Apply

f@@expr or Apply[f,expr]

replaces the head of expr by f.

Apply[f,expr,levelspec]

replaces heads in parts of expr specified by levelspec.

Apply[f]

represents an operator form of Apply that can be applied to an expression.

Details and Options

Apply uses standard level specifications:
n levels 1 through n

Infinity levels 1 through Infinity

{n} level n only

{n₁,n₂} levels n₁ through n₂
The default value for levelspec in Apply is {0}.
Apply[f,expr,{1}] is equivalent to MapApply[f,expr] or f@@@expr. »
A positive level n consists of all parts of expr specified by n indices.
A negative level -n consists of all parts of expr with depth n.
Level -1 consists of numbers, symbols, and other objects that do not have subparts.
Level 0 corresponds to the whole expression.
With the option setting Heads->True, Apply will apply inside the heads of parts in addition to the parts themselves. »
Apply always effectively constructs a complete new expression and then evaluates it.
Apply operates on SparseArray objects and structured arrays just as it would on the corresponding ordinary lists. »
Apply on Association objects operates on values only. »
Apply[f][expr] is equivalent to Apply[f,expr].
Parallelize[Apply[f,expr,levelspec]] computes Apply[f,expr,levelspec] in parallel on all subkernels. »

Examples

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Basic Examples (6)

Replace the head of a list with f:

Equivalently:

Sum a list by replacing the head with Plus:

Apply gets rid of a level of lists:

Use the operator form of Apply:

Applying f to an Association keeps only values:

Applying a List to an Association is equivalent to Values:

Scope (15)

Level Specifications (10)

Apply at level 0 (default):

Apply at level 1:

Apply at levels 0 and 1:

Apply down to level 2 (excluding level 0):

Apply at levels 0 through 2:

Apply at all levels, starting at level 1:

Apply also at level 0:

Negative levels:

Positive and negative levels can be mixed:

Different heads at each level:

Apply also inside heads at the levels specified:

Types of Expressions (5)

Apply works with any head, not just List:

Apply works on sparse arrays:

Use Apply with structured arrays, such as SymmetrizedArray:

Use Apply to apply a function to the rows of a structured array of type QuantityArray:

Apply f at the second level of an association; the association head is kept:

Apply f at several levels:

Options (2)

Heads (2)

Apply inside heads as well as arguments:

The option has no effect if including level zero:

Applications (4)

Display the factorization of an integer using superscripts:

Create a table from a list of range specifications:

Turn a function that takes several arguments into one that takes a list of arguments:

Find random co-prime integers:

Properties & Relations (6)

Leaves are visited before roots:

Total does effectively the same thing as applying Plus to a list:

Using ## in a pure function has the same effect as using Apply:

Three ways to apply a function at level 1:

Using Map:

Using MapApply:

Ordinary function application takes the list as a single argument:

Apply takes the elements of the list as separate arguments:

Compute Apply in parallel:

Possible Issues (1)

Applying to atomic objects that do not have subparts effectively does nothing:

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Apply

Details and Options

Examples

Basic Examples (6)