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<a href="#func-members">Functions</a> </div>
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<div class="headertitle"><div class="title">Householder transform of a vector<div class="ingroups"><a class="el" href="group__groupMatrix.html">Matrix Functions</a></div></div></div>
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</div><!--header-->
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ga2ac1a8e5e186599ae8ca5a67206c19c4"><td class="memItemLeft" align="right" valign="top">float16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__MatrixHouseholder.html#ga2ac1a8e5e186599ae8ca5a67206c19c4">arm_householder_f16</a> (const float16_t *pSrc, const float16_t threshold, uint32_t <a class="el" href="arm__variance__example__f32_8c.html#ab6558f40a619c2502fbc24c880fd4fb0">blockSize</a>, float16_t *pOut)</td></tr>
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<tr class="memdesc:ga2ac1a8e5e186599ae8ca5a67206c19c4"><td class="mdescLeft"> </td><td class="mdescRight">Householder transform of a half floating point vector. <a href="group__MatrixHouseholder.html#ga2ac1a8e5e186599ae8ca5a67206c19c4">More...</a><br /></td></tr>
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<tr class="separator:ga2ac1a8e5e186599ae8ca5a67206c19c4"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga4dcb8af2a65875bf84da6ed35c436537"><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__MatrixHouseholder.html#ga4dcb8af2a65875bf84da6ed35c436537">arm_householder_f32</a> (const <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pSrc, const <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> threshold, uint32_t <a class="el" href="arm__variance__example__f32_8c.html#ab6558f40a619c2502fbc24c880fd4fb0">blockSize</a>, <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pOut)</td></tr>
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<tr class="memdesc:ga4dcb8af2a65875bf84da6ed35c436537"><td class="mdescLeft"> </td><td class="mdescRight">Householder transform of a floating point vector. <a href="group__MatrixHouseholder.html#ga4dcb8af2a65875bf84da6ed35c436537">More...</a><br /></td></tr>
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<tr class="separator:ga4dcb8af2a65875bf84da6ed35c436537"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga62826e5b9e3c7787147e4e4de21015fc"><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__MatrixHouseholder.html#ga62826e5b9e3c7787147e4e4de21015fc">arm_householder_f64</a> (const <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> *pSrc, const <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> threshold, uint32_t <a class="el" href="arm__variance__example__f32_8c.html#ab6558f40a619c2502fbc24c880fd4fb0">blockSize</a>, <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> *pOut)</td></tr>
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<tr class="memdesc:ga62826e5b9e3c7787147e4e4de21015fc"><td class="mdescLeft"> </td><td class="mdescRight">Householder transform of a double floating point vector. <a href="group__MatrixHouseholder.html#ga62826e5b9e3c7787147e4e4de21015fc">More...</a><br /></td></tr>
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<tr class="separator:ga62826e5b9e3c7787147e4e4de21015fc"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Description</h2>
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<p >Computes the Householder transform of a vector x.</p>
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<p >The Householder transform of x is a vector v with</p>
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<p class="formulaDsp">
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\[ v_0 = 1 \]
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</p>
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<p >and a scalar \(\beta\) such that:</p>
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<p class="formulaDsp">
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\[ P = I - \beta v v^T \]
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</p>
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<p >is an orthogonal matrix and</p>
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<p class="formulaDsp">
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\[ P x = ||x||_2 e_1 \]
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</p>
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<p >So P is an hyperplane reflection such that the image of x is proportional to \(e_1\).</p>
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<p >\(e_1\) is the vector of coordinates:</p>
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<p class="formulaDsp">
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\[ \begin{pmatrix} 1 \\ 0 \\ \vdots \\ \end{pmatrix} \]
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</p>
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<p >If x is already proportional to \(e_1\) then the matrix P should be the identity.</p>
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<p >Thus, \(\beta\) should be 0 and in this case the vector v can also be null.</p>
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<p >But how do we detect that x is already proportional to \(e_1\).</p>
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<p >If x </p><p class="formulaDsp">
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\[ x = \begin{pmatrix} x_0 \\ xr \\ \end{pmatrix} \]
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</p>
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<p >where \(xr\) is a vector.</p>
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<p >The algorithm is computing the norm squared of this vector:</p>
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<p class="formulaDsp">
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\[ ||xr||^2 \]
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</p>
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<p >and this value is compared to a <code>threshold</code>. If the value is smaller than the <code>threshold</code>, the algorithm is returning 0 for \(\beta\) and the householder vector.</p>
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<p >This <code>threshold</code> is an argument of the function.</p>
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<p >Default values are provided in the header <code><a class="el" href="matrix__functions_8h.html">dsp/matrix_functions.h</a></code> like for instance <code>DEFAULT_HOUSEHOLDER_THRESHOLD_F32</code> </p>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="ga2ac1a8e5e186599ae8ca5a67206c19c4" name="ga2ac1a8e5e186599ae8ca5a67206c19c4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga2ac1a8e5e186599ae8ca5a67206c19c4">◆ </a></span>arm_householder_f16()</h2>
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<td class="memname">float16_t arm_householder_f16 </td>
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<td>(</td>
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<td class="paramtype">const float16_t * </td>
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<td class="paramname"><em>pSrc</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const float16_t </td>
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<td class="paramname"><em>threshold</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">uint32_t </td>
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<td class="paramname"><em>blockSize</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">float16_t * </td>
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<td class="paramname"><em>pOut</em> </td>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">pSrc</td><td>points to the input vector. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">threshold</td><td>norm2 threshold. <br />
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</td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">blockSize</td><td>dimension of the vector space. </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOut</td><td>points to the output vector. </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>beta return the scaling factor beta </dd></dl>
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</div>
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</div>
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<a id="ga4dcb8af2a65875bf84da6ed35c436537" name="ga4dcb8af2a65875bf84da6ed35c436537"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga4dcb8af2a65875bf84da6ed35c436537">◆ </a></span>arm_householder_f32()</h2>
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<td class="memname"><a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> arm_householder_f32 </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> * </td>
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<td class="paramname"><em>pSrc</em>, </td>
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</tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> </td>
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<td class="paramname"><em>threshold</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">uint32_t </td>
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<td class="paramname"><em>blockSize</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype"><a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> * </td>
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<td class="paramname"><em>pOut</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">pSrc</td><td>points to the input vector. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">threshold</td><td>norm2 threshold. <br />
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</td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">blockSize</td><td>dimension of the vector space. </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOut</td><td>points to the output vector. </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>beta return the scaling factor beta </dd></dl>
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</div>
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</div>
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<a id="ga62826e5b9e3c7787147e4e4de21015fc" name="ga62826e5b9e3c7787147e4e4de21015fc"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga62826e5b9e3c7787147e4e4de21015fc">◆ </a></span>arm_householder_f64()</h2>
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<div class="memitem">
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<td class="memname"><a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> arm_householder_f64 </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> * </td>
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<td class="paramname"><em>pSrc</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> </td>
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<td class="paramname"><em>threshold</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">uint32_t </td>
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<td class="paramname"><em>blockSize</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype"><a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> * </td>
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<td class="paramname"><em>pOut</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</div><div class="memdoc">
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">pSrc</td><td>points to the input vector. </td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">threshold</td><td>norm2 threshold. <br />
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</td></tr>
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<tr><td class="paramdir">[in]</td><td class="paramname">blockSize</td><td>dimension of the vector space. </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOut</td><td>points to the output vector. </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>beta return the scaling factor beta </dd></dl>
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