2.2.3 Applying Functions to Lists and Other ExpressionsIn an expression like f[{a, b, c}] you are giving a list as the argument to a function. Often you need instead to apply a function directly to the elements of a list, rather than to the list as a whole. You can do this in Mathematica using Apply. | This makes each element of the list an argument of the function f. | |
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Apply[f, {a, b, c}]
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| This gives Plus[a, b, c] which yields the sum of the elements in the list. | |
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Apply[Plus, {a, b, c}]
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| Here is the definition of the statistical mean, written using Apply. | |
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mean[list_] := Apply[Plus, list] / Length[list]
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| Apply[f, {a, b, ... }] | apply f to a list, giving f[a, b, ... ] | | Apply[f, expr] or f @@ expr | apply f to the top level of an expression | | Apply[f, expr, {1}] or f @@@ expr | apply f at the first level in an expression | | Apply[f, expr, lev] | apply f at the specified levels in an expression |
Applying functions to lists and other expressions. | What Apply does in general is to replace the head of an expression with the function you specify. Here it replaces Plus by List. | |
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Apply[List, a + b + c]
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| Here is a matrix. | |
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m = {{a, b, c}, {b, c, d}}
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| Using Apply without an explicit level specification replaces the top-level list with f. | |
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| This applies f only to parts of m at level 1. | |
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| This applies f at levels 0 through 1. | |
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Apply[f, m, {0, 1}]
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