The key function contains two parameters, the scale and the shape, and so the gradient is two-dimensional. Current implementation assumes that scaled dist is x/scale, not x/width
keyfct.grad.hz(distance, key.scale, key.shape, shape = FALSE)matrix of derivatives of the hazard rate key function w.r.t. the scale parameter and the shape parameter.
perpendicular distance vector
vector of scale values
vector of shape values
is the gradient parameter the shape parameter? Defaults to FALSE
d key / d scale = (shape * exp(-(1/ (x/scale) ^ shape)) / ((x/scale) ^ shape ) * scale) d key / d shape = - ((log(x / scale) * exp(-(1/ (x/scale) ^ shape))) / (x/scale) ^ shape)
When distance = 0, the gradients are also zero. However, the equation below will result in NaN and (-)Inf due to operations such as log(0) or division by zero. We correct for this in line 33.