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title="Links to Section Contents" popup="false"><f family="Arial" charset="0" size="11"><b><u><inlineAttr font-style="normal" line-through="false"><c val="#808000">UTILITIES</c></inlineAttr></u></b></f><f family="Arial" charset="0" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#808000"><sp /></c></inlineAttr></b></f></link></p></text></region><region region-id="1345" left="36" top="72.75" width="92.25" height="13.5" align-x="36" align-y="84" 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="Sous-titre" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Arial" charset="0" size="12"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#800000">Batch Processing</c></inlineAttr></f></p></text><indexes><phrase>batch processing</phrase></indexes></region><region region-id="1346" left="36" top="103.5" width="81" height="12.75" align-x="36" align-y="114" 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="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Times New Roman" charset="0" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#800000">batchn(func,data)</c></inlineAttr></b></f></p></text><indexes><phrase>batchn</phrase></indexes></region><region region-id="1347" left="156" top="103.5" width="90.75" height="12.75" align-x="156" align-y="114" 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="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Times New Roman" charset="0" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#800000">Automation window</c></inlineAttr></b></f></p></text><indexes><phrase>automation window</phrase></indexes></region><region region-id="1348" left="36" top="134.25" width="301.5" height="96" align-x="36" align-y="144" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Mathcad programming can be used to both create and manipulate nested sets of data to use as sequential arguments to a function in batch mode. Results for each set of nested data can either be returned individually as elements of a vector, or the data can be assembled into a single matrix and processed simultaneously. In addition, Mathcad's scripting window can be used to automate whole worksheets.</c></inlineAttr></f></p></text></region><region region-id="1349" left="36" top="241.5" width="132" height="12.75" align-x="36" align-y="252" 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"><f family="Times New Roman" charset="0" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#800000">Batching data with programs</c></inlineAttr></b></f></p></text><indexes><phrase>batching data with programs</phrase></indexes></region><region region-id="1350" left="36" top="260.25" width="286.5" height="36" align-x="36" align-y="270" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">For example, if you have several sets of data packed in a nested matrix, and you wish to find the mean of the second column in each data set:</c></inlineAttr></f></p></text></region><region region-id="1296" left="66" top="309" width="36.75" height="12.75" align-x="74.25" align-y="318" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:id>i</ml:id><ml:range><ml:real>0</ml:real><ml:real>20</ml:real></ml:range></ml:define></math><rendering item-idref="4" /></region><region 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show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:id>y2</ml:id><ml:apply><ml:id>runif</ml:id><ml:sequence><ml:real>21</ml:real><ml:real>1</ml:real><ml:real>2</ml:real></ml:sequence></ml:apply></ml:define></math><rendering item-idref="7" /></region><region region-id="1305" left="66" top="333" width="96" height="18" align-x="99" align-y="342" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>0</ml:real></ml:apply><ml:apply><ml:id>augment</ml:id><ml:sequence><ml:id>x</ml:id><ml:id>y</ml:id></ml:sequence></ml:apply></ml:define></math><rendering item-idref="8" /></region><region region-id="1306" left="222" top="333" width="100.5" height="18" align-x="255" align-y="342" 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:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>1</ml:real></ml:apply><ml:apply><ml:id>augment</ml:id><ml:sequence><ml:id>x</ml:id><ml:id>y2</ml:id></ml:sequence></ml:apply></ml:define></math><rendering item-idref="9" /></region><region region-id="1351" left="36" top="362.25" width="297" height="24" align-x="36" align-y="372" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Displaying the data will show you the rows-by-column sizes of the nested matrices of data:</c></inlineAttr></f></p></text></region><region region-id="1104" left="66" top="396.75" width="79.5" height="29.25" align-x="93.75" align-y="414" 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>spots</ml:id></ml:eval></math><rendering item-idref="10" /></region><region region-id="1352" left="36" top="434.25" width="187.5" height="12" align-x="36" align-y="444" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Definition of a sample batch function:</c></inlineAttr></f></p></text><indexes><phrase>batch functions</phrase></indexes></region><region region-id="1127" left="66" top="453" width="279" height="72.75" align-x="189" align-y="462" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>batch1</ml:id><ml:boundVars><ml:id>func_name</ml:id><ml:id>data</ml:id><ml:id>col</ml:id></ml:boundVars></ml:function><ml:program><ml:localDefine><ml:id>n</ml:id><ml:apply><ml:id>length</ml:id><ml:id>data</ml:id></ml:apply></ml:localDefine><ml:for><ml:id>i</ml:id><ml:range><ml:real>0</ml:real><ml:apply><ml:minus /><ml:id>n</ml:id><ml:real>1</ml:real></ml:apply></ml:range><ml:localDefine><ml:apply><ml:indexer /><ml:id>OUT</ml:id><ml:id>i</ml:id></ml:apply><ml:apply><ml:id>func_name</ml:id><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>data</ml:id><ml:id>i</ml:id></ml:apply></ml:parens><ml:id>col</ml:id></ml:apply></ml:apply></ml:localDefine></ml:for><ml:id>OUT</ml:id></ml:program></ml:define></math><rendering item-idref="11" /></region><region region-id="1353" left="36" top="536.25" width="316.5" height="60" align-x="36" align-y="546" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">This function takes a function, a collection of nested data, and a column selector, specifying the column from each data set that should be used as an argument to the function. We'll use this to find the mean over column 1 for each data set. For this to work, we must specify the 1-argument version of mean:</c></inlineAttr></f></p></text></region><region region-id="1268" left="66" top="603" width="82.5" height="12.75" align-x="108.75" align-y="612" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>mean1</ml:id><ml:boundVars><ml:id>x</ml:id></ml:boundVars></ml:function><ml:apply><ml:id>mean</ml:id><ml:id>x</ml:id></ml:apply></ml:define></math><rendering item-idref="12" /></region><region region-id="1354" left="0" top="624" width="6000" height="-6" align-x="0" align-y="618" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="1355" left="36" top="626.25" width="321.75" height="12" align-x="36" align-y="636" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Compare the batched output with the calculation done by hand:</c></inlineAttr></f></p></text></region><region region-id="1269" left="66" top="645.75" width="117" height="23.25" align-x="150" align-y="660" 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>mean1</ml:id><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>0</ml:real></ml:apply></ml:parens><ml:real>1</ml:real></ml:apply></ml:apply></ml:eval></math><rendering item-idref="13" /></region><region region-id="1272" left="228" top="645.75" width="117" height="23.25" align-x="312" align-y="660" 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>mean1</ml:id><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>1</ml:real></ml:apply></ml:parens><ml:real>1</ml:real></ml:apply></ml:apply></ml:eval></math><rendering item-idref="14" /></region><region region-id="1271" left="66" top="672.75" width="148.5" height="29.25" align-x="167.25" align-y="690" 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>batch1</ml:id><ml:sequence><ml:id>mean1</ml:id><ml:id>spots</ml:id><ml:real>1</ml:real></ml:sequence></ml:apply></ml:eval></math><rendering item-idref="15" /></region><region region-id="1356" left="36" top="704.25" width="258" height="12" align-x="36" align-y="714" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">In each case we've drawn column 1 from the data. </c></inlineAttr></f></p></text></region><region region-id="1357" left="36" top="734.25" width="341.25" height="60" align-x="36" align-y="744" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">In a more general way, we can write composing functions that allow you to specify different numbers of arguments, depending on how many columns of the data are needed to perform the desired operation. For example, consider the composing functions for the 1, 2 and 3 argument cases:</c></inlineAttr></f></p></text></region><region region-id="1266" left="66" top="801.75" width="126.75" height="18" align-x="113.25" align-y="816" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>arg1</ml:id><ml:boundVars><ml:id>f</ml:id><ml:id>c1</ml:id></ml:boundVars></ml:function><ml:localDefine><ml:function><ml:id>g</ml:id><ml:boundVars><ml:id>M</ml:id></ml:boundVars></ml:function><ml:apply><ml:id>f</ml:id><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:id>c1</ml:id></ml:apply></ml:apply></ml:localDefine></ml:define></math><rendering item-idref="16" /></region><region region-id="1173" left="216" top="801.75" width="168.75" height="18" align-x="276.75" align-y="816" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>arg2</ml:id><ml:boundVars><ml:id>f</ml:id><ml:id>c1</ml:id><ml:id>c2</ml:id></ml:boundVars></ml:function><ml:localDefine><ml:function><ml:id>g</ml:id><ml:boundVars><ml:id>M</ml:id></ml:boundVars></ml:function><ml:apply><ml:id>f</ml:id><ml:sequence><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:id>c1</ml:id></ml:apply><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:id>c2</ml:id></ml:apply></ml:sequence></ml:apply></ml:localDefine></ml:define></math><rendering item-idref="17" /></region><region region-id="1267" left="66" top="831.75" width="210.75" height="18" align-x="140.25" align-y="846" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>arg3</ml:id><ml:boundVars><ml:id>f</ml:id><ml:id>c1</ml:id><ml:id>c2</ml:id><ml:id>c3</ml:id></ml:boundVars></ml:function><ml:localDefine><ml:function><ml:id>g</ml:id><ml:boundVars><ml:id>M</ml:id></ml:boundVars></ml:function><ml:apply><ml:id>f</ml:id><ml:sequence><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:id>c1</ml:id></ml:apply><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:id>c2</ml:id></ml:apply><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:id>c3</ml:id></ml:apply></ml:sequence></ml:apply></ml:localDefine></ml:define></math><rendering item-idref="18" /></region><region region-id="1358" left="36" top="860.25" width="319.5" height="36" align-x="36" align-y="870" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">The first of these, arg1, </c></inlineAttr></f><f family="Verdana" charset="0" size="10"><i><inlineAttr font-weight="normal" underline="false" line-through="false"><c val="#000">returns a function</c></inlineAttr></i></f><f family="Verdana" charset="0" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000"> expecting a data matrix, M, from which it will draw a single column, and apply the function f.</c></inlineAttr></f></p></text></region><region region-id="1258" left="66" top="903" width="111" height="12.75" align-x="130.5" align-y="912" 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>arg1</ml:id><ml:sequence><ml:id>mean1</ml:id><ml:real>1</ml:real></ml:sequence></ml:apply></ml:eval></math><rendering item-idref="19" /></region><region region-id="1359" left="36" top="926.25" width="327" height="24" align-x="36" align-y="936" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">The generalized batch function can now be written to expect the output of these composing functions.</c></inlineAttr></f></p></text></region><region region-id="1259" left="66" top="963" width="238.5" height="67.5" align-x="173.25" align-y="972" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>batchn</ml:id><ml:boundVars><ml:id>func_name</ml:id><ml:id>data</ml:id></ml:boundVars></ml:function><ml:program><ml:localDefine><ml:id>n</ml:id><ml:apply><ml:id>length</ml:id><ml:id>data</ml:id></ml:apply></ml:localDefine><ml:for><ml:id>i</ml:id><ml:range><ml:real>0</ml:real><ml:apply><ml:minus /><ml:id>n</ml:id><ml:real>1</ml:real></ml:apply></ml:range><ml:localDefine><ml:apply><ml:indexer /><ml:id>OUT</ml:id><ml:id>i</ml:id></ml:apply><ml:apply><ml:id>func_name</ml:id><ml:apply><ml:indexer /><ml:id>data</ml:id><ml:id>i</ml:id></ml:apply></ml:apply></ml:localDefine></ml:for><ml:id>OUT</ml:id></ml:program></ml:define></math><rendering item-idref="20" /></region><region region-id="1260" left="66" top="1044.75" width="174" height="29.25" align-x="192.75" align-y="1062" 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>batchn</ml:id><ml:sequence><ml:apply><ml:id>arg1</ml:id><ml:sequence><ml:id>mean1</ml:id><ml:real>1</ml:real></ml:sequence></ml:apply><ml:id>spots</ml:id></ml:sequence></ml:apply></ml:eval></math><rendering item-idref="21" /></region><region region-id="1360" left="246" top="1052.25" width="129" height="12" align-x="246" align-y="1062" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">called with one argument.</c></inlineAttr></f></p></text></region><region region-id="1361" left="282" top="1082.25" width="75.75" height="24" align-x="282" align-y="1092" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">called with two arguments.</c></inlineAttr></f></p></text></region><region region-id="1263" left="66" top="1080.75" width="207" height="29.25" align-x="221.25" align-y="1098" 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>batchn</ml:id><ml:sequence><ml:apply><ml:id>arg2</ml:id><ml:sequence><ml:id>supsmooth</ml:id><ml:real>0</ml:real><ml:real>1</ml:real></ml:sequence></ml:apply><ml:id>spots</ml:id></ml:sequence></ml:apply></ml:eval><resultFormat><general radix="dec" complex-threshold="10" precision="3" show-trailing-zeros="false" exponential-threshold="3" /><matrix display-style="auto" expand-nested-arrays="false" /><unit format-units="false" simplify-units="false" /></resultFormat></math><rendering item-idref="22" /></region><region region-id="1362" left="36" top="1124.25" width="324" height="24" align-x="36" align-y="1134" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Further, a specialized batch function that rolls the data batching in with non-data arguments:</c></inlineAttr></f></p></text></region><region region-id="1394" left="36" top="1161" width="352.5" height="89.25" align-x="175.5" align-y="1170" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>batch_interp</ml:id><ml:boundVars><ml:id>data</ml:id><ml:id>func</ml:id><ml:id>c1</ml:id><ml:id>c2</ml:id><ml:id>x</ml:id></ml:boundVars></ml:function><ml:program><ml:localDefine><ml:id>n</ml:id><ml:apply><ml:id>length</ml:id><ml:id>data</ml:id></ml:apply></ml:localDefine><ml:localDefine><ml:id>VS</ml:id><ml:apply><ml:id>batchn</ml:id><ml:sequence><ml:apply><ml:id>arg2</ml:id><ml:sequence><ml:id>func</ml:id><ml:id>c1</ml:id><ml:id>c2</ml:id></ml:sequence></ml:apply><ml:id>data</ml:id></ml:sequence></ml:apply></ml:localDefine><ml:for><ml:id>i</ml:id><ml:range><ml:real>0</ml:real><ml:apply><ml:minus /><ml:id>n</ml:id><ml:real>1</ml:real></ml:apply></ml:range><ml:localDefine><ml:apply><ml:indexer /><ml:id>OUT</ml:id><ml:id>i</ml:id></ml:apply><ml:apply><ml:id>interp</ml:id><ml:sequence><ml:apply><ml:indexer /><ml:id>VS</ml:id><ml:id>i</ml:id></ml:apply><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>data</ml:id><ml:id>i</ml:id></ml:apply></ml:parens><ml:id>c1</ml:id></ml:apply><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>data</ml:id><ml:id>i</ml:id></ml:apply></ml:parens><ml:id>c2</ml:id></ml:apply><ml:id>x</ml:id></ml:sequence></ml:apply></ml:localDefine></ml:for><ml:id>OUT</ml:id></ml:program></ml:define></math><rendering item-idref="23" /></region><region region-id="1375" left="0" top="1260" width="6000" height="6" align-x="0" align-y="1260" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="1264" left="66" top="1263" width="179.25" height="12.75" align-x="105.75" align-y="1272" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:id>at_point</ml:id><ml:apply><ml:id>batch_interp</ml:id><ml:sequence><ml:id>spots</ml:id><ml:id>cspline</ml:id><ml:real>0</ml:real><ml:real>1</ml:real></ml:sequence></ml:apply></ml:define></math><rendering item-idref="24" /></region><region region-id="1273" left="66" top="1290.75" width="143.25" height="41.25" align-x="137.25" align-y="1314" 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>at_point</ml:id><ml:real>1945.5</ml:real></ml:apply></ml:eval></math><rendering item-idref="25" /></region><region region-id="1289" left="228" top="1305" width="49.5" height="12.75" align-x="237.75" align-y="1314" 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:range><ml:sequence><ml:real>0</ml:real><ml:real>.1</ml:real></ml:sequence><ml:real>20</ml:real></ml:range></ml:define></math><rendering item-idref="26" /></region><region region-id="1275" left="66" top="1338" width="257.25" height="196.5" align-x="66" align-y="1338" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><plot disable-calc="false" item-idref="27" /><rendering item-idref="28" /></region><region region-id="1364" left="36" top="1556.25" width="314.25" height="36" align-x="36" align-y="1566" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">You can modify this program to suit your particular application, including adding additional arguments for functions which require guess values or other input.</c></inlineAttr></f></p></text></region><region region-id="1365" left="36" top="1609.5" width="138" height="12.75" align-x="36" align-y="1620" 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"><f family="Times New Roman" charset="0" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#800000">Assembling multiple data sets</c></inlineAttr></b></f></p></text><indexes><phrase>multiple data sets, assembling</phrase></indexes></region><region region-id="1366" left="36" top="1634.25" width="338.25" height="36" align-x="36" align-y="1644" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Here is an alternate version of the program which concatenates nested datasets into a single array before performing the requested calculation.</c></inlineAttr></f></p></text></region><region region-id="1018" left="66" top="1689" width="230.25" height="89.25" align-x="177.75" align-y="1698" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>batch_a</ml:id><ml:boundVars><ml:id>func_name</ml:id><ml:id>data</ml:id></ml:boundVars></ml:function><ml:program><ml:localDefine><ml:id>M</ml:id><ml:apply><ml:indexer /><ml:id>data</ml:id><ml:real>0</ml:real></ml:apply></ml:localDefine><ml:localDefine><ml:id>n</ml:id><ml:apply><ml:id>last</ml:id><ml:id>data</ml:id></ml:apply></ml:localDefine><ml:for><ml:id>i</ml:id><ml:range><ml:real>1</ml:real><ml:id>n</ml:id></ml:range><ml:localDefine><ml:id>M</ml:id><ml:apply><ml:id>stack</ml:id><ml:sequence><ml:id>M</ml:id><ml:apply><ml:indexer /><ml:id>data</ml:id><ml:id>n</ml:id></ml:apply></ml:sequence></ml:apply></ml:localDefine></ml:for><ml:localDefine><ml:id>OUT</ml:id><ml:apply><ml:id>func_name</ml:id><ml:id>M</ml:id></ml:apply></ml:localDefine></ml:program></ml:define></math><rendering item-idref="29" /></region><region region-id="1367" left="36" top="1790.25" width="328.5" height="24" align-x="36" align-y="1800" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Compare the assembled batched output with the calculation done by hand, for the single column case:</c></inlineAttr></f></p></text></region><region region-id="1014" left="66" top="1827.75" width="158.25" height="23.25" align-x="195.75" align-y="1842" 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>mean</ml:id><ml:sequence><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>0</ml:real></ml:apply></ml:parens><ml:real>1</ml:real></ml:apply><ml:apply><ml:matcol /><ml:parens><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>1</ml:real></ml:apply></ml:parens><ml:real>1</ml:real></ml:apply></ml:sequence></ml:apply></ml:eval></math><rendering item-idref="30" /></region><region region-id="1015" left="66" top="1863" width="159.75" height="12.75" align-x="197.25" align-y="1872" 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>batch_a</ml:id><ml:sequence><ml:apply><ml:id>arg1</ml:id><ml:sequence><ml:id>mean1</ml:id><ml:real>1</ml:real></ml:sequence></ml:apply><ml:id>spots</ml:id></ml:sequence></ml:apply></ml:eval><resultFormat><general radix="dec" complex-threshold="10" precision="3" show-trailing-zeros="false" exponential-threshold="3" /><matrix display-style="auto" expand-nested-arrays="false" /><unit format-units="false" simplify-units="false" /></resultFormat></math><rendering item-idref="31" /></region><region region-id="1376" left="0" top="1884" width="6000" height="6" align-x="0" align-y="1884" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="1369" left="36" top="1892.25" width="125.25" height="12" align-x="36" align-y="1902" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">And for multiple columns:</c></inlineAttr></f></p></text></region><region region-id="1324" left="66" top="1911" width="109.5" height="18" align-x="81" align-y="1920" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:id>M</ml:id><ml:apply><ml:id>stack</ml:id><ml:sequence><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>0</ml:real></ml:apply><ml:apply><ml:indexer /><ml:id>spots</ml:id><ml:real>1</ml:real></ml:apply></ml:sequence></ml:apply></ml:define></math><rendering item-idref="32" /></region><region region-id="1325" left="66" top="1930.5" width="179.25" height="23.25" align-x="143.25" align-y="1950" 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:transpose /><ml:apply><ml:id>line</ml:id><ml:sequence><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:real>0</ml:real></ml:apply><ml:apply><ml:matcol /><ml:id>M</ml:id><ml:real>1</ml:real></ml:apply></ml:sequence></ml:apply></ml:apply></ml:eval></math><rendering item-idref="33" /></region><region region-id="1327" left="66" top="1965" width="236.25" height="18.75" align-x="200.25" align-y="1980" 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:transpose /><ml:apply><ml:id>batch_a</ml:id><ml:sequence><ml:apply><ml:id>arg2</ml:id><ml:sequence><ml:id>line</ml:id><ml:real>0</ml:real><ml:real>1</ml:real></ml:sequence></ml:apply><ml:id>spots</ml:id></ml:sequence></ml:apply></ml:apply></ml:eval></math><rendering item-idref="34" /></region><region region-id="1370" left="42" top="1994.25" width="316.5" height="24" align-x="42" align-y="2004" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">For more tips on batch reading of data files, see the section on </c></inlineAttr></f><link href="./inout.xmcd" title="Links to section" popup="false"><f family="Verdana" charset="0" size="10"><b><u><inlineAttr font-style="normal" line-through="false"><c val="#000">File Input a</c></inlineAttr></u></b></f><b><u><inlineAttr font-style="normal" line-through="false"><c val="#000"><f family="Verdana" charset="0" size="10">nd Output</f></c></inlineAttr></u></b><f family="Verdana" charset="0" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000"> .</c></inlineAttr></f></link></p></text></region><region region-id="1371" left="42" top="2041.5" width="90.75" height="12.75" align-x="65.25" align-y="2052" 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"><f family="Times New Roman" charset="0" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#800000">Automation window</c></inlineAttr></b></f></p></text><indexes><phrase>automation window</phrase></indexes></region><region region-id="1372" left="42" top="2060.25" width="327.75" height="96" align-x="42" align-y="2070" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">If you wish to batch process an entire worksheet, use Mathcad's Automation tools to drive the worksheet and its input values from a script. Such scripts can be run from within a scripting environment, such as Windows Scripting Host from Microsoft, from other Windows Applications that support scripting, such as Excel or Word, or from a custom application, written, for example, in Visual Basic. See the </c></inlineAttr></f><f family="Verdana" charset="0" size="10"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#000">Developer's Reference</c></inlineAttr></b></f><f family="Verdana" charset="0" size="10"><c val="#000"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> under the </inlineAttr></c></f><f family="Verdana" charset="0" size="10"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#000">Help</c></inlineAttr></b></f><f family="Verdana" charset="0" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000"> menu.</c></inlineAttr></f></p></text></region><region region-id="1373" left="42" top="2174.25" width="321.75" height="84" align-x="42" align-y="2184" 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" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">Mathcad includes a scripting window that can be used to drive Mathcad worksheets in a batched fashion. Press </c></inlineAttr></f><f family="Verdana" charset="0" size="10"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#000">[Ctrl][Alt][Shift]S</c></inlineAttr></b></f><f family="Verdana" charset="0" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000"> to bring up the window. You should see a window titled "Mathcad Scripting Host", with a large text box for entering scripts, and a choice between JScript and VBScript languages. The scripts should refer to Mathcad automation methods and objects, such as </c></inlineAttr></f></p></text><indexes><phrase>scripting window</phrase></indexes></region><region region-id="1391" left="78" top="2277" width="234" height="144" align-x="78" align-y="2286" 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"><f family="Courier New" charset="0">dim cwd, result</f></p><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"><f family="Courier New" charset="0">For i = 0 To 2</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">cwd = ActiveWorksheet.GetValue ("CWD")</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">'get the worksheet's path from Mathcad</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">ActiveWorksheet.SetValue "Index", i</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">ActiveWorksheet.Recalculate</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">FileName = cwd &amp; "loop" &amp; i &amp; ".htm"</f></p><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"><f family="Courier New" charset="0">result = ActiveWorksheet.GetValue ("b")</f></p><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"><f family="Courier New" charset="0">Echo(result)</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">Echo("writing " &amp; FileName)</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">ActiveWorksheet.SaveAs FileName, 2</f></p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Courier New" charset="0">Next</f></p></text></region><region region-id="1392" left="0" top="2436" width="6000" height="6" align-x="0" align-y="2436" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="1379" left="36" top="2444.25" width="318.75" height="132" align-x="36" align-y="2454" 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 Mathcad scripting window identifies the open worksheet as the ActiveWorksheet.<sp count="2" />It loops through values of i, and sets a variable named Index to each value of i in the script.<sp count="2" />It recalculates the worksheet with the new value of Index set, and saves the worksheet as an HTML version of itself with the resulting values (to store results).<sp count="2" />The number 2 after the SaveAs Filename method is the switch which sets the save to HTML format.<sp count="2" />Other available methods are 9 for version 12 MCD format, or 13 for version 12 XML format.<sp count="2" />Additional formats, and many other automation commands are described in the Developer's reference.</p></text></region><region region-id="1400" left="36" top="2588.25" width="302.25" height="60" align-x="36" align-y="2598" 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">You'll find that the scripting window also gives an approximate measure of how long it took to run the script, which can give you a measure of worksheet calculation time.<sp count="2" />It reports timing in ticks, which are roughly equivalent to a millisecond.</p></text></region><region region-id="1398" left="36" top="2660.25" width="322.5" height="60" align-x="36" align-y="2670" 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">Try this example with the sample looping worksheet provided by following the link to <b><u><link href="./loop.xmcd" title="Links to example file" popup="false">loop.xmcd</link></u></b>, copying the contents to a blank document in your main Mathcad window, saving the worksheet (so that the CWD variable is found) and running the script in the window as described.</p></text></region><region region-id="1399" left="6" top="2736" width="427.5" height="5.25" align-x="6" align-y="2736" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><png item-idref="35" display-width="435" display-height="3.75" /><rendering item-idref="36" /></region></regions><binaryContent><item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4zMuw6CMBgF4P5tuYoyOf8mLjZh4hmIk4mPQErFW0I0yODb66HgbpvTy9fm
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