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list-style-type="inherit" tabs="inherit">The routines <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">sort</c></inlineAttr></b></f>, <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">csort</c></inlineAttr></b></f>, and <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">rsort</c></inlineAttr></b></f> all use heap sorting to rearrange the elements, columns, and rows of a vector or matrix. 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disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:id>weights</ml:id><ml:apply><ml:matcol /><ml:id>data</ml:id><ml:real>1</ml:real></ml:apply></ml:define></math><rendering item-idref="12" /></region><region region-id="625" left="300" top="705.75" width="60.75" height="18" align-x="324.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:id>ages</ml:id><ml:apply><ml:matcol /><ml:id>data</ml:id><ml:real>2</ml:real></ml:apply></ml:define></math><rendering item-idref="13" /></region><region region-id="626" left="36" top="739.5" width="25.5" height="12.75" align-x="36" align-y="750" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag="rank"><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Rank</p></text><indexes><phrase>Rank</phrase></indexes></region><region region-id="381" left="36" top="758.25" width="291" height="48" align-x="36" align-y="768" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Given a set of data values, the rank of each value is the position at which that value appears in a sorted list of the data. 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The rank of the first sorted value is 1.</p></text></region><region region-id="633" left="0" top="1242" width="6000" height="6" align-x="0" align-y="1242" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="425" left="36" top="1255.5" width="57.75" height="12.75" align-x="36" align-y="1266" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Sorted index</p></text><indexes><phrase>sorted index</phrase></indexes></region><region region-id="428" left="36" top="1274.25" width="328.5" height="36" align-x="50.25" align-y="1284" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">Order</c></inlineAttr></b></f> gives a sorted index related to the rank, a statistical measure. Order returns the index of each value in an array when sorted.</p></text></region><region region-id="523" left="36" top="1322.25" width="326.25" height="36" align-x="36" align-y="1332" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The vector shown has repeated values. Multiple occurrences are indexed sequentially in order of their occurrence in the original vector.</p></text></region><region region-id="530" left="66" top="1373.25" width="47.25" height="128.25" align-x="75" align-y="1440" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:id>x</ml:id></ml:eval></math><rendering item-idref="21" /></region><region region-id="531" left="144" top="1373.25" width="69" height="128.25" align-x="181.5" align-y="1440" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:apply><ml:id>order</ml:id><ml:id>x</ml:id></ml:apply></ml:eval></math><rendering item-idref="22" /></region><region region-id="621" left="246" top="1431" width="54" height="12.75" align-x="282.75" align-y="1440" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:id>ORIGIN</ml:id></ml:eval></math><rendering item-idref="23" /></region><region region-id="538" left="36" top="1514.25" width="259.5" height="12" align-x="48" align-y="1524" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">A vector with unique values is treated as usual:</p></text></region><region region-id="635" left="246" top="1545" width="49.5" height="12.75" align-x="283.5" align-y="1554" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:id>ORIGIN</ml:id><ml:real>2</ml:real></ml:define></math><rendering item-idref="24" /></region><region region-id="529" left="66" top="1547.25" width="47.25" height="128.25" align-x="75.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:id>x</ml:id><ml:matrix rows="8" cols="1"><ml:real>0.5</ml:real><ml:real>0.01</ml:real><ml:real>0.2</ml:real><ml:real>0.44</ml:real><ml:real>0.1</ml:real><ml:real>0.3</ml:real><ml:real>0.4</ml:real><ml:real>0.9</ml:real></ml:matrix></ml:define></math><rendering item-idref="25" /></region><region region-id="535" left="144" top="1547.25" width="69" height="128.25" align-x="181.5" align-y="1614" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:apply><ml:id>order</ml:id><ml:id>x</ml:id></ml:apply></ml:eval></math><rendering item-idref="26" /></region><region region-id="619" left="36" top="1694.25" width="331.5" height="24" align-x="36" align-y="1704" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The order function will begin indexing according to the current value of ORIGIN.</p></text></region><region region-id="603" left="6" top="1734" width="427.5" height="5.25" align-x="6" align-y="1734" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><png item-idref="27" /><rendering item-idref="28" /></region></regions><binaryContent><item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4zMuw6CMBgF4P5tuYoyOf8mLjZh4hmIk4mPQErFW0I0yODb66HgbpvTy9fm
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