Once the system has been built, you can create a local copy of an
diff --git a/docs/articles/Howto.html b/docs/articles/Howto.html
index 87795ae..0d9ab32 100644
--- a/docs/articles/Howto.html
+++ b/docs/articles/Howto.html
@@ -12,11 +12,12 @@
-
+
-
+
+
This tutorial requires ubiquity 2.04 or greater. Currently
+this is only available using the development version off of
+github
+
Sometimes we need to analyze data where the independent variable is
+not time. You can do this with ubiquity and this tutorial will highlight
+how that is done. If you have not done so already, please review the
+naive-pooled parameter estimation tutorial because this will build on
+the concepts covered there. The workshop (workshop.ubiquity.tools)
+provides an example of how to analyize static in vitro data. To make a
+copy of these scripts and other supporting files in the current working
+directory run the following:
This should create the following files in your current working
+direcotry:
+
+
+system-in_vitro.txt - System file that can be run both
+in vivo and in vitro
+
+
+in_vitro_er_data.csv- In vitro data file
+
+mk_data_in_vitro.R- Script to generate in vitro
+data
+
+analysis_in_vitro.R- Script to perform parameter
+estimation using the in vitro data
+
+
This example uses a system from Chakraborty
+and Jusko. J Pharm Sci 91(5), 1334-1342. Specifically equation 5
+from that article where the effect of two drugs, A and B, is driven by
+their concentrations (C_A, and C_B):
This has been implemented in the PKPD system file
+(system-in_vitro.txt) shown at the bottom. This
+implementation is dynamic meaning the effect changes with the PK of the
+drug. However the effect is considered instantaneous and typically
+analyzed from in vitro data using algebraic relationships. For this
+system consider the following data:
+
+Here both the concentrations of drug A and B are altered (independent
+variable) and the Effect is measured (dependent variable).
+
+
+
The sysem file: system-in_vitro.txt
+
+
First lets discuss the way the system file is structured. There is
+bolus dosing for the PK specified, but the initial conditions of the
+effect compartments are also defined in terms of system parameters:
+
<I> Cp_A = C_A0
+<I> Cp_B = C_B0
+
These system parameters (C_A0 and C_B0)
+have a default value of zero. So by default the system would run like
+any in vivo PKPD system. But these initial condition placeholders will
+be used when performing in vitro analyses. This allows you to
+use the same system file for both in vitro and in vivo analyses. This is
+useful because you do not have to do your static in vitro analysis in
+one system file and then copy and paste to your in vivo dynamic
+system.
+
+
+
The dataset: in_vitro_er_data.csv
+
+
This table contains a snapshot of the relevant columns of the
+dataset:
+
+
+
+
+
C_A0
+
C_B0
+
Effect
+
treat
+
samp_time
+
+
+
+
0.001
+
0.1
+
102.15401
+
A_0_001_B_0_1
+
1
+
+
+
0.001
+
0.1
+
100.78589
+
A_0_001_B_0_1
+
1
+
+
+
0.001
+
0.1
+
91.14621
+
A_0_001_B_0_1
+
1
+
+
+
0.001
+
100
+
93.38012
+
A_0_001_B_100
+
1
+
+
+
0.001
+
100
+
91.03467
+
A_0_001_B_100
+
1
+
+
+
0.001
+
100
+
86.20118
+
A_0_001_B_100
+
1
+
+
+
0.001
+
500
+
51.76744
+
A_0_001_B_500
+
1
+
+
+
0.001
+
500
+
48.95016
+
A_0_001_B_500
+
1
+
+
+
0.001
+
500
+
52.68611
+
A_0_001_B_500
+
1
+
+
+
0.001
+
1000
+
28.46122
+
A_0_001_B_1000
+
1
+
+
+
+
+
The C_A0 and C_B0 columns correspond to the
+concentrations that elicit the Effect. The
+treat column is a unique name for the combination of the
+two drug combinations. It has only letters numbers and underscores. This
+is intentional so I can use this as a cohort name when I’m constructing
+the estimation script below. The samp_time column is set to
+1. This is arbitrary because the mapping in the cohort definitions
+requires a time column. You’ll see why it is arbitrary below.
+
+
+
The analysis script: analysis_in_vitro.R
+
+
This analysis scripts has some aspects that are unique to the in
+vitro analysis being performed.
+
+
Output times
+
+
First is the output times. When you run simulations (which is what
+happens when performing a parameter estimation) more output times
+results in slower simulations. So it is important to only include the
+ncesssary output times. In this case we only have two output times (0
+and 1):
+
+cfg=system_set_option(cfg, group ="simulation",
+ option ="output_times",
+seq(0,1,1))
+
The final value of 1 was chosen because that corresponds to the time
+column (samp_time) in the analysis dataset.
+
+
+
Making a dynamic simulation static:
+
+
Next we set the simulation option dynamic
+to FALSE:
+
+cfg=system_set_option(cfg, group ="simulation",
+ option ="dynamic",
+ value =FALSE)
+
What this does is fix the values of the differential equations to 0
+for the purposes of the subsequent simulations.
+
+
+
Datasets
+
+
For the dataset we are reading it into a dataframe and loading it
+that way. This was done so the dataset could be used internally with
+ubiqiuty and also to construct the analysis below:
In the estimation tutorial cohorts are defined individually. We could
+do that here too but it would be rather tedious. See we need a cohort
+for every unique combination of C_A0 and C_B0
+in the dataset. To do this we are going to loop through each unique
+value in the treat column and create a cohort. The variable
+tmp_treat contains the value of the current treatment so
+the first thing we do is get the records for the current treatment:
This subset of the data is used to define the initial condition
+parameters for the current cohort using the cp field (see
+the help for system_define_cohort() for more information
+about this option). Because of the way the treat column was
+constructed we can use this as the cohort name. This will allow us to
+link the simulated output below to the original dataset in the post
+processing section below. The inputs are set to NULL here
+and we do not have to change them because there is no dosing.
Because we set the simulation option dynamic to
+FALSE, the initial condition is set to the values for the
+current treatment, and there are no inputs, then the system is
+effectively behaving like an in vitro system.
+
+
+
Postprocessing
+
+
You cannot rely on the normal figure generation and reporting
+elements. In this example we can take the simulated output at the
+estimation erp and the original data dataset
+er_data to create meaningful VPCs. This is because we can
+link the two datasets using the treat column from the
+original dataset to the COHORT column in
+erp$pred:
These functions take two bracketed arguments. The first argument is
diff --git a/docs/articles/NCA.html b/docs/articles/NCA.html
index f2fc6de..c3dc8dc 100644
--- a/docs/articles/NCA.html
+++ b/docs/articles/NCA.html
@@ -12,11 +12,12 @@
-
+
-
+
+
Simulating an Indiv
the celarance to a value of .015 you could simply use:
parameters$CL = 0.15.
Next different simulation options can be set. For example the
-following will set the duration of the simulation to three months
-
+following will set the duration of the simulation to three months \left(3\ \mbox{months} \times
+4\frac{\mbox{weeks}}{\mbox{month}}\times7\frac{\mbox{days}}{\mbox{week}}\right)
in days:
cfg=system_set_option(cfg, group ="simulation",
diff --git a/docs/articles/Titration.html b/docs/articles/Titration.html
index 009b609..63bba93 100644
--- a/docs/articles/Titration.html
+++ b/docs/articles/Titration.html
@@ -12,11 +12,12 @@
-
+
-
+
+
Skip to contents
@@ -47,6 +48,7 @@
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t||!t.unexpandable:yn.hasOwnProperty(e)&&!yn[e].primitive}}const 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Vn{constructor(e,t){this.mode=void 0,this.gullet=void 0,this.settings=void 0,this.leftrightDepth=void 0,this.nextToken=void 0,this.mode="math",this.gullet=new Hn(e,t,this.mode),this.settings=t,this.leftrightDepth=0}expect(e,t){if(void 0===t&&(t=!0),this.fetch().text!==e)throw new n("Expected '"+e+"', got '"+this.fetch().text+"'",this.fetch());t&&this.consume()}consume(){this.nextToken=null}fetch(){return null==this.nextToken&&(this.nextToken=this.gullet.expandNextToken()),this.nextToken}switchMode(e){this.mode=e,this.gullet.switchMode(e)}parse(){this.settings.globalGroup||this.gullet.beginGroup(),this.settings.colorIsTextColor&&this.gullet.macros.set("\\color","\\textcolor");try{const e=this.parseExpression(!1);return this.expect("EOF"),this.settings.globalGroup||this.gullet.endGroup(),e}finally{this.gullet.endGroups()}}subparse(e){const t=this.nextToken;this.consume(),this.gullet.pushToken(new Nr("}")),this.gullet.pushTokens(e);const r=this.parseExpression(!1);return 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0,r(6469)),l=r(505),c=r(5884);e.DirectionVH=((r={})[1]="v",r[2]="h",r),e.CommonMoMixin=function(t){return o(e,n=t),e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1),this.protoBBox(t),this.node.attributes.get("symmetric")&&2!==this.stretch.dir&&(e=this.getCenterOffset(t),t.h+=e,t.d-=e),this.node.getProperty("mathaccent")&&(0===this.stretch.dir||0<=this.size)&&(t.w=0)},e.prototype.protoBBox=function(t){var e=0!==this.stretch.dir;e&&null===this.size&&this.getStretchedVariant([0]),e&&this.size<0||(n.prototype.computeBBox.call(this,t),this.copySkewIC(t))},e.prototype.getAccentOffset=function(){var t=a.BBox.empty();return this.protoBBox(t),-t.w/2},e.prototype.getCenterOffset=function(t){return(t=void 0===t?null:t)||(t=a.BBox.empty(),n.prototype.computeBBox.call(this,t)),(t.h+t.d)/2+this.font.params.axis_height-t.h},e.prototype.getVariant=function(){this.node.attributes.get("largeop")?this.variant=this.node.attributes.get("displaystyle")?"-largeop":"-smallop":this.node.attributes.getExplicit("mathvariant")||!1!==this.node.getProperty("pseudoscript")?n.prototype.getVariant.call(this):this.variant="-tex-variant"},e.prototype.canStretch=function(t){if(0!==this.stretch.dir)return this.stretch.dir===t;if(!this.node.attributes.get("stretchy"))return!1;var e=this.getText();if(1!==Array.from(e).length)return!1;e=this.font.getDelimiter(e.codePointAt(0));return this.stretch=e&&e.dir===t?e:c.NOSTRETCH,0!==this.stretch.dir},e.prototype.getStretchedVariant=function(t,e){var r,n;if(void 0===e&&(e=!1),0!==this.stretch.dir){var o=this.getWH(t),i=this.getSize("minsize",0),a=this.getSize("maxsize",1/0),s=this.node.getProperty("mathaccent"),o=Math.max(i,Math.min(a,o)),a=this.font.params.delimiterfactor/1e3,l=this.font.params.delimitershortfall,c=i||e?o:s?Math.min(o/a,o+l):Math.max(o*a,o-l),u=this.stretch,p=u.c||this.getText().codePointAt(0),h=0;if(u.sizes)try{for(var d=y(u.sizes),f=d.next();!f.done;f=d.next()){if(f.value>=c)return s&&h&&h--,this.variant=this.font.getSizeVariant(p,h),this.size=h,void(u.schar&&u.schar[h]&&(this.stretch=m(m({},this.stretch),{c:u.schar[h]})));h++}}catch(t){r={error:t}}finally{try{f&&!f.done&&(n=d.return)&&n.call(d)}finally{if(r)throw r.error}}u.stretch?(this.size=-1,this.invalidateBBox(),this.getStretchBBox(t,this.checkExtendedHeight(o,u),u)):(this.variant=this.font.getSizeVariant(p,h-1),this.size=h-1)}},e.prototype.getSize=function(t,e){var r=this.node.attributes;return e=r.isSet(t)?this.length2em(r.get(t),1,1):e},e.prototype.getWH=function(t){if(0===t.length)return 0;if(1===t.length)return t[0];var t=s(t,2),e=t[0],t=t[1],r=this.font.params.axis_height;return this.node.attributes.get("symmetric")?2*Math.max(e-r,t+r):e+t},e.prototype.getStretchBBox=function(t,e,r){r.hasOwnProperty("min")&&r.min>e&&(e=r.min);var n=s(r.HDW,3),o=n[0],i=n[1],n=n[2];1===this.stretch.dir?(o=(t=s(this.getBaseline(t,e,r),2))[0],i=t[1]):n=e,this.bbox.h=o,this.bbox.d=i,this.bbox.w=n},e.prototype.getBaseline=function(t,e,r){var n=2===t.length&&t[0]+t[1]===e,o=this.node.attributes.get("symmetric"),t=s(n?t:[e,0],2),e=t[0],t=t[1],i=s([e+t,0],2),a=i[0],i=i[1];return i=o?(o=this.font.params.axis_height,(a=n?2*Math.max(e-o,t+o):a)/2-o):n?t:(o=(e=s(r.HDW||[.75,.25],2))[0],(n=e[1])*(a/(o+n))),[a-i,i]},e.prototype.checkExtendedHeight=function(t,e){var r;return e.fullExt&&(r=(e=s(e.fullExt,2))[0],t=(e=e[1])+Math.ceil(Math.max(0,t-e)/r)*r),t},e.prototype.remapChars=function(t){var e=this.node.getProperty("primes");return e?(0,l.unicodeChars)(e):(1===t.length&&(e=this.node.coreParent().parent,e=this.isAccent&&!e.isKind("mrow")?"accent":"mo",(e=this.font.getRemappedChar(e,t[0]))&&(t=this.unicodeChars(e,this.variant))),t)},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonInferredMrowMixin=e.CommonMrowMixin=void 0,r(6469));e.CommonMrowMixin=function(t){return o(e,s=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),e.prototype.stretchChildren=function(){var t,e,r,n,o,i,a=[];try{for(var s=x(this.childNodes),l=s.next();!l.done;l=s.next())(S=l.value).canStretch(1)&&a.push(S)}catch(e){t={error:e}}finally{try{l&&!l.done&&(e=s.return)&&e.call(s)}finally{if(t)throw t.error}}var c=a.length,u=this.childNodes.length;if(c&&1p&&(p=g),(b*=v)>h&&(h=b))}}catch(t){r={error:t}}finally{try{m&&!m.done&&(n=f.return)&&n.call(f)}finally{if(r)throw r.error}}try{for(var S,O=x(a),M=O.next();!M.done;M=O.next())(S=M.value).coreMO().getStretchedVariant([p,h])}catch(t){o={error:t}}finally{try{M&&!M.done&&(i=O.return)&&i.call(O)}finally{if(o)throw o.error}}}},e;function e(){for(var e,t,r=[],n=0;nthis.surdH?(t.h+t.d-(this.surdH-2*e-r/2))/2:e+r/4]},e.prototype.getRootDimens=function(t,e){return[0,0,0,0]},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},s=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMtableMixin=void 0,r(6469)),l=r(505),u=r(7875);e.CommonMtableMixin=function(t){return i(e,o=t),Object.defineProperty(e.prototype,"tableRows",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.findContainer=function(){for(var t=this,e=t.parent;e&&(e.node.notParent||e.node.isKind("mrow"));)e=(t=e).parent;this.container=e,this.containerI=t.node.childPosition()},e.prototype.getPercentageWidth=function(){var t;this.hasLabels?this.bbox.pwidth=s.BBox.fullWidth:(t=this.node.attributes.get("width"),(0,l.isPercent)(t)&&(this.bbox.pwidth=t))},e.prototype.stretchRows=function(){for(var t=this.node.attributes.get("equalrows"),e=t?this.getEqualRowHeight():0,r=t?this.getTableData():{H:[0],D:[0]},n=r.H,o=r.D,i=this.tableRows,a=0;ao[r]&&(o[r]=c),u>i[r]&&(i[r]=u),s
a[e]&&(a[e]=l),s},e.prototype.extendHD=function(t,e,r,n){n=(n-(e[t]+r[t]))/2;n<1e-5||(e[t]+=n,r[t]+=n)},e.prototype.recordPWidthCell=function(t,e){t.childNodes[0]&&t.childNodes[0].getBBox().pwidth&&this.pwidthCells.push([t,e])},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var e=this.getTableData(),r=e.H,e=e.D,r=(n=this.node.attributes.get("equalrows")?(n=this.getEqualRowHeight(),(0,u.sum)([].concat(this.rLines,this.rSpace))+n*this.numRows):(0,u.sum)(r.concat(e,this.rLines,this.rSpace)),n+=2*(this.fLine+this.fSpace[1]),this.getComputedWidths()),e=(0,u.sum)(r.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),r=this.node.attributes.get("width"),n=("auto"!==r&&(e=Math.max(this.length2em(r,0)+2*this.fLine,e)),p(this.getBBoxHD(n),2)),o=n[0],n=n[1],o=(t.h=o,t.d=n,t.w=e,p(this.getBBoxLR(),2)),n=o[0],e=o[1];t.L=n,t.R=e,(0,l.isPercent)(r)||this.setColumnPWidths()},e.prototype.setChildPWidths=function(t,e,r){var n=this.node.attributes.get("width");if(!(0,l.isPercent)(n))return!1;this.hasLabels||(this.bbox.pwidth="",this.container.bbox.pwidth="");var o=this.bbox,i=o.w,a=o.L,o=o.R,s=this.node.attributes.get("data-width-includes-label"),n=Math.max(i,this.length2em(n,Math.max(e,a+i+o)))-(s?a+o:0),e=this.node.attributes.get("equalcolumns")?Array(this.numCols).fill(this.percent(1/Math.max(1,this.numCols))):this.getColumnAttributes("columnwidth",0),s=(this.cWidths=this.getColumnWidthsFixed(e,n),this.getComputedWidths());return this.pWidth=(0,u.sum)(s.concat(this.cLines,this.cSpace))+2*(this.fLine+this.fSpace[0]),this.isTop&&(this.bbox.w=this.pWidth),this.setColumnPWidths(),this.pWidth!==i&&this.parent.invalidateBBox(),this.pWidth!==i},e.prototype.setColumnPWidths=function(){var t,e,r=this.cWidths;try{for(var n=_(this.pwidthCells),o=n.next();!o.done;o=n.next()){var i=p(o.value,2),a=i[0],s=i[1];a.setChildPWidths(!1,r[s])&&(a.invalidateBBox(),a.getBBox())}}catch(e){t={error:e}}finally{try{o&&!o.done&&(e=n.return)&&e.call(n)}finally{if(t)throw t.error}}},e.prototype.getBBoxHD=function(t){var e,r=p(this.getAlignmentRow(),2),n=r[0],r=r[1];if(null===r)return{top:[0,t],center:[e=t/2,e],bottom:[t,0],baseline:[e,e],axis:[e+(o=this.font.params.axis_height),e-o]}[n]||[e,e];var o=this.getVerticalPosition(r,n);return[o,t-o]},e.prototype.getBBoxLR=function(){var t,e,r,n;return this.hasLabels?(t=(n=this.node.attributes).get("side"),e=(r=p(this.getPadAlignShift(t),2))[0],r=r[1],(n=this.hasLabels&&!!n.get("data-width-includes-label"))&&this.frame&&this.fSpace[0]&&(e-=this.fSpace[0]),"center"!==r||n?"left"===t?[e,0]:[0,e]:[e,e]):[0,0]},e.prototype.getPadAlignShift=function(t){var e=this.getTableData().L+this.length2em(this.node.attributes.get("minlabelspacing")),r=p(null==this.styles?["",""]:[this.styles.get("padding-left"),this.styles.get("padding-right")],2),n=r[0],r=r[1],n=((n||r)&&(e=Math.max(e,this.length2em(n||"0"),this.length2em(r||"0"))),p(this.getAlignShift(),2)),r=n[0],n=n[1];return[e,r,n=r===t?"left"===t?Math.max(e,n)-e:Math.min(-e,n)+e:n]},e.prototype.getAlignShift=function(){return this.isTop?o.prototype.getAlignShift.call(this):[this.container.getChildAlign(this.containerI),0]},e.prototype.getWidth=function(){return this.pWidth||this.getBBox().w},e.prototype.getEqualRowHeight=function(){var t=this.getTableData(),e=t.H,r=t.D,t=Array.from(e.keys()).map(function(t){return e[t]+r[t]});return Math.max.apply(Math,t)},e.prototype.getComputedWidths=function(){var e=this,r=this.getTableData().W,t=Array.from(r.keys()).map(function(t){return("number"==typeof e.cWidths[t]?e.cWidths:r)[t]});return t=this.node.attributes.get("equalcolumns")?Array(t.length).fill((0,u.max)(t)):t},e.prototype.getColumnWidths=function(){var t=this.node.attributes.get("width");if(this.node.attributes.get("equalcolumns"))return this.getEqualColumns(t);var e=this.getColumnAttributes("columnwidth",0);return"auto"===t?this.getColumnWidthsAuto(e):(0,l.isPercent)(t)?this.getColumnWidthsPercent(e):this.getColumnWidthsFixed(e,this.length2em(t))},e.prototype.getEqualColumns=function(t){var e,r=Math.max(1,this.numCols);return t="auto"===t?(e=this.getTableData().W,(0,u.max)(e)):(0,l.isPercent)(t)?this.percent(1/r):(e=(0,u.sum)([].concat(this.cLines,this.cSpace))+2*this.fSpace[0],Math.max(0,this.length2em(t)-e)/r),Array(this.numCols).fill(t)},e.prototype.getColumnWidthsAuto=function(t){var e=this;return t.map(function(t){return"auto"===t||"fit"===t?null:(0,l.isPercent)(t)?t:e.length2em(t)})},e.prototype.getColumnWidthsPercent=function(r){var n=this,o=0<=r.indexOf("fit"),i=(o?this.getTableData():{W:null}).W;return Array.from(r.keys()).map(function(t){var e=r[t];return"fit"===e?null:"auto"===e?o?i[t]:null:(0,l.isPercent)(e)?e:n.length2em(e)})},e.prototype.getColumnWidthsFixed=function(r,t){var n=this,e=Array.from(r.keys()),o=e.filter(function(t){return"fit"===r[t]}),i=e.filter(function(t){return"auto"===r[t]}),i=o.length||i.length,a=(i?this.getTableData():{W:null}).W,s=t-(0,u.sum)([].concat(this.cLines,this.cSpace))-2*this.fSpace[0],l=s,c=(e.forEach(function(t){var e=r[t];l-="fit"===e||"auto"===e?a[t]:n.length2em(e,s)}),i&&0this.numRows?null:t-1]},e.prototype.getColumnAttributes=function(t,e){var r=this.numCols-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getRowAttributes=function(t,e){var r=this.numRows-(e=void 0===e?1:e),n=this.getAttributeArray(t);if(0===n.length)return null;for(;n.lengthr&&n.splice(r),n},e.prototype.getAttributeArray=function(t){var e=this.node.attributes.get(t);return e?(0,l.split)(e):[this.node.attributes.getDefault(t)]},e.prototype.addEm=function(t,e){var r=this;return void 0===e&&(e=1),t?t.map(function(t){return r.em(t/e)}):null},e.prototype.convertLengths=function(t){var e=this;return t?t.map(function(t){return e.length2em(t)}):null},e;function e(){for(var t=[],e=0;e=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")};Object.defineProperty(e,"__esModule",{value:!0}),e.CommonMlabeledtrMixin=e.CommonMtrMixin=void 0,e.CommonMtrMixin=function(t){return o(e,r=t),Object.defineProperty(e.prototype,"fixesPWidth",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"numCells",{get:function(){return this.childNodes.length},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"labeled",{get:function(){return!1},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"tableCells",{get:function(){return this.childNodes},enumerable:!1,configurable:!0}),e.prototype.getChild=function(t){return this.childNodes[t]},e.prototype.getChildBBoxes=function(){return this.childNodes.map(function(t){return t.getBBox()})},e.prototype.stretchChildren=function(t){void 0===t&&(t=null);var e,r,n,o,i=[],a=this.labeled?this.childNodes.slice(1):this.childNodes;try{for(var s=M(a),l=s.next();!l.done;l=s.next())(_=l.value.childNodes[0]).canStretch(1)&&i.push(_)}catch(t){u={error:t}}finally{try{l&&!l.done&&(c=s.return)&&c.call(s)}finally{if(u)throw u.error}}var c=i.length,u=this.childNodes.length;if(c&&1=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},a=(Object.defineProperty(e,"__esModule",{value:!0}),e.CommonScriptbaseMixin=void 0,r(9007));e.CommonScriptbaseMixin=function(t){var o;return i(e,o=t),Object.defineProperty(e.prototype,"baseChild",{get:function(){return this.childNodes[this.node.base]},enumerable:!1,configurable:!0}),Object.defineProperty(e.prototype,"scriptChild",{get:function(){return this.childNodes[1]},enumerable:!1,configurable:!0}),e.prototype.getBaseCore=function(){for(var t=this.getSemanticBase()||this.childNodes[0];t&&(1===t.childNodes.length&&(t.node.isKind("mrow")||t.node.isKind("TeXAtom")&&t.node.texClass!==a.TEXCLASS.VCENTER||t.node.isKind("mstyle")||t.node.isKind("mpadded")||t.node.isKind("mphantom")||t.node.isKind("semantics"))||t.node.isKind("munderover")&&t.isMathAccent);)this.setBaseAccentsFor(t),t=t.childNodes[0];return t||(this.baseHasAccentOver=this.baseHasAccentUnder=!1),t||this.childNodes[0]},e.prototype.setBaseAccentsFor=function(t){t.node.isKind("munderover")&&(null===this.baseHasAccentOver&&(this.baseHasAccentOver=!!t.node.attributes.get("accent")),null===this.baseHasAccentUnder&&(this.baseHasAccentUnder=!!t.node.attributes.get("accentunder")))},e.prototype.getSemanticBase=function(){var t=this.node.attributes.getExplicit("data-semantic-fencepointer");return this.getBaseFence(this.baseChild,t)},e.prototype.getBaseFence=function(t,e){var r,n;if(!t||!t.node.attributes||!e)return null;if(t.node.attributes.getExplicit("data-semantic-id")===e)return t;try{for(var o=O(t.childNodes),i=o.next();!i.done;i=o.next()){var a=i.value,s=this.getBaseFence(a,e);if(s)return s}}catch(t){r={error:t}}finally{try{i&&!i.done&&(n=o.return)&&n.call(o)}finally{if(r)throw r.error}}return null},e.prototype.getBaseScale=function(){for(var t=this.baseCore,e=1;t&&t!==this;)e*=t.getOuterBBox().rscale,t=t.parent;return e},e.prototype.getBaseIc=function(){return this.baseCore.getOuterBBox().ic*this.baseScale},e.prototype.getAdjustedIc=function(){var t=this.baseCore.getOuterBBox();return(t.ic?1.05*t.ic+.05:0)*this.baseScale},e.prototype.isCharBase=function(){var t=this.baseCore;return(t.node.isKind("mo")&&null===t.size||t.node.isKind("mi")||t.node.isKind("mn"))&&1===t.bbox.rscale&&1===Array.from(t.getText()).length},e.prototype.checkLineAccents=function(){this.node.isKind("munderover")&&(this.node.isKind("mover")?this.isLineAbove=this.isLineAccent(this.scriptChild):this.node.isKind("munder")?this.isLineBelow=this.isLineAccent(this.scriptChild):(this.isLineAbove=this.isLineAccent(this.overChild),this.isLineBelow=this.isLineAccent(this.underChild)))},e.prototype.isLineAccent=function(t){t=t.coreMO().node;return t.isToken&&"―"===t.getText()},e.prototype.getBaseWidth=function(){var t=this.baseChild.getOuterBBox();return t.w*t.rscale-(this.baseRemoveIc?this.baseIc:0)+this.font.params.extra_ic},e.prototype.computeBBox=function(t,e){void 0===e&&(e=!1);var r=this.getBaseWidth(),n=y(this.getOffset(),2),o=n[0],n=n[1];t.append(this.baseChild.getOuterBBox()),t.combine(this.scriptChild.getOuterBBox(),r+o,n),t.w+=this.font.params.scriptspace,t.clean(),this.setChildPWidths(e)},e.prototype.getOffset=function(){return[0,0]},e.prototype.baseCharZero=function(t){var e=!!this.baseCore.node.attributes.get("largeop"),r=this.baseScale;return this.baseIsChar&&!e&&1===r?0:t},e.prototype.getV=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.length2em(this.node.attributes.get("subscriptshift"),r.sub1);return Math.max(this.baseCharZero(t.d*this.baseScale+r.sub_drop*e.rscale),n,e.h*e.rscale-.8*r.x_height)},e.prototype.getU=function(){var t=this.baseCore.getOuterBBox(),e=this.scriptChild.getOuterBBox(),r=this.font.params,n=this.node.attributes.getList("displaystyle","superscriptshift"),o=this.node.getProperty("texprimestyle")?r.sup3:n.displaystyle?r.sup1:r.sup2,n=this.length2em(n.superscriptshift,o);return Math.max(this.baseCharZero(t.h*this.baseScale-r.sup_drop*e.rscale),n,e.d*e.rscale+.25*r.x_height)},e.prototype.hasMovableLimits=function(){var t=this.node.attributes.get("displaystyle"),e=this.baseChild.coreMO().node;return!t&&!!e.attributes.get("movablelimits")},e.prototype.getOverKU=function(t,e){var r=this.node.attributes.get("accent"),n=this.font.params,e=e.d*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentOver?o:0,o=this.isLineAbove?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing1,n.big_op_spacing3-Math.max(0,e)))-i;return[r,t.h*t.rscale+r+e]},e.prototype.getUnderKV=function(t,e){var r=this.node.attributes.get("accentunder"),n=this.font.params,e=e.h*e.rscale,o=n.rule_thickness*n.separation_factor,i=this.baseHasAccentUnder?o:0,o=this.isLineBelow?3*n.rule_thickness:o,r=(r?o:Math.max(n.big_op_spacing2,n.big_op_spacing4-e))-i;return[r,-(t.d*t.rscale+r+e)]},e.prototype.getDeltaW=function(e,t){void 0===t&&(t=[0,0,0]);var r,n,o,i,a=this.node.attributes.get("align"),s=e.map(function(t){return t.w*t.rscale}),l=(s[0]-=this.baseRemoveIc&&!this.baseCore.node.attributes.get("largeop")?this.baseIc:0,Math.max.apply(Math,g([],y(s),!1))),c=[],u=0;try{for(var p=O(s.keys()),h=p.next();!h.done;h=p.next()){var d=h.value;c[d]=("center"===a?(l-s[d])/2:"right"===a?l-s[d]:0)+t[d],c[d]=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},u=this&&this.__read||function(t,e){var r="function"==typeof Symbol&&t[Symbol.iterator];if(!r)return t;var n,o,i=r.call(t),a=[];try{for(;(void 0===e||0=t.length?void 0:t)&&t[n++],done:!t}}};throw new TypeError(e?"Object is not iterable.":"Symbol.iterator is not defined.")},o=this&&this.__importDefault||function(t){return t&&t.__esModule?t:{default:t}},i=(Object.defineProperty(e,"__esModule",{value:!0}),e.Menu=void 0,r(5713)),c=r(4474),a=r(9515),s=r(7233),l=r(5865),p=r(473),h=r(4414),d=r(4922),f=r(6914),m=r(3463),y=r(7309),g=o(r(5445)),b=a.MathJax,v="undefined"!=typeof window&&window.navigator&&"Mac"===window.navigator.platform.substr(0,3);function _(t,e){void 0===e&&(e={});var r=this;this.settings=null,this.defaultSettings=null,this.menu=null,this.MmlVisitor=new p.MmlVisitor,this.jax={CHTML:null,SVG:null},this.rerenderStart=c.STATE.LAST,this.about=new d.Info('MathJax v'+i.mathjax.version,function(){var t=[];return t.push("Input Jax: "+r.document.inputJax.map(function(t){return t.name}).join(", ")),t.push("Output Jax: "+r.document.outputJax.name),t.push("Document Type: "+r.document.kind),t.join(" ")},'www.mathjax.org'),this.help=new d.Info("MathJax Help",function(){return["
MathJax is a JavaScript library that allows page"," authors to include mathematics within their web pages."," As a reader, you don't need to do anything to make that happen.
","
Browsers: MathJax works with all modern browsers including"," Edge, Firefox, Chrome, Safari, Opera, and most mobile browsers.
","
Math Menu: MathJax adds a contextual menu to equations."," Right-click or CTRL-click on any mathematics to access the menu.
",'
',"
Show Math As: These options allow you to view the formula's"," source markup (as MathML or in its original format).
","
Copy to Clipboard: These options copy the formula's source markup,"," as MathML or in its original format, to the clipboard"," (in browsers that support that).
","
Math Settings: These give you control over features of MathJax,"," such the size of the mathematics, and the mechanism used"," to display equations.
","
Accessibility: MathJax can work with screen"," readers to make mathematics accessible to the visually impaired."," Turn on the explorer to enable generation of speech strings"," and the ability to investigate expressions interactively.
","
Language: This menu lets you select the language used by MathJax"," for its menus and warning messages. (Not yet implemented in version 3.)
","
","
Math Zoom: If you are having difficulty reading an"," equation, MathJax can enlarge it to help you see it better, or"," you can scall all the math on the page to make it larger."," Turn these features on in the Math Settings menu.
","
Preferences: MathJax uses your browser's localStorage database"," to save the preferences set via this menu locally in your browser. These"," are not used to track you, and are not transferred or used remotely by"," MathJax in any way.