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<a name="Dimensions-and-related-operations"></a>
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<a name="Dimensions-and-related-operations-_0028ap_005fdimension_002eh_0029"></a>
<h2 class="section">Dimensions and related operations (‘<tt>ap_dimension.h</tt>’)</h2>
<dl>
<dt><a name="index-ap_005fdim_005ft"></a><u>datatype:</u> <b>ap_dim_t</b></dt>
<dd><table><tr><td> </td><td><pre class="example">typedef unsigned int ap_dim_t;
</pre></td></tr></table>
<p>Datatype for dimensions.
</p></dd></dl>
<dl>
<dt><a name="index-AP_005fDIM_005fMAX"></a><u>Macro:</u> <b>AP_DIM_MAX</b></dt>
<dd><p>Special value used for sparse representations, means: "to be
ignored". Also used as a result when an error occurs.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimension_005ft"></a><u>datatype:</u> <b>ap_dimension_t</b></dt>
<dd><table><tr><td> </td><td><pre class="example">typedef struct ap_dimension_t {
size_t intdim; /* Number of integer dimensions */
size_t realdim; /* Number of real dimensions */
} ap_dimension_t;
</pre></td></tr></table>
<p>Datatype for specifying the dimensionality of an abstract value.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange_005ft"></a><u>datatype:</u> <b>ap_dimchange_t</b></dt>
<dd><table><tr><td> </td><td><pre class="example">typedef struct ap_dimchange_t {
ap_dim_t* dim; /* Assumed to be an array of size intdim+realdim */
size_t intdim ; /* Number of integer dimensions to add/remove */
size_t realdim; /* Number of real dimensions to add/remove */
} ap_dimchange_t;
</pre></td></tr></table>
<p>Datatype for specifying change of dimension.
</p>
<p>The semantics is the following:
</p><dl compact="compact">
<dt> <strong>Addition of dimensions</strong></dt>
<dd>
<p><code>dimchange.dim[k]</code> means: add one dimension at dimension k
and shift the already existing dimensions greater than or equal to
<code>k</code> one step on the right (or increment them).
</p>
<p>if <code>k</code> is equal to the size of the vector, then it means: add
a dimension at the end.
</p>
<p>Repetion are allowed, and means that one inserts more than one dimensions.
</p>
<p>Example: <code>linexpr0_add_dimensions([i0 i1 r0 r1], { [0 1 2 2
4],3,1 })</code> returns <code>[0 i0 0 i1 0 0 r0 r1 0]</code>, considered as
a vector with 5 integer dimensions and 4 real dimensions.
</p>
</dd>
<dt> <strong>Removal of dimensions</strong></dt>
<dd>
<p><code>dimchange.dim[k]</code>: remove the dimension <code>k</code> and shift
the dimensions greater than <code>k</code> one step on the left (or
decrement them).
</p>
<p>Repetitions are meaningless (and are not correct specification).
</p>
<p>Example: <code>linexpr0_remove_dimensions([i0 i1 i2 r0 r1 r2], {
[0 2 4],2,1 })</code> returns <code>[i1 r0 r2]</code>, considered as a vector with 1
integer dimensions and 2 real dimensions.
</p></dd>
</dl>
</dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange2_005ft"></a><u>datatype:</u> <b>ap_dimchange2_t</b></dt>
<dd><table><tr><td> </td><td><pre class="example">typedef struct ap_dimchange_2t {
ap_dimchange_t* add; /* If not NULL, specifies the adding new dimensions */
ap_dimchange_t* remove; /* If not NULL, specifies the removal of dimensions */
} ap_dimchange2_t;
</pre></td></tr></table>
<p>Datatype for specifying a transformation composed of the addition and
the removal of dimensions. Used by functions
<code>ap_abstract0_apply_dimchange2</code>,
<code>ap_environment_dimchange2</code>, and
<code>ap_abstract1_change_environment.</code>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimperm_005ft"></a><u>datatype:</u> <b>ap_dimperm_t</b></dt>
<dd><table><tr><td> </td><td><pre class="example">typedef struct ap_dimperm_t {
ap_dim_t* dim; /* Array assumed to be of size size */
size_t size;
} ap_dimperm_t;
</pre></td></tr></table>
<p>Datatype for permutations.
</p>
<p>Represents the permutation <code>i -> dimperm.p[i]</code> for
<code>0<=i<dimperm.size</code>.
</p></dd></dl>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top"><a href="#Manipulating-changes-of-dimensions">Manipulating changes of dimensions</a></td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top"><a href="#Manipulating-permutations-of-dimensions">Manipulating permutations of dimensions</a></td><td> </td><td align="left" valign="top">
</td></tr>
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<a name="Manipulating-changes-of-dimensions-1"></a>
<h3 class="subsection">Manipulating changes of dimensions</h3>
<dl>
<dt><a name="index-ap_005fdimchange_005finit"></a><u>Function:</u> void <b>ap_dimchange_init</b><i> (ap_dimchange_t* <var>dimchange</var>, size_t <var>intdim</var>, size_t <var>realdim</var>)</i></dt>
<dt><a name="index-ap_005fdimchange_005fclear"></a><u>Function:</u> void <b>ap_dimchange_clear</b><i> (ap_dimchange_t* <var>dimchange</var>)</i></dt>
<dd><p>Initialize and clear a dimchange structure.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange_005falloc"></a><u>Function:</u> ap_dimchange_t* <b>ap_dimchange_alloc</b><i> (size_t <var>intdim</var>, size_t <var>realdim</var>)</i></dt>
<dt><a name="index-ap_005fdimchange_005ffree"></a><u>Function:</u> void <b>ap_dimchange_free</b><i> (ap_dimchange_t* <var>dimchange</var>)</i></dt>
<dd><p>Allocate and free a dimchange structure.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange_005ffprint"></a><u>Function:</u> void <b>ap_dimchange_fprint</b><i> (FILE* <var>stream</var>, ap_dimchange_t* <var>dimchange</var>)</i></dt>
<dd><p>Print the change of dimension.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange_005fadd_005finvert"></a><u>Function:</u> void <b>ap_dimchange_add_invert</b><i> (ap_dimchange_t* <var>dimchange</var>)</i></dt>
<dd><p>Assuming that dimchange is a transformation for the addition of dimensions,
invert it to obtain the inverse transformation for removing dimensions.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange2_005finit"></a><u>Function:</u> void <b>ap_dimchange2_init</b><i> (ap_dimchange2_t* <var>dimchange2</var>, ap_dimchange_t* <var>add</var>, ap_dimchange_t* <var>remove</var>)</i></dt>
<dt><a name="index-ap_005fdimchange2_005fclear"></a><u>Function:</u> void <b>ap_dimchange2_clear</b><i> (ap_dimchange2_t* <var>dimchange2</var>)</i></dt>
<dd><p>Initialize (with <var>add</var> and <var>remove</var>) and clear a dimchange2
structure.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange2_005falloc"></a><u>Function:</u> ap_dimchange2_t* <b>ap_dimchange2_alloc</b><i> (ap_dimchange_t* <var>add</var>, ap_dimchange_t* <var>remove</var>)</i></dt>
<dt><a name="index-ap_005fdimchange2_005ffree"></a><u>Function:</u> void <b>ap_dimchange2_free</b><i> (ap_dimchange2_t* <var>dimchange2</var>)</i></dt>
<dd><p>Allocate and free a dimchange2 structure.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimchange2_005ffprint"></a><u>Function:</u> void <b>ap_dimchange2_fprint</b><i> (FILE* <var>stream</var>, ap_dimchange2_t* <var>dimchange2</var>)</i></dt>
<dd><p>Print the change of dimension.
</p></dd></dl>
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<a name="Manipulating-permutations-of-dimensions-1"></a>
<h3 class="subsection">Manipulating permutations of dimensions</h3>
<dl>
<dt><a name="index-ap_005fdimperm_005finit"></a><u>Function:</u> void <b>ap_dimperm_init</b><i> (ap_dimperm_t* <var>perm</var>, size_t <var>size</var>)</i></dt>
<dt><a name="index-ap_005fdimperm_005fclear"></a><u>Function:</u> void <b>ap_dimperm_clear</b><i> (ap_dimperm_t* <var>perm</var>)</i></dt>
<dd><p>Initialize and clear a dimperm structure.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimperm_005falloc"></a><u>Function:</u> ap_dimperm_t* <b>ap_dimperm_alloc</b><i> (size_t <var>size</var>)</i></dt>
<dt><a name="index-ap_005fdimperm_005ffree"></a><u>Function:</u> void <b>ap_dimperm_free</b><i> (ap_dimperm_t* <var>perm</var>)</i></dt>
<dd><p>Allocate and free a dimperm structure.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimperm_005ffprint"></a><u>Function:</u> void <b>ap_dimperm_fprint</b><i> (FILE* <var>stream</var>, ap_dimperm_t* <var>perm</var>)</i></dt>
<dd><p>Print the permutation.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimperm_005fset_005fid"></a><u>Function:</u> void <b>ap_dimperm_set_id</b><i> (ap_dimperm_t* <var>perm</var>)</i></dt>
<dd><p>Fill the already allocated <var>perm</var> with the identity permutation.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimperm_005fcompose"></a><u>Function:</u> void <b>ap_dimperm_compose</b><i> (ap_dimperm_t* <var>perm</var>, ap_dimperm_t* <var>perm1</var>, ap_dimperm_t* <var>perm2</var>)</i></dt>
<dd><p>Compose the 2 permutations <var>perm1</var> and <var>perm2</var> (in this order)
and store the result the already allocated perm.
The sizes of permutations are supposed to be equal.
At exit, we have <code>perm.dim[i] = perm2.dim[perm1.dim[i]]</code>.
</p></dd></dl>
<dl>
<dt><a name="index-ap_005fdimperm_005finvert"></a><u>Function:</u> void <b>ap_dimperm_invert</b><i> (ap_dimperm_t* <var>nperm</var>, ap_dimperm_t* <var>perm</var>)</i></dt>
<dd><p>Invert the permutation <var>perm</var> and store it in the already
allocated <var>nperm</var>. The sizes of permutations are supposed to
be equal.
</p></dd></dl>
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