable wcserr and send messages to stderr. */
  wcserr_enable(1);
  wcsprintf_set(stderr);

  ...

  if (wcsset(&wcs) {
    wcsperr(&wcs);
    return wcs.err->status;
  }
@endverbatim
In this example, if an error was generated in one of the prjset() functions,
wcsperr() would print an error traceback starting with wcsset(), then
celset(), and finally the particular projection-setting function that
generated the error.  For each of them it would print the status return value,
function name, source file, line number, and an error message which may be
more specific and informative than the general error messages reported in the
first example.  For example, in response to a deliberately generated error,
the @c twcs test program, which tests wcserr among other things, produces a
traceback similar to this:
@verbatim
ERROR 5 in wcsset() at line 1564 of file wcs.c:
  Invalid parameter value.
ERROR 2 in celset() at line 196 of file cel.c:
  Invalid projection parameters.
ERROR 2 in bonset() at line 5727 of file prj.c:
  Invalid parameters for Bonne's projection.
@endverbatim

Each of the @ref structs "structs" in @ref overview "WCSLIB" includes a
pointer, called @a err, to a wcserr struct.  When an error occurs, a struct is
allocated and error information stored in it.  The wcserr pointers and the
@ref memory "memory" allocated for them are managed by the routines that
manage the various structs such as wcsini() and wcsfree().

wcserr messaging is an opt-in system enabled via wcserr_enable(), as in the
example above.  If enabled, when an error occurs it is the user's
responsibility to free the memory allocated for the error message using
wcsfree(), celfree(), prjfree(), etc.  Failure to do so before the struct goes
out of scope will result in memory leaks (if execution continues beyond the
error).
*/


/** @page vector Vector API

WCSLIB's API is vector-oriented.  At the least, this allows the function call
overhead to be amortised by spreading it over multiple coordinate
transformations.  However, vector computations may provide an opportunity for
caching intermediate calculations and this can produce much more significant
efficiencies.  For example, many of the spherical projection equations are
partially or fully separable in the mathematical sense, i.e. @f$ (x,y) =
f(\phi) g(\theta) @f$, so if @f$ \theta @f$ was invariant for a set of
coordinate transformations then @f$ g(\theta) @f$ would only need to be
computed once.  Depending on the circumstances, this may well lead to speedups
of a factor of two or more.

WCSLIB has two different categories of vector API:

- Certain steps in the WCS algorithm chain operate on coordinate vectors as a
  whole rather than particular elements of it.  For example, the linear
  transformation takes one or more pixel coordinate vectors, multiples by the
  transformation matrix, and returns whole intermediate world coordinate
  vectors.
  @n
  The routines that implement these steps, wcsp2s(), wcss2p(), linp2x(),
  linx2p(), tabx2s(), and tabs2x(), accept and return two-dimensional arrays,
  i.e. a number of coordinate vectors.  Because WCSLIB permits these arrays to
  contain unused elements, three parameters are needed to describe them:
  - @a  naxis: the number of coordinate elements, as per the FITS @c NAXIS or
               @c WCSAXES keyvalues,
  - @a ncoord: the number of coordinate vectors,
  - @a  nelem: the total number of elements in each vector, unused as well as
               used.  Clearly, @a nelem must equal or exceed @a naxis.  (Note
               that when @a ncoord is unity, @a nelem is irrelevant and so is
               ignored.  It may be set to 0.)
  .
  @a ncoord and @a nelem are specified as function arguments while @a naxis is
  provided as a member of the wcsprm (or linprm) struct.
  @n
  For example, wcss2p() accepts an array of world coordinate vectors,
  <EM>world[ncoord][nelem]</EM>.  In the following example, @a naxis = 4,
  @a ncoord = 5, and @a nelem = 7:
  @verbatim
    s1  x1  y1  t1  u   u   u
    s2  x2  y2  t2  u   u   u
    s3  x3  y3  t3  u   u   u
    s4  x4  y4  t4  u   u   u
    s5  x5  y5  t5  u   u   u
  @endverbatim
  where @a u indicates unused array elements, and the array is laid out in
  memory as
  @verbatim
    s1  x1  y1  t1  u   u   u   s2  x2  y2  ...
  @endverbatim
  @b Note that the <EM>stat[]</EM> vector returned by routines in this
  category is of length @a ncoord, as are the intermediate <EM>phi[]</EM> and
  <EM>theta[]</EM> vectors returned by wcsp2s() and wcss2p().
  @n
  @b Note also that the function prototypes for routines in this category
  have to declare these two-dimensional arrays as one-dimensional vectors in
  order to avoid warnings from the C compiler about declaration of "incomplete
  types".  This was considered preferable to declaring them as simple
  pointers-to-double which gives no indication that storage is associated with
  them.

- Other steps in the WCS algorithm chain typically operate only on a part of
  the coordinate vector.  For example, a spectral transformation operates on
  only one element of an intermediate world coordinate that may also contain
  celestial coordinate elements.  In the above example, spcx2s() might operate
  only on the @a s (spectral) coordinate elements.
  @n
  Routines like spcx2s() and celx2s() that implement these steps accept and
  return one-dimensional vectors in which the coordinate element of interest
  is specified via a starting address, a length, and a stride.  To continue
  the previous example, the starting address for the spectral elements is
  @a s1, the length is 5, and the stride is 7.

@section lengths Vector lengths

Routines such as spcx2s() and celx2s() accept and return either one coordinate
vector, or a pair of coordinate vectors (one-dimensional C arrays).  As
explained above, the coordinate elements of interest are usually embedded in a
two-dimensional array and must be selected by specifying a starting point,
length and stride through the array.  For routines such as spcx2s() that
operate on a single element of each coordinate vector these parameters have a
straightforward interpretation.

However, for routines such as celx2s() that operate on a pair of elements in
each coordinate vector, WCSLIB allows these parameters to be specified
independently for each input vector, thereby providing a much more general
interpretation than strictly needed to traverse an array.

This is best described by illustration.  The following diagram describes the
situation for cels2x(), as a specific example, with <EM>nlng = 5</EM>, and
<EM>nlat = 3:</EM>

@verbatim
             lng[0]   lng[1]   lng[2]  lng[3]   lng[4]
             ------   ------   ------  ------   ------
  lat[0]  |  x,y[0]   x,y[1]   x,y[2]  x,y[3]   x,y[4]
  lat[1]  |  x,y[5]   x,y[6]   x,y[7]  x,y[8]   x,y[9]
  lat[2]  |  x,y[10]  x,y[11]  x,y[12] x,y[13]  x,y[14]
@endverbatim

In this case, while only 5 longitude elements and 3 latitude elements are
specified, the world-to-pixel routine would calculate <EM>nlng * nlat = 15
(x,y)</EM> coordinate pairs.  It is the responsibility of the caller to ensure
that sufficient space has been allocated in <EM><B>all</B></EM> of the output
arrays, in this case <EM>phi[]</EM>, <EM>theta[]</EM>, <EM>x[]</EM>,
<EM>y[]</EM> and <EM>stat[]</EM>.

Vector computation will often be required where neither @a lng nor @a lat is
constant.  This is accomplished by setting @a nlat = 0 which is interpreted to
mean <EM>nlat = nlng</EM> but only the matrix diagonal is to be computed.
Thus, for <EM>nlng = 3</EM> and <EM>nlat = 0</EM> only three <EM>(x,y)</EM>
coordinate pairs are computed:

@verbatim
             lng[0]   lng[1]   lng[2]
             ------   ------   ------
  lat[0]  |  x,y[0]
  lat[1]  |           x,y[1]
  lat[2]  |                    x,y[2]
@endverbatim

Note how this differs from <EM>nlng = 3, nlat = 1</EM>:

@verbatim
             lng[0]   lng[1]   lng[2]
             ------   ------   ------
  lat[0]  |  x,y[0]   x,y[1]   x,y[2]
@endverbatim

The situation for celx2s() is similar; the <EM>x</EM>-coordinate (like @a lng)
varies fastest.

Similar comments can be made for all routines that accept arguments specifying
vector length(s) and stride(s).  (tabx2s() and tabs2x() do not fall into this
category because the @c -TAB algorithm is fully <EM>N</EM>-dimensional so
there is no way to know in advance how many coordinate elements may be
involved.)

The reason that WCSLIB allows this generality is related to the aforementioned
opportunities that vector computations may provide for caching intermediate
calculations and the significant efficiencies that can result.  The high-level
routines, wcsp2s() and wcss2p(), look for opportunities to collapse a set of
coordinate transformations where one of the coordinate elements is invariant,
and the low-level routines take advantage of such to cache intermediate
calculations.


@section strides Vector strides

As explained above, the vector stride arguments allow the caller to specify
that successive elements of a vector are not contiguous in memory.  This
applies equally to vectors given to, or returned from a function.

As a further example consider the following two arrangements in memory of the
elements of four <EM>(x,y)</EM> coordinate pairs together with an @a s
coordinate element (e.g. spectral):

- <EM>x1 x2 x3 x4 y1 y2 y3 y4 s1 s2 s3 s4</EM> @n
  the address of <EM>x[]</EM> is @a x1, its stride is 1, and length 4, @n
  the address of <EM>y[]</EM> is @a y1, its stride is 1, and length 4, @n
  the address of <EM>s[]</EM> is @a s1, its stride is 1, and length 4.

- <EM>x1 y1 s1 x2 y2 s2 x3 y3 s3 x4 y4 s4</EM> @n
  the address of <EM>x[]</EM> is @a x1, its stride is 3, and length 4, @n
  the address of <EM>y[]</EM> is @a y1, its stride is 3, and length 4, @n
  the address of <EM>s[]</EM> is @a s1, its stride is 3, and length 4.

For routines such as cels2x(), each of the pair of input vectors is assumed to
have the same stride.  Each of the output vectors also has the same stride,
though it may differ from the input stride.  For example, for cels2x() the
input <EM>lng[]</EM> and <EM>lat[]</EM> vectors each have vector stride
@a sll, while the <EM>x[]</EM> and <EM>y[]</EM> output vectors have stride
@a sxy.  However, the intermediate <EM>phi[]</EM> and <EM>theta[]</EM> arrays
each have unit stride, as does the <EM>stat[]</EM> vector.

If the vector length is 1 then the stride is irrelevant and so ignored.  It
may be set to 0.
*/


/** @page threads Thread-safety

With the following exceptions WCSLIB 5.17 is thread-safe:

- The C code generated by Flex is not re-entrant.  Flex does have the capacity
  for producing re-entrant scanners but they have a different API.  This may
  be handled by a compile-time option in future but in the meantime calls to
  the header parsers should be serialized via a mutex.

- The low-level functions wcsnpv() and wcsnps() are not thread-safe but within
  the library itself they are only used by the Flex scanners wcspih() and
  wcsbth().  They would rarely need to be used by application programmers.

- Diagnostic functions that print the contents of the various structs, namely
  celprt(), linprt(), prjprt(), spcprt(), tabprt(), wcsprt(), and wcsperr()
  use printf() which is thread-safe by the POSIX requirement on @c stdio.
  However, this is only at the function level.  Where multiple threads invoke
  these functions simultaneously their output is likely to be interleaved.

- wcserr_enable() sets a static variable and so is not thread-safe.  However,
  this facility is not intended to be used dynamically.  If detailed error
  messages are required, enable wcserr when execution starts and don't change
  it.
*/


/** @page testing Example code, testing and verification

WCSLIB has an extensive test suite that also provides programming templates
as well as demonstrations.  Test programs, with names that indicate the main
WCSLIB routine under test, reside in @c ./{C,Fortran}/test and each contains a
brief description of its purpose.

The high- and middle-level test programs are more instructive for applications
programming, while the low-level tests are vital for verifying the integrity
of the mathematical routines.

- High level:
  @n
  @a twcstab provides an example of high-level applications programming using
  WCSLIB and @ref software "CFITSIO".  It constructs an input FITS test file,
  specifically for testing TAB coordinates, partly using @c wcstab.keyrec, and
  then extracts the coordinate description from it following the steps
  outlined in wcshdr.h.
  @n@n
  @a tpih1 and @a tpih2 verify wcspih().  The first prints the contents of the
  structs returned by wcspih() using wcsprt() and the second uses @a cpgsbox()
  to draw coordinate graticules.  Input for these comes from a FITS WCS test
  header implemented as a list of keyrecords, @c wcs.keyrec, one keyrecord per
  line, together with a program, @a tofits, that compiles these into a valid
  FITS file.
  @n@n
  @a tfitshdr also uses @c wcs.keyrec to test the generic FITS header parsing
  routine.
  @n@n
  @a twcsfix sets up a wcsprm struct containing various non-standard
  constructs and then invokes wcsfix() to translate them all to standard
  usage.

- Middle level:
  @n
  @a twcs tests closure of wcss2p() and wcsp2s() for a number of selected
  projections.  @a twcsmix verifies wcsmix() on the @f$1^\circ@f$ grid of
  celestial longitude and latitude for a number of selected projections.  It
  plots a test grid for each projection and indicates the location of
  successful and failed solutions.  @a twcssub tests the extraction of a
  coordinate description for a subimage from a wcsprm struct by wcssub().
  @n@n
  @a tunits tests wcsutrne(), wcsunitse() and wcsulexe(), the units
  specification translator, converter and parser, either interactively or
  using a list of units specifications contained in units_test.

- Low level:
  @n
  @a tlin, @a tlog, @a tprj1, @a tsph, @a tspc, @a tspc, and ttab1 test
  "closure" of the respective routines.  Closure tests apply the forward and
  reverse transformations in sequence and compare the result with the original
  value.  Ideally, the result should agree exactly, but because of floating
  point rounding errors there is usually a small discrepancy so it is only
  required to agree within a "closure tolerance".
  @n@n
  @a tprj1 tests for closure separately for longitude and latitude except at
  the poles where it only tests for closure in latitude.  Note that closure in
  longitude does not deal with angular displacements on the sky.  This is
  appropriate for many projections such as the cylindricals where circumpolar
  parallels are projected at the same length as the equator.  On the other
  hand, @a tsph does test for closure in angular displacement.
  @n@n
  The tolerance for reporting closure discrepancies is set at @f$10^{-10}@f$
  degree for most projections; this is slightly less than 3 microarcsec.  The
  worst case closure figure is reported for each projection and this is
  usually better than the reporting tolerance by several orders of magnitude.
  @a tprj1 and @a tsph test closure at all points on the @f$1^\circ@f$ grid of
  native longitude and latitude and to within @f$5^\circ@f$ of any latitude of
  divergence for those projections that cannot represent the full sphere.
  Closure is also tested at a sequence of points close to the reference point
  (@a tprj1) or pole (@a tsph).
  @n@n
  Closure has been verified at all test points for SUN workstations.  However,
  non-closure may be observed for other machines near native latitude
  @f$-90^\circ@f$ for the zenithal, cylindrical and conic equal area
  projections (<TT><B>ZEA</B></TT>, <TT><B>CEA</B></TT> and
  <TT><B>COE</B></TT>), and near divergent latitudes of projections such as
  the azimuthal perspective and stereographic projections (<TT><B>AZP</B></TT>
  and <TT><B>STG</B></TT>).   Rounding errors may also carry points between
  faces of the quad-cube projections (<TT><B>CSC</B></TT>,
  <TT><B>QSC</B></TT>, and <TT><B>TSC</B></TT>).  Although such excursions may
  produce long lists of non-closure points, this is not necessarily indicative
  of a fundamental problem.
  @n@n
  Note that the inverse of the COBE quad-qube projection (<TT><B>CSC</B></TT>)
  is a polynomial approximation and its closure tolerance is intrinsically
  poor.
  @n@n
  Although tests for closure help to verify the internal consistency of the
  routines they do not verify them in an absolute sense.  This is partly
  addressed by @a tcel1, @a tcel2, @a tprj2, @a ttab2 and @a ttab3 which plot
  graticules for visual inspection of scaling, orientation, and other
  macroscopic characteristics of the projections.
*/


/** @page fortran WCSLIB Fortran wrappers

The Fortran subdirectory contains wrappers, written in C, that allow Fortran
programs to use WCSLIB.

A prerequisite for using the wrappers is an understanding of the usage of the
associated C routines, in particular the data structures they are based on.
The principle difficulty in creating the wrappers was the need to manage these
C structs from within Fortran, particularly as they contain pointers to
allocated memory, pointers to C functions, and other structs that themselves
contain similar entities.

To this end, routines have been provided to set and retrieve values of the
various structs, for example @c WCSPUT and @c WCSGET for the wcsprm struct,
and @c CELPUT and @c CELGET for the celprm struct.  These must be used in
conjunction with wrappers on the routines provided to manage the structs in C,
for example @c WCSINI, @c WCSSUB, @c WCSCOPY, @c WCSFREE, and @c WCSPRT which
wrap wcsini(), wcssub(), wcscopy(), wcsfree(), and wcsprt().

The various @c *PUT and @c *GET routines are based on codes defined in Fortran
include files (*.inc), if your Fortran compiler does not support the
@c INCLUDE statement then you will need to include these manually wherever
necessary.  Codes are defined as parameters with names like @c WCS_CRPIX which
refers to wcsprm::crpix (if your Fortran compiler does not support long
symbolic names then you will need to rename these).

The include files also contain parameters, such as @c WCSLEN, that define the
length of an @c INTEGER array that must be declared to hold the struct.  This
length may differ for different platforms depending on how the C compiler
aligns data within the structs.  A test program for the C library, @a twcs,
prints the size of the struct in <EM>sizeof(int)</EM> units and the values in
the Fortran include files must equal or exceed these.  On some platforms, such
as Suns, it is important that the start of the @c INTEGER array be
<EM><B>aligned on a @c DOUBLE @c PRECISION boundary</B></EM>, otherwise a
@c BUS error may result.  This may be achieved via an @c EQUIVALENCE with a
@c DOUBLE @c PRECISION variable, or by sequencing variables in a @c COMMON
block so that the @c INTEGER array follows immediately after a @c DOUBLE
@c PRECISION variable.

The @c *PUT routines set only one element of an array at a time; the final one
or two integer arguments of these routines specify 1-relative array indices
(N.B. not 0-relative as in C).  The one exception is the prjprm::pv array.

The @c *PUT routines also reset the @a flag element to signal that the struct
needs to be reinitialized.  Therefore, if you wanted to set wcsprm::flag
itself to -1 prior to the first call to @c WCSINI, for example, then that
@c WCSPUT must be the last one before the call.

The @c *GET routines retrieve whole arrays at a time and expect array
arguments of the appropriate length where necessary.  Note that they do not
initialize the structs.

A basic coding fragment is

@verbatim
      INTEGER   LNGIDX, STATUS
      CHARACTER CTYPE1*72

      INCLUDE 'wcs.inc'

*     WCSLEN is defined as a parameter in wcs.inc.
      INTEGER   WCS(WCSLEN)
      DOUBLE PRECISION DUMMY
      EQUIVALENCE (WCS, DUMMY)

*     Allocate memory and set default values for 2 axes.
      STATUS = WCSPUT (WCS, WCS_FLAG, -1, 0, 0)
      STATUS = WCSINI (2, WCS)

*     Set CRPIX1, and CRPIX2; WCS_CRPIX is defined in wcs.inc.
      STATUS = WCSPUT (WCS, WCS_CRPIX, 512D0, 1, 0)
      STATUS = WCSPUT (WCS, WCS_CRPIX, 512D0, 2, 0)

*     Set PC1_2 to 5.0 (I = 1, J = 2).
      STATUS = WCSPUT (WCS, WCS_PC, 5D0, 1, 2)

*     Set CTYPE1 to 'RA---SIN'; N.B. must be given as CHARACTER*72.
      CTYPE1 = 'RA---SIN'
      STATUS = WCSPUT (WCS, WCS_CTYPE, CTYPE1, 1, 0)

*     Set PV1_3 to -1.0 (I = 1, M = 3).
      STATUS = WCSPUT (WCS, WCS_PV, -1D0, 1, 3)

      etc.

*     Initialize.
      STATUS = WCSSET (WCS)
      IF (STATUS.NE.0) THEN
        CALL FLUSH(6)
        STATUS = WCSPERR(WCS, CHAR(0))
      ENDIF

*     Find the "longitude" axis.
      STATUS = WCSGET (WCS, WCS_LNG, LNGIDX)

*     Free memory.
      STATUS = WCSFREE (WCS)
@endverbatim

Refer to the various Fortran test programs for further programming examples.
In particular, @a twcs and @a twcsmix show how to retrieve elements of the
celprm and prjprm structs contained within the wcsprm struct.

Note that the data type of the third argument to the @c *PUT and @c *GET
routines differs depending on the data type of the corresponding C struct
member, be it @a int, @a double, or @a char[].  It is essential that the
Fortran data type match that of the C struct for @a int and @a double types,
and be a @c CHARACTER variable of the correct length for @a char[] types.
Compilers (e.g. g77) may warn of inconsistent usage of this argument but this
can (usually) be safely ignored.  If these warnings become annoying,
type-specific variants are provided for each of the @c *PUT routines, @c *PTI,
@c *PTD, and @c *PTC for @a int, @a double, or @a char[] and likewise @c *GTI,
@c *GTD, and @c *GTC for the @c *GET routines.

When calling wrappers for C functions that print to @a stdout, such as
@c WCSPRT, and @c WCSPERR, or that may print to @a stderr, such as @c WCSPIH,
@c WCSBTH, @c WCSULEXE, or @c WCSUTRNE, it may be necessary to flush the
Fortran I/O buffers beforehand so that the output appears in the correct
order.  The wrappers for these functions do call @c fflush(NULL), but
depending on the particular system, this may not succeed in flushing the
Fortran I/O buffers.  Most Fortran compilers provide the non-standard
intrinsic @c FLUSH(), which is called with unit number 6 to flush @a stdout
(as in the example above), and unit 0 for @a stderr.

A basic assumption made by the wrappers is that an @c INTEGER variable is no
less than half the size of a @c DOUBLE @c PRECISION.
*/


/** @page pgsbox PGSBOX

@c PGSBOX, which is provided as a separate part of WCSLIB, is a @ref software
"PGPLOT" routine (PGPLOT being a Fortran graphics library) that draws and
labels curvilinear coordinate grids.  Example @c PGSBOX grids can be seen at
http://www.atnf.csiro.au/people/Mark.Calabretta/WCS/PGSBOX/index.html.

The prologue to pgsbox.f contains usage instructions.  pgtest.f and cpgtest.c
serve as test and demonstration programs in Fortran and C and also as well-
documented examples of usage.

@c PGSBOX requires a separate routine, @c EXTERNAL @c NLFUNC, to define the
coordinate transformation.  Fortran subroutine @c PGCRFN (pgcrfn.f) is
provided to define separable pairs of non-linear coordinate systems.  Linear,
logarithmic and power-law axis types are currently defined; further types may
be added as required.  A C function, @a pgwcsl_(), with Fortran-like interface
defines an @c NLFUNC that interfaces to WCSLIB 4.x for @c PGSBOX to draw
celestial coordinate grids.

@ref software "PGPLOT" is implemented as a Fortran library with a set of C
wrapper routines that are generated by a software tool.  However, @c PGSBOX
has a more complicated interface than any of the standard PGPLOT routines,
especially in having an @c EXTERNAL function in its argument list.
Consequently, @c PGSBOX is implemented in Fortran but with a hand-coded C
wrapper, @a cpgsbox().

As an example, in this suite the C test/demo program, @a cpgtest, calls the C
wrapper, @a cpgsbox(), passing it a pointer to @a pgwcsl_().  In turn,
@a cpgsbox() calls @c PGSBOX, which invokes @a pgwcsl_() as an @c EXTERNAL
subroutine.  In this sequence, a complicated C struct defined by @a cpgtest is
passed through @c PGSBOX to @a pgwcsl_() as an @c INTEGER array.

While there are no formal standards for calling Fortran from C, there are some
fairly well established conventions.  Nevertheless, it's possible that you may
need to modify the code if you use a combination of Fortran and C compilers
with linkage conventions that differ from that of the GNU compilers, gcc and
g77.
*/

/** @page versioning WCSLIB version numbers

The full WCSLIB/PGSBOX version number is composed of three integers in fields
separated by periods:

 - <B>Major</B>: the first number changes only when the ABI changes, a rare
   occurence (and the API never changes).  Typically, the ABI changes when the
   contents of a struct change.  For example, the contents of the
   <I>linprm</I> struct changed between 4.25.1 and 5.0.

   In practical terms, this number becomes the major version number of the
   WCSLIB sharable library, <B>libwcs.so.<major></B>.  To avoid possible
   segmentation faults or bus errors that may arise from the altered ABI, the
   dynamic (runtime) linker will not allow an application linked to a sharable
   library with a particular major version number to run with that of a
   different major version number.

   Application code must be recompiled and relinked to use a newer version of
   the WCSLIB sharable library with a new major version number.

 - <B>Minor</B>: the second number changes when existing code is changed,
   whether due to added functionality or bug fixes.  This becomes the minor
   version number of the WCSLIB sharable library,
   <B>libwcs.so.<major>.<minor></B>.

   Because the ABI remains unchanged, older applications can use the new
   sharable library without needing to be recompiled, thus obtaining the
   benefit of bug fixes, speed enhancements, etc.

   Application code written subsequently to use the added functionality would,
   of course, need to be recompiled.

 - <B>Patch</B>: the third number, which is often omitted, indicates a change
   to the build procedures, documentation, or test suite.  It may also
   indicate changes to the utility applications (<I>wcsware</I>,
   <I>HPXcvt</I>, etc.), including the addition of new ones.

   However, the library itself, including the definitions in the header files,
   remains unaltered, so there is no point in recompiling applications.

The following describes what happens (or should happen) when WCSLIB's
installation procedures are used on a typical Linux system using the GNU gcc
compiler and GNU linker.

The sharable library should be installed as libwcs.so.<major>.<minor>, say
libwcs.so.5.4 for concreteness, and a number of symbolic links created as
follows:

@verbatim
  libwcs.so     -> libwcs.so.5
  libwcs.so.5   -> libwcs.so.5.4
  libwcs.so.5.4
@endverbatim

When an application is linked using '-lwcs', the linker finds libwcs.so and
the symlinks lead it to libwcs.so.5.4.  However, that library's SONAME is
actually 'libwcs.so.5', by virtue of linker options used when the sharable
library was created, as can be seen by running

@verbatim
  readelf -d libwcs.so.5.4
@endverbatim

Thus, when an application that was compiled and linked to libwcs.so.5.4 begins
execution, the dynamic linker, ld.so, will attempt to bind it to libwcs.so.5,
as can be seen by running

@verbatim
  ldd <application>
@endverbatim

Later, when WCSLIB  5.5 is installed, the library symbolic links will become

@verbatim
  libwcs.so     -> libwcs.so.5
  libwcs.so.5   -> libwcs.so.5.5
  libwcs.so.5.4
  libwcs.so.5.5
@endverbatim

Thus, even without being recompiled, existing applications will link
automatically to libwcs.so.5.5 at runtime.  In fact, libwcs.so.5.4 would no
longer be used and could be deleted.

If WCSLIB 6.0 were to be installed at some later time, then the libwcs.so.6
libraries would be used for new compilations.  However, the libwcs.so.5
libraries must be left in place for existing executables that still require
them:

@verbatim
  libwcs.so     -> libwcs.so.6
  libwcs.so.6   -> libwcs.so.6.0
  libwcs.so.6.0
  libwcs.so.5   -> libwcs.so.5.5
  libwcs.so.5.5
@endverbatim
*/
