vectors.texi

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@comment 
@comment The new vector is only a view of the block underlying the original
@comment vector, @var{v}.  The block is not owned by the new vector.  When the new
@comment vector is deallocated the original vector @var{v} and its block will
@comment continue to exist.  The original memory can only be deallocated by
@comment freeing the original vector.  Of course, the original vector should not
@comment be deallocated while the new vector is still in use.
@comment @end deftypefun

@node Copying vectors
@subsection Copying vectors

Common operations on vectors such as addition and multiplication are
available in the @sc{blas} part of the library (@pxref{BLAS
Support}).  However, it is useful to have a small number of utility
functions which do not require the full @sc{blas} code.  The following
functions fall into this category.

@deftypefun int gsl_vector_memcpy (gsl_vector * @var{dest}, const gsl_vector * @var{src})
This function copies the elements of the vector @var{src} into the
vector @var{dest}.  The two vectors must have the same length.
@end deftypefun

@deftypefun int gsl_vector_swap (gsl_vector * @var{v}, gsl_vector * @var{w})
This function exchanges the elements of the vectors @var{v} and @var{w}
by copying.  The two vectors must have the same length.
@end deftypefun


@node Exchanging elements
@subsection Exchanging elements

The following function can be used to exchange, or permute, the elements
of a vector.

@deftypefun int gsl_vector_swap_elements (gsl_vector * @var{v}, size_t @var{i}, size_t @var{j})
This function exchanges the @var{i}-th and @var{j}-th elements of the
vector @var{v} in-place.
@end deftypefun

@deftypefun int gsl_vector_reverse (gsl_vector * @var{v})
This function reverses the order of the elements of the vector @var{v}.
@end deftypefun


@node Vector operations
@subsection Vector operations

The following operations are only defined for real vectors.

@deftypefun int gsl_vector_add (gsl_vector * @var{a}, const gsl_vector * @var{b})
This function adds the elements of vector @var{b} to the elements of
vector @var{a}, @math{a'_i = a_i + b_i}. The two vectors must have the
same length.
@end deftypefun

@deftypefun int gsl_vector_sub (gsl_vector * @var{a}, const gsl_vector * @var{b})
This function subtracts the elements of vector @var{b} from the elements of
vector @var{a}, @math{a'_i = a_i - b_i}. The two vectors must have the
same length.
@end deftypefun

@deftypefun int gsl_vector_mul (gsl_vector * @var{a}, const gsl_vector * @var{b})
This function multiplies the elements of vector @var{a} by the elements of
vector @var{b}, @math{a'_i = a_i * b_i}. The two vectors must have the
same length.
@end deftypefun

@deftypefun int gsl_vector_div (gsl_vector * @var{a}, const gsl_vector * @var{b})
This function divides the elements of vector @var{a} by the elements of
vector @var{b}, @math{a'_i = a_i / b_i}. The two vectors must have the
same length.
@end deftypefun

@deftypefun int gsl_vector_scale (gsl_vector * @var{a}, const double @var{x})
This function multiplies the elements of vector @var{a} by the constant
factor @var{x}, @math{a'_i = x a_i}.
@end deftypefun

@deftypefun int gsl_vector_add_constant (gsl_vector * @var{a}, const double @var{x})
This function adds the constant value @var{x} to the elements of the
vector @var{a}, @math{a'_i = a_i + x}.
@end deftypefun

@node Finding maximum and minimum elements of vectors
@subsection Finding maximum and minimum elements of vectors

@deftypefun double gsl_vector_max (const gsl_vector * @var{v})
This function returns the maximum value in the vector @var{v}.
@end deftypefun

@deftypefun double gsl_vector_min (const gsl_vector * @var{v})
This function returns the minimum value in the vector @var{v}.
@end deftypefun

@deftypefun void gsl_vector_minmax (const gsl_vector * @var{v}, double * @var{min_out}, double * @var{max_out})
This function returns the minimum and maximum values in the vector
@var{v}, storing them in @var{min_out} and @var{max_out}.
@end deftypefun

@deftypefun size_t gsl_vector_max_index (const gsl_vector * @var{v})
This function returns the index of the maximum value in the vector @var{v}.
When there are several equal maximum elements then the lowest index is
returned.
@end deftypefun

@deftypefun size_t gsl_vector_min_index (const gsl_vector * @var{v})
This function returns the index of the minimum value in the vector @var{v}.
When there are several equal minimum elements then the lowest index is
returned.
@end deftypefun

@deftypefun void gsl_vector_minmax_index (const gsl_vector * @var{v}, size_t * @var{imin}, size_t * @var{imax})
This function returns the indices of the minimum and maximum values in
the vector @var{v}, storing them in @var{imin} and @var{imax}. When
there are several equal minimum or maximum elements then the lowest
indices are returned.
@end deftypefun

@node Vector properties
@subsection Vector properties

@deftypefun int gsl_vector_isnull (const gsl_vector * @var{v})
This function returns 1 if all the elements of the vector @var{v} are
zero, and 0 otherwise.
@end deftypefun

@node Example programs for vectors
@subsection Example programs for vectors

This program shows how to allocate, initialize and read from a vector
using the functions @code{gsl_vector_alloc}, @code{gsl_vector_set} and
@code{gsl_vector_get}.

@example
@verbatiminclude examples/vector.c
@end example
@comment
@noindent
Here is the output from the program.  The final loop attempts to read
outside the range of the vector @code{v}, and the error is trapped by
the range-checking code in @code{gsl_vector_get}.

@example
v_0 = 1.23
v_1 = 2.23
v_2 = 3.23
gsl: vector_source.c:12: ERROR: index out of range
IOT trap/Abort (core dumped)
@end example
@comment
@noindent
The next program shows how to write a vector to a file.

@example
@verbatiminclude examples/vectorw.c
@end example
@comment
@noindent
After running this program the file @file{test.dat} should contain the
elements of @code{v}, written using the format specifier
@code{%.5g}.  The vector could then be read back in using the function
@code{gsl_vector_fscanf (f, v)} as follows:

@example
@verbatiminclude examples/vectorr.c
@end example


@node Matrices
@section Matrices
@cindex matrices
@cindex physical dimension, matrices
@cindex trailing dimension, matrices
@cindex leading dimension, matrices

Matrices are defined by a @code{gsl_matrix} structure which describes a
generalized slice of a block.  Like a vector it represents a set of
elements in an area of memory, but uses two indices instead of one.

The @code{gsl_matrix} structure contains six components, the two
dimensions of the matrix, a physical dimension, a pointer to the memory
where the elements of the matrix are stored, @var{data}, a pointer to
the block owned by the matrix @var{block}, if any, and an ownership
flag, @var{owner}.  The physical dimension determines the memory layout
and can differ from the matrix dimension to allow the use of
submatrices.  The @code{gsl_matrix} structure is very simple and looks
like this,

@example
typedef struct
@{
  size_t size1;
  size_t size2;
  size_t tda;
  double * data;
  gsl_block * block;
  int owner;
@} gsl_matrix;
@end example
@comment
@noindent
Matrices are stored in row-major order, meaning that each row of
elements forms a contiguous block in memory.  This is the standard
"C-language ordering" of two-dimensional arrays. Note that @sc{fortran}
stores arrays in column-major order. The number of rows is @var{size1}.
The range of valid row indices runs from 0 to @code{size1-1}.  Similarly
@var{size2} is the number of columns.  The range of valid column indices
runs from 0 to @code{size2-1}.  The physical row dimension @var{tda}, or
@dfn{trailing dimension}, specifies the size of a row of the matrix as
laid out in memory.

For example, in the following matrix @var{size1} is 3, @var{size2} is 4,
and @var{tda} is 8.  The physical memory layout of the matrix begins in
the top left hand-corner and proceeds from left to right along each row
in turn.

@example
@group
00 01 02 03 XX XX XX XX
10 11 12 13 XX XX XX XX
20 21 22 23 XX XX XX XX
@end group
@end example
@noindent
Each unused memory location is represented by ``@code{XX}''.  The
pointer @var{data} gives the location of the first element of the matrix
in memory.  The pointer @var{block} stores the location of the memory
block in which the elements of the matrix are located (if any).  If the
matrix owns this block then the @var{owner} field is set to one and the
block will be deallocated when the matrix is freed.  If the matrix is
only a slice of a block owned by another object then the @var{owner} field is
zero and any underlying block will not be freed.

The functions for allocating and accessing matrices are defined in
@file{gsl_matrix.h}

@menu
* Matrix allocation::           
* Accessing matrix elements::   
* Initializing matrix elements::  
* Reading and writing matrices::  
* Matrix views::                
* Creating row and column views::  
* Copying matrices::            
* Copying rows and columns::    
* Exchanging rows and columns::  
* Matrix operations::           
* Finding maximum and minimum elements of matrices::  
* Matrix properties::           
* Example programs for matrices::  
@end menu

@node Matrix allocation
@subsection Matrix allocation

The functions for allocating memory to a matrix follow the style of
@code{malloc} and @code{free}.  They also perform their own error
checking.  If there is insufficient memory available to allocate a vector
then the functions call the GSL error handler (with an error number of
@code{GSL_ENOMEM}) in addition to returning a null pointer.  Thus if you
use the library error handler to abort your program then it isn't
necessary to check every @code{alloc}.

@deftypefun {gsl_matrix *} gsl_matrix_alloc (size_t @var{n1}, size_t @var{n2})
This function creates a matrix of size @var{n1} rows by @var{n2}
columns, returning a pointer to a newly initialized matrix struct. A new
block is allocated for the elements of the matrix, and stored in the
@var{block} component of the matrix struct.  The block is ``owned'' by the
matrix, and will be deallocated when the matrix is deallocated.
@end deftypefun

@deftypefun {gsl_matrix *} gsl_matrix_calloc (size_t @var{n1}, size_t @var{n2})
This function allocates memory for a matrix of size @var{n1} rows by
@var{n2} columns and initializes all the elements of the matrix to zero.
@end deftypefun

@deftypefun void gsl_matrix_free (gsl_matrix * @var{m})
This function frees a previously allocated matrix @var{m}.  If the
matrix was created using @code{gsl_matrix_alloc} then the block
underlying the matrix will also be deallocated.  If the matrix has been
created from another object then the memory is still owned by that
object and will not be deallocated.
@end deftypefun

@node Accessing matrix elements
@subsection Accessing matrix elements
@cindex matrices, range-checking
@cindex range-checking for matrices

The functions for accessing the elements of a matrix use the same range
checking system as vectors.  You can turn off range checking by recompiling
your program with the preprocessor definition
@code{GSL_RANGE_CHECK_OFF}.

The elements of the matrix are stored in "C-order", where the second
index moves continuously through memory.  More precisely, the element
accessed by the function @code{gsl_matrix_get(m,i,j)} and
@code{gsl_matrix_set(m,i,j,x)} is