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<a href="#func-members">Functions</a> </div>
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<div class="headertitle"><div class="title">QR decomposition of a Matrix<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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<div class="contents">
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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:ga6b783c1917e0744ef7a088812ffcd1cf"><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__MatrixQR.html#ga6b783c1917e0744ef7a088812ffcd1cf">arm_mat_qr_f16</a> (const <a class="el" href="structarm__matrix__instance__f16.html">arm_matrix_instance_f16</a> *pSrc, const float16_t threshold, <a class="el" href="structarm__matrix__instance__f16.html">arm_matrix_instance_f16</a> *pOutR, <a class="el" href="structarm__matrix__instance__f16.html">arm_matrix_instance_f16</a> *pOutQ, float16_t *pOutTau, float16_t *pTmpA, float16_t *pTmpB)</td></tr>
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<tr class="memdesc:ga6b783c1917e0744ef7a088812ffcd1cf"><td class="mdescLeft"> </td><td class="mdescRight">QR decomposition of a m x n half floating point matrix with m >= n. <a href="group__MatrixQR.html#ga6b783c1917e0744ef7a088812ffcd1cf">More...</a><br /></td></tr>
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<tr class="separator:ga6b783c1917e0744ef7a088812ffcd1cf"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gae4b129d8c645a812914da44ad1fc4f50"><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__MatrixQR.html#gae4b129d8c645a812914da44ad1fc4f50">arm_mat_qr_f32</a> (const <a class="el" href="structarm__matrix__instance__f32.html">arm_matrix_instance_f32</a> *pSrc, const <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> threshold, <a class="el" href="structarm__matrix__instance__f32.html">arm_matrix_instance_f32</a> *pOutR, <a class="el" href="structarm__matrix__instance__f32.html">arm_matrix_instance_f32</a> *pOutQ, <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pOutTau, <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pTmpA, <a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> *pTmpB)</td></tr>
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<tr class="memdesc:gae4b129d8c645a812914da44ad1fc4f50"><td class="mdescLeft"> </td><td class="mdescRight">QR decomposition of a m x n floating point matrix with m >= n. <a href="group__MatrixQR.html#gae4b129d8c645a812914da44ad1fc4f50">More...</a><br /></td></tr>
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<tr class="separator:gae4b129d8c645a812914da44ad1fc4f50"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaa222c153ee1753dce2904b4b01189eb4"><td class="memItemLeft" align="right" valign="top"><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__MatrixQR.html#gaa222c153ee1753dce2904b4b01189eb4">arm_mat_qr_f64</a> (const <a class="el" href="structarm__matrix__instance__f64.html">arm_matrix_instance_f64</a> *pSrc, const <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> threshold, <a class="el" href="structarm__matrix__instance__f64.html">arm_matrix_instance_f64</a> *pOutR, <a class="el" href="structarm__matrix__instance__f64.html">arm_matrix_instance_f64</a> *pOutQ, <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> *pOutTau, <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> *pTmpA, <a class="el" href="arm__math__types_8h.html#ac55f3ae81b5bc9053760baacf57e47f4">float64_t</a> *pTmpB)</td></tr>
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<tr class="memdesc:gaa222c153ee1753dce2904b4b01189eb4"><td class="mdescLeft"> </td><td class="mdescRight">QR decomposition of a m x n double floating point matrix with m >= n. <a href="group__MatrixQR.html#gaa222c153ee1753dce2904b4b01189eb4">More...</a><br /></td></tr>
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<tr class="separator:gaa222c153ee1753dce2904b4b01189eb4"><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 QR decomposition of a matrix M using Householder algorithm.</p>
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<p class="formulaDsp">
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\[ M = Q R \]
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</p>
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<p >where Q is an orthogonal matrix and R is upper triangular. No pivoting strategy is used.</p>
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<p >The returned value for R is using a format a bit similar to LAPACK : it is not just containing the matrix R but also the Householder reflectors.</p>
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<p >The function is also returning a vector \(\tau\) that is containing the scaling factor for the reflectors.</p>
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<p >Returned value R has the structure:</p>
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<p class="formulaDsp">
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\[ \begin{pmatrix} r_{11} & r_{12} & \dots & r_{1n} \\ v_{12} & r_{22} & \dots & r_{2n} \\ v_{13} & v_{22} & \dots & r_{3n} \\ \vdots & \vdots & \ddots & \vdots \\ v_{1m} & v_{2(m-1)} & \dots & r_{mn} \\ \end{pmatrix} \]
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</p>
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<p >where</p>
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<p class="formulaDsp">
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\[ v_1 = \begin{pmatrix} 1 \\ v_{12} \\ \vdots \\ v_{1m} \\ \end{pmatrix} \]
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</p>
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<p >is the first householder reflector.</p>
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<p >The Householder Matrix is given by \(H_1\)</p>
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<p class="formulaDsp">
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\[ H_1 = I - \tau_1 v_1 v_1^T \]
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</p>
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<p >The Matrix Q is the product of the Householder matrices:</p>
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<p class="formulaDsp">
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\[ Q = H_1 H_2 \dots H_n \]
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</p>
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<p >The computation of the matrix Q by this function is optional.</p>
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<p >And the matrix R, would be the returned value R without the householder reflectors:</p>
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<p class="formulaDsp">
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\[ \begin{pmatrix} r_{11} & r_{12} & \dots & r_{1n} \\ 0 & r_{22} & \dots & r_{2n} \\ 0 & 0 & \dots & r_{3n} \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \dots & r_{mn} \\ \end{pmatrix} \]
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</p>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="ga6b783c1917e0744ef7a088812ffcd1cf" name="ga6b783c1917e0744ef7a088812ffcd1cf"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga6b783c1917e0744ef7a088812ffcd1cf">◆ </a></span>arm_mat_qr_f16()</h2>
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname"><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> arm_mat_qr_f16 </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="structarm__matrix__instance__f16.html">arm_matrix_instance_f16</a> * </td>
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<td class="paramname"><em>pSrc</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">const float16_t </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"><a class="el" href="structarm__matrix__instance__f16.html">arm_matrix_instance_f16</a> * </td>
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<td class="paramname"><em>pOutR</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="structarm__matrix__instance__f16.html">arm_matrix_instance_f16</a> * </td>
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<td class="paramname"><em>pOutQ</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">float16_t * </td>
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<td class="paramname"><em>pOutTau</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">float16_t * </td>
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<td class="paramname"><em>pTmpA</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">float16_t * </td>
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<td class="paramname"><em>pTmpB</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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<p >QR decomposition of a m x n floating point matrix with m >= n.</p>
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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 input matrix structure. The source matrix is modified by the function. </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">[out]</td><td class="paramname">pOutR</td><td>points to output R matrix structure of dimension m x n </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOutQ</td><td>points to output Q matrix structure of dimension m x m (can be NULL) </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOutTau</td><td>points to Householder scaling factors of dimension n </td></tr>
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<tr><td class="paramdir">[in,out]</td><td class="paramname">pTmpA</td><td>points to a temporary vector of dimension m. </td></tr>
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<tr><td class="paramdir">[in,out]</td><td class="paramname">pTmpB</td><td>points to a temporary vector of dimension m. </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>execution status<ul>
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<li><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6a9f8b2a10bd827fb4600e77d455902eb0">ARM_MATH_SUCCESS</a> : Operation successful</li>
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<li><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6a7071b92f1f6bc3c5c312a237ea91105b">ARM_MATH_SIZE_MISMATCH</a> : Matrix size check failed</li>
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</ul>
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</dd></dl>
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<dl class="section user"><dt>pOutQ is optional:</dt><dd>pOutQ can be a NULL pointer. In this case, the argument will be ignored and the output Q matrix won't be computed.</dd></dl>
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<dl class="section user"><dt>f16 implementation</dt><dd>The f16 implementation is not very accurate.</dd></dl>
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<dl class="section user"><dt>Norm2 threshold </dt><dd>For the meaning of this argument please refer to the <a class="el" href="group__MatrixHouseholder.html">Householder transform of a vector</a> documentation </dd></dl>
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</div>
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</div>
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<a id="gae4b129d8c645a812914da44ad1fc4f50" name="gae4b129d8c645a812914da44ad1fc4f50"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gae4b129d8c645a812914da44ad1fc4f50">◆ </a></span>arm_mat_qr_f32()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname"><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> arm_mat_qr_f32 </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="structarm__matrix__instance__f32.html">arm_matrix_instance_f32</a> * </td>
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<td class="paramname"><em>pSrc</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">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"><a class="el" href="structarm__matrix__instance__f32.html">arm_matrix_instance_f32</a> * </td>
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<td class="paramname"><em>pOutR</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="structarm__matrix__instance__f32.html">arm_matrix_instance_f32</a> * </td>
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<td class="paramname"><em>pOutQ</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"><a class="el" href="arm__math__types_8h.html#a4611b605e45ab401f02cab15c5e38715">float32_t</a> * </td>
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<td class="paramname"><em>pOutTau</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>pTmpA</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>pTmpB</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 input matrix structure. The source matrix is modified by the function. </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">[out]</td><td class="paramname">pOutR</td><td>points to output R matrix structure of dimension m x n </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOutQ</td><td>points to output Q matrix structure of dimension m x m (can be NULL) </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">pOutTau</td><td>points to Householder scaling factors of dimension n </td></tr>
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<tr><td class="paramdir">[in,out]</td><td class="paramname">pTmpA</td><td>points to a temporary vector of dimension m. </td></tr>
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<tr><td class="paramdir">[in,out]</td><td class="paramname">pTmpB</td><td>points to a temporary vector of dimension m. </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>execution status<ul>
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<li><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6a9f8b2a10bd827fb4600e77d455902eb0">ARM_MATH_SUCCESS</a> : Operation successful</li>
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<li><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6a7071b92f1f6bc3c5c312a237ea91105b">ARM_MATH_SIZE_MISMATCH</a> : Matrix size check failed</li>
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</ul>
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</dd></dl>
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<dl class="section user"><dt>pOutQ is optional:</dt><dd>pOutQ can be a NULL pointer. In this case, the argument will be ignored and the output Q matrix won't be computed.</dd></dl>
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<dl class="section user"><dt>Norm2 threshold </dt><dd>For the meaning of this argument please refer to the <a class="el" href="group__MatrixHouseholder.html">Householder transform of a vector</a> documentation </dd></dl>
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</div>
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</div>
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<a id="gaa222c153ee1753dce2904b4b01189eb4" name="gaa222c153ee1753dce2904b4b01189eb4"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gaa222c153ee1753dce2904b4b01189eb4">◆ </a></span>arm_mat_qr_f64()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname"><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6">arm_status</a> arm_mat_qr_f64 </td>
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<td>(</td>
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<td class="paramtype">const <a class="el" href="structarm__matrix__instance__f64.html">arm_matrix_instance_f64</a> * </td>
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<td class="paramname"><em>pSrc</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">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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</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="structarm__matrix__instance__f64.html">arm_matrix_instance_f64</a> * </td>
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<td class="paramname"><em>pOutR</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="structarm__matrix__instance__f64.html">arm_matrix_instance_f64</a> * </td>
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<td class="paramname"><em>pOutQ</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>pOutTau</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>pTmpA</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>pTmpB</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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<p >QR decomposition of a m x n floating point matrix with m >= n.</p>
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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 input matrix structure. The source matrix is modified by the function. </td></tr>
|
|
<tr><td class="paramdir">[in]</td><td class="paramname">threshold</td><td>norm2 threshold. <br />
|
|
</td></tr>
|
|
<tr><td class="paramdir">[out]</td><td class="paramname">pOutR</td><td>points to output R matrix structure of dimension m x n </td></tr>
|
|
<tr><td class="paramdir">[out]</td><td class="paramname">pOutQ</td><td>points to output Q matrix structure of dimension m x m (can be NULL) </td></tr>
|
|
<tr><td class="paramdir">[out]</td><td class="paramname">pOutTau</td><td>points to Householder scaling factors of dimension n </td></tr>
|
|
<tr><td class="paramdir">[in,out]</td><td class="paramname">pTmpA</td><td>points to a temporary vector of dimension m. </td></tr>
|
|
<tr><td class="paramdir">[in,out]</td><td class="paramname">pTmpB</td><td>points to a temporary vector of dimension m. </td></tr>
|
|
</table>
|
|
</dd>
|
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</dl>
|
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<dl class="section return"><dt>Returns</dt><dd>execution status<ul>
|
|
<li><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6a9f8b2a10bd827fb4600e77d455902eb0">ARM_MATH_SUCCESS</a> : Operation successful</li>
|
|
<li><a class="el" href="arm__math__types_8h.html#a5e459c6409dfcd2927bb8a57491d7cf6a7071b92f1f6bc3c5c312a237ea91105b">ARM_MATH_SIZE_MISMATCH</a> : Matrix size check failed</li>
|
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</ul>
|
|
</dd></dl>
|
|
<dl class="section user"><dt>pOutQ is optional:</dt><dd>pOutQ can be a NULL pointer. In this case, the argument will be ignored and the output Q matrix won't be computed.</dd></dl>
|
|
<dl class="section user"><dt>Norm2 threshold </dt><dd>For the meaning of this argument please refer to the <a class="el" href="group__MatrixHouseholder.html">Householder transform of a vector</a> documentation </dd></dl>
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</div>
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