Changes between Version 18 and Version 19 of DataParallel/Regular

Timestamp:

01/17/10 21:29:31 (3 years ago)

Author:

gckeller

Comment:

--

DataParallel/Regular

@@ -149 +149 @@
 
 The `map` operation takes a function over element types and applies it to every
-data element of the DArray, which can have arbitrary dimensionality. Note that 
-it is not possible to use this function to apply an operation for example to every
-row or column of a matrix. We will discuss how this can be done later on.
-
-{{{map:: (U.Elt a, U.Elt b, A.Shape dim) =>  (a -> b) -> DArray dim a -> DArray dim b}}}
+data element of the DArray, which can have arbitrary dimensionality.
+{{{
+map:: (U.Elt a, U.Elt b, A.Shape dim) =>  (a -> b) -> DArray dim a -> DArray dim b
+}}}
 
 Similarily, `zip` and `zipWith` apply to every data element in the array as well. Both arguments
@@ -280 +279 @@
 to be done at run time using assertions.
 
+== `Nesting' Array Functions ==
+
+We already introduced the `map` function, which applies a given function to all data elements
+of an array:
+{{{
+map:: (U.Elt a, U.Elt b, A.Shape dim) =>  (a -> b) -> DArray dim a -> DArray dim b
+}}}
+We can't use `map`, however, to apply a function to all columns, rows, or other sub-arrays of 
+a multidimensional array, and generalising `map` to be able to handle this wouldn't make sense
+in this framework. Consider, for example, a function `filter`, which takes a one-dimensional 
+array and creates a new array containing only the even elements of the argument array. If we mapped
+this function over all the rows of a two-dimensional array, the resulting structure would, in general,
+not be a two dimensional array anymore, since each row might potentially have a different length. 
+Therefore, we restrict the class of functions that can be mapped over sub-arrays to functions where 
+the shape of the argument determines the shape of the result. In other words, it can't depend on the data
+values. 
+
+
+
 == Open Questions ==