I have two positive-valued vectors x,y of the same length in R. Using plot(x, y, "l",...), gives me a continuous line plot in 2 dimensions out of my finite vectors x and y. Is there a way to compute a definite integral over some range of this line plot in R?
edit1: I've looked into the integrate function in R. I'm not sure however how to make a function out of two vectors to pass to it, as my vectors are both finite.
edit2: For some more background, The length of x and y ~ 10,000. I've written a function to find periods, [xi, xj], of abnormalities in the data I'm observing. For each of these abnormalities, I've used plot to see what's going on in these snippets of my data. Now i need to compute statistics concerning the values of the integrals in these abnormal periods, so I'm trying to get as accurate as a number as possible to match with my graphs. X is a time variable, and I've taken very fine intervals of time.
The approxfun function will take 2 vectors and return a function that gives the linear interpolation between the points. This can then be passed to functions like integrate. The splinefun function will also do interpolation, but based on a spline rather than piecewise linear.
In the piecewise linear case the integral will just be the sum of the trapezoids, it may be faster/simpler to just sum the areas of the trapezoids (the width, difference in x's