ColumnwiseValue

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`ColumnwiseValue`

New in 14.2[Experimental]

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ColumnwiseValue[cbody]

denotes that cbody, a part of the body of a function, will be evaluated once in columnwise form before using that function to transform rows in TransformColumns or ConstructColumns operations.

Details

ColumnwiseValue is typically used as part of the Function body of the transformations performed on tabular data, to precompute some partial results.
When transforming a Tabular object tab with Function[head[…,ColumnwiseValue[cbody],…]], any instances of #col in cbody will be replaced with the entire column tab[[All,col]] and then evaluated to get the value cval. The transformation function becomes Function[head[…,cval,…]].

Examples

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Basic Examples (1)Summary of the most common use cases

Compute the mean of a column and subtract it from all the entries of that column:

In[1]:=1

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https://wolfram.com/xid/0v5mv0udffube-2o9k85

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0v5mv0udffube-t03oys

Out[2]=2

Scope (2)Survey of the scope of standard use cases

Use ColumnwiseValue to subtract the mean of a column from its values:

In[1]:=1

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https://wolfram.com/xid/0v5mv0udffube-sxnuzz

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0v5mv0udffube-cg0m4r

Out[2]=2

This is equivalent to first computing the mean value once and then subtracting it in every row:

In[3]:=3

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https://wolfram.com/xid/0v5mv0udffube-b8tieg

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0v5mv0udffube-jcvhqu

Out[4]=4

Find which elements in a column are above the median:

In[1]:=1

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https://wolfram.com/xid/0v5mv0udffube-gap13g

Out[1]=1

Include a constant column with the median value:

In[2]:=2

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https://wolfram.com/xid/0v5mv0udffube-d5mt8y

Out[2]=2

Compute the median only once by using the operator form:

In[3]:=3

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https://wolfram.com/xid/0v5mv0udffube-b3ac3u

Out[3]=3

Applications (1)Sample problems that can be solved with this function

Take a Tabular object of numbers:

In[1]:=1

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https://wolfram.com/xid/0v5mv0udffube-45kiln

Out[1]=1

Standardize the "obs" column by acting on the column as a whole:

In[2]:=2

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https://wolfram.com/xid/0v5mv0udffube-02lo8m

Out[2]=2

Properties & Relations (2)Properties of the function, and connections to other functions

Use ColumnwiseThread to compute a vector-valued transformation of an entire column:

In[1]:=1

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https://wolfram.com/xid/0v5mv0udffube-ki8x4y

Out[2]=2

With ColumnwiseValue, you get the same list for each row:

In[3]:=3

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https://wolfram.com/xid/0v5mv0udffube-d1tcxw

Out[3]=3

Take a Tabular object:

In[1]:=1

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https://wolfram.com/xid/0v5mv0udffube-bbmm5q

Out[1]=1

TransformColumns by default operates sequentially on each row:

In[2]:=2

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https://wolfram.com/xid/0v5mv0udffube-8poffd

Out[2]=2

TransformColumns with ColumnwiseValue[expr] evaluates expr once first, then acts on each row:

In[3]:=3

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https://wolfram.com/xid/0v5mv0udffube-p36zm8

Out[3]=3

TransformColumns with ColumnwiseThread[expr] evaluates expr once, acting on whole columns:

In[4]:=4

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https://wolfram.com/xid/0v5mv0udffube-6b2fjx

Out[4]=4

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