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<title>Matrices - GNU Scientific Library -- Reference Manual</title>
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<a name="Matrices"></a>
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<h3 class="section">8.4 Matrices</h3>
<p><a name="index-matrices-907"></a><a name="index-physical-dimension_002c-matrices-908"></a><a name="index-trailing-dimension_002c-matrices-909"></a><a name="index-leading-dimension_002c-matrices-910"></a>
Matrices are defined by a <code>gsl_matrix</code> 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.
<p>The <code>gsl_matrix</code> 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</var>, a pointer to
the block owned by the matrix <var>block</var>, if any, and an ownership
flag, <var>owner</var>. The physical dimension determines the memory layout
and can differ from the matrix dimension to allow the use of
submatrices. The <code>gsl_matrix</code> structure is very simple and looks
like this,
<pre class="example"> typedef struct
{
size_t size1;
size_t size2;
size_t tda;
double * data;
gsl_block * block;
int owner;
} gsl_matrix;
</pre>
<p class="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 <span class="sc">fortran</span>
stores arrays in column-major order. The number of rows is <var>size1</var>.
The range of valid row indices runs from 0 to <code>size1-1</code>. Similarly
<var>size2</var> is the number of columns. The range of valid column indices
runs from 0 to <code>size2-1</code>. The physical row dimension <var>tda</var>, or
<dfn>trailing dimension</dfn>, specifies the size of a row of the matrix as
laid out in memory.
<p>For example, in the following matrix <var>size1</var> is 3, <var>size2</var> is 4,
and <var>tda</var> 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.
<pre class="example"> 00 01 02 03 XX XX XX XX
10 11 12 13 XX XX XX XX
20 21 22 23 XX XX XX XX
</pre>
<p class="noindent">Each unused memory location is represented by “<code>XX</code>”. The
pointer <var>data</var> gives the location of the first element of the matrix
in memory. The pointer <var>block</var> 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</var> 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</var> field is
zero and any underlying block will not be freed.
<p>The functions for allocating and accessing matrices are defined in
<samp><span class="file">gsl_matrix.h</span></samp>
<ul class="menu">
<li><a accesskey="1" href="Matrix-allocation.html">Matrix allocation</a>
<li><a accesskey="2" href="Accessing-matrix-elements.html">Accessing matrix elements</a>
<li><a accesskey="3" href="Initializing-matrix-elements.html">Initializing matrix elements</a>
<li><a accesskey="4" href="Reading-and-writing-matrices.html">Reading and writing matrices</a>
<li><a accesskey="5" href="Matrix-views.html">Matrix views</a>
<li><a accesskey="6" href="Creating-row-and-column-views.html">Creating row and column views</a>
<li><a accesskey="7" href="Copying-matrices.html">Copying matrices</a>
<li><a accesskey="8" href="Copying-rows-and-columns.html">Copying rows and columns</a>
<li><a accesskey="9" href="Exchanging-rows-and-columns.html">Exchanging rows and columns</a>
<li><a href="Matrix-operations.html">Matrix operations</a>
<li><a href="Finding-maximum-and-minimum-elements-of-matrices.html">Finding maximum and minimum elements of matrices</a>
<li><a href="Matrix-properties.html">Matrix properties</a>
<li><a href="Example-programs-for-matrices.html">Example programs for matrices</a>
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