|
Packit |
67cb25 |
.. index:: multisets
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
*********
|
|
Packit |
67cb25 |
Multisets
|
|
Packit |
67cb25 |
*********
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. include:: include.rst
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This chapter describes functions for creating and manipulating multisets. A
|
|
Packit |
67cb25 |
multiset :math:`c` is represented by an array of :math:`k` integers in the range
|
|
Packit |
67cb25 |
0 to :math:`n - 1`, where each value :math:`c_i` may occur more than once. The
|
|
Packit |
67cb25 |
multiset :math:`c` corresponds to indices of :math:`k` elements chosen from an
|
|
Packit |
67cb25 |
:math:`n` element vector with replacement. In mathematical terms, :math:`n` is
|
|
Packit |
67cb25 |
the cardinality of the multiset while :math:`k` is the maximum multiplicity of
|
|
Packit |
67cb25 |
any value. Multisets are useful, for example, when iterating over the indices
|
|
Packit |
67cb25 |
of a :math:`k`-th order symmetric tensor in :math:`n`-space.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
The functions described in this chapter are defined in the header file
|
|
Packit |
67cb25 |
:file:`gsl_multiset.h`.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
The Multiset struct
|
|
Packit |
67cb25 |
===================
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. type:: gsl_multiset
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
A multiset is defined by a structure containing three components, the
|
|
Packit |
67cb25 |
values of :math:`n` and :math:`k`, and a pointer to the multiset array.
|
|
Packit |
67cb25 |
The elements of the multiset array are all of type :code:`size_t`, and
|
|
Packit |
67cb25 |
are stored in increasing order. The :type:`gsl_multiset` structure
|
|
Packit |
67cb25 |
looks like this::
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
typedef struct
|
|
Packit |
67cb25 |
{
|
|
Packit |
67cb25 |
size_t n;
|
|
Packit |
67cb25 |
size_t k;
|
|
Packit |
67cb25 |
size_t *data;
|
|
Packit |
67cb25 |
} gsl_multiset;
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Multiset allocation
|
|
Packit |
67cb25 |
===================
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: gsl_multiset * gsl_multiset_alloc (size_t n, size_t k)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function allocates memory for a new multiset with parameters :data:`n`,
|
|
Packit |
67cb25 |
:data:`k`. The multiset is not initialized and its elements are undefined. Use
|
|
Packit |
67cb25 |
the function :func:`gsl_multiset_calloc` if you want to create a multiset which
|
|
Packit |
67cb25 |
is initialized to the lexicographically first multiset element. A null pointer
|
|
Packit |
67cb25 |
is returned if insufficient memory is available to create the multiset.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: gsl_multiset * gsl_multiset_calloc (size_t n, size_t k)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function allocates memory for a new multiset with parameters :data:`n`,
|
|
Packit |
67cb25 |
:data:`k` and initializes it to the lexicographically first multiset element. A
|
|
Packit |
67cb25 |
null pointer is returned if insufficient memory is available to create the
|
|
Packit |
67cb25 |
multiset.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: void gsl_multiset_init_first (gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function initializes the multiset :data:`c` to the lexicographically first
|
|
Packit |
67cb25 |
multiset element, i.e. :math:`0` repeated :math:`k` times.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: void gsl_multiset_init_last (gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function initializes the multiset :data:`c` to the lexicographically last
|
|
Packit |
67cb25 |
multiset element, i.e. :math:`n-1` repeated :math:`k` times.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: void gsl_multiset_free (gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function frees all the memory used by the multiset :data:`c`.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_memcpy (gsl_multiset * dest, const gsl_multiset * src)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function copies the elements of the multiset :data:`src` into the
|
|
Packit |
67cb25 |
multiset :data:`dest`. The two multisets must have the same size.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Accessing multiset elements
|
|
Packit |
67cb25 |
===========================
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
The following function can be used to access the elements of a multiset.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: size_t gsl_multiset_get (const gsl_multiset * c, const size_t i)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function returns the value of the :data:`i`-th element of the
|
|
Packit |
67cb25 |
multiset :data:`c`. If :data:`i` lies outside the allowed range of 0 to
|
|
Packit |
67cb25 |
:math:`k - 1` then the error handler is invoked and 0 is returned. |inlinefn|
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Multiset properties
|
|
Packit |
67cb25 |
===================
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: size_t gsl_multiset_n (const gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function returns the range (:math:`n`) of the multiset :data:`c`.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: size_t gsl_multiset_k (const gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function returns the number of elements (:math:`k`) in the multiset :data:`c`.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: size_t * gsl_multiset_data (const gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function returns a pointer to the array of elements in the
|
|
Packit |
67cb25 |
multiset :data:`c`.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. index::
|
|
Packit |
67cb25 |
single: checking multiset for validity
|
|
Packit |
67cb25 |
single: testing multiset for validity
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_valid (gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function checks that the multiset :data:`c` is valid. The :data:`k`
|
|
Packit |
67cb25 |
elements should lie in the range 0 to :math:`n - 1`, with each
|
|
Packit |
67cb25 |
value occurring in nondecreasing order.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Multiset functions
|
|
Packit |
67cb25 |
==================
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. index:: iterating through multisets
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_next (gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function advances the multiset :data:`c` to the next multiset element in
|
|
Packit |
67cb25 |
lexicographic order and returns :macro:`GSL_SUCCESS`. If no further multisets
|
|
Packit |
67cb25 |
elements are available it returns :macro:`GSL_FAILURE` and leaves :data:`c`
|
|
Packit |
67cb25 |
unmodified. Starting with the first multiset and repeatedly applying this
|
|
Packit |
67cb25 |
function will iterate through all possible multisets of a given order.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_prev (gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function steps backwards from the multiset :data:`c` to the previous
|
|
Packit |
67cb25 |
multiset element in lexicographic order, returning :macro:`GSL_SUCCESS`. If no
|
|
Packit |
67cb25 |
previous multiset is available it returns :macro:`GSL_FAILURE` and leaves :data:`c`
|
|
Packit |
67cb25 |
unmodified.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Reading and writing multisets
|
|
Packit |
67cb25 |
=============================
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
The library provides functions for reading and writing multisets to a
|
|
Packit |
67cb25 |
file as binary data or formatted text.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_fwrite (FILE * stream, const gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function writes the elements of the multiset :data:`c` to the
|
|
Packit |
67cb25 |
stream :data:`stream` in binary format. The function returns
|
|
Packit |
67cb25 |
:macro:`GSL_EFAILED` if there was a problem writing to the file. Since the
|
|
Packit |
67cb25 |
data is written in the native binary format it may not be portable
|
|
Packit |
67cb25 |
between different architectures.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_fread (FILE * stream, gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function reads elements from the open stream :data:`stream` into the
|
|
Packit |
67cb25 |
multiset :data:`c` in binary format. The multiset :data:`c` must be
|
|
Packit |
67cb25 |
preallocated with correct values of :math:`n` and :math:`k` since the
|
|
Packit |
67cb25 |
function uses the size of :data:`c` to determine how many bytes to read.
|
|
Packit |
67cb25 |
The function returns :macro:`GSL_EFAILED` if there was a problem reading
|
|
Packit |
67cb25 |
from the file. The data is assumed to have been written in the native
|
|
Packit |
67cb25 |
binary format on the same architecture.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_fprintf (FILE * stream, const gsl_multiset * c, const char * format)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function writes the elements of the multiset :data:`c`
|
|
Packit |
67cb25 |
line-by-line to the stream :data:`stream` using the format specifier
|
|
Packit |
67cb25 |
:data:`format`, which should be suitable for a type of :code:`size_t`.
|
|
Packit |
67cb25 |
In ISO C99 the type modifier :code:`z` represents :code:`size_t`, so
|
|
Packit |
67cb25 |
:code:`"%zu\n"` is a suitable format [#f1]_.
|
|
Packit |
67cb25 |
The function returns :macro:`GSL_EFAILED` if there was a problem writing to the file.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. function:: int gsl_multiset_fscanf (FILE * stream, gsl_multiset * c)
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
This function reads formatted data from the stream :data:`stream` into the
|
|
Packit |
67cb25 |
multiset :data:`c`. The multiset :data:`c` must be preallocated with
|
|
Packit |
67cb25 |
correct values of :math:`n` and :math:`k` since the function uses the size of :data:`c` to
|
|
Packit |
67cb25 |
determine how many numbers to read. The function returns
|
|
Packit |
67cb25 |
:macro:`GSL_EFAILED` if there was a problem reading from the file.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Examples
|
|
Packit |
67cb25 |
========
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
The example program below prints all multisets elements containing the values
|
|
Packit |
67cb25 |
:math:`{0,1,2,3}` ordered by size. Multiset elements of the same size are
|
|
Packit |
67cb25 |
ordered lexicographically.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. include:: examples/multiset.c
|
|
Packit |
67cb25 |
:code:
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
Here is the output from the program,
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. include:: examples/multiset.txt
|
|
Packit |
67cb25 |
:code:
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
All 70 multisets are generated and sorted lexicographically.
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. rubric:: Footnotes
|
|
Packit |
67cb25 |
|
|
Packit |
67cb25 |
.. [#f1] In versions of the GNU C library prior to the ISO C99 standard,
|
|
Packit |
67cb25 |
the type modifier :code:`Z` was used instead.
|