54 lines
1.8 KiB
Factor
54 lines
1.8 KiB
Factor
USING: help.markup help.syntax ;
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IN: math.derivatives
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HELP: derivative ( x function -- m )
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{ $values { "x" "a position on the function" } { "function" "a differentiable function" } }
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{ $description
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"Approximates the slope of the tangent line by using Ridders' "
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"method of computing derivatives, from the chapter \"Accurate computation "
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"of F'(x) and F'(x)F''(x)\", from \"Advances in Engineering Software, Vol. 4, pp. 75-76 ."
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}
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{ $examples
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{ $example
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"USING: math.derivatives prettyprint ;"
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"[ sq ] 4 derivative ."
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"8"
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}
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{ $notes
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"For applied scientists, you may play with the settings "
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"in the source file to achieve arbitrary accuracy."
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}
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} ;
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HELP: fast-derivative ( x function -- m )
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{ $values { "x" "a x-position on the function" } { "function" "a differentiable function" } }
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{ $description
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"Approximates the slope of the tangent line of the provided function "
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"by using a secant line with very near points. This implementation is "
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"naive and is only provided because it is used in the much more "
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"accurate " { $link derivative } " word. Use this word if accuracy "
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"is of no importance."
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} ;
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HELP: derivative-func ( function -- der )
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{ $values { "func" "a differentiable function" } { "der" "the derivative" } }
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{ $description
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"Provides the derivative of the function. The implementation simply "
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"attaches the " { $link derivative } " word to the end of the function."
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}
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{ $examples
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{ $example
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"USING: math.derivatives prettyprint ;"
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"[ sq ] derivative-func ."
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"[ [ sq ] derivative ]"
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}
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} ;
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ARTICLE: "derivatives" "The Derivative Toolkit"
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"A toolkit for computing the derivative of functions."
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{ $subsection derivative }
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{ $subsection derivative-func }
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{ $subsection fast-derivative } ;
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ABOUT: "derivatives"
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