Difference between revisions of "Template:Cts-solve"
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| − | {{#expr:{{{low|0}}} - ({{#expr:( ( {{{high|0}}} - {{{low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }} | + | <includeonly>{{#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|0.5}}} }}) + {{{add|0}}} {{#ifeq:{{{digit|0}}}|1|round0|round2}} }}</includeonly> |
<noinclude> | <noinclude> | ||
| − | + | This template is used to generate values for scaling which uses the [[Scaling#.28cTS.29_combatTalentScale| combatTalentScale]] function. See also: [[Template:cts]]. | |
| + | |||
| + | ===Format=== | ||
<pre> | <pre> | ||
| Line 13: | Line 15: | ||
|shift= (default 0, optional) | |shift= (default 0, optional) | ||
|add= (default 0, optional) | |add= (default 0, optional) | ||
| + | |digit= (default 0, optional) | ||
}} | }} | ||
</pre> | </pre> | ||
| + | ===Use=== | ||
| + | |||
| + | When given a function of type: | ||
| + | |||
| + | <pre> | ||
| + | combatTalentScale(t, 4, 15, 0.75, 1, 2, true) | ||
| + | </pre> | ||
| + | |||
| + | These values map to: | ||
| + | |||
| + | <pre> | ||
| + | combatTalentScale(t, low, high, power, shift, add) | ||
| + | </pre> | ||
| + | |||
| + | And 'raw' or 'log' is not currently implemented. ''t'' is always the talent level value you want to generate the final result for! | ||
| + | |||
| + | Therefore, we can use the following: | ||
| + | |||
| + | combatTalentScale(t, 4, 15, 0.75, 1, 2) for t=3 is {{cts-solve|t=3|low=4|high=15|power=0.75|shift=1|add=2}} | ||
| + | |||
| + | ===Other parameters=== | ||
| + | |||
| + | ''x_low'' is the talent level for which we expect the result to be ''low'', and defaults to 1 | ||
| + | |||
| + | ''x_high'' is the talent level for which we expect to result to be ''high'', and defaults to 5 | ||
| + | |||
| + | ''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=== | ||
Input: power(=0), add(=0), shift(=0), x_low (=1), x_high(=5), low, high, (raw or log), t | Input: power(=0), add(=0), shift(=0), x_low (=1), x_high(=5), low, high, (raw or log), t | ||
| Line 27: | Line 62: | ||
* '''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> | * '''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> | ||
</noinclude> | </noinclude> | ||
Latest revision as of 14:35, 1 March 2016
This template is used to generate values for scaling which uses the combatTalentScale function. See also: Template:cts.
Contents
Format
{{cts-solve
|high=
|low=
|t=
|x_high= (default 5, optional)
|x_low= (default 1, optional)
|power= (default 0.5, optional)
|shift= (default 0, optional)
|add= (default 0, optional)
|digit= (default 0, optional)
}}
Use
When given a function of type:
combatTalentScale(t, 4, 15, 0.75, 1, 2, true)
These values map to:
combatTalentScale(t, low, high, power, shift, add)
And 'raw' or 'log' is not currently implemented. t is always the talent level value you want to generate the final result for!
Therefore, we can use the following:
combatTalentScale(t, 4, 15, 0.75, 1, 2) for t=3 is 11.86
Other parameters
x_low is the talent level for which we expect the result to be low, and defaults to 1
x_high is the talent level for which we expect to result to be high, and defaults to 5
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
Input: power(=0), add(=0), shift(=0), x_low (=1), x_high(=5), low, high, (raw or log), t
Psuedo code for m:
- m = (high - low) / ( (x_high+shift)^power - (x_low+shift)^power )
- Expr for m: {{#expr:( ( {{{high|0}}} - {{{low|0}}} )/( ( {{{x_high|5}}} + {{{shift|0}}} )^ {{{power|0.5}}} - ( {{{x_low|1}}} + {{{shift|0}}} )^ {{{power|0.5}}} )) }}
Psuedo code for b:
- b = low - m*(x_low+shift)^power
- Expr for b (unexpanded): {{#expr:{{{low|0}}} - (m)*({{{xlow|1}}}+{{{shift|0}}})^{{{power|0.75}}} }}
- Expr for b (expanded): {{#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}}} }}
Psuedo code for the whole thing:
- Output = m * (t+shift)^power + b + add
- Expr for output (unexpanded): (m)* {{#expr:({{{t|0}}}+{{{shift|0}}})^{{{power|0.5}}} }} + (b) + add
- Expr for output (expanded): {{#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}}} }}
