PadLeft

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`PadLeft`

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PadLeft[list,n]

makes a list of length n by padding list with zeros on the left.

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PadLeft[list,n,x]

pads by repeating the element x.

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PadLeft[list,n,{x₁,x₂,…}]

pads by cyclically repeating the elements x_i.

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PadLeft[list,n,padding,m]

leaves a margin of m elements of padding on the right.

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PadLeft[list,{n₁,n₂,…}]

makes a nested list with length n_i at level i.

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PadLeft[list]

pads a ragged array list with zeros to make it full.

Details

PadLeft[list,n,…] always returns a list of length n, except in some special cases where padding is {}.
With padding {x₁,x₂,…,x_s}, cyclic repetitions of the x_i are effectively laid down and then the list is superimposed on top of them, with the last element of the list lying on an occurrence of x_s. »
PadLeft[list,n,padding,-m] truncates the last m elements of list.
A margin of Round[(n-Length[list])/2] effectively centers list.
PadLeft[list,n,list] effectively treats list as cyclic.
PadLeft[list,n,{xlist}] can be used to repeat an individual element that is itself a list.
PadLeft[{},n,{x₁,x₂,…}] repeats the sequence of x_i as many times as fit in a list of length n.
PadLeft[list,{n₁,n₂,…}] creates a full array with dimensions {n₁,n₂,…} even if list is ragged. »
PadLeft[list,Automatic,x] pads with x to make a full array.
Negative n_i specify to pad on the right.
PadLeft[list,{n₁,n₂},{{x₁₁,x₁₂,…},{x₂₁,…},…}] pads by repeating the block of x_ij.
PadLeft[list,{n₁,n₂,…},list] effectively treats list as cyclic in every dimension.
PadLeft[list,{n₁,n₂,…},padding,{m₁,m₂,…}] uses margin m_i at level i.
The object list need not have head List.
PadLeft can be used on SparseArray objects.

Examples

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Basic Examples (6)Summary of the most common use cases

Pad with 0 to make the list be of length 10:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-kfw

Out[1]=1

Pad with x:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-pmf

Out[1]=1

Pad by repeating {x,y,z}:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-uv3

Out[1]=1

Leave margin 2 on the right:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-y4l

Out[1]=1

Pad to make a 3×5 array:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-omm

Pad to make a full array:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-zaz

Scope (3)Survey of the scope of standard use cases

Negative length specifications pad on the right:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-qwt

Out[1]=1

Lay down repetitions of the padding, then superimpose the original array:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-tld

Use different margins for rows and columns:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-qi1

Generalizations & Extensions (1)Generalized and extended use cases

Use a head other than List:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-ubl

Out[1]=1

Applications (3)Sample problems that can be solved with this function

Put a 1 at the center of a list of 0s:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-uy9

Out[1]=1

Pad digit lists to be the same length:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-yk5

Out[1]=1

Lay out an array of tiles:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-cwe

Out[1]=1

Properties & Relations (1)Properties of the function, and connections to other functions

PadLeft[list,n] and PadRight[list,n] pad to make a list of length n:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-kqmb9k

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0tzuc5u6-c3x83m

Out[2]=2

ArrayPad[list,n] pads with n additional elements on each side:

In[3]:=3

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https://wolfram.com/xid/0tzuc5u6-bhmmq

Out[3]=3

Possible Issues (1)Common pitfalls and unexpected behavior

Pad with an element that is itself a list:

In[1]:=1

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https://wolfram.com/xid/0tzuc5u6-t6p

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0tzuc5u6-h3r

Out[2]=2

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