Dimensions

Dimensions[expr]

gives a list of the dimensions of expr.

Dimensions[expr,n]

gives a list of the dimensions of expr down to level n.

Details and Options

  • expr must be a full array, with all the pieces of expr at a particular level having the same length. (The elements of expr can then be thought of as filling up a hyper‐rectangular region.)
  • For special array objects like SparseArray, NumericArray and QuantityArray, Dimensions yields the dimensions of the corresponding ordinary lists.
  • The following options can be given:
  • AllowedHeads Automaticwhat heads to allow at each level of the array
  • Settings for the AllowedHeads option include:
  • Automaticdefault settings
    Inheritedallow only Head[expr] at any level
    hallow only head h at any level
    {h1,…}allow any of h1,… at different levels
    h1|h2|…allow the hi at the same or different levels
    Allallow any head at different levels
    "ListLike"allow List and related heads
    Fullallow any head at any level
  • The setting AllowedHeads"ListLike" allows all heads recognized by ArrayQ, which include List, SparseArray and structured array heads like QuantityArray and SymmetrizedArray.
  • With the default setting AllowedHeads->Automatic, successive levels in expr must have the same head, except that ordinary lists, sparse arrays and structured arrays are considered the same head.

Examples

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Basic Examples  (1)

Find the dimensions of a matrix:

Scope  (5)

Dimensions counts only dimensions at which an expression is not "ragged":

Dimensions works with arrays of any depth:

Give dimensions only down to level 2:

Dimensions works with special array types, including SparseArray objects:

SymmetrizedArray objects:

NumericArray objects:

Find the dimensions of a matrix that is a mixture of List and different special array heads:

Dimensions works with any head, not just List:

Options  (4)

AllowedHeads  (4)

Only consider nested expressions with head List:

By default, rectangular nested expressions with any head are considered arrays:

Allow lists and numeric arrays at different levels:

Different heads cannot be mixed at the same level:

Allow a mixture of both heads at the same level:

Allow List as well as other general array representations:

Only allow the head List:

Both settings disallow general heads:

Allow any head at each level of the array:

An array has a consistent head at each level:

Completely ignore heads, looking only at the tree structure of the expression:

Applications  (2)

Create a version of MatrixQ that only accepts list matrices:

Create several expressions to test:

The function matrixQ gives True only for listMat, which both is a matrix and has head List:

MatrixQ gives True for matrices of any known array type:

Find dimensions of regions filled by 10 steps of cellular automaton evolution:

Properties & Relations  (7)

Dimensions always returns a list:

The default value of the option AllowedHeads allows mixtures of list, sparse and structured arrays:

It also allows any single head at successive levels:

Use AllowedHeads"ListLike" to allow any list-like array while excluding other heads:

VectorQ, MatrixQ and ArrayQ effectively use AllowedHeads"ListLike":

The setting AllowedHeads"ListLike" does not include ByteArray and NumericArray:

Combine "ListLike" with the additional heads to allow the combination:

Length[Dimensions[expr]] equals ArrayDepth[expr]:

Dimensions[Array[h,dims]] gives dims:

If Dimensions[expr] is non-empty, its first element equals Length[expr]:

Possible Issues  (1)

Numeric expressions report dimensions based of the structure of their FullForm:

To treat all numeric expressions as scalars, use the setting List or "ListLike" for AllowedHeads:

Wolfram Research (1988), Dimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/Dimensions.html (updated 2020).

Text

Wolfram Research (1988), Dimensions, Wolfram Language function, https://reference.wolfram.com/language/ref/Dimensions.html (updated 2020).

CMS

Wolfram Language. 1988. "Dimensions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/Dimensions.html.

APA

Wolfram Language. (1988). Dimensions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Dimensions.html

BibTeX

@misc{reference.wolfram_2022_dimensions, author="Wolfram Research", title="{Dimensions}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/Dimensions.html}", note=[Accessed: 03-June-2023 ]}

BibLaTeX

@online{reference.wolfram_2022_dimensions, organization={Wolfram Research}, title={Dimensions}, year={2020}, url={https://reference.wolfram.com/language/ref/Dimensions.html}, note=[Accessed: 03-June-2023 ]}