{"id":663,"date":"2012-12-15T15:32:15","date_gmt":"2012-12-15T14:32:15","guid":{"rendered":"http:\/\/inprompt.service.tu-berlin.de\/wordMOSAIC\/?page_id=663"},"modified":"2024-07-14T15:01:46","modified_gmt":"2024-07-14T14:01:46","slug":"use-of-functions-ii-applications-using-indices","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=663","title":{"rendered":"Use of Functions II &#8211; Applications Using Indices"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">On this page<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Model-description\" >Model description<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Workflow\" >Workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Notation-of-equation-system\" >Notation of equation system<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Equations\" >Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Notation-and-definition-of-function\" >Notation and definition of function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Equation-system\" >Equation system<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Evaluation-Simulation\" >Evaluation \/ Simulation<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mosaic-modeling.de\/?page_id=663\/#Initialization-and-results\" >Initialization and results<\/a><\/li><\/ul><\/nav><\/div>\n<address style=\"text-align: justify;\">\u00a0<\/address>\n<p style=\"text-align: justify;\">This tutorial introduces the use of indices in function applications.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Model-description\"><\/span>Model description<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The following example will solve the following equation system:<\/p>\n<p><p class=\"ql-left-displayed-equation\" style=\"line-height: 42px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-add6cd950d17755c9bfb7b88182e6511_l3.png\" height=\"42\" width=\"89\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;&#38;&#120;&#95;&#105;&#32;&#61;&#32;&#97;&#95;&#105;&#32;&#43;&#32;&#98;&#95;&#105;&#32;&#92;&#92;&#38;&#115;&#95;&#105;&#32;&#61;&#32;&#121;&#95;&#105;&#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<p>As in the previous example, a function shall be used to calculate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-761333a1d61654bd1cb5c7224b0d1994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/>. This function has the same formula as before:<\/p>\n<p style=\"text-align: justify;\"><p class=\"ql-left-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-394026ec9b54ea734866255d53ed13aa_l3.png\" height=\"19\" width=\"225\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#121;&#95;&#105;&#32;&#61;&#32;&#102;&#40;&#97;&#95;&#105;&#44;&#32;&#98;&#95;&#105;&#41;&#32;&#61;&#32;&#48;&#46;&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#97;&#95;&#105;&#43;&#98;&#95;&#105;&#41;&#46;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Workflow\"><\/span>Workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"Notation-of-equation-system\"><\/span>Notation of equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>For the notation of the equation, we need to set up all base names of symbols that appear in the equations, i.e.<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0e55b0b3943237ccfc96979505679274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, parameter<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"\/>, parameter<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ad69adf868bc701e561aa555db995f1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/>, parameter<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c74288aabc0e2ca280d25d92bf1a1ec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, parameter<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, additional value s (new)<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>, iteration variable<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/>, iteration variable<\/li>\n<\/ul>\n<p>As indices are now involved, we also need to define the index <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>:<\/p>\n<ul>\n<li style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>, index of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/> \u00a01..N (new)<\/li>\n<\/ul>\n<p>The resulting notation has ID 182662.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equations\"><\/span>Equations<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">Next, we can define the equations of the model. Therefore, we open the equation editor, load the notation we just created, and enter the equations as stated above in the model description. The formulated equations are available with the IDs 182663 and 182664.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Notation-and-definition-of-function\"><\/span>Notation and definition of function<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Because we use exactly the same function, we do not have to define and save a notation and the function itself again, but we will simply re-use this function and apply it on our new variables. The function is available with ID 182656.<\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Equation-system\"><\/span>Equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\">We are now able to construct our new equation system based on the new equations and the function saved in the previous example:<\/p>\n<ol>\n<li style=\"text-align: justify;\">Go to &#8220;Equation System&#8221; and load the notation <strong>for the equations<\/strong><\/li>\n<li>Add the two equations to your system in the Connected Elements tab<\/li>\n<li>Go to the Functions tab. To use the general function created above, it must be added to the equation system and applied on the variables within this problem. In this context, applying means specifying which variable names in the equation system are supposed to be the corresponding input and output variables of the function.<\/li>\n<li>Click on &#8220;Add Function&#8221; at the bottom of the screen and open your function in the opening popup window. After loading the function, you should see the expression for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> as a function of the inputs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5f813d35bd704e28ab3db49ea879d509_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#111;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/>. On the left hand side of the dialog, you see the Output Naming<span style=\"text-align: justify; color: initial;\"> and the Input Naming<\/span><span style=\"text-align: justify; color: initial;\"> as defined in the function.\u00a0<\/span><\/li>\n<li>On the right hand side of the dialog there is a section called Applications (Function Calls), which contains the tables Output Variable, Input Variables, and Parameters. Click on &#8220;Add Application&#8221;, which opens another popup window.<\/li>\n<li>In this dialog, double click into the field Applied Naming<span style=\"text-align: justify; color: initial;\"> or click on &#8220;Edit Output&#8221; <\/span><span style=\"text-align: justify; color: initial;\">below that field. This opens another dialog where you can enter the naming of the output variable in the equation system.<\/span><\/li>\n<li>Enter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-761333a1d61654bd1cb5c7224b0d1994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/> into the Tex Expression, render, and confirm<\/li>\n<li>Double click into the table row of the variable naming <em>o<\/em> or select this row and click &#8220;Edit Input&#8221;. Again a dialog is shown in which a variable naming can be entered. Enter <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0ea7aa2fd00c5c5980e75b075179d117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"\/>, render, and confirm; then repeat this step for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/> with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b7f20c534e11222b0ca7a34c5c1f7591_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"13\" style=\"vertical-align: -3px;\"\/> being the applied input<\/li>\n<li>Confirm these matches at the bottom of the window. When clicking on &#8216;A&#8217; in the Applications, you should now find the match of the inputs (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-bc1e96b0d98a614ad47829a68fe2880e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#111;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#97;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: -3px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-56f5fe2202af4dec6754bc0559b7daa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#98;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"50\" style=\"vertical-align: -4px;\"\/>)<\/li>\n<li>Confirm in this window at the bottom and save your equation system<\/li>\n<\/ol>\n<p>This equation system is available with ID 182665.\u00a0<\/p>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Evaluation-Simulation\"><\/span>Evaluation \/ Simulation<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Your model is now complete and you can move on to the &#8220;Simulation&#8221; section of MOSAICmodeling.<\/p>\n<ol style=\"text-align: justify;\">\n<li>Enter a suitable description<\/li>\n<li>Select the tab Equation System and load the system created in the previous steps. Go to Indexing and set <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#78;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> to 2<\/li>\n<li>If you now go to the tab Instantiated System and then to the Functions tab, you will notice that you still have one application but two usages, because the function is applied on all instances of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>, i.e., for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-13d95f188571688bc02e58b2e7f0d322_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: 0px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5c96c7b068fad34bdb27fa5586ef2fb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#32;&#61;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: 0px;\"\/><\/li>\n<li>Select the tab Specifications. In the list ALL VARIABLES, you will find the variables as defined in your model notation. Therein, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-761333a1d61654bd1cb5c7224b0d1994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"\/> will be of type &#8220;CALCULATED_VALUE&#8221; because it is determined by a function<\/li>\n<li>Classify the variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0ea7aa2fd00c5c5980e75b075179d117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b7f20c534e11222b0ca7a34c5c1f7591_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"13\" style=\"vertical-align: -3px;\"\/> as design variables by selecting this category from the dropdown menu in the Type column. You can also assign the variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2071979c45a4a9e06d8cccc739ffc771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/> as &#8220;ITERATION_VALUE&#8221;<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Initialization-and-results\"><\/span>Initialization and results<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This example is solved with the initial guesses for the variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-2071979c45a4a9e06d8cccc739ffc771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"\/> given in Table 1. After having assigned the initial guesses and the parameter values, you can save the variable specification and then the simulation. This simulation is available with ID 182666 with variable specification 182667. The solution for all iteration variables is also given in Table 1.<\/p>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Name<\/th><th class=\"has-text-align-left\" data-align=\"left\">Description<\/th><th class=\"has-text-align-left\" data-align=\"left\">Value \/ Initial guess<\/th><th class=\"has-text-align-left\" data-align=\"left\">Solution<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-64a1d8239f3e5a23a975af05c0607f93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-48bb8b6f5e81e3221498ce8b1dedf94f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"32\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\">1.5<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c26d99186c2b3ab0ea2d7aa2a3768ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"30\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\">3.0<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4ecac524f2b1f42b968d9875419141ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\">3.5<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-043c5ea5c2e0923cacb6a916b385c6f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Explicitly calculable value<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><td class=\"has-text-align-left\" data-align=\"left\">2.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-a7c974b1412028469bbf1cfc2a0d6855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Explicitly calculable value<\/td><td class=\"has-text-align-left\" data-align=\"left\"><\/td><td class=\"has-text-align-left\" data-align=\"left\">2.5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5abbdea805fa4b76e97874079f9edffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"30\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Iteration variable<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><td class=\"has-text-align-left\" data-align=\"left\">2.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e752bdf8e454f465694796464a688d8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Iteration variable<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><td class=\"has-text-align-left\" data-align=\"left\">2.5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5f82b7b0a49514733976c2fdbd97b4fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#123;&#105;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"32\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Iteration variable<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><td class=\"has-text-align-left\" data-align=\"left\">4.0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-516a5a8e71d8e4b2e6a9cd57061f4e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#123;&#105;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"33\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Iteration variable<\/td><td class=\"has-text-align-left\" data-align=\"left\">0.0<\/td><td class=\"has-text-align-left\" data-align=\"left\">5.0<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Overview of parameter values, initial guesses, and the solution.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0 This tutorial introduces the use of indices in function applications. Model description The following example will solve the following equation system: &nbsp; &nbsp; As in the previous example, a function shall be used to calculate . This function has the same formula as before: &nbsp; &nbsp; Workflow Notation of equation system For the notation [&hellip;]<\/p>\n","protected":false},"author":188,"featured_media":0,"parent":307,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-663","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/663","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/users\/188"}],"replies":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=663"}],"version-history":[{"count":48,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/663\/revisions"}],"predecessor-version":[{"id":6151,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/663\/revisions\/6151"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/307"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}