Creation of temporary copies of arrays when using x[[a]]=b

*To*: mathgroup at smc.vnet.net*Subject*: [mg80869] Creation of temporary copies of arrays when using x[[a]]=b*From*: andrew.j.moylan at gmail.com]*Date*: Tue, 4 Sep 2007 06:35:41 -0400 (EDT)

Please consider this input, which creates a large array of real numbers, and then changes one element of that array, and tracks the memory used by this process: $HistoryLength = 0; Print[{MemoryInUse[], MaxMemoryUsed[]}]; Module[ {x}, x = RandomReal[1, {1000000}]; Print[{MemoryInUse[], MaxMemoryUsed[]}]; x[[2345]] = 5.6; Print[{MemoryInUse[], MaxMemoryUsed[]}]; ]; Print[{MemoryInUse[], MaxMemoryUsed[]}]; Here is the output (on my machine): {5812072,5837352} {13812760,13812920} {13812776,21813128} {5810712,21813128} The second line of output shows that the code "x = RandomReal[1, {1000000}];" used 8MB of memory, as expected for 1000000 real numbers. The third line of output shows that the code x[[2345]]=5.6 uses *another* 8MB of memory, temporarily. Presumably this is because x[[a]]=b is equivalent to x=ReplacePart[x,a->b], which would result in the temporary creation of the 8MB object ReplacePart[x,a->b]. Question 1. Can anyone confirm that these are equivalent? Because of this, an algorithm that relies on repeatedly changing single elements of a large list by using x[[a]]=b is very slow. Question 2. What is the simplest way to have lists for which the reassignment of a single element is efficient? Is an external package necessary, or can the built-in Mathematica functions be used for this purpose? I note that if you take the input and enclose it in Compile[{},...][], then then output becomes: {5840208,5864960} {13840296,13840440} {13840296,13840648} {13840296,13840648} No temporary 8MB array is created in this case. However, I can only make this work when x is defined *inside* the compiled function. If I move the definition of x outside Compile[], then temporary objects are created again. Question 3. Is there a more comprehensive set of documentation for Compile than that found in the Mathematica documentation centre? I would like to know the answer to questions like: How does Compile decide what assumptions to make about the types of expressions found in the code to be compiled?