Programming with Variable Lengths
UpTo is a symbolic specification that can be used to represent up to a given number of objects or positions. Many functions support this new specification, which makes programming with expressions of variable lengths very easy.
Take up to the first 5 elements of a binary list of unknown size.
In[1]:=
list = RandomInteger[1, RandomInteger[{1, 10}]];
Take[list, UpTo[5]]
Out[1]=
Obtain the 6 most common elements of a list, or as many as there are if fewer.
In[2]:=
Commonest[{b, a, c, 2, a, b, 1, 2}, UpTo[6]]
Out[2]=
Create a ragged partition into blocks of up to 3 elements long, where the last sublists can be shorter.
In[3]:=
Partition[{a, b, c, d, e, f, g}, UpTo[3]]
Out[3]=
In[4]:=
Partition[{a, b, c, d, e, f, g}, UpTo[3], 1]
Out[4]=
Partition an image so that lengths are up to 36 pixels and heights are up to 28 pixels.
In[5]:=
img = \!\(\*
GraphicsBox[
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"], {{0, 122}, {150,
0}}, {0, 255},
ColorFunction->RGBColor],
BoxForm`ImageTag[
"Byte", ColorSpace -> "RGB", ImageSize -> All,
Interleaving -> True],
Selectable->False],
BaseStyle->"ImageGraphics",
ImageSize->Automatic,
ImageSizeRaw->{150, 122},
PlotRange->{{0, 150}, {0, 122}}]\)
Out[5]=
In[6]:=
ImagePartition[img, {UpTo[36], UpTo[28]}] // Grid
Out[6]=