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alt="Logo" src="madlib.png" height="50" style="padding-left:0.5em;" border="0"/
></a></td>
+ <td style="padding-left: 0.5em;">
+ <div id="projectname">
+ <span id="projectnumber">1.11</span>
+ </div>
+ <div id="projectbrief">User Documentation for MADlib</div>
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+<div id="doc-content">
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+ name="MSearchResults" id="MSearchResults">
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+
+<div class="header">
+ <div class="summary">
+<a href="#func-members">Functions</a> </div>
+ <div class="headertitle">
+<div class="title">linalg.sql_in File Reference</div> </div>
+</div><!--header-->
+<div class="contents">
+
+<p>SQL functions for linear algebra.
+<a href="#details">More...</a></p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a
name="func-members"></a>
+Functions</h2></td></tr>
+<tr class="memitem:a300300fe4b8576ba0b97b95d8dea3057"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a300300fe4b8576ba0b97b95d8dea3057">norm1</a>
(float8[] x)</td></tr>
+<tr class="memdesc:a300300fe4b8576ba0b97b95d8dea3057"><td
class="mdescLeft"> </td><td class="mdescRight">1-norm of a vector <a
href="#a300300fe4b8576ba0b97b95d8dea3057">More...</a><br /></td></tr>
+<tr class="separator:a300300fe4b8576ba0b97b95d8dea3057"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a50fdfe30cc0edc6888a909dbb4b4c239"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a50fdfe30cc0edc6888a909dbb4b4c239">norm2</a>
(float8[] x)</td></tr>
+<tr class="memdesc:a50fdfe30cc0edc6888a909dbb4b4c239"><td
class="mdescLeft"> </td><td class="mdescRight">2-norm of a vector <a
href="#a50fdfe30cc0edc6888a909dbb4b4c239">More...</a><br /></td></tr>
+<tr class="separator:a50fdfe30cc0edc6888a909dbb4b4c239"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a31fa9f2f5b45507c09f136464fdad1db"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a31fa9f2f5b45507c09f136464fdad1db">dist_inf_norm</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:a31fa9f2f5b45507c09f136464fdad1db"><td
class="mdescLeft"> </td><td class="mdescRight">Infinity-norm of the
difference between two vectors. <a
href="#a31fa9f2f5b45507c09f136464fdad1db">More...</a><br /></td></tr>
+<tr class="separator:a31fa9f2f5b45507c09f136464fdad1db"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ad9cc156ae57bf7c0a2fe90798259105a"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#ad9cc156ae57bf7c0a2fe90798259105a">dist_pnorm</a>
(float8[] x, float8[] y, float8 p)</td></tr>
+<tr class="memdesc:ad9cc156ae57bf7c0a2fe90798259105a"><td
class="mdescLeft"> </td><td class="mdescRight">p-norm of the difference
between two vectors <a
href="#ad9cc156ae57bf7c0a2fe90798259105a">More...</a><br /></td></tr>
+<tr class="separator:ad9cc156ae57bf7c0a2fe90798259105a"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:aad193850e79c4b9d811ca9bc53e13476"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#aad193850e79c4b9d811ca9bc53e13476">dist_norm1</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:aad193850e79c4b9d811ca9bc53e13476"><td
class="mdescLeft"> </td><td class="mdescRight">1-norm of the difference
between two vectors <a
href="#aad193850e79c4b9d811ca9bc53e13476">More...</a><br /></td></tr>
+<tr class="separator:aad193850e79c4b9d811ca9bc53e13476"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:aa58e51526edea6ea98db30b6f250adb4"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#aa58e51526edea6ea98db30b6f250adb4">dist_norm2</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:aa58e51526edea6ea98db30b6f250adb4"><td
class="mdescLeft"> </td><td class="mdescRight">2-norm of the difference
between two vectors <a
href="#aa58e51526edea6ea98db30b6f250adb4">More...</a><br /></td></tr>
+<tr class="separator:aa58e51526edea6ea98db30b6f250adb4"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a1782f2ba00d9f9fab20894a576079f87"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a1782f2ba00d9f9fab20894a576079f87">cosine_similarity</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:a1782f2ba00d9f9fab20894a576079f87"><td
class="mdescLeft"> </td><td class="mdescRight">cosine similarity score
between two vectors <a
href="#a1782f2ba00d9f9fab20894a576079f87">More...</a><br /></td></tr>
+<tr class="separator:a1782f2ba00d9f9fab20894a576079f87"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a00a08e69f27524f2096032214e15b668"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a00a08e69f27524f2096032214e15b668">squared_dist_norm2</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:a00a08e69f27524f2096032214e15b668"><td
class="mdescLeft"> </td><td class="mdescRight">Squared 2-norm of the
difference between two vectors. <a
href="#a00a08e69f27524f2096032214e15b668">More...</a><br /></td></tr>
+<tr class="separator:a00a08e69f27524f2096032214e15b668"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a8c7b9281a72ff22caf06161701b27e84"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a8c7b9281a72ff22caf06161701b27e84">dist_angle</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:a8c7b9281a72ff22caf06161701b27e84"><td
class="mdescLeft"> </td><td class="mdescRight">Angle between two vectors.
<a href="#a8c7b9281a72ff22caf06161701b27e84">More...</a><br /></td></tr>
+<tr class="separator:a8c7b9281a72ff22caf06161701b27e84"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:afa13b4c6122b99422d666dedea136c18"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#afa13b4c6122b99422d666dedea136c18">dist_tanimoto</a>
(float8[] x, float8[] y)</td></tr>
+<tr class="memdesc:afa13b4c6122b99422d666dedea136c18"><td
class="mdescLeft"> </td><td class="mdescRight">Tanimoto distance between
two vectors. <a href="#afa13b4c6122b99422d666dedea136c18">More...</a><br
/></td></tr>
+<tr class="separator:afa13b4c6122b99422d666dedea136c18"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ac1397ac9f4a35b3b67c3be05b5e1a828"><td class="memItemLeft"
align="right" valign="top">float8 </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#ac1397ac9f4a35b3b67c3be05b5e1a828">dist_jaccard</a>
(text[] x, text[] y)</td></tr>
+<tr class="memdesc:ac1397ac9f4a35b3b67c3be05b5e1a828"><td
class="mdescLeft"> </td><td class="mdescRight">Jaccard distance between
two vectors (treated as sets) <a
href="#ac1397ac9f4a35b3b67c3be05b5e1a828">More...</a><br /></td></tr>
+<tr class="separator:ac1397ac9f4a35b3b67c3be05b5e1a828"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a8239fac12096a5dc2720f6cb35b011e5"><td class="memItemLeft"
align="right" valign="top">closest_column_result </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a8239fac12096a5dc2720f6cb35b011e5">_closest_column</a>
(float8[] m, float8[] x, regproc dist, text dist_dn)</td></tr>
+<tr class="separator:a8239fac12096a5dc2720f6cb35b011e5"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:acf6628dfa4d73dfce65a582aa5c5a3db"><td class="memItemLeft"
align="right" valign="top">closest_column_result </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#acf6628dfa4d73dfce65a582aa5c5a3db">closest_column</a>
(float8[] m, float8[] x, regproc dist="squared_dist_norm2")</td></tr>
+<tr class="memdesc:acf6628dfa4d73dfce65a582aa5c5a3db"><td
class="mdescLeft"> </td><td class="mdescRight">Given matrix <img
class="formulaInl" alt="$ M $" src="form_175.png"/> and vector <img
class="formulaInl" alt="$ \vec x $" src="form_176.png"/> compute the column of
<img class="formulaInl" alt="$ M $" src="form_175.png"/> that is closest to
<img class="formulaInl" alt="$ \vec x $" src="form_176.png"/>. <a
href="#acf6628dfa4d73dfce65a582aa5c5a3db">More...</a><br /></td></tr>
+<tr class="separator:acf6628dfa4d73dfce65a582aa5c5a3db"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a31c8d60f9a631c27f5f91964e0108da9"><td class="memItemLeft"
align="right" valign="top">closest_column_result </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a31c8d60f9a631c27f5f91964e0108da9">closest_column</a>
(float8[] m, float8[] x)</td></tr>
+<tr class="separator:a31c8d60f9a631c27f5f91964e0108da9"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a37fd07274dbc9a7f779346b8572ec989"><td class="memItemLeft"
align="right" valign="top">closest_columns_result </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a37fd07274dbc9a7f779346b8572ec989">_closest_columns</a>
(float8[] m, float8[] x, integer num, regproc dist, text dist_dn)</td></tr>
+<tr class="memdesc:a37fd07274dbc9a7f779346b8572ec989"><td
class="mdescLeft"> </td><td class="mdescRight">Given matrix <img
class="formulaInl" alt="$ M $" src="form_175.png"/> and vector <img
class="formulaInl" alt="$ \vec x $" src="form_176.png"/> compute the columns of
<img class="formulaInl" alt="$ M $" src="form_175.png"/> that are closest to
<img class="formulaInl" alt="$ \vec x $" src="form_176.png"/>. <a
href="#a37fd07274dbc9a7f779346b8572ec989">More...</a><br /></td></tr>
+<tr class="separator:a37fd07274dbc9a7f779346b8572ec989"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ad864339591086b635d12015db993b5bc"><td class="memItemLeft"
align="right" valign="top">closest_columns_result </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#ad864339591086b635d12015db993b5bc">closest_columns</a>
(float8[] m, float8[] x, integer num, regproc dist)</td></tr>
+<tr class="separator:ad864339591086b635d12015db993b5bc"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:aa5da5470cc84963a059714faa238a07d"><td class="memItemLeft"
align="right" valign="top">closest_columns_result </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#aa5da5470cc84963a059714faa238a07d">closest_columns</a>
(float8[] m, float8[] x, integer num)</td></tr>
+<tr class="separator:aa5da5470cc84963a059714faa238a07d"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:aaea269f4746f952faadffed9d9b107d7"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#aaea269f4746f952faadffed9d9b107d7">avg_vector_transition</a>
(float8[] state, float8[] x)</td></tr>
+<tr class="separator:aaea269f4746f952faadffed9d9b107d7"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a5ac255c13e1f2d91274b829ff0383e44"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a5ac255c13e1f2d91274b829ff0383e44">avg_vector_merge</a>
(float8[] state_left, float8[] state_right)</td></tr>
+<tr class="separator:a5ac255c13e1f2d91274b829ff0383e44"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ad468b52a7caa9b47a0650d39e32d9c50"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#ad468b52a7caa9b47a0650d39e32d9c50">avg_vector_final</a>
(float8[] state)</td></tr>
+<tr class="separator:ad468b52a7caa9b47a0650d39e32d9c50"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a1aa37f73fb1cd8d7d106aa518dd8c0b4"><td class="memItemLeft"
align="right" valign="top">aggregate float8 [] </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a1aa37f73fb1cd8d7d106aa518dd8c0b4">avg</a> (float8[]
x)</td></tr>
+<tr class="memdesc:a1aa37f73fb1cd8d7d106aa518dd8c0b4"><td
class="mdescLeft"> </td><td class="mdescRight">Compute the average of
vectors. <a href="#a1aa37f73fb1cd8d7d106aa518dd8c0b4">More...</a><br
/></td></tr>
+<tr class="separator:a1aa37f73fb1cd8d7d106aa518dd8c0b4"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ad5863fed5eb4813ba0044abc268d03ce"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#ad5863fed5eb4813ba0044abc268d03ce">normalized_avg_vector_transition</a>
(float8[] state, float8[] x)</td></tr>
+<tr class="separator:ad5863fed5eb4813ba0044abc268d03ce"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a1c22ee0672d6c550f5bb966f78ce738a"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a1c22ee0672d6c550f5bb966f78ce738a">normalized_avg_vector_final</a>
(float8[] state)</td></tr>
+<tr class="separator:a1c22ee0672d6c550f5bb966f78ce738a"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a0b04663ca206f03e66aed5ea2b4cc461"><td class="memItemLeft"
align="right" valign="top">aggregate float8 [] </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a0b04663ca206f03e66aed5ea2b4cc461">normalized_avg</a>
(float8[] x)</td></tr>
+<tr class="memdesc:a0b04663ca206f03e66aed5ea2b4cc461"><td
class="mdescLeft"> </td><td class="mdescRight">Compute the normalized
average of vectors. <a
href="#a0b04663ca206f03e66aed5ea2b4cc461">More...</a><br /></td></tr>
+<tr class="separator:a0b04663ca206f03e66aed5ea2b4cc461"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ac2d98e204b4fccab518aa20edef4ec41"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#ac2d98e204b4fccab518aa20edef4ec41">matrix_agg_transition</a>
(float8[] state, float8[] x)</td></tr>
+<tr class="separator:ac2d98e204b4fccab518aa20edef4ec41"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:adb012de82ecdc71ac54f3498e88e59d0"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#adb012de82ecdc71ac54f3498e88e59d0">matrix_agg_final</a>
(float8[] state)</td></tr>
+<tr class="separator:adb012de82ecdc71ac54f3498e88e59d0"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a9c439706f35d6cac89f151d553a5f111"><td class="memItemLeft"
align="right" valign="top">aggregate float8 [] </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a9c439706f35d6cac89f151d553a5f111">matrix_agg</a>
(float8[] x)</td></tr>
+<tr class="memdesc:a9c439706f35d6cac89f151d553a5f111"><td
class="mdescLeft"> </td><td class="mdescRight">Combine vectors to a
matrix. <a href="#a9c439706f35d6cac89f151d553a5f111">More...</a><br
/></td></tr>
+<tr class="separator:a9c439706f35d6cac89f151d553a5f111"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:aed3a33f3d3d43a056c5ec591661d34d8"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#aed3a33f3d3d43a056c5ec591661d34d8">matrix_column</a>
(float8[] matrix, integer col)</td></tr>
+<tr class="memdesc:aed3a33f3d3d43a056c5ec591661d34d8"><td
class="mdescLeft"> </td><td class="mdescRight">Return the column of a
matrix. <a href="#aed3a33f3d3d43a056c5ec591661d34d8">More...</a><br
/></td></tr>
+<tr class="separator:aed3a33f3d3d43a056c5ec591661d34d8"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a21d0a134f1674f71b3e872aacc5f3789"><td class="memItemLeft"
align="right" valign="top">set< record > </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#a21d0a134f1674f71b3e872aacc5f3789">deconstruct_2d_array</a>
(float8[] in_array)</td></tr>
+<tr class="memdesc:a21d0a134f1674f71b3e872aacc5f3789"><td
class="mdescLeft"> </td><td class="mdescRight">Construct a M-column N-row
table of 2-D array. <a
href="#a21d0a134f1674f71b3e872aacc5f3789">More...</a><br /></td></tr>
+<tr class="separator:a21d0a134f1674f71b3e872aacc5f3789"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:ab67d0a074625d4fb90950d047dc2794e"><td class="memItemLeft"
align="right" valign="top">set< record > </td><td
class="memItemRight" valign="bottom"><a class="el"
href="linalg_8sql__in.html#ab67d0a074625d4fb90950d047dc2794e">__deconstruct_lower_triangle</a>
(float8[] in_array)</td></tr>
+<tr class="memdesc:ab67d0a074625d4fb90950d047dc2794e"><td
class="mdescLeft"> </td><td class="mdescRight">Construct a M-column M-row
table of using lower triangle of 2-D array. <a
href="#ab67d0a074625d4fb90950d047dc2794e">More...</a><br /></td></tr>
+<tr class="separator:ab67d0a074625d4fb90950d047dc2794e"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a71304c333a999e69ac1430c285c35181"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a71304c333a999e69ac1430c285c35181">array_to_1d</a>
(float8[] in_array)</td></tr>
+<tr class="memdesc:a71304c333a999e69ac1430c285c35181"><td
class="mdescLeft"> </td><td class="mdescRight">Return the input array as
1-D. <a href="#a71304c333a999e69ac1430c285c35181">More...</a><br /></td></tr>
+<tr class="separator:a71304c333a999e69ac1430c285c35181"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a0799a4ccb93a699a280861126c3e1a74"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a0799a4ccb93a699a280861126c3e1a74">array_to_2d</a>
(float8[] in_array)</td></tr>
+<tr class="memdesc:a0799a4ccb93a699a280861126c3e1a74"><td
class="mdescLeft"> </td><td class="mdescRight">Return A 2-D matrix that
the number of rows is encoded as the first element of the input array and the
number of cols second. <a
href="#a0799a4ccb93a699a280861126c3e1a74">More...</a><br /></td></tr>
+<tr class="separator:a0799a4ccb93a699a280861126c3e1a74"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:abe23dd6c6963093863c2a107425f6384"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#abe23dd6c6963093863c2a107425f6384">index_2d_array</a>
(float8[] in_2d_array, integer index)</td></tr>
+<tr class="memdesc:abe23dd6c6963093863c2a107425f6384"><td
class="mdescLeft"> </td><td class="mdescRight">Return A 1-D form of the
specified row of the given 2-D array. <a
href="#abe23dd6c6963093863c2a107425f6384">More...</a><br /></td></tr>
+<tr class="separator:abe23dd6c6963093863c2a107425f6384"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:af6b905fcac7746ef0ed0c36df4a1e070"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#af6b905fcac7746ef0ed0c36df4a1e070">get_row</a>
(float8[] in_2d_array, integer index)</td></tr>
+<tr class="memdesc:af6b905fcac7746ef0ed0c36df4a1e070"><td
class="mdescLeft"> </td><td class="mdescRight">Get an indexed row of the
given matrix (2-D array) <a
href="#af6b905fcac7746ef0ed0c36df4a1e070">More...</a><br /></td></tr>
+<tr class="separator:af6b905fcac7746ef0ed0c36df4a1e070"><td
class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:a20f34c9e661191e5225cca7bc23252c5"><td class="memItemLeft"
align="right" valign="top">float8 [] </td><td class="memItemRight"
valign="bottom"><a class="el"
href="linalg_8sql__in.html#a20f34c9e661191e5225cca7bc23252c5">get_col</a>
(float8[] in_2d_array, integer index)</td></tr>
+<tr class="memdesc:a20f34c9e661191e5225cca7bc23252c5"><td
class="mdescLeft"> </td><td class="mdescRight">Get an indexed col of the
given matrix (2-D array) <a
href="#a20f34c9e661191e5225cca7bc23252c5">More...</a><br /></td></tr>
+<tr class="separator:a20f34c9e661191e5225cca7bc23252c5"><td
class="memSeparator" colspan="2"> </td></tr>
+</table>
+<a name="details" id="details"></a><h2 class="groupheader">Detailed
Description</h2>
+<div class="textblock"><dl class="section see"><dt>See also</dt><dd>For an
overview of linear-algebra functions, see the module description <a class="el"
href="group__grp__linalg.html">Norms and Distance functions</a>. </dd></dl>
+</div><h2 class="groupheader">Function Documentation</h2>
+<a id="ab67d0a074625d4fb90950d047dc2794e"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ab67d0a074625d4fb90950d047dc2794e">◆ </a></span>__deconstruct_lower_triangle()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">set<record> __deconstruct_lower_triangle
</td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_array</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_array</td><td>2-D array </td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="a8239fac12096a5dc2720f6cb35b011e5"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a8239fac12096a5dc2720f6cb35b011e5">◆ </a></span>_closest_column()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">closest_column_result _closest_column </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>m</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">regproc </td>
+ <td class="paramname"><em>dist</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">text </td>
+ <td class="paramname"><em>dist_dn</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a37fd07274dbc9a7f779346b8572ec989"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a37fd07274dbc9a7f779346b8572ec989">◆ </a></span>_closest_columns()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">closest_columns_result _closest_columns </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>m</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>num</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">regproc </td>
+ <td class="paramname"><em>dist</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">text </td>
+ <td class="paramname"><em>dist_dn</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<p>This function does essentially the same as <a class="el"
href="linalg_8sql__in.html#acf6628dfa4d73dfce65a582aa5c5a3db">closest_column()</a>,
except that it allows to specify the number of closest columns to return. The
return value is a composite value:</p><ul>
+<li><code>columns_ids INTEGER[]</code> - The 0-based indices of the
<code>num</code> columns of <img class="formulaInl" alt="$ M $"
src="form_175.png"/> that are closest to <img class="formulaInl" alt="$ x $"
src="form_179.png"/>. In case of ties, the first such indices are returned.</li>
+<li><code>distances DOUBLE PRECISION[]</code> - The distances between the
columns of <img class="formulaInl" alt="$ M $" src="form_175.png"/> with
indices in <code>columns_ids</code> and <img class="formulaInl" alt="$ x $"
src="form_179.png"/>. That is, <code>distances[i]</code> contains <img
class="formulaInl" alt="$ \operatorname{dist}(\vec{m_j}, \vec x) $"
src="form_182.png"/>, where <img class="formulaInl" alt="$ j = $"
src="form_183.png"/> <code>columns_ids[i]</code>. </li>
+</ul>
+
+</div>
+</div>
+<a id="a71304c333a999e69ac1430c285c35181"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a71304c333a999e69ac1430c285c35181">◆ </a></span>array_to_1d()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] array_to_1d </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_array</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_array</td><td>1-D or 2-D array </td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="a0799a4ccb93a699a280861126c3e1a74"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a0799a4ccb93a699a280861126c3e1a74">◆ </a></span>array_to_2d()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] array_to_2d </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_array</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_array</td><td>Input array with first 2
elements describing dimensions </td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="a1aa37f73fb1cd8d7d106aa518dd8c0b4"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a1aa37f73fb1cd8d7d106aa518dd8c0b4">◆ </a></span>avg()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">aggregate float8 [] avg </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<p>Given vectors <img class="formulaInl" alt="$ x_1, \dots, x_n $"
src="form_184.png"/>, compute the average <img class="formulaInl" alt="$ \frac
1n \sum_{i=1}^n x_i $" src="form_185.png"/>.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Point <img class="formulaInl" alt="$
x_i $" src="form_63.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>Average <img class="formulaInl"
alt="$ \frac 1n \sum_{i=1}^n x_i $" src="form_185.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="ad468b52a7caa9b47a0650d39e32d9c50"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ad468b52a7caa9b47a0650d39e32d9c50">◆ </a></span>avg_vector_final()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] avg_vector_final </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a5ac255c13e1f2d91274b829ff0383e44"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a5ac255c13e1f2d91274b829ff0383e44">◆ </a></span>avg_vector_merge()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] avg_vector_merge </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state_left</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state_right</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="aaea269f4746f952faadffed9d9b107d7"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#aaea269f4746f952faadffed9d9b107d7">◆ </a></span>avg_vector_transition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] avg_vector_transition </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="acf6628dfa4d73dfce65a582aa5c5a3db"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#acf6628dfa4d73dfce65a582aa5c5a3db">◆ </a></span>closest_column()
<span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">closest_column_result closest_column </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>m</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">regproc </td>
+ <td class="paramname"><em>dist</em> =
<code>"squared_dist_norm2"</code> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">M</td><td>Matrix <img class="formulaInl" alt="$
M = (\vec{m_0} \dots \vec{m_{l-1}}) \in \mathbb{R}^{k \times l} $"
src="form_177.png"/> </td></tr>
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x \in \mathbb R^k $" src="form_178.png"/> </td></tr>
+ <tr><td class="paramname">dist</td><td>The metric <img class="formulaInl"
alt="$ \operatorname{dist} $" src="form_142.png"/>. This needs to be a function
with signature <code>DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE
PRECISION</code>.</td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>A composite value:<ul>
+<li><code>columns_id INTEGER</code> - The 0-based index of the column of <img
class="formulaInl" alt="$ M $" src="form_175.png"/> that is closest to <img
class="formulaInl" alt="$ x $" src="form_179.png"/>. In case of ties, the first
such index is returned. That is, <code>columns_id</code> is the minimum element
in the set <img class="formulaInl" alt="$ \arg\min_{i=0,\dots,l-1}
\operatorname{dist}(\vec{m_i}, \vec x) $" src="form_180.png"/>.</li>
+<li><code>distance DOUBLE PRECISION</code> - The minimum distance between any
column of <img class="formulaInl" alt="$ M $" src="form_175.png"/> and <img
class="formulaInl" alt="$ x $" src="form_179.png"/>. That is, <img
class="formulaInl" alt="$ \min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i},
\vec x) $" src="form_181.png"/>. </li>
+</ul>
+</dd></dl>
+
+</div>
+</div>
+<a id="a31c8d60f9a631c27f5f91964e0108da9"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a31c8d60f9a631c27f5f91964e0108da9">◆ </a></span>closest_column()
<span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">closest_column_result closest_column </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>m</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="ad864339591086b635d12015db993b5bc"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ad864339591086b635d12015db993b5bc">◆ </a></span>closest_columns()
<span class="overload">[1/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">closest_columns_result closest_columns </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>m</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>num</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">regproc </td>
+ <td class="paramname"><em>dist</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="aa5da5470cc84963a059714faa238a07d"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#aa5da5470cc84963a059714faa238a07d">◆ </a></span>closest_columns()
<span class="overload">[2/2]</span></h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">closest_columns_result closest_columns </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>m</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>num</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a1782f2ba00d9f9fab20894a576079f87"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a1782f2ba00d9f9fab20894a576079f87">◆ </a></span>cosine_similarity()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 cosine_similarity </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\frac{\langle \vec x, \vec y \rangle} {\| \vec x \| \cdot \| \vec y \|} $"
src="form_169.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="a21d0a134f1674f71b3e872aacc5f3789"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a21d0a134f1674f71b3e872aacc5f3789">◆ </a></span>deconstruct_2d_array()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">set<record> deconstruct_2d_array </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_array</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_array</td><td>2-D array </td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="a8c7b9281a72ff22caf06161701b27e84"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a8c7b9281a72ff22caf06161701b27e84">◆ </a></span>dist_angle()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_angle </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\arccos\left(\frac{\langle \vec x, \vec y \rangle} {\| \vec x \| \cdot \| \vec
y \|}\right) $" src="form_171.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="a31fa9f2f5b45507c09f136464fdad1db"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a31fa9f2f5b45507c09f136464fdad1db">◆ </a></span>dist_inf_norm()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_inf_norm </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x - y \|_\infty = \max_{i=1}^n \|x_i - y_i\| $" src="form_164.png"/>
</dd></dl>
+
+</div>
+</div>
+<a id="ac1397ac9f4a35b3b67c3be05b5e1a828"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ac1397ac9f4a35b3b67c3be05b5e1a828">◆ </a></span>dist_jaccard()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_jaccard </td>
+ <td>(</td>
+ <td class="paramtype">text [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">text [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_m) $" src="form_173.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
1 - \frac{|x \cap y|}{|x \cup y|} $" src="form_174.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="aad193850e79c4b9d811ca9bc53e13476"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#aad193850e79c4b9d811ca9bc53e13476">◆ </a></span>dist_norm1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_norm1 </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x - y \|_1 = \sum_{i=1}^n |x_i - y_i| $" src="form_167.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="aa58e51526edea6ea98db30b6f250adb4"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#aa58e51526edea6ea98db30b6f250adb4">◆ </a></span>dist_norm2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_norm2 </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x - y \|_2 = \sqrt{\sum_{i=1}^n (x_i - y_i)^2} $" src="form_168.png"/>
</dd></dl>
+
+</div>
+</div>
+<a id="ad9cc156ae57bf7c0a2fe90798259105a"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ad9cc156ae57bf7c0a2fe90798259105a">◆ </a></span>dist_pnorm()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_pnorm </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 </td>
+ <td class="paramname"><em>p</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ <tr><td class="paramname">p</td><td>Scalar <img class="formulaInl" alt="$
p > 0 $" src="form_165.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x - y \|_p = (\sum_{i=1}^n \|x_i - y_i\|^p)^{\frac{1}{p}} $"
src="form_166.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="afa13b4c6122b99422d666dedea136c18"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#afa13b4c6122b99422d666dedea136c18">◆ </a></span>dist_tanimoto()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 dist_tanimoto </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
1 - \frac{\langle \vec x, \vec y \rangle} {\| \vec x \|^2 \cdot \| \vec y \|^2
- \langle \vec x, \vec y \rangle} $" src="form_172.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="a20f34c9e661191e5225cca7bc23252c5"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a20f34c9e661191e5225cca7bc23252c5">◆ </a></span>get_col()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] get_col </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_2d_array</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>index</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_2d_array</td><td>Input 2-D array </td></tr>
+ <tr><td class="paramname">index</td><td></td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="af6b905fcac7746ef0ed0c36df4a1e070"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#af6b905fcac7746ef0ed0c36df4a1e070">◆ </a></span>get_row()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] get_row </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_2d_array</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>index</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_2d_array</td><td>Input 2-D array </td></tr>
+ <tr><td class="paramname">index</td><td></td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="abe23dd6c6963093863c2a107425f6384"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#abe23dd6c6963093863c2a107425f6384">◆ </a></span>index_2d_array()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] index_2d_array </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>in_2d_array</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>index</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">in_2d_array</td><td>Input 2-D array </td></tr>
+ <tr><td class="paramname">index</td><td></td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="a9c439706f35d6cac89f151d553a5f111"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a9c439706f35d6cac89f151d553a5f111">◆ </a></span>matrix_agg()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">aggregate float8 [] matrix_agg </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<p>Given vectors <img class="formulaInl" alt="$ \vec x_1, \dots, \vec x_n \in
\mathbb R^m $" src="form_188.png"/>, return matrix <img class="formulaInl"
alt="$ ( \vec x_1 \dots \vec x_n ) \in \mathbb R^{m \times n}$"
src="form_189.png"/>.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
x_i $" src="form_63.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>Matrix with columns <img
class="formulaInl" alt="$ x_1, \dots, x_n $" src="form_184.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="adb012de82ecdc71ac54f3498e88e59d0"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#adb012de82ecdc71ac54f3498e88e59d0">◆ </a></span>matrix_agg_final()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] matrix_agg_final </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="ac2d98e204b4fccab518aa20edef4ec41"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ac2d98e204b4fccab518aa20edef4ec41">◆ </a></span>matrix_agg_transition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] matrix_agg_transition </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="aed3a33f3d3d43a056c5ec591661d34d8"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#aed3a33f3d3d43a056c5ec591661d34d8">◆ </a></span>matrix_column()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] matrix_column </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>matrix</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">integer </td>
+ <td class="paramname"><em>col</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">matrix</td><td>Two-dimensional matrix </td></tr>
+ <tr><td class="paramname">col</td><td>Column of the matrix to return
(0-based index) </td></tr>
+ </table>
+ </dd>
+</dl>
+
+</div>
+</div>
+<a id="a300300fe4b8576ba0b97b95d8dea3057"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a300300fe4b8576ba0b97b95d8dea3057">◆ </a></span>norm1()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 norm1 </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x \|_1 = \sum_{i=1}^n |x_i| $" src="form_161.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="a50fdfe30cc0edc6888a909dbb4b4c239"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a50fdfe30cc0edc6888a909dbb4b4c239">◆ </a></span>norm2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 norm2 </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x \|_2 = \sqrt{\sum_{i=1}^n x_i^2} $" src="form_162.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="a0b04663ca206f03e66aed5ea2b4cc461"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a0b04663ca206f03e66aed5ea2b4cc461">◆ </a></span>normalized_avg()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">aggregate float8 [] normalized_avg </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<p>Given vectors <img class="formulaInl" alt="$ x_1, \dots, x_n $"
src="form_184.png"/>, define <img class="formulaInl" alt="$ \widetilde{x} :=
\frac 1n \sum_{i=1}^n \frac{x_i}{\| x_i \|} $" src="form_186.png"/>, and
compute the normalized average <img class="formulaInl" alt="$
\frac{\widetilde{x}}{\| \widetilde{x} \|} $" src="form_187.png"/>.</p>
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Point <img class="formulaInl" alt="$
x_i $" src="form_63.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd>Normalized average <img
class="formulaInl" alt="$ \frac{\widetilde{x}}{\| \widetilde{x} \|} $"
src="form_187.png"/> </dd></dl>
+
+</div>
+</div>
+<a id="a1c22ee0672d6c550f5bb966f78ce738a"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a1c22ee0672d6c550f5bb966f78ce738a">◆ </a></span>normalized_avg_vector_final()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] normalized_avg_vector_final </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state</em></td><td>)</td>
+ <td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="ad5863fed5eb4813ba0044abc268d03ce"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#ad5863fed5eb4813ba0044abc268d03ce">◆ </a></span>normalized_avg_vector_transition()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 [] normalized_avg_vector_transition </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>state</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+
+</div>
+</div>
+<a id="a00a08e69f27524f2096032214e15b668"></a>
+<h2 class="memtitle"><span class="permalink"><a
href="#a00a08e69f27524f2096032214e15b668">◆ </a></span>squared_dist_norm2()</h2>
+
+<div class="memitem">
+<div class="memproto">
+ <table class="memname">
+ <tr>
+ <td class="memname">float8 squared_dist_norm2 </td>
+ <td>(</td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>x</em>, </td>
+ </tr>
+ <tr>
+ <td class="paramkey"></td>
+ <td></td>
+ <td class="paramtype">float8 [] </td>
+ <td class="paramname"><em>y</em> </td>
+ </tr>
+ <tr>
+ <td></td>
+ <td>)</td>
+ <td></td><td></td>
+ </tr>
+ </table>
+</div><div class="memdoc">
+<dl class="params"><dt>Parameters</dt><dd>
+ <table class="params">
+ <tr><td class="paramname">x</td><td>Vector <img class="formulaInl" alt="$
\vec x = (x_1, \dots, x_n) $" src="form_160.png"/> </td></tr>
+ <tr><td class="paramname">y</td><td>Vector <img class="formulaInl" alt="$
\vec y = (y_1, \dots, y_n) $" src="form_163.png"/> </td></tr>
+ </table>
+ </dd>
+</dl>
+<dl class="section return"><dt>Returns</dt><dd><img class="formulaInl" alt="$
\| x - y \|_2^2 = \sum_{i=1}^n (x_i - y_i)^2 $" src="form_170.png"/> </dd></dl>
+
+</div>
+</div>
+</div><!-- contents -->
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