Apply
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
open all close allBasic Examples (6)
Replace the head of a list with f:
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)
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:
Options (2)
Applications (4)
Properties & Relations (5)
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:
Text
Wolfram Research (1988), Apply, Wolfram Language function, https://reference.wolfram.com/language/ref/Apply.html (updated 2014).
CMS
Wolfram Language. 1988. "Apply." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Apply.html.
APA
Wolfram Language. (1988). Apply. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Apply.html