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Create a list from a function—Wolfram Documentation

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• See Also
  • Table
  • ConstantArray
  • SparseArray
  • Grid
  • ArrayPlot
  • Tuples
  • ArrayFlatten
• Related Guides
  • Constructing Matrices
  • Constructing Lists
  • Tensors
  • Operations on Vectors
  • List Manipulation
  • Handling Arrays of Data
  • Language Overview
  • Creating & Importing Signals
• Workflows
  • Create a Matrix
  • Make a Grid of Output Data
• Tech Notes
  • Vectors and Matrices
  • Tensors

Array[f,n]

generates a list of length n, with elements f[i].

Array[f,n,r]

generates a list using the index origin r.

Array[f,n,{a,b}]

generates a list using n values from a to b.

Array[f,{n₁,n₂,…}]

generates an n₁×n₂×… array of nested lists, with elements f[i₁,i₂,…].

Array[f,{n₁,n₂,…},{r₁,r₂,…}]

generates a list using the index origins r_i (default 1).

Array[f,{n₁,n₂,…},{{a₁,b₁},{a₂,b₂},…}]

generates a list using n_i values from a_i to b_i.

Array[f,dims,origin,h]

uses head h, rather than List, for each level of the array.

Generate a 3×2 array:

Generate a 3×4 array:

Use index origin 0 instead of 1:

Start with indices 0 and 4 instead of 1:

Sample between 0 and 1:

Use ranges {-1/2,1/2} and {0,1}:

Create a 3×2 array using an indexed symbol:

Create a 4×4 array using a subscript:

Create a Hilbert matrix:

Use named function slots:

Compare with the built-in function:

Create a constant array:

Use ## to pick up a sequence of indices:

Create a 1D array:

Create a 1D array, starting the indices at 0:

Create a 3×2 array:

Create a 4×3×2 array with index-dependent origins:

Use a non-default head for each level of the array:

Use Plus instead of List to combine elements:

Any symbol with attribute Flat would produce the same shape:

Totally antisymmetric tensor:

Compare with the built-in LeviCivitaTensor:

Lower-triangular matrix:

Matrix with generic symbolic entries:

Use it to see the effects of some linear algebra functions:

Sample a function uniformly on an interval:

ConstantArray[c,dims] and Array[c&,dims] are equivalent:

When c is a machine number, ConstantArray is much faster for large arrays:

Array[f,dims] can be generated using Table:

Set up the Table limit specifications:

Use Apply to splice them into a Table command:

The result is identical to the array generated using Array:

SparseArray[{i_,j_}->f[i,j],dims] gives a sparse representation of Array[f,dims]:

The results are Equal:

The objects are not identical, but the represented arrays are:

Compute Array in parallel:

Array of powers:

Array of GCDs:

Array of arrays:

Introduced in 1988 (1.0) | Updated in 1999 (4.0) ▪ 2000 (4.1) ▪ 2002 (4.2) ▪ 2012 (9.0)

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