Robert Smith avatar Robert Smith committed 9bf14e9

give example of derivative computation using dual numbers

Comments (0)

Files changed (1)

       (dual (expt a b)
             (+ (* p b (expt a (1- b)))  ; Factor out aᵇ?
                (* q (log a) (expt a b)))))))
+
+;;; To evaluate the derivative of f at x, compute f(〈x, 1〉) and the
+;;; result will be 〈f(x), f′(x)〉.
+;;; 
+;;; For example, √sin(x) can be computed by
+
+#+#:example
+(defun sqrt-sin (x)
+  (dual-sqrt (dual-sin (dual x 1))))
+
+;;; The derivative at x=3 is -1.317... and our computation gives...
+;;; 
+;;;   CL-USER> (sqrt-sin 3.0)
+;;;   #<0.37565944 - 1.3176728ε>
Tip: Filter by directory path e.g. /media app.js to search for public/media/app.js.
Tip: Use camelCasing e.g. ProjME to search for ProjectModifiedEvent.java.
Tip: Filter by extension type e.g. /repo .js to search for all .js files in the /repo directory.
Tip: Separate your search with spaces e.g. /ssh pom.xml to search for src/ssh/pom.xml.
Tip: Use ↑ and ↓ arrow keys to navigate and return to view the file.
Tip: You can also navigate files with Ctrl+j (next) and Ctrl+k (previous) and view the file with Ctrl+o.
Tip: You can also navigate files with Alt+j (next) and Alt+k (previous) and view the file with Alt+o.