Lecture 10: Functions in R are objects, just like everything else, and so can be both arguments to and return values of functions, with no special machinery required. Examples from math (especially calculus) of functions with other functions as arguments. Some R syntax relating to functions. Examples with curve. Using sapply to extend functions of single numbers to functions of vectors; its combination with curve. We write functions with lower-level functions as arguments to abstract out a common pattern of operations. Example: calculating a gradient. Numerical gradients by first differences, done two different ways. (Limitations of taking derivatives by first differences.) Incorporating this as a part of a larger algorithm, such as gradient descent. Using adapters, like wrapper functions and anonymous functions, to fit different functions together. Examples from math (especially calculus) of operators, which turn one function into another. The importance of scoping when using functions as return values. Example: creating a linear predictor. Example: implementing the gradient operator (two different ways). Example: writing surface, as a two-dimensional analog to the standard curve. The use of eval and substitute to control when and in what context an expression is evaluated. Three increasingly refined versions of surface, employing eval.
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