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@c Copyright (C) 2007-2011 John W. Eaton and David Bateman
@c Copyright (C) 2007 Paul Thomas and Christoph Spiel
@c
@c This file is part of Octave.
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@node Dynamically Linked Functions
@appendix Dynamically Linked Functions
@cindex dynamic-linking

Octave has the possibility of including compiled code as dynamically
linked extensions and then using these extensions as if they were part
of Octave itself.  Octave can call C++ code
through its native oct-file interface or C code through its mex
interface.  It can also indirectly call functions written in any other
language through a simple wrapper.  The reasons to write code in a
compiled language might be either to link to an existing piece of code
and allow it to be used within Octave, or to allow improved performance
for key pieces of code.

Before going further, you should first determine if you really need to
use dynamically linked functions at all.  Before proceeding with writing
any dynamically linked function to improve performance you should
address ask yourself

@itemize @bullet
@item
Can I get the same functionality using the Octave scripting language only?

@item
Is it thoroughly optimized Octave code?  Vectorization of Octave code,
doesn't just make it concise, it generally significantly improves its
performance.  Above all, if loops must be used, make sure that the
allocation of space for variables takes place outside the loops using an
assignment to a matrix of the right size, or zeros.

@item
Does it make as much use as possible of existing built-in library
routines?  These are highly optimized and many do not carry the overhead
of being interpreted.

@item
Does writing a dynamically linked function represent useful investment
of your time, relative to staying in Octave?
@end itemize

Also, as oct- and mex-files are dynamically linked to Octave, they
introduce the possibility of Octave crashing due to errors in
the user code.  For example a segmentation violation in the user's code
will cause Octave to abort.

@menu
* Oct-Files::                   
* Mex-Files::                   
* Standalone Programs::         
@end menu

@node Oct-Files
@section Oct-Files
@cindex oct-files
@cindex mkoctfile
@cindex oct

@menu
* Getting Started with Oct-Files::  
* Matrices and Arrays in Oct-Files::  
* Character Strings in Oct-Files::  
* Cell Arrays in Oct-Files::    
* Structures in Oct-Files::  
* Sparse Matrices in Oct-Files::  
* Accessing Global Variables in Oct-Files::  
* Calling Octave Functions from Oct-Files::  
* Calling External Code from Oct-Files::  
* Allocating Local Memory in Oct-Files::  
* Input Parameter Checking in Oct-Files::  
* Exception and Error Handling in Oct-Files::  
* Documentation and Test of Oct-Files::  
@c * Application Programming Interface for Oct-Files::  
@end menu

@node Getting Started with Oct-Files
@subsection Getting Started with Oct-Files

The basic command to build oct-files is @code{mkoctfile} and it can be
call from within octave or from the command line.

@c mkoctfile scripts/miscellaneous/mkoctfile.m
@anchor{doc-mkoctfile}
@deftypefn {Command} {} mkoctfile [-options] file @dots{}

The @code{mkoctfile} function compiles source code written in C,
C++, or Fortran.  Depending on the options used with @code{mkoctfile}, the
compiled code can be called within Octave or can be used as a stand-alone
application.

@code{mkoctfile} can be called from the shell prompt or from the Octave
prompt.

@code{mkoctfile} accepts the following options, all of which are optional
except for the file name of the code you wish to compile:

@table @samp
@item -I DIR
Add the include directory DIR to compile commands.

@item -D DEF
Add the definition DEF to the compiler call.

@item -l LIB
Add the library LIB to the link command.

@item -L DIR
Add the library directory DIR to the link command.

@item -M
@itemx --depend
Generate dependency files (.d) for C and C++ source files.

@item -R DIR
Add the run-time path to the link command.

@item -Wl,@dots{}
Pass flags though the linker like "-Wl,-rpath=@dots{}".
The quotes are needed since commas are interpreted as command
separators.

@item -W@dots{}
Pass flags though the compiler like "-Wa,OPTION".

@item -c
Compile but do not link.

@item -g
Enable debugging options for compilers.

@item -o FILE
@itemx --output FILE
Output file name.  Default extension is .oct
(or .mex if @samp{--mex} is specified) unless linking
a stand-alone executable.

@item -p VAR
@itemx --print VAR
Print the configuration variable VAR@.  Recognized variables are:

@example
   ALL_CFLAGS                FFTW_LIBS
   ALL_CXXFLAGS              FLIBS
   ALL_FFLAGS                FPICFLAG
   ALL_LDFLAGS               INCFLAGS
   BLAS_LIBS                 LDFLAGS
   CC                        LD_CXX
   CFLAGS                    LD_STATIC_FLAG
   CPICFLAG                  LFLAGS
   CPPFLAGS                  LIBCRUFT
   CXX                       LIBOCTAVE
   CXXFLAGS                  LIBOCTINTERP
   CXXPICFLAG                LIBREADLINE
   DEPEND_EXTRA_SED_PATTERN  LIBS
   DEPEND_FLAGS              OCTAVE_LIBS
   DL_LD                     RDYNAMIC_FLAG
   DL_LDFLAGS                RLD_FLAG
   F2C                       SED
   F2CFLAGS                  XTRA_CFLAGS
   F77                       XTRA_CXXFLAGS
   FFLAGS
@end example

@item --link-stand-alone
Link a stand-alone executable file.

@item --mex
Assume we are creating a MEX file.  Set the default output extension
to ".mex".

@item -s
@itemx --strip
Strip the output file.

@item -v
@itemx --verbose
Echo commands as they are executed.

@item file
The file to compile or link.  Recognized file types are

@example
@group
                  .c    C source
                  .cc   C++ source
                  .C    C++ source
                  .cpp  C++ source
                  .f    Fortran source (fixed form)
                  .F    Fortran source (fixed form)
                  .f90  Fortran source (free form)
                  .F90  Fortran source (free form)
                  .o    object file
                  .a    library file
@end group
@end example

@end table
@end deftypefn


Consider the short C++ example:

@example
@group
@verbatim
#include <octave/oct.h>

DEFUN_DLD (helloworld, args, nargout,
  "Hello World Help String")
{
  int nargin = args.length ();
  octave_stdout << "Hello World has " << nargin
        << " input arguments and "
        << nargout << " output arguments.\n";
  return octave_value_list ();
}
@end verbatim

@end group
@end example

This example although short introduces the basics of writing a C++
function that can be dynamically linked to Octave.  The easiest way to
make available most of the definitions that might be necessary for a C++
oct-file in Octave is to use the @code{#include <octave/oct.h>} header.
Note that @file{octave/oct.h} is a C++ header and cannot be directly
@code{#include}'ed in a C source file, nor any other language.  What
follows is mostly C++, with a discussion of other languages in section
@ref{Calling External Code from Oct-Files}.

The macro that defines the entry point into the dynamically loaded
function is @w{@code{DEFUN_DLD}}.  This macro takes four arguments, these being

@enumerate 1
@item The function name as it will be seen in Octave,

@item The list of arguments to the function of type @code{octave_value_list},

@item The number of output arguments, which can and often is omitted if
not used, and

@item The string that will be seen as the help text of the function.
@end enumerate

The return type of functions defined with @w{@code{DEFUN_DLD}} is always
@code{octave_value_list}.

There are a couple of important considerations in the choice of function
name.  Firstly, it must be a valid Octave function name and so must be a
sequence of letters, digits and underscores, not starting with a
digit.  Secondly, as Octave uses the function name to define the filename
it attempts to find the function in, the function name in the
@w{@code{DEFUN_DLD}} macro must match the filename of the oct-file.  Therefore,
the above function should be in a file @file{helloworld.cc}, and it should be
compiled to an oct-file using the command

@example
mkoctfile helloworld.cc
@end example

This will create a file called @file{helloworld.oct}, that is the compiled
version of the function.  It should be noted that it is perfectly
acceptable to have more than one @w{@code{DEFUN_DLD}} function in a source
file.  However, there must either be a symbolic link to the oct-file for
each of the functions defined in the source code with the @w{@code{DEFUN_DLD}}
macro or the autoload (@ref{Function Files}) function should be used.

The rest of this function then shows how to find the number of input
arguments, how to print through the octave pager, and return from the
function.  After compiling this function as above, an example of its use
is

@example
@group
helloworld (1, 2, 3)
@print{} Hello World has 3 input arguments and 0 output arguments.
@end group
@end example

@node Matrices and Arrays in Oct-Files
@subsection Matrices and Arrays in Oct-Files

Octave supports a number of different array and matrix classes, the
majority of which are based on the Array class.  The exception is the
sparse matrix types discussed separately below.  There are three basic
matrix types

@table @code
@item Matrix
A double precision matrix class defined in dMatrix.h,

@item ComplexMatrix
A complex matrix class defined in CMatrix.h, and

@item BoolMatrix
A boolean matrix class defined in boolMatrix.h.
@end table

These are the basic two-dimensional matrix types of octave.  In
additional there are a number of multi-dimensional array types, these
being

@table @code
@item NDArray
A double precision array class defined in @file{dNDArray.h}

@item ComplexNDarray
A complex array class defined in @file{CNDArray.h}

@item boolNDArray
A boolean array class defined in @file{boolNDArray.h}

@item int8NDArray
@itemx int16NDArray
@itemx int32NDArray
@itemx int64NDArray
8, 16, 32 and 64-bit signed array classes defined in
@file{int8NDArray.h}, @file{int16NDArray.h}, etc.

@item uint8NDArray
@itemx uint16NDArray
@itemx uint32NDArray
@itemx uint64NDArray
8, 16, 32 and 64-bit unsigned array classes defined in
@file{uint8NDArray.h}, @file{uint16NDArray.h}, etc.
@end table

There are several basic means of constructing matrices of
multi-dimensional arrays.  Considering the @code{Matrix} type as an
example

@itemize @bullet
@item
We can create an empty matrix or array with the empty constructor.  For
example

@example
Matrix a;
@end example

This can be used on all matrix and array types

@item
Define the dimensions of the matrix or array with a dim_vector.  For
example

@example
@group
dim_vector dv (2);
dv(0) = 2; dv(1) = 2;
Matrix a (dv);
@end group
@end example

This can be used on all matrix and array types

@item
Define the number of rows and columns in the matrix.  For example:

@example
Matrix a (2, 2)
@end example

However, this constructor can only be used with the matrix types.
@end itemize

These types all share a number of basic methods and operators, a
selection of which include

@deftypefn  Method T& {operator ()} (octave_idx_type)
@deftypefnx Method T& elem (octave_idx_type)
The @code{()} operator or @code{elem} method allow the values of the
matrix or array to be read or set.  These can take a single argument,
which is of type @code{octave_idx_type}, that is the index into the matrix or
array.  Additionally, the matrix type allows two argument versions of the
@code{()} operator and elem method, giving the row and column index of the
value to obtain or set.
@end deftypefn

Note that these functions do significant error checking and so in some
circumstances the user might prefer to access the data of the array or
matrix directly through the @nospell{fortran_vec} method discussed below.

@deftypefn Method octave_idx_type nelem (void) const
The total number of elements in the matrix or array.
@end deftypefn

@deftypefn Method size_t byte_size (void) const
The number of bytes used to store the matrix or array.
@end deftypefn

@deftypefn Method dim_vector dims (void) const
The dimensions of the matrix or array in value of type dim_vector.
@end deftypefn

@deftypefn Method void resize (const dim_vector&)
A method taking either an argument of type @code{dim_vector}, or in the
case of a matrix two arguments of type @code{octave_idx_type} defining
the number of rows and columns in the matrix.
@end deftypefn

@deftypefn Method T* fortran_vec (void)
This method returns a pointer to the underlying data of the matrix or a
array so that it can be manipulated directly, either within Octave or by
an external library.
@end deftypefn

Operators such an @code{+}, @code{-}, or @code{*} can be used on the
majority of the above types.  In addition there are a number of methods
that are of interest only for matrices such as @code{transpose},
@code{hermitian}, @code{solve}, etc.

The typical way to extract a matrix or array from the input arguments of
@w{@code{DEFUN_DLD}} function is as follows

@example
@group
@verbatim
#include <octave/oct.h>

DEFUN_DLD (addtwomatrices, args, , "Add A to B")
{
  int nargin = args.length ();
  if (nargin != 2)
    print_usage ();
  else
    {
      NDArray A = args(0).array_value ();
      NDArray B = args(1).array_value ();
      if (! error_state)
        return octave_value (A + B);
    }
  return octave_value_list ();
}
@end verbatim

@end group
@end example

To avoid segmentation faults causing Octave to abort, this function
explicitly checks that there are sufficient arguments available before
accessing these arguments.  It then obtains two multi-dimensional arrays
of type @code{NDArray} and adds these together.  Note that the array_value
method is called without using the @code{is_matrix_type} type, and instead the
error_state is checked before returning @code{A + B}.  The reason to
prefer this is that the arguments might be a type that is not an
@code{NDArray}, but it would make sense to convert it to one.  The
@code{array_value} method allows this conversion to be performed
transparently if possible, and sets @code{error_state} if it is not.

@code{A + B}, operating on two @code{NDArray}'s returns an
@code{NDArray}, which is cast to an @code{octave_value} on the return
from the function.  An example of the use of this demonstration function
is

@example
@group
addtwomatrices (ones (2, 2), ones (2, 2))
      @result{}  2  2
          2  2
@end group
@end example

A list of the basic @code{Matrix} and @code{Array} types, the methods to
extract these from an @code{octave_value} and the associated header is
listed below.

@multitable @columnfractions .3 .4 .3
@item @code{RowVector} @tab @code{row_vector_value} @tab @file{dRowVector.h}
@item @code{ComplexRowVector} @tab @code{complex_row_vector_value} @tab @file{CRowVector.h}
@item @code{ColumnVector} @tab @code{column_vector_value} @tab @file{dColVector.h}
@item @code{ComplexColumnVector} @tab @code{complex_column_vector_value} @tab @file{CColVector.h}
@item @code{Matrix} @tab @code{matrix_value} @tab @file{dMatrix.h}
@item @code{ComplexMatrix} @tab @code{complex_matrix_value} @tab @file{CMatrix.h}
@item @code{boolMatrix} @tab @code{bool_matrix_value} @tab @file{boolMatrix.h}
@item @code{charMatrix} @tab @code{char_matrix_value} @tab @file{chMatrix.h}
@item @code{NDArray} @tab @code{array_value} @tab @file{dNDArray.h}
@item @code{ComplexNDArray} @tab @code{complex_array_value} @tab @file{CNDArray.h}
@item @code{boolNDArray} @tab @code{bool_array_value} @tab @file{boolNDArray.h}
@item @code{charNDArray} @tab @code{char_array_value} @tab @file{charNDArray.h}
@item @code{int8NDArray} @tab @code{int8_array_value} @tab @file{int8NDArray.h}
@item @code{int16NDArray} @tab @code{int16_array_value} @tab @file{int16NDArray.h}
@item @code{int32NDArray} @tab @code{int32_array_value} @tab @file{int32NDArray.h}
@item @code{int64NDArray} @tab @code{int64_array_value} @tab @file{int64NDArray.h}
@item @code{uint8NDArray} @tab @code{uint8_array_value} @tab @file{uint8NDArray.h}
@item @code{uint16NDArray} @tab @code{uint16_array_value} @tab @file{uint16NDArray.h}
@item @code{uint32NDArray} @tab @code{uint32_array_value} @tab @file{uint32NDArray.h}
@item @code{uint64NDArray} @tab @code{uint64_array_value} @tab @file{uint64NDArray.h}
@end multitable

@node Character Strings in Oct-Files
@subsection Character Strings in Oct-Files

In Octave a character string is just a special @code{Array} class.
Consider the example:

@example
@verbatim
#include <octave/oct.h>

DEFUN_DLD (stringdemo, args, , "String Demo")
{
  int nargin = args.length();
  octave_value_list retval;

  if (nargin != 1)
    print_usage ();
  else
    {
      charMatrix ch = args(0).char_matrix_value ();

      if (! error_state)
        {
          if (args(0).is_sq_string ())
            retval(1) = octave_value (ch, true);
          else
            retval(1) = octave_value (ch, true, '\'');

          octave_idx_type nr = ch.rows();
          for (octave_idx_type i = 0; i < nr / 2; i++)
            {
              std::string tmp = ch.row_as_string (i);
              ch.insert (ch.row_as_string(nr-i-1).c_str(),
                         i, 0);
              ch.insert (tmp.c_str(), nr-i-1, 0);
            }
          retval(0) = octave_value (ch, true);
        }
    }
  return retval;
}
@end verbatim

@end example

An example of the use of this function is

@example
@group
s0 = ["First String"; "Second String"];
[s1,s2] = stringdemo (s0)
@result{} s1 = Second String
        First String

@result{} s2 = First String
        Second String

typeinfo (s2)
@result{} sq_string
typeinfo (s1)
@result{} string
@end group
@end example

One additional complication of strings in Octave is the difference
between single quoted and double quoted strings.  To find out if an
@code{octave_value} contains a single or double quoted string an example is

@example
@group
    if (args(0).is_sq_string ())
      octave_stdout << 
        "First argument is a singularly quoted string\n";
    else if (args(0).is_dq_string ())
      octave_stdout << 
        "First argument is a doubly quoted string\n";
@end group
@end example

Note however, that both types of strings are represented by the
@code{charNDArray} type, and so when assigning to an
@code{octave_value}, the type of string should be specified.  For example:

@example
@group
octave_value_list retval;
charNDArray c;
@dots{}
// Create single quoted string
retval(1) = octave_value (ch, true, '\'');

// Create a double quoted string
retval(0) = octave_value (ch, true);
@end group
@end example

@node Cell Arrays in Oct-Files
@subsection Cell Arrays in Oct-Files

Octave's cell type is equally accessible within oct-files.  A cell
array is just an array of @code{octave_value}s, and so each element of the cell
array can then be treated just like any other @code{octave_value}.  A simple
example is

@example
@group
@verbatim
#include <octave/oct.h>
#include <octave/Cell.h>

DEFUN_DLD (celldemo, args, , "Cell Demo")
{
  octave_value_list retval;
  int nargin = args.length ();

  if (nargin != 1)
    print_usage ();
  else
    {
      Cell c = args (0).cell_value ();
      if (! error_state)
        for (octave_idx_type i = 0; i < c.nelem (); i++)
          retval(i) = c.elem (i);
    }

  return retval;
}
@end verbatim

@end group
@end example

Note that cell arrays are used less often in standard oct-files and so
the @file{Cell.h} header file must be explicitly included.  The rest of this
example extracts the @code{octave_value}s one by one from the cell array and
returns be as individual return arguments.  For example consider

@example
@group
[b1, b2, b3] = celldemo (@{1, [1, 2], "test"@})
@result{}
b1 =  1
b2 =

   1   2

b3 = test
@end group
@end example

@node Structures in Oct-Files
@subsection Structures in Oct-Files

A structure in Octave is map between a number of fields represented and
their values.  The Standard Template Library @code{map} class is used,
with the pair consisting of a @code{std::string} and an octave
@code{Cell} variable.

A simple example demonstrating the use of structures within oct-files is

@example
@verbatim
#include <octave/oct.h>
#include <octave/ov-struct.h>

DEFUN_DLD (structdemo, args, , "Struct demo.")
{
  int nargin = args.length ();
  octave_value retval;

  if (args.length () == 2)
    {
      octave_scalar_map arg0 = args(0).scalar_map_value ();

      if (! error_state)
        {
          std::string arg1 = args(1).string_value ();

          if (! error_state)
            {
              octave_value tmp = arg0.contents (arg1);

              if (tmp.is_defined ())
                {
                  octave_scalar_map st;

                  st.assign ("selected", tmp);

                  retval = octave_value (st);
                }
              else
                error ("sruct does not contain field named '%s'\n",
                       arg1.c_str ());
            }
          else
            error ("expecting character string as second argument");
        }
      else
        error ("expecting struct as first argument");
    }
  else
    print_usage ();

  return retval;
}

@end verbatim

@end example

An example of its use is

@example
@group
x.a = 1; x.b = "test"; x.c = [1, 2];
structdemo (x, "b")
@result{} selected = test
@end group
@end example

The commented code above demonstrates how to iterate over all of the
fields of the structure, where as the following code demonstrates finding
a particular field in a more concise manner.

As can be seen the @code{contents} method of the @code{Octave_map} class
returns a @code{Cell} which allows structure arrays to be represented.
Therefore, to obtain the underlying @code{octave_value} we write

@example
octave_value tmp = arg0.contents (p1) (0);
@end example

@noindent
where the trailing (0) is the () operator on the @code{Cell} object.  We
can equally iterate of the elements of the Cell array to address the
elements of the structure array.

@node Sparse Matrices in Oct-Files
@subsection Sparse Matrices in Oct-Files

There are three classes of sparse objects that are of interest to the
user.

@table @code
@item SparseMatrix
A double precision sparse matrix class

@item SparseComplexMatrix
A complex sparse matrix class

@item SparseBoolMatrix
A boolean sparse matrix class
@end table

All of these classes inherit from the @code{Sparse<T>} template class,
and so all have similar capabilities and usage.  The @code{Sparse<T>}
class was based on Octave @code{Array<T>} class, and so users familiar
with Octave's @code{Array} classes will be comfortable with the use of
the sparse classes.

The sparse classes will not be entirely described in this section, due
to their similarity with the existing @code{Array} classes.  However,
there are a few differences due the different nature of sparse objects,
and these will be described.  Firstly, although it is fundamentally
possible to have N-dimensional sparse objects, the Octave sparse classes do
not allow them at this time.  So all operations of the sparse classes
must be 2-dimensional.  This means that in fact @code{SparseMatrix} is
similar to Octave's @code{Matrix} class rather than its
@code{NDArray} class.

@menu
* Array and Sparse Differences::  
* Creating Sparse Matrices in Oct-Files::  
* Using Sparse Matrices in Oct-Files::  
@end menu

@node Array and Sparse Differences
@subsubsection The Differences between the Array and Sparse Classes

The number of elements in a sparse matrix is considered to be the number
of non-zero elements rather than the product of the dimensions.  Therefore

@example
@group
SparseMatrix sm;
@dots{}
int nel = sm.nelem ();
@end group
@end example

@noindent
returns the number of non-zero elements.  If the user really requires the
number of elements in the matrix, including the non-zero elements, they
should use @code{numel} rather than @code{nelem}.  Note that for very
large matrices, where the product of the two dimensions is larger than
the representation of an unsigned int, then @code{numel} can overflow.
An example is @code{speye(1e6)} which will create a matrix with a million
rows and columns, but only a million non-zero elements.  Therefore the
number of rows by the number of columns in this case is more than two
hundred times the maximum value that can be represented by an unsigned int.
The use of @code{numel} should therefore be avoided useless it is known
it won't overflow.

Extreme care must be take with the elem method and the "()" operator,
which perform basically the same function.  The reason is that if a
sparse object is non-const, then Octave will assume that a
request for a zero element in a sparse matrix is in fact a request
to create this element so it can be filled.  Therefore a piece of
code like

@example
@group
SparseMatrix sm;
@dots{}
for (int j = 0; j < nc; j++)
  for (int i = 0; i < nr; i++)
    std::cerr << " (" << i << "," << j << "): " << sm(i,j)
              << std::endl;
@end group
@end example

@noindent
is a great way of turning the sparse matrix into a dense one, and a
very slow way at that since it reallocates the sparse object at each
zero element in the matrix.

An easy way of preventing the above from happening is to create a temporary
constant version of the sparse matrix.  Note that only the container for
the sparse matrix will be copied, while the actual representation of the
data will be shared between the two versions of the sparse matrix.  So this
is not a costly operation.  For example, the above would become

@example
@group
SparseMatrix sm;
@dots{}
const SparseMatrix tmp (sm);
for (int j = 0; j < nc; j++)
  for (int i = 0; i < nr; i++)
    std::cerr << " (" << i << "," << j << "): " << tmp(i,j)
              << std::endl;
@end group
@end example

Finally, as the sparse types aren't just represented as a contiguous
block of memory, the @nospell{@code{fortran_vec}} method of the @code{Array<T>}
is not available.  It is however replaced by three separate methods
@code{ridx}, @code{cidx} and @code{data}, that access the raw compressed
column format that the Octave sparse matrices are stored in.
Additionally, these methods can be used in a manner similar to @code{elem},
to allow the matrix to be accessed or filled.  However, in that case it is
up to the user to respect the sparse matrix compressed column format
discussed previous.

@node Creating Sparse Matrices in Oct-Files
@subsubsection Creating Sparse Matrices in Oct-Files

You have several alternatives for creating a sparse matrix.
You can first create the data as three vectors representing the
row and column indexes and the data, and from those create the matrix.
Or alternatively, you can create a sparse matrix with the appropriate
amount of space and then fill in the values.  Both techniques have their
advantages and disadvantages.

Here is an example of how to create a small sparse matrix with the first
technique

@example
@group
int nz = 4, nr = 3, nc = 4;

ColumnVector ridx (nz);
ColumnVector cidx (nz);
ColumnVector data (nz);

ridx(0) = 0; ridx(1) = 0; ridx(2) = 1; ridx(3) = 2;
cidx(0) = 0; cidx(1) = 1; cidx(2) = 3; cidx(3) = 3;
data(0) = 1; data(1) = 2; data(2) = 3; data(3) = 4;

SparseMatrix sm (data, ridx, cidx, nr, nc);
@end group
@end example

@noindent
which creates the matrix given in section
@ref{Storage of Sparse Matrices}.  Note that the compressed matrix
format is not used at the time of the creation of the matrix itself,
however it is used internally.

As previously mentioned, the values of the sparse matrix are stored
in increasing column-major ordering.  Although the data passed by the
user does not need to respect this requirement, the pre-sorting the
data significantly speeds up the creation of the sparse matrix.

The disadvantage of this technique of creating a sparse matrix is
that there is a brief time where two copies of the data exists.  Therefore
for extremely memory constrained problems this might not be the right
technique to create the sparse matrix.

The alternative is to first create the sparse matrix with the desired
number of non-zero elements and then later fill those elements in.  The
easiest way to do this is

@example
@group
int nz = 4, nr = 3, nc = 4;
SparseMatrix sm (nr, nc, nz);
sm(0,0) = 1; sm(0,1) = 2; sm(1,3) = 3; sm(2,3) = 4;
@end group
@end example

That creates the same matrix as previously.  Again, although it is not
strictly necessary, it is significantly faster if the sparse matrix is
created in this manner that the elements are added in column-major
ordering.  The reason for this is that if the elements are inserted
at the end of the current list of known elements then no element
in the matrix needs to be moved to allow the new element to be
inserted.  Only the column indexes need to be updated.

There are a few further points to note about this technique of creating
a sparse matrix.  Firstly, it is possible to create a sparse matrix
with fewer elements than are actually inserted in the matrix.  Therefore

@example
@group
int nz = 4, nr = 3, nc = 4;
SparseMatrix sm (nr, nc, 0);
sm(0,0) = 1; sm(0,1) = 2; sm(1,3) = 3; sm(2,3) = 4;
@end group
@end example

@noindent 
is perfectly valid.  However it is a very bad idea.  The reason is that
as each new element is added to the sparse matrix the space allocated
to it is increased by reallocating the memory.  This is an expensive
operation, that will significantly slow this means of creating a sparse
matrix.  Furthermore, it is possible to create a sparse matrix with
too much storage, so having @var{nz} above equaling 6 is also valid.
The disadvantage is that the matrix occupies more memory than strictly
needed.

It is not always easy to know the number of non-zero elements prior
to filling a matrix.  For this reason the additional storage for the
sparse matrix can be removed after its creation with the
@dfn{maybe_compress} function.  Furthermore, the maybe_compress can
deallocate the unused storage, but it can equally remove zero elements
from the matrix.  The removal of zero elements from the matrix is
controlled by setting the argument of the @dfn{maybe_compress} function
to be @samp{true}.  However, the cost of removing the zeros is high because it
implies resorting the elements.  Therefore, if possible it is better
is the user doesn't add the zeros in the first place.  An example of
the use of @dfn{maybe_compress} is

@example
@group
  int nz = 6, nr = 3, nc = 4;

  SparseMatrix sm1 (nr, nc, nz);
  sm1(0,0) = 1; sm1(0,1) = 2; sm1(1,3) = 3; sm1(2,3) = 4;
  sm1.maybe_compress ();  // No zero elements were added

  SparseMatrix sm2 (nr, nc, nz);
  sm2(0,0) = 1; sm2(0,1) = 2; sm(0,2) = 0; sm(1,2) = 0;
  sm1(1,3) = 3; sm1(2,3) = 4;
  sm2.maybe_compress (true);  // Zero elements were added
@end group
@end example

The use of the @dfn{maybe_compress} function should be avoided if
possible, as it will slow the creation of the matrices.

A third means of creating a sparse matrix is to work directly with
the data in compressed row format.  An example of this technique might
be

@c Note the @verbatim environment is a relatively new addition to Texinfo.
@c Therefore use the @example environment and replace @, with @@,
@c { with @{, etc

@example
octave_value arg;
@dots{}
int nz = 6, nr = 3, nc = 4;   // Assume we know the max no nz
SparseMatrix sm (nr, nc, nz);
Matrix m = arg.matrix_value ();

int ii = 0;
sm.cidx (0) = 0;
for (int j = 1; j < nc; j++)
  @{
    for (int i = 0; i < nr; i++)
      @{
        double tmp = foo (m(i,j));
        if (tmp != 0.)
          @{
            sm.data(ii) = tmp;
            sm.ridx(ii) = i;
            ii++;
          @}
      @}
    sm.cidx(j+1) = ii;
 @}
sm.maybe_compress ();  // If don't know a-priori 
                       // the final no of nz.
@end example

@noindent
which is probably the most efficient means of creating the sparse matrix.

Finally, it might sometimes arise that the amount of storage initially
created is insufficient to completely store the sparse matrix.  Therefore,
the method @code{change_capacity} exists to reallocate the sparse memory.
The above example would then be modified as

@example
octave_value arg;
@dots{}
int nz = 6, nr = 3, nc = 4;   // Assume we know the max no nz
SparseMatrix sm (nr, nc, nz);
Matrix m = arg.matrix_value ();

int ii = 0;
sm.cidx (0) = 0;
for (int j = 1; j < nc; j++)
  @{
    for (int i = 0; i < nr; i++)
      @{
        double tmp = foo (m(i,j));
        if (tmp != 0.)
          @{
            if (ii == nz)
              @{
                nz += 2;   // Add 2 more elements
                sm.change_capacity (nz);
              @}
            sm.data(ii) = tmp;
            sm.ridx(ii) = i;
            ii++;
          @}
      @}
    sm.cidx(j+1) = ii;
 @}
sm.maybe_mutate ();  // If don't know a-priori 
                     // the final no of nz.
@end example

Note that both increasing and decreasing the number of non-zero elements in
a sparse matrix is expensive, as it involves memory reallocation.  Also as
parts of the matrix, though not its entirety, exist as the old and new copy
at the same time, additional memory is needed.  Therefore if possible this
should be avoided.

@node Using Sparse Matrices in Oct-Files
@subsubsection Using Sparse Matrices in Oct-Files

Most of the same operators and functions on sparse matrices that are
available from the Octave are equally available with oct-files.
The basic means of extracting a sparse matrix from an @code{octave_value}
and returning them as an @code{octave_value}, can be seen in the
following example.

@example
@group
octave_value_list retval;

SparseMatrix sm = args(0).sparse_matrix_value ();
SparseComplexMatrix scm = 
    args(1).sparse_complex_matrix_value ();
SparseBoolMatrix sbm = args(2).sparse_bool_matrix_value ();
@dots{}
retval(2) = sbm;
retval(1) = scm;
retval(0) = sm;
@end group
@end example

The conversion to an octave-value is handled by the sparse
@code{octave_value} constructors, and so no special care is needed.

@node Accessing Global Variables in Oct-Files
@subsection Accessing Global Variables in Oct-Files

Global variables allow variables in the global scope to be
accessed.  Global variables can easily be accessed with oct-files using
the support functions @code{get_global_value} and
@code{set_global_value}.  @code{get_global_value} takes two arguments,
the first is a string representing the variable name to obtain.  The
second argument is a boolean argument specifying what to do in the case
that no global variable of the desired name is found.  An example of the
use of these two functions is

@example
@verbatim
#include <octave/oct.h>

DEFUN_DLD (globaldemo, args, , "Global demo.")
{
  int nargin = args.length ();
  octave_value retval;

  if (nargin != 1)
    print_usage ();
  else
    {
      std::string s = args(0).string_value ();
      if (! error_state)
        {
          octave_value tmp = get_global_value (s, true);
          if (tmp.is_defined ())
            retval = tmp;
          else
            retval = "Global variable not found";

          set_global_value ("a", 42.0);
        }
    }
  return retval;
}
@end verbatim

@end example

An example of its use is

@example
@group
global a b
b = 10;
globaldemo ("b")
@result{} 10
globaldemo ("c")
@result{} "Global variable not found"
num2str (a)
@result{} 42
@end group
@end example

@node Calling Octave Functions from Oct-Files
@subsection Calling Octave Functions from Oct-Files

There is often a need to be able to call another octave function from
within an oct-file, and there are many examples of such within octave
itself.  For example the @code{quad} function is an oct-file that
calculates the definite integral by quadrature over a user supplied
function.

There are also many ways in which a function might be passed.  It might
be passed as one of

@enumerate 1
@item Function Handle

@item Anonymous Function Handle

@item Inline Function

@item String
@end enumerate

The example below demonstrates an example that accepts all four means of
passing a function to an oct-file.

@example
@verbatim
#include <octave/oct.h>
#include <octave/parse.h>

DEFUN_DLD (funcdemo, args, nargout, "Function Demo")
{
  int nargin = args.length();
  octave_value_list retval;

  if (nargin < 2)
    print_usage ();
  else
    {
      octave_value_list newargs;
      for (octave_idx_type i = nargin - 1; i > 0; i--)
        newargs (i - 1) = args(i);
      if (args(0).is_function_handle ()
          || args(0).is_inline_function ())
        {
          octave_function *fcn = args(0).function_value ();
          if (! error_state)
            retval = feval (fcn, newargs, nargout);
        }
      else if (args(0).is_string ())
        {
          std::string fcn = args (0).string_value ();
          if (! error_state)
            retval = feval (fcn, newargs, nargout);
        }
      else
        error ("funcdemo: expected string,",
               " inline or function handle");
    }
  return retval;
}
@end verbatim

@end example

The first argument to this demonstration is the user supplied function
and the following arguments are all passed to the user function.

@example
@group
funcdemo (@@sin,1)
@result{} 0.84147
funcdemo (@@(x) sin(x), 1)
@result{} 0.84147
funcdemo (inline ("sin(x)"), 1)
@result{} 0.84147
funcdemo ("sin",1)
@result{} 0.84147
funcdemo (@@atan2, 1, 1)
@result{} 0.78540
@end group
@end example

When the user function is passed as a string, the treatment of the
function is different.  In some cases it is necessary to always have the
user supplied function as an @code{octave_function} object.  In that
case the string argument can be used to create a temporary function like

@example
@group
std::octave fcn_name = unique_symbol_name ("__fcn__");
std::string fname = "function y = ";
fname.append (fcn_name);
fname.append ("(x) y = ");
fcn = extract_function (args(0), "funcdemo", fcn_name,
                        fname, "; endfunction");
@dots{}
if (fcn_name.length ())
  clear_function (fcn_name);
@end group
@end example

There are two important things to know in this case.  The number of input
arguments to the user function is fixed, and in the above is a single
argument, and secondly to avoid leaving the temporary function in the
Octave symbol table it should be cleared after use.

@node Calling External Code from Oct-Files
@subsection Calling External Code from Oct-Files

Linking external C code to Octave is relatively simple, as the C
functions can easily be called directly from C++.  One possible issue is
the declarations of the external C functions might need to be explicitly
defined as C functions to the compiler.  If the declarations of the
external C functions are in the header @code{foo.h}, then the manner in
which to ensure that the C++ compiler treats these declarations as C
code is

@example
@group
#ifdef __cplusplus
extern "C"
@{
#endif
#include "foo.h"
#ifdef __cplusplus
@}  /* end extern "C" */
#endif
@end group
@end example

Calling Fortran code however can pose some difficulties.  This is due to
differences in the manner in compilers treat the linking of Fortran code
with C or C++ code.  Octave supplies a number of macros that allow
consistent behavior across a number of compilers.

The underlying Fortran code should use the @code{XSTOPX} function to
replace the Fortran @code{STOP} function.  @code{XSTOPX} uses the Octave
exception handler to treat failing cases in the Fortran code
explicitly.  Note that Octave supplies its own replacement @sc{blas}
@code{XERBLA} function, which uses @code{XSTOPX}.

If the underlying code calls @code{XSTOPX}, then the @w{@code{F77_XFCN}}
macro should be used to call the underlying Fortran function.  The Fortran
exception state can then be checked with the global variable
@code{f77_exception_encountered}.  If @code{XSTOPX} will not be called,
then the @w{@code{F77_FCN}} macro should be used instead to call the Fortran
code.

There is no harm in using @w{@code{F77_XFCN}} in all cases, except that for
Fortran code that is short running and executes a large number of times,
there is potentially an overhead in doing so.  However, if @w{@code{F77_FCN}}
is used with code that calls @code{XSTOP}, Octave can generate a
segmentation fault.

An example of the inclusion of a Fortran function in an oct-file is
given in the following example, where the C++ wrapper is

@example
@verbatim
#include <octave/oct.h>
#include <octave/f77-fcn.h>

extern "C"
{
  F77_RET_T
  F77_FUNC (fortsub, FORTSUB)
        (const int&, double*, F77_CHAR_ARG_DECL
         F77_CHAR_ARG_LEN_DECL);
}

DEFUN_DLD (fortdemo , args , , "Fortran Demo.")
{
  octave_value_list retval;
  int nargin = args.length();
  if (nargin != 1)
    print_usage ();
  else
    {
      NDArray a = args(0).array_value ();
      if (! error_state)
        {
          double *av = a.fortran_vec ();
          octave_idx_type na = a.nelem ();
          OCTAVE_LOCAL_BUFFER (char, ctmp, 128);

          F77_XFCN (fortsub, FORTSUB, (na, av, ctmp
                    F77_CHAR_ARG_LEN (128)));

          retval(1) = std::string (ctmp);
          retval(0) = a;
        }
    }
  return retval;
}
@end verbatim

@end example

@noindent
and the Fortran function is

@example
@verbatim
      subroutine fortsub (n, a, s)
      implicit none
      character*(*) s
      real*8 a(*)
      integer*4 i, n, ioerr
      do i = 1, n
        if (a(i) .eq. 0d0) then
          call xstopx ('fortsub: divide by zero')
        else
          a(i) = 1d0 / a(i)
        endif
      enddo
      write (unit = s, fmt = '(a,i3,a,a)', iostat = ioerr)
     $       'There are ', n,
     $       ' values in the input vector', char(0)
      if (ioerr .ne. 0) then
        call xstopx ('fortsub: error writing string')
      endif
      return
      end

@end verbatim

@end example

This example demonstrates most of the features needed to link to an
external Fortran function, including passing arrays and strings, as well
as exception handling.  An example of the behavior of this function is

@example
@group
[b, s] = fortdemo (1:3)
@result{}
  b = 1.00000   0.50000   0.33333
  s = There are   3 values in the input vector
[b, s] = fortdemo(0:3)
error: fortsub:divide by zero
error: exception encountered in Fortran subroutine fortsub_
error: fortdemo: error in Fortran
@end group
@end example

@node Allocating Local Memory in Oct-Files
@subsection Allocating Local Memory in Oct-Files

Allocating memory within an oct-file might seem easy as the C++
new/delete operators can be used.  However, in that case care must be
taken to avoid memory leaks.  The preferred manner in which to allocate
memory for use locally is to use the @w{@code{OCTAVE_LOCAL_BUFFER}} macro.
An example of its use is

@example
OCTAVE_LOCAL_BUFFER (double, tmp, len)
@end example

@noindent
that returns a pointer @code{tmp} of type @code{double *} of length
@code{len}.

@node Input Parameter Checking in Oct-Files
@subsection Input Parameter Checking in Oct-Files

As oct-files are compiled functions they have the possibility of causing
Octave to abort abnormally.  It is therefore important that
each and every function has the minimum of parameter
checking needed to ensure that Octave behaves well.

The minimum requirement, as previously discussed, is to check the number
of input arguments before using them to avoid referencing a non existent
argument.  However, it some case this might not be sufficient as the
underlying code imposes further constraints.  For example an external
function call might be undefined if the input arguments are not
integers, or if one of the arguments is zero.  Therefore, oct-files often
need additional input parameter checking.

There are several functions within Octave that might be useful for the
purposes of parameter checking.  These include the methods of the
octave_value class like @code{is_real_matrix}, etc., but equally include
more specialized functions.  Some of the more common ones are
demonstrated in the following example.

@example
@verbatim
#include <octave/oct.h>

DEFUN_DLD (paramdemo, args, nargout,
           "Parameter Check Demo.")
{
  int nargin = args.length ();
  octave_value retval;

  if (nargin != 1)
    print_usage();
  else if (nargout != 0)
    error ("paramdemo: function has no output arguments");
  else
    {
      NDArray m = args(0).array_value();
      double min_val = -10.0;
      double max_val = 10.0;
      octave_stdout << "Properties of input array:\n";
      if (m.any_element_is_negative ())
        octave_stdout << "  includes negative values\n";
      if (m.any_element_is_inf_or_nan())
        octave_stdout << "  includes Inf or NaN values\n";
      if (m.any_element_not_one_or_zero())
        octave_stdout <<
          "  includes other values than 1 and 0\n";
      if (m.all_elements_are_int_or_inf_or_nan())
        octave_stdout <<
          "  includes only int, Inf or NaN values\n";
      if (m.all_integers (min_val, max_val))
        octave_stdout <<
          "  includes only integers in [-10,10]\n";
    }
  return retval;
}
@end verbatim

@end example

@noindent
An example of its use is:

@example
@group
paramdemo ([1, 2, NaN, Inf])
@result{} Properties of input array:
      includes Inf or NaN values
      includes other values than 1 and 0
      includes only int, Inf or NaN values
@end group
@end example

@node Exception and Error Handling in Oct-Files
@subsection Exception and Error Handling in Oct-Files

Another important feature of Octave is its ability to react to the user
typing @kbd{Control-C} even during calculations.  This ability is based on the
C++ exception handler, where memory allocated by the C++ new/delete
methods are automatically released when the exception is treated.  When
writing an oct-file, to allow Octave to treat the user typing @kbd{Control-C},
the @w{@code{OCTAVE_QUIT}} macro is supplied.  For example:

@example
@group
for (octave_idx_type i = 0; i < a.nelem (); i++)
  @{
    OCTAVE_QUIT;
    b.elem(i) = 2. * a.elem(i);
  @}
@end group
@end example

The presence of the @w{@code{OCTAVE_QUIT}} macro in the inner loop allows
Octave to treat the user request with the @kbd{Control-C}.  Without this macro,
the user must either wait for the function to return before the interrupt is
processed, or press @kbd{Control-C} three times to force Octave to exit.

The @w{@code{OCTAVE_QUIT}} macro does impose a very small speed penalty, and so
for loops that are known to be small it might not make sense to include
@w{@code{OCTAVE_QUIT}}.

When creating an oct-file that uses an external libraries, the function
might spend a significant portion of its time in the external
library.  It is not generally possible to use the @w{@code{OCTAVE_QUIT}} macro
in this case.  The alternative in this case is

@example
@group
BEGIN_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
@dots{}  some code that calls a "foreign" function @dots{}
END_INTERRUPT_IMMEDIATELY_IN_FOREIGN_CODE;
@end group
@end example

The disadvantage of this is that if the foreign code allocates any
memory internally, then this memory might be lost during an interrupt,
without being deallocated.  Therefore, ideally Octave itself should
allocate any memory that is needed by the foreign code, with either the
@nospell{fortran_vec} method or the @w{@code{OCTAVE_LOCAL_BUFFER}} macro.

The Octave unwind_protect mechanism (@ref{The @code{unwind_protect} Statement})
can also be used in oct-files.  In conjunction with the exception
handling of Octave, it is important to enforce that certain code is run
to allow variables, etc. to be restored even if an exception occurs.  An
example of the use of this mechanism is

@example
@verbatim
#include <octave/oct.h>
#include <octave/unwind-prot.h>

void
err_hand (const char *fmt, ...)
{
  // Do nothing!!
}

DEFUN_DLD (unwinddemo, args, nargout, "Unwind Demo")
{
  int nargin = args.length();
  octave_value retval;
  if (nargin < 2)
    print_usage ();
  else
    {
      NDArray a = args(0).array_value ();
      NDArray b = args(1).array_value ();

      if (! error_state)
        {
          unwind_protect::begin_frame ("Funwinddemo");
          unwind_protect_ptr (current_liboctave_warning_handler);
          set_liboctave_warning_handler(err_hand);
          retval = octave_value (quotient (a, b));
          unwind_protect::run_frame ("Funwinddemo");
        }
    }
  return retval;
}
@end verbatim

@end example

As can be seen in the example:

@example
@group
unwinddemo (1, 0)
@result{} Inf
1 / 0
@result{} warning: division by zero
   Inf
@end group
@end example

The division by zero (and in fact all warnings) is disabled in the
@code{unwinddemo} function.

@node Documentation and Test of Oct-Files
@subsection Documentation and Test of Oct-Files

The documentation of an oct-file is the fourth string parameter of the
@w{@code{DEFUN_DLD}} macro.  This string can be formatted in the same manner
as the help strings for user functions (@ref{Documentation Tips}),
however there are some issue that are particular to the formatting of
help strings within oct-files.

The major issue is that the help string will typically be longer than a
single line of text, and so the formatting of long help strings need to
be taken into account.  There are several manners in which to treat this
issue, but the most common is illustrated in the following example,

@example
@group
DEFUN_DLD (do_what_i_want, args, nargout, 
  "-*- texinfo -*-\n\
@@deftypefn @{Function File@} @{@} do_what_i_say (@@var@{n@})\n\
A function that does what the user actually wants rather\n\
than what they requested.\n\
@@end deftypefn")
@{
@dots{}
@}
@end group
@end example

@noindent
where, as can be seen, end line of text within the help string is
terminated by @code{\n\} which is an embedded new-line in the string
together with a C++ string continuation character.  Note that the final
@code{\} must be the last character on the line.

Octave also includes the ability to embed the test and demonstration
code for a function within the code itself (@ref{Test and Demo Functions}).
This can be used from within oct-files (or in fact any file) with
certain provisos.  Firstly, the test and demo functions of Octave look
for a @code{%!} as the first characters on a new-line to identify test
and demonstration code.  This is equally a requirement for
oct-files.  Furthermore the test and demonstration code must be included
in a comment block of the compiled code to avoid it being interpreted by
the compiler.  Finally, the Octave test and demonstration code must have
access to the source code of the oct-file and not just the compiled code
as the tests are stripped from the compiled code.  An example in an
oct-file might be

@example
@group
/*

%!error (sin())
%!error (sin(1,1))
%!assert (sin([1,2]),[sin(1),sin(2)])

*/
@end group
@end example

@c @node Application Programming Interface for Oct-Files
@c @subsection Application Programming Interface for Oct-Files
@c 
@c WRITE ME, using Coda section 1.3 as a starting point.

@node Mex-Files
@section Mex-Files
@cindex mex-files
@cindex mex

Octave includes an interface to allow legacy mex-files to be compiled
and used with Octave.  This interface can also be used to share code
between Octave and @sc{matlab} users.  However, as mex-files expose the
@sc{matlab}'s internal API, and the internal structure of Octave is
different, a mex-file can never have the same performance in Octave as
the equivalent oct-file.  In particular to support the manner in which
mex-files access the variables passed to mex functions, there are a
significant number of additional copies of memory when calling or
returning from a mex function.  For this reason, new code should be
written using the oct-file interface discussed above if possible.

@menu
* Getting Started with Mex-Files::  
* Working with Matrices and Arrays in Mex-Files::  
* Character Strings in Mex-Files::  
* Cell Arrays with Mex-Files::  
* Structures with Mex-Files::  
* Sparse Matrices with Mex-Files::  
* Calling Other Functions in Mex-Files::  
@c * Application Programming Interface for Mex-Files::  
@end menu

@node Getting Started with Mex-Files
@subsection Getting Started with Mex-Files

The basic command to build a mex-file is either @code{mkoctfile --mex}
or @code{mex}.  The first can either be used from within Octave or from
the command line.  However, to avoid issues with @sc{matlab}'s own @code{mex}
command, the use of the command @code{mex} is limited to within Octave.

@c mex scripts/miscellaneous/mex.m
@anchor{doc-mex}
@deftypefn {Function File} {} mex [options] file @dots{}
Compile source code written in C, C++, or Fortran, to a MEX file.
This is equivalent to @code{mkoctfile --mex [options] file}.
@seealso{@ref{doc-mkoctfile,,mkoctfile}}
@end deftypefn


@c mexext scripts/miscellaneous/mexext.m
@anchor{doc-mexext}
@deftypefn {Function File} {} mexext ()
Return the filename extension used for MEX files.
@end deftypefn


One important difference with the use of @code{mex} between @sc{matlab} and
Octave is that the header file "matrix.h" is implicitly included through
the inclusion of "mex.h".  This is to avoid a conflict with the Octave
file "Matrix.h" with operating systems and compilers that don't
distinguish between filenames in upper and lower case

Consider the short example:

@example
@group
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray *plhs[], int nrhs, 
             const mxArray *prhs[])
{
  mxArray *v = mxCreateDoubleMatrix (1, 1, mxREAL);
  double *data = mxGetPr (v);
  *data = 1.23456789;
  plhs[0] = v;
}
@end verbatim

@end group
@end example

This simple example demonstrates the basics of writing a mex-file.  The
entry point into the mex-file is defined by @code{mexFunction}.  Note
that the function name is not explicitly included in the
@code{mexFunction} and so there can only be a single @code{mexFunction}
entry point per-file.  Also the name of the function is determined by the
name of the mex-file itself.  Therefore if the above function is in the
file @file{firstmexdemo.c}, it can be compiled with

@example
mkoctfile --mex firstmexdemo.c
@end example

@noindent
which creates a file @file{firstmexdemo.mex}.  The function can then be run
from Octave as

@example
@group
firstmexdemo()
@result{} 1.2346
@end group
@end example

It should be noted that the mex-file contains no help string for the
functions it contains.  To document mex-files, there should exist an
m-file in the same directory as the mex-file itself.  Taking the above as
an example, we would therefore have a file @file{firstmexdemo.m} that might
contain the text

@example
%FIRSTMEXDEMO Simple test of the functionality of a mex-file.
@end example

In this case, the function that will be executed within Octave will be
given by the mex-file, while the help string will come from the
m-file.  This can also be useful to allow a sample implementation of the
mex-file within the Octave language itself for testing purposes.

Although we cannot have multiple entry points into a single mex-file,
we can use the @code{mexFunctionName} function to determine what name
the mex-file was called with.  This can be used to alter the behavior of
the mex-file based on the function name.  For example if

@example
@group
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray *plhs[], int nrhs, 
             const mxArray *prhs[])
{
  const char *nm;
  nm = mexFunctionName ();
  mexPrintf ("You called function: %s\n", nm);
  if (strcmp (nm, "myfunc") == 0)
    mexPrintf ("This is the principal function\n", nm);
  return; 
}
@end verbatim

@end group
@end example

@noindent
is in file @file{myfunc.c}, and it is compiled with

@example
@group
mkoctfile --mex myfunc.c
ln -s myfunc.mex myfunc2.mex
@end group
@end example

Then as can be seen by

@example
@group
myfunc()
@result{} You called function: myfunc
    This is the principal function
myfunc2()
@result{} You called function: myfunc2
@end group
@end example

@noindent
the behavior of the mex-file can be altered depending on the functions
name.

Allow the user should only include @code{mex.h} in their code, Octave
declares additional functions, typedefs, etc., available to the user to
write mex-files in the headers @code{mexproto.h} and @code{mxarray.h}.

@node Working with Matrices and Arrays in Mex-Files
@subsection Working with Matrices and Arrays in Mex-Files

The basic mex type of all variables is @code{mxArray}.  All variables,
such as matrices, cell arrays or structures are all stored in this basic
type, and this type serves basically the same purpose as the
octave_value class in oct-files.  That is it acts as a container for the
more specialized types.

The @code{mxArray} structure contains at a minimum, the variable it
represents name, its dimensions, its type and whether the variable is
real or complex.  It can however contain a number of additional fields
depending on the type of the @code{mxArray}.  There are a number of
functions to create @code{mxArray} structures, including
@code{mxCreateCellArray}, @code{mxCreateSparse} and the generic
@code{mxCreateNumericArray}.

The basic functions to access the data contained in an array is
@code{mxGetPr}.  As the mex interface assumes that the real and imaginary
parts of a complex array are stored separately, there is an equivalent
function @code{mxGetPi} that get the imaginary part.  Both of these
functions are for use only with double precision matrices.  There also
exists the generic function @code{mxGetData} and @code{mxGetImagData}
that perform the same operation on all matrix types.  For example:

@example
@group
mxArray *m;
mwSize *dims;
UINT32_T *pr;

dims = (mwSize *) mxMalloc (2 * sizeof(mwSize));
dims[0] = 2;
dims[1] = 2;
m = mxCreateNumericArray (2, dims, mxUINT32_CLASS, mxREAL);
pr =  = (UINT32_T *) mxGetData (m);
@end group
@end example

There are also the functions @code{mxSetPr}, etc., that perform the
inverse, and set the data of an Array to use the block of memory pointed
to by the argument of @code{mxSetPr}.

Note the type @code{mwSize} used above, and @code{mwIndex} are defined
as the native precision of the indexing in Octave on the platform on
which the mex-file is built.  This allows both 32- and 64-bit platforms
to support mex-files.  @code{mwSize} is used to define array dimension
and maximum number or elements, while @code{mwIndex} is used to define
indexing into arrays.

An example that demonstration how to work with arbitrary real or complex
double precision arrays is given by the file @file{mypow2.c} as given
below.

@example
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray* plhs[], int nrhs, 
             const mxArray* prhs[])
{
  mwIndex i;
  mwSize n;
  double *vri, *vro;
  
  if (nrhs != 1 || ! mxIsNumeric (prhs[0]))
    mexErrMsgTxt ("expects matrix");

  n = mxGetNumberOfElements (prhs[0]);
  plhs[0] = (mxArray *) mxCreateNumericArray 
    (mxGetNumberOfDimensions (prhs[0]),
     mxGetDimensions (prhs[0]), mxGetClassID (prhs[0]),
     mxIsComplex (prhs[0]));
  vri = mxGetPr (prhs[0]);
  vro = mxGetPr (plhs[0]);

  if (mxIsComplex (prhs[0]))
    {
      double *vii, *vio;
      vii = mxGetPi (prhs[0]);
      vio = mxGetPi (plhs[0]);

      for (i = 0; i < n; i++)
        {
          vro [i] = vri [i] * vri [i] - vii [i] * vii [i];
          vio [i] = 2 * vri [i] * vii [i];
        }
    }
  else
    {
      for (i = 0; i < n; i++)
        vro [i] = vri [i] * vri [i];
    }
}
@end verbatim

@end example

@noindent
with an example of its use

@example
@group
b = randn(4,1) + 1i * randn(4,1);
all(b.^2 == mypow2(b))
@result{} 1
@end group
@end example


The example above uses the functions @code{mxGetDimensions},
@code{mxGetNumberOfElements}, and @code{mxGetNumberOfDimensions} to work
with the dimensions of multi-dimensional arrays.  The functions
@code{mxGetM}, and @code{mxGetN} are also available to find the number
of rows and columns in a matrix.

@node Character Strings in Mex-Files
@subsection Character Strings in Mex-Files

As mex-files do not make the distinction between single and double
quoted strings within Octave, there is perhaps less complexity in the
use of strings and character matrices in mex-files.  An example of their
use, that parallels the demo in @file{stringdemo.cc}, is given in the
file @file{mystring.c}, as seen below.

@example
@verbatim
#include <string.h>
#include "mex.h"

void
mexFunction (int nlhs, mxArray *plhs[], int nrhs, 
             const mxArray *prhs[])
{
  mwIndex i, j;
  mwSize m, n;
  mxChar *pi, *po;

  if (nrhs != 1 || ! mxIsChar (prhs[0]) || 
      mxGetNumberOfDimensions (prhs[0]) > 2)
    mexErrMsgTxt ("expecting char matrix");

  m = mxGetM (prhs[0]);
  n = mxGetN (prhs[0]);
  pi = mxGetChars (prhs[0]);
  plhs[0] = mxCreateNumericMatrix (m, n, mxCHAR_CLASS, 
                                   mxREAL);
  po = mxGetChars (plhs[0]);

  for (j = 0; j < n; j++)
    for (i = 0; i < m; i++)
      po [j*m + m - 1 - i] = pi [j*m + i];
}
@end verbatim

@end example

@noindent
An example of its expected output is

@example
@group
mystring(["First String"; "Second String"])
@result{} s1 = Second String
        First String
@end group
@end example

Other functions in the mex interface for handling character strings are
@code{mxCreateString}, @code{mxArrayToString}, and
@code{mxCreateCharMatrixFromStrings}.  In a mex-file, a character string
is considered to be a vector rather than a matrix.  This is perhaps an
arbitrary distinction as the data in the mxArray for the matrix is
consecutive in any case.

@node Cell Arrays with Mex-Files
@subsection Cell Arrays with Mex-Files

We can perform exactly the same operations in Cell arrays in mex-files
as we can in oct-files.  An example that reduplicates the functional of
the @file{celldemo.cc} oct-file in a mex-file is given by
@file{mycell.c} as below

@example
@group
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray* plhs[], int nrhs, 
             const mxArray* prhs[])
{
  mwSize n;
  mwIndex i;

  if (nrhs != 1 || ! mxIsCell (prhs[0]))
    mexErrMsgTxt ("expects cell");

  n = mxGetNumberOfElements (prhs[0]);
  n = (n > nlhs ? nlhs : n);
  
  for (i = 0; i < n; i++)
    plhs[i] = mxDuplicateArray (mxGetCell (prhs[0], i));
}
@end verbatim

@end group
@end example

@noindent
which as can be seen below has exactly the same behavior as the oct-file
version.

@example
@group
[b1, b2, b3] = mycell (@{1, [1, 2], "test"@})
@result{}
b1 =  1
b2 =

   1   2

b3 = test
@end group
@end example

Note in the example the use of the @code{mxDuplicateArray} function.  This
is needed as the @code{mxArray} pointer returned by @code{mxGetCell}
might be deallocated.  The inverse function to @code{mxGetCell} is
@code{mcSetCell} and is defined as

@example
void mxSetCell (mxArray *ptr, int idx, mxArray *val);
@end example

Finally, to create a cell array or matrix, the appropriate functions are

@example
@group
mxArray *mxCreateCellArray (int ndims, const int *dims);
mxArray *mxCreateCellMatrix (int m, int n);
@end group
@end example

@node Structures with Mex-Files
@subsection Structures with Mex-Files

The basic function to create a structure in a mex-file is
@code{mxCreateStructMatrix}, which creates a structure array with a two
dimensional matrix, or @code{mxCreateStructArray}.

@example
@group
mxArray *mxCreateStructArray (int ndims, int *dims, 
                              int num_keys, 
                              const char **keys);
mxArray *mxCreateStructMatrix (int rows, int cols, 
                               int num_keys, 
                               const char **keys);
@end group
@end example

Accessing the fields of the structure can then be performed with the
@code{mxGetField} and @code{mxSetField} or alternatively with the
@code{mxGetFieldByNumber} and @code{mxSetFieldByNumber} functions.

@example
@group
mxArray *mxGetField (const mxArray *ptr, mwIndex index,
                     const char *key);
mxArray *mxGetFieldByNumber (const mxArray *ptr, 
                             mwIndex index, int key_num);
void mxSetField (mxArray *ptr, mwIndex index, 
                 const char *key, mxArray *val);
void mxSetFieldByNumber (mxArray *ptr, mwIndex index, 
                         int key_num, mxArray *val);
@end group
@end example

A difference between the oct-file interface to structures and the
mex-file version is that the functions to operate on structures in
mex-files directly include an @code{index} over the elements of the
arrays of elements per @code{field}.  Whereas the oct-file structure
includes a Cell Array per field of the structure.

An example that demonstrates the use of structures in mex-file can be
found in the file @file{mystruct.c}, as seen below

@example
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray* plhs[], int nrhs, 
             const mxArray* prhs[])
{
  int i;
  mwIndex j;
  mxArray *v;
  const char *keys[] = { "this", "that" };

  if (nrhs != 1 || ! mxIsStruct (prhs[0]))
    mexErrMsgTxt ("expects struct");

  for (i = 0; i < mxGetNumberOfFields (prhs[0]); i++)
    for (j = 0; j < mxGetNumberOfElements (prhs[0]); j++)
      {
        mexPrintf ("field %s(%d) = ", 
                   mxGetFieldNameByNumber (prhs[0], i), j);
        v = mxGetFieldByNumber (prhs[0], j, i);
        mexCallMATLAB (0, 0, 1, &v, "disp");
      }

  v = mxCreateStructMatrix (2, 2, 2, keys);

  mxSetFieldByNumber (v, 0, 0, mxCreateString ("this1"));
  mxSetFieldByNumber (v, 0, 1, mxCreateString ("that1"));
  mxSetFieldByNumber (v, 1, 0, mxCreateString ("this2"));
  mxSetFieldByNumber (v, 1, 1, mxCreateString ("that2"));
  mxSetFieldByNumber (v, 2, 0, mxCreateString ("this3"));
  mxSetFieldByNumber (v, 2, 1, mxCreateString ("that3"));
  mxSetFieldByNumber (v, 3, 0, mxCreateString ("this4"));
  mxSetFieldByNumber (v, 3, 1, mxCreateString ("that4"));

  if (nlhs)
    plhs[0] = v;
}
@end verbatim

@end example

An example of the behavior of this function within Octave is then

@example
a(1).f1 = "f11"; a(1).f2 = "f12"; 
a(2).f1 = "f21"; a(2).f2 = "f22";
b = mystruct(a)
@result{} field f1(0) = f11
    field f1(1) = f21
    field f2(0) = f12
    field f2(1) = f22
    b =
    @{
      this =
    
      (,
        [1] = this1
        [2] = this2
        [3] = this3
        [4] = this4
      ,)
    
      that =
    
      (,
        [1] = that1
        [2] = that2
        [3] = that3
        [4] = that4
      ,)
    
    @}
@end example

@node Sparse Matrices with Mex-Files
@subsection Sparse Matrices with Mex-Files

The Octave format for sparse matrices is identical to the mex format in
that it is a compressed column sparse format.  Also in both, sparse
matrices are required to be two-dimensional.  The only difference is that
the real and imaginary parts of the matrix are stored separately.

The mex-file interface, as well as using @code{mxGetM}, @code{mxGetN},
@code{mxSetM}, @code{mxSetN}, @code{mxGetPr}, @code{mxGetPi},
@code{mxSetPr} and @code{mxSetPi}, the mex-file interface supplies the
functions

@example
@group
mwIndex *mxGetIr (const mxArray *ptr);
mwIndex *mxGetJc (const mxArray *ptr);
mwSize mxGetNzmax (const mxArray *ptr);

void mxSetIr (mxArray *ptr, mwIndex *ir);
void mxSetJc (mxArray *ptr, mwIndex *jc);
void mxSetNzmax (mxArray *ptr, mwSize nzmax);
@end group
@end example

@noindent
@code{mxGetNzmax} gets the maximum number of elements that can be stored
in the sparse matrix.  This is not necessarily the number of non-zero
elements in the sparse matrix.  @code{mxGetJc} returns an array with one
additional value than the number of columns in the sparse matrix.  The
difference between consecutive values of the array returned by
@code{mxGetJc} define the number of non-zero elements in each column of
the sparse matrix.  Therefore

@example
@group
mwSize nz, n;
mwIndex *Jc;
mxArray *m;
@dots{}
n = mxGetN (m);
Jc = mxGetJc (m);
nz = Jc[n];
@end group
@end example

@noindent
returns the actual number of non-zero elements stored in the matrix in
@code{nz}.  As the arrays returned by @code{mxGetPr} and @code{mxGetPi}
only contain the non-zero values of the matrix, we also need a pointer
to the rows of the non-zero elements, and this is given by
@code{mxGetIr}.  A complete example of the use of sparse matrices in
mex-files is given by the file @file{mysparse.c} as seen below

@example
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray *plhs[], int nrhs, 
             const mxArray *prhs[])
{
  mwSize n, m, nz;
  mxArray *v;
  mwIndex i;
  double *pr, *pi;
  double *pr2, *pi2;
  mwIndex *ir, *jc;
  mwIndex *ir2, *jc2;
  
  if (nrhs != 1 || ! mxIsSparse (prhs[0]))
    mexErrMsgTxt ("expects sparse matrix");

  m = mxGetM (prhs [0]);
  n = mxGetN (prhs [0]);
  nz = mxGetNzmax (prhs [0]);
  
  if (mxIsComplex (prhs[0]))
    {
      mexPrintf ("Matrix is %d-by-%d complex",
                 " sparse matrix", m, n);
      mexPrintf (" with %d elements\n", nz);

      pr = mxGetPr (prhs[0]);
      pi = mxGetPi (prhs[0]);
      ir = mxGetIr (prhs[0]);
      jc = mxGetJc (prhs[0]);

      i = n;
      while (jc[i] == jc[i-1] && i != 0) i--;
      mexPrintf ("last non-zero element (%d, %d) =", 
                 ir[nz-1]+ 1, i);
      mexPrintf (" (%g, %g)\n", pr[nz-1], pi[nz-1]);

      v = mxCreateSparse (m, n, nz, mxCOMPLEX);
      pr2 = mxGetPr (v);
      pi2 = mxGetPi (v);
      ir2 = mxGetIr (v);
      jc2 = mxGetJc (v);
      
      for (i = 0; i < nz; i++)
        {
          pr2[i] = 2 * pr[i];
          pi2[i] = 2 * pi[i];
          ir2[i] = ir[i];
        }
      for (i = 0; i < n + 1; i++)
        jc2[i] = jc[i];

      if (nlhs > 0)
        plhs[0] = v;
    }
  else if (mxIsLogical (prhs[0]))
    {
      bool *pbr, *pbr2;
      mexPrintf ("Matrix is %d-by-%d logical",
                 " sparse matrix", m, n);
      mexPrintf (" with %d elements\n", nz);

      pbr = mxGetLogicals (prhs[0]);
      ir = mxGetIr (prhs[0]);
      jc = mxGetJc (prhs[0]);

      i = n;
      while (jc[i] == jc[i-1] && i != 0) i--;
      mexPrintf ("last non-zero element (%d, %d) = %d\n",
                 ir[nz-1]+ 1, i, pbr[nz-1]);

      v = mxCreateSparseLogicalMatrix (m, n, nz);
      pbr2 = mxGetLogicals (v);
      ir2 = mxGetIr (v);
      jc2 = mxGetJc (v);
      
      for (i = 0; i < nz; i++)
        {
          pbr2[i] = pbr[i];
          ir2[i] = ir[i];
        }
      for (i = 0; i < n + 1; i++)
        jc2[i] = jc[i];

      if (nlhs > 0)
        plhs[0] = v;
    }
  else
    {
      mexPrintf ("Matrix is %d-by-%d real",
                 " sparse matrix", m, n);
      mexPrintf (" with %d elements\n", nz);

      pr = mxGetPr (prhs[0]);
      ir = mxGetIr (prhs[0]);
      jc = mxGetJc (prhs[0]);

      i = n;
      while (jc[i] == jc[i-1] && i != 0) i--;
      mexPrintf ("last non-zero element (%d, %d) = %g\n",
                ir[nz-1]+ 1, i, pr[nz-1]);

      v = mxCreateSparse (m, n, nz, mxREAL);
      pr2 = mxGetPr (v);
      ir2 = mxGetIr (v);
      jc2 = mxGetJc (v);
      
      for (i = 0; i < nz; i++)
        {
          pr2[i] = 2 * pr[i];
          ir2[i] = ir[i];
        }
      for (i = 0; i < n + 1; i++)
        jc2[i] = jc[i];

      if (nlhs > 0)
        plhs[0] = v;
    }
}
@end verbatim

@end example

@node Calling Other Functions in Mex-Files
@subsection Calling Other Functions in Mex-Files

It is also possible call other Octave functions from within a mex-file
using @code{mexCallMATLAB}.  An example of the use of
@code{mexCallMATLAB} can be see in the example below

@example
@verbatim
#include "mex.h"

void
mexFunction (int nlhs, mxArray* plhs[], int nrhs, 
             const mxArray* prhs[])
{
  char *str;

  mexPrintf ("Hello, World!\n");

  mexPrintf ("I have %d inputs and %d outputs\n", nrhs,
             nlhs);

  if (nrhs < 1 || ! mxIsString (prhs[0])) 
    mexErrMsgTxt ("function name expected");

  str = mxArrayToString (prhs[0]);

  mexPrintf ("I'm going to call the function %s\n", str);

  mexCallMATLAB (nlhs, plhs, nrhs-1, prhs+1, str);

  mxFree (str);
}
@end verbatim

@end example

If this code is in the file @file{myfeval.c}, and is compiled to
@file{myfeval.mex}, then an example of its use is

@example
@group
myfeval("sin", 1)
a = myfeval("sin", 1)
@result{} Hello, World!
    I have 2 inputs and 1 outputs
    I'm going to call the interpreter function sin
    a =  0.84147
@end group
@end example

Note that it is not possible to use function handles or inline functions
within a mex-file.

@c @node Application Programming Interface for Mex-Files
@c @subsection Application Programming Interface for Mex-Files
@c 
@c WRITE ME, refer to mex.h and mexproto.h

@node Standalone Programs
@section Standalone Programs

The libraries Octave itself uses, can be utilized in standalone
applications.  These applications then have access, for example, to the
array and matrix classes as well as to all the Octave algorithms.  The
following C++ program, uses class Matrix from @file{liboctave.a} or
@file{liboctave.so}.

@example
@group
@verbatim
#include <iostream>
#include <octave/oct.h>

int
main (void)
{
  std::cout << "Hello Octave world!\n";
  int n = 2;
  Matrix a_matrix = Matrix (n, n);
  for (octave_idx_type i = 0; i < n; i++)
    {
      for (octave_idx_type j = 0; j < n; j++)
        {
          a_matrix (i, j) = (i + 1) * 10 + (j + 1);
        }
    }
  std::cout << a_matrix;
  return 0;
}
@end verbatim

@end group
@end example

@noindent
mkoctfile can then be used to build a standalone application with a
command like

@example
@group
$ mkoctfile --link-stand-alone standalone.cc -o standalone
$ ./standalone
Hello Octave world!
  11 12
  21 22
$
@end group
@end example

Note that the application @code{hello} will be dynamically linked
against the octave libraries and any octave support libraries.  The above
allows the Octave math libraries to be used by an application.  It does
not however allow the script files, oct-files or builtin functions of
Octave to be used by the application.  To do that the Octave interpreter
needs to be initialized first.  An example of how to do this can then be
seen in the code

@example
@group
@verbatim
#include <iostream>
#include <octave/oct.h>
#include <octave/octave.h>
#include <octave/parse.h>

int
main (void)
{
  string_vector argv (2);
  argv(0) = "embedded";
  argv(1) = "-q";

  octave_main (2, argv.c_str_vec(), 1);

  octave_idx_type n = 2;
  Matrix a_matrix = Matrix (1, 2);

  std::cout << "GCD of [";
  for (octave_idx_type i = 0; i < n; i++)
    {
      a_matrix (i) = 5 * (i + 1);
      if (i != 0)
        std::cout << ", " << 5 * (i + 2);
      else
        std::cout << 5 * (i + 2);
    }
  std::cout << "] is ";

  octave_value_list in = octave_value (a_matrix);
  octave_value_list out = feval ("gcd", in, 1);

  if (!error_state && out.length () > 0)
    {
      a_matrix = out(0).matrix_value ();
      if (a_matrix.numel () == 1)
        std::cout << a_matrix(0) << "\n";
      else
        std::cout << "invalid\n";
    }
  else
    std::cout << "invalid\n";

  return 0;
}
@end verbatim

@end group
@end example

@noindent
which is compiled and run as before as a standalone application with

@example
@group
$ mkoctfile --link-stand-alone embedded.cc -o embedded
$ ./embedded
GCD of [10, 15] is 5
$
@end group
@end example

