The diff function accomplishes the equivalent of numerical differentiation on equally spaced values (up to a constant factor) so finding maximum (or minimum) values can be used to identify location of steepest ascent (or descent):
z <- exp(-seq(0,3, by=0.1)^2 )
plot(z)
plot(diff(z))
z[ which(abs(diff(z))==max(abs(diff(z))) )]
# [1] 0.6126264
# could have also tested for min() instead of max(abs())
plot(z)
abline( v = which(abs(diff(z))==max(abs(diff(z))) ) )
abline( h = z[which(abs(diff(z))==max(abs(diff(z))) ) ] )
With an x-difference of 1, the slope is just the difference at that point:
diff(z) [ which(abs(diff(z))==max(abs(diff(z))) ) ]
[1] -0.08533397
... but I question whether that is really of much interest. I would have thought that getting the index (which would be the melting point subject to an offset) would be the value of interest.
