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CenterArray
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CenterArray

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creates a list of length n with the elements of a at the center and zeros elsewhere.

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CenterArray[a,{n1,n2,…}]

creates an n1×n2×… array with the array a at the center and zeros elsewhere.

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CenterArray[a,nspec,pad]

uses pad instead of zero for the background.

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CenterArray[nspec]

creates an array with a single 1 at the center and zeros elsewhere.

Details

  • The input a can be a list, full array, ragged array, or any form of array, such as a SparseArray object.
  • CenterArray always generates a full array.
  • CenterArray[a,nspec,pad,SparseArray] creates a SparseArray object.
  • CenterArray[expr,…] is equivalent to CenterArray[{expr},…] if expr is not a list.
  • CenterArray[a,n] attempts if possible to put equal padding on both sides of a. If this is not possible, additional padding is placed on the right.
  • In the form CenterArray[a,{n1,n2,…}], any of the ni can be Inherited, in which case it is assumed to be the corresponding dimension of a, and no padding is added at this level.
  • If the resulting array has a higher rank, a is centered at the deepest level.
  • For possible settings of padding value pad, see the reference page for ArrayPad.

Examples

open allclose all

Basic Examples  (3)Summary of the most common use cases

Create a list of length 5 with a single 1 at the center:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-felh2
Out[1]=1

Create a list of length 5 with the specified element at the center:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-oudv4b
Out[1]=1

Place an element at the center of a 2D array:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-mcyxei

Scope  (11)Survey of the scope of standard use cases

Data  (9)

Center a list in a 2D array:

In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-d83lqj

Create a sparse array:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-dxuil4
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-4beo7v

Center a matrix to have 3 rows:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-l8iojr

Center a matrix so its dimensions are {3,4}:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-ki6e1g

Center a ragged array:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-sxgvmk

Center a mixed input:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-56crk4

Create an array with more rows and fewer columns:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-e2i8df

Center a 2D sparse array:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-8hlav7
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-ri110a

Create a 2D sparse array:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-idsv8p
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-bhl3s2

Output Dimensions  (1)

Return a smaller list:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-80nnsl
Out[1]=1

Padding  (1)

The default padding is zero:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-2m5hnq
Out[1]=1

Specify a different padding:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-yu1i6v
Out[1]=1

Use "Extrapolated" padding instead:

In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-s74c1o
Out[2]=2

Applications  (6)Sample problems that can be solved with this function

Crop the center of an array:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-v3kuyb
Out[1]=1

Conform a list of arrays so they have commensurate dimensions:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-t5sgqp
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-ceuxgb
In[3]:=3
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https://wolfram.com/xid/0b8crjyp6y-lupn7n
Out[3]=3

Conform elements of a list so they are all of length 3:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-ipkn8r
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-oshpkn
Out[2]=2

Apply a dimension-sensitive operator to the conformed elements:

In[3]:=3
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https://wolfram.com/xid/0b8crjyp6y-jdjlh4
Out[3]=3

Make a full array from a ragged list of full arrays:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-793c8k
Out[1]=1

Create a sharpening kernel from a lowpass kernel:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-8jcpu6
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-b3bjen

Sharpen an image by convolving with the computed kernel:

In[3]:=3
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https://wolfram.com/xid/0b8crjyp6y-6tg2ey
Out[3]=3

Show a collection of graphs with missing graphics:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-3mkuap
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-f8vzjl
Out[2]=2

By default, GraphicsGrid has empty spaces at the ends:

In[3]:=3
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https://wolfram.com/xid/0b8crjyp6y-eljy58
Out[3]=3

Properties & Relations  (3)Properties of the function, and connections to other functions

If the amount of padding is an odd number, additional padding is placed on the right:

In[3]:=3
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https://wolfram.com/xid/0b8crjyp6y-4ky6dm
Out[3]=3

2D input:

In[4]:=4
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https://wolfram.com/xid/0b8crjyp6y-kmuabf
Out[4]=4

The background value of sparse arrays is preserved, irrespective of the specified padding value:

In[1]:=1
✖
https://wolfram.com/xid/0b8crjyp6y-c7dl46
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-ibjix7
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0b8crjyp6y-rilp2t
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0b8crjyp6y-dndmb8
Out[4]=4

The precision of the result is the minimum of the precisions of the input array and the padding value:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-owf8br
In[2]:=2
✖
https://wolfram.com/xid/0b8crjyp6y-vkhxci
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0b8crjyp6y-mcuuy3
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0b8crjyp6y-yi3uei
Out[4]=4

Possible Issues  (2)Common pitfalls and unexpected behavior

Padding with nonconstant values may not be possible with empty list inputs:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-80p6dy
Out[1]=1

Use constant padding instead:

In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-rb7apf
Out[2]=2

This ragged input cannot be centered because it is not a list of full arrays with the same depths:

In[1]:=1
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https://wolfram.com/xid/0b8crjyp6y-etcv05
In[2]:=2
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https://wolfram.com/xid/0b8crjyp6y-wstysy
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0b8crjyp6y-4haf3h
Out[3]=3

Use a specific target depth instead:

In[4]:=4
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https://wolfram.com/xid/0b8crjyp6y-e9h7jk
Out[4]=4

Center the resulting array in an array of rank 3:

In[5]:=5
✖
https://wolfram.com/xid/0b8crjyp6y-5ekuf9
Out[5]=5
Wolfram Research (2016), CenterArray, Wolfram Language function, https://reference.wolfram.com/language/ref/CenterArray.html.
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Wolfram Research (2016), CenterArray, Wolfram Language function, https://reference.wolfram.com/language/ref/CenterArray.html.

Text

Wolfram Research (2016), CenterArray, Wolfram Language function, https://reference.wolfram.com/language/ref/CenterArray.html.

✖
Wolfram Research (2016), CenterArray, Wolfram Language function, https://reference.wolfram.com/language/ref/CenterArray.html.

CMS

Wolfram Language. 2016. "CenterArray." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CenterArray.html.

✖
Wolfram Language. 2016. "CenterArray." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CenterArray.html.

APA

Wolfram Language. (2016). CenterArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CenterArray.html

✖
Wolfram Language. (2016). CenterArray. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CenterArray.html

BibTeX

@misc{reference.wolfram_2025_centerarray, author="Wolfram Research", title="{CenterArray}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/CenterArray.html}", note=[Accessed: 18-June-2025 ]}

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@misc{reference.wolfram_2025_centerarray, author="Wolfram Research", title="{CenterArray}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/CenterArray.html}", note=[Accessed: 18-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_centerarray, organization={Wolfram Research}, title={CenterArray}, year={2016}, url={https://reference.wolfram.com/language/ref/CenterArray.html}, note=[Accessed: 18-June-2025 ]}

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@online{reference.wolfram_2025_centerarray, organization={Wolfram Research}, title={CenterArray}, year={2016}, url={https://reference.wolfram.com/language/ref/CenterArray.html}, note=[Accessed: 18-June-2025 ]}