Example: Using the Comparison Option with the Lookup Functions

Functions > Vector and Matrix > Other Array Functions > Example: Using the Comparison Option with the Lookup Functions

1. Define two input matrices A and B of equal dimensions

2. Define variable z

3. Use the match function to find elements in matrix A that match z exactly

The function returns the row-column coordinates of the two matched elements in matrix A.

4. Write a program to display the elements found by the match function

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 <math resultRef="101">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <function>
 <id labels="VARIABLE" xml:space="preserve">F</id>
 <boundVars>
 <id labels="VARIABLE" xml:space="preserve">z</id>
 <id labels="VARIABLE" xml:space="preserve">f</id>
 </boundVars>
 </function>
 <program>
 <if>
 <test>
 <apply>
 <equal />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">f</id>
 <real>0</real>
 </apply>
 </test>
 <then>
 <program>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">M</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">match</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">z</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
 </sequence>
 </apply>
 </localDefine>
 </program>
 </then>
 <else>
 <program>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">M</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">match</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">z</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">f</id>
 </sequence>
 </apply>
 </localDefine>
 </program>
 </else>
 </if>
 <for>
 <id labels="VARIABLE" xml:space="preserve">p</id>
 <range>
 <real>0</real>
 <apply>
 <minus />
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">rows</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 </apply>
 <real>1</real>
 </apply>
 </range>
 <program>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">r</id>
 <apply>
 <indexer />
 <parens>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">p</id>
 </apply>
 </parens>
 <real>0</real>
 </apply>
 </localDefine>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">c</id>
 <apply>
 <indexer />
 <parens>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">p</id>
 </apply>
 </parens>
 <real>1</real>
 </apply>
 </localDefine>
 <localDefine>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve">Q</id>
 <id labels="*" xml:space="preserve">p</id>
 </apply>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">r</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
 </sequence>
 </apply>
 </localDefine>
 </program>
 </for>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Q</id>
 </program>
 </define>
 <resultFormat>
 <matrix size="12,1" offset="1,0" show-indices="false" expand-nested-arrays="false" />
 </resultFormat>
 </math>
</region>

5. Use the program to display the exactly matched elements when z=57

6. Use the lookup function to find elements in matrix B that correspond to the matched elements in matrix A

The function returns the matched elements themselves and not their row-column coordinates.

7. Write a program to display the elements found by the lookup function

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 <math resultRef="107">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <function>
 <id labels="VARIABLE" xml:space="preserve">L</id>
 <boundVars>
 <id labels="VARIABLE" xml:space="preserve">z</id>
 <id labels="VARIABLE" xml:space="preserve">f</id>
 </boundVars>
 </function>
 <program>
 <if>
 <test>
 <apply>
 <equal />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">f</id>
 <real>0</real>
 </apply>
 </test>
 <then>
 <program>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">M</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">lookup</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">z</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">B</id>
 </sequence>
 </apply>
 </localDefine>
 </program>
 </then>
 <else>
 <program>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">M</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">lookup</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">z</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">B</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">f</id>
 </sequence>
 </apply>
 </localDefine>
 </program>
 </else>
 </if>
 </program>
 </define>
 </math>
</region>

8. Use the program to display the matched elements of matrix B when z=57

9. Use the two programs to display the elements found by the match and lookup functions using the comparison function f1

This comparison option matches matrix A element values within the r1 range:

10. Use the two programs to display the elements found by the match and lookup functions using the comparison function f2

This comparison option matches matrix A element values outside the r2 range:

11. Write a program to convert a matrix to a vector

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 <math resultRef="135">
 <define xmlns="http://schemas.mathsoft.com/math50">
 <function>
 <id labels="VARIABLE" xml:space="preserve">S</id>
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 <id labels="VARIABLE" xml:space="preserve">M</id>
 </boundVars>
 </function>
 <program>
 <localDefine>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve">T</id>
 <real>0</real>
 </apply>
 <real>0</real>
 </localDefine>
 <for>
 <id labels="VARIABLE" xml:space="preserve">c</id>
 <range>
 <real>0</real>
 <apply>
 <minus />
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cols</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 </apply>
 <real>1</real>
 </apply>
 </range>
 <program>
 <localDefine>
 <id labels="VARIABLE" xml:space="preserve">T</id>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">stack</id>
 <sequence>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">T</id>
 <apply>
 <matcol />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">c</id>
 </apply>
 </sequence>
 </apply>
 </localDefine>
 </program>
 </for>
 <for>
 <id labels="VARIABLE" xml:space="preserve">d</id>
 <range>
 <real>1</real>
 <apply>
 <mult />
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">rows</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 </apply>
 <apply>
 <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cols</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">M</id>
 </apply>
 </apply>
 </range>
 <program>
 <localDefine>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve">S</id>
 <apply>
 <minus />
 <id labels="*" xml:space="preserve">d</id>
 <real>1</real>
 </apply>
 </apply>
 <apply>
 <indexer />
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">T</id>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">d</id>
 </apply>
 </localDefine>
 </program>
 </for>
 <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">S</id>
 </program>
 </define>
 <resultFormat>
 <matrix size="13,1" offset="5,0" show-indices="false" expand-nested-arrays="false" />
 </resultFormat>
 </math>
</region>

12. Use the program to convert matrix A to vector V

13. Find the length of the vector of points matched in matrix A

14. Write a program to insert the matched points into a new vector of equal length as V. The program writes -100 in unpopulated positions.

15. Plot the two vectors in a way that hides the -100 points of MV. Use horizontal markers to show the two levels of r2.

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 </trace>
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 <graph-size width="438.4" height="230.4" />
 <axes>
 <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="11">
 <axisLine position="ticknumberlock" positionticmark="1" legendWidth="61.7533333333333" />
 <axisGrid>
 <gridFrequency>12</gridFrequency>
 <gridLabels display="true" />
 <gridLines />
 <tickMarks display="true" />
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 <axisLabel />
 <markers />
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 <minus />
 <id xml:space="preserve">l1</id>
 <real>1</real>
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 <yAxis rank="1" legend-position="PlotBoundaryLeft" start="-20" end="180">
 <axisLine position="left" positionticmark="-1" legendWidth="96.53" />
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 <gridLines />
 <tickMarks display="true" />
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 <marker resultRef="159" display="true" color="#FFED1D2F" line-style="Dash" value="28.5">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">
 r2<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">lo</Subscript>
 </id>
 </marker>
 <marker resultRef="161" display="true" color="#FFED1D2F" line-style="Dash" value="85.5">
 <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">
 r2<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">hi</Subscript>
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 <indexer />
 <parens>
 <id xml:space="preserve">MV</id>
 </parens>
 <id xml:space="preserve">n</id>
 </apply>
 </math>
 <math resultRef="172">
 <placeholder xmlns="http://schemas.mathsoft.com/math50" />
 </math>
 </plotEquation>
 </plotEquations>
 <xyDomain scale-type="linear" auto-scale="true">
 <startValue resultRef="164">
 <apply xmlns="http://schemas.mathsoft.com/math50">
 <neg />
 <id xml:space="preserve">offset</id>
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 <secondTickValue resultRef="166">
 <real xmlns="http://schemas.mathsoft.com/math50">0</real>
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 <plus />
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 <id xml:space="preserve">max</id>
 <id xml:space="preserve">A</id>
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 <id xml:space="preserve">offset</id>
 </apply>
 </endValue>
 </xyDomain>
 </yAxis>
 </axes>
 </xyPlot>
 </plot>
</region>

Of the twelve elements of vector V (or matrix A), the five matched elements fall outside the specified range of r2.