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MapIndexed

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

MapIndexed[f, expr]
    Applies f to the elements of expr, giving the part specification
    of each element as a second argument to f: {f[e1, {1}],
    f[e2, {2}], ...}.
MapIndexed[f, expr, levelspec]
    Applies f to all parts of expr on the levels specified by
    levelspec:
      n            levels 1 through n
      Infinity     levels 1 through Infinity
      {n}          level n only
      {n1, n2}     levels n1 through n2
    The default is {1}. A positive level n consists of all parts
    specified by n indices; a negative level -n consists of all parts
    with depth n, so level -1 is the atoms. Level 0 is the whole
    expression, whose position is {}.
    The position handed to f is the one Part and Extract take, so
    Extract[expr, #2] is #1. Over an association the position of a
    value is {Key[k]}, and keys are preserved.
    With Heads -> True the function is applied to heads as well, a
    head having index 0 in its position.
    MapIndexed always effectively constructs a complete new expression
    and then evaluates it.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= MapIndexed[f, {10, 20, 30}]
Out[1]= {f[10, {1}], f[20, {2}], f[30, {3}]}

In[2]:= MapIndexed[First[#2] + f[#1] &, {a, b, c, d}]
Out[2]= {1 + f[a], 2 + f[b], 3 + f[c], 4 + f[d]}

In[3]:= MapIndexed[f, {{a, b}, {c, d, e}}, {2}]
Out[3]= {{f[a, {1, 1}], f[b, {1, 2}]}, {f[c, {2, 1}], f[d, {2, 2}], f[e, {2, 3}]}}

In[4]:= MapIndexed[f, {{a, b}, {c, d, {e}}}, {-1}]
Out[4]= {{f[a, {1, 1}], f[b, {1, 2}]}, {f[c, {2, 1}], f[d, {2, 2}], {f[e, {2, 3, 1}]}}}

In[5]:= MapIndexed[f, h0[h1[h2[h3[h4[a]]]]], {2, -3}]
Out[5]= h0[h1[f[h2[f[h3[h4[a]], {1, 1, 1}]], {1, 1}]]]

In[6]:= MapIndexed[f, {a, b}, {0, 1}]
Out[6]= f[{f[a, {1}], f[b, {2}]}, {}]

In[7]:= MapIndexed[f, p[x][a, b, c], Infinity, Heads -> True]
Out[7]= f[f[p, {0, 0}][f[x, {0, 1}]], {0}][f[a, {1}], f[b, {2}], f[c, {3}]]

In[8]:= MapIndexed[f, <|"a" -> 10, "b" -> 20|>]
Out[8]= <|"a" -> f[10, {Key["a"]}], "b" -> f[20, {Key["b"]}]|>

Implementation notes

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References