View source for Template:Cs-solve

<includeonly>{{#expr: ({{#expr:( ( {{{y_high|0}}} - {{{y_low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }} ) * {{#expr:({{{x|0}}}+{{{shift|0}}})^{{{power|0.5}}} }} + ({{#expr:{{{y_low|0}}} - ({{#expr:( ( {{{y_high|0}}} - {{{y_low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }} ) *({{{x_low|1}}}+{{{shift|0}}})^{{{power|0.5}}} }}) + {{{add|0}}} {{#ifeq:{{{digit|0}}}|1|round0|round2}}  }}</includeonly>
<noinclude>
This template is used to generate values for scaling which uses the [[Scaling#cS| combatScale]] function. See also: [[Template:cs]].

===Format===

<pre>
{{cs-solve
|x=
|y_low=
|x_low=
|y_high=
|x_high= 
|power= (default 0.5, optional)
|shift= (default 0, optional)
|add= (default 0, optional)
|digit= (default 0, optional)
}}
</pre>

===Use===

When given a function of type: 

<pre>
combatScale(self:getStr(7, true) * self:getTalentLevel(t), 5, 0, 40, 35)
</pre>

These values map to:

<pre>
combatScale(x, y_low, x_low, y_high, x_high, power, add, shift)
</pre>

And 'raw' or 'log' is not currently implemented. 

''x'' is always the changing value you want to generate the final result for. This may be a combination of talents, stats, or something else; it's up to you to provide meaningful values. In the example above, ''x'' is defined as 0.07*Str*talent_level.

Therefore, we can use the following:

*x=(input desired value)
*y_low=5
*x_low=0
*y_high=40
*x_high=35
*power, shift, add have default values

Therefore:

combatScale(self:getStr(7, true) * self:getTalentLevel(t), 5, 0, 40, 35) for (str=30, talent_level=3) is: 

<pre>{{cs-solve|x=6.3|y_low=5|x_low=0|y_high=40|x_high=35}}</pre> = {{cs-solve|x=6.3|y_low=5|x_low=0|y_high=40|x_high=35}}



===Other parameters===

''digit'' defines the rounding of the final result. If digit=1, it will be rounded to the nearest whole number. Otherwise (if omitted), it will be rounded to two decimal places. 

You should not usually need to override these.


===Math=== 
(replace all 'high' with 'y_high', 'low' with 'y_low')
Input: power(=0), add(=0), shift(=0), x_low (=1), x_high(=5), y_low, y_high, (raw or log), t 

Psuedo code for '''m''':
*'''m''' = (y_high - y_low) / ( (x_high+shift)^power - (x_low+shift)^power )
* '''Expr for m''': <nowiki>{{#expr:( ( {{{high|0}}} - {{{low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }}</nowiki>

Psuedo code for '''b''':
* '''b''' = low - m*(x_low+shift)^power
* '''Expr for b''' (unexpanded): <nowiki>{{#expr:{{{low|0}}} - (m)*({{{xlow|1}}}+{{{shift|0}}})^{{{power|0.75}}} }}</nowiki>
* '''Expr for b''' (expanded):  <nowiki>{{#expr:{{{low|0}}} - ({{#expr:( ( {{{high|0}}} - {{{low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }}   )*({{{x_low|1}}}+{{{shift|0}}})^{{{power|0.75}}} }}</nowiki>

Psuedo code for '''the whole thing''':

*'''Output''' = m * (t+shift)^power + b + add
* '''Expr for output''' (unexpanded): <nowiki>(m)* {{#expr:({{{t|0}}}+{{{shift|0}}})^{{{power|0.5}}} }} + (b) + add</nowiki>
* '''Expr for output''' (expanded): <nowiki>{{#expr: ({{#expr:( ( {{{high|0}}} - {{{low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }} ) * {{#expr:({{{t|0}}}+{{{shift|0}}})^{{{power|0.5}}} }} + ({{#expr:{{{low|0}}} - ({{#expr:( ( {{{high|0}}} - {{{low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }} ) *({{{x_low|1}}}+{{{shift|0}}})^{{{power|0.50}}} }}) + {{{add|0.5}}} }}</nowiki>
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