--- title: "UpTo" language: "en" type: "Symbol" summary: "UpTo[n] represents up to n objects or positions. If n objects or positions are available, all are used. If fewer are available, only those available are used." keywords: - up to - at most - not more than - with limit - not beyond canonical_url: "https://reference.wolfram.com/language/ref/UpTo.html" source: "Wolfram Language Documentation" related_guides: - title: "Graphics Shape & Size" link: "https://reference.wolfram.com/language/guide/GraphicsShapeAndSize.en.md" - title: "Elements of Lists" link: "https://reference.wolfram.com/language/guide/ElementsOfLists.en.md" related_functions: - title: "Take" link: "https://reference.wolfram.com/language/ref/Take.en.md" - title: "Drop" link: "https://reference.wolfram.com/language/ref/Drop.en.md" - title: "Partition" link: "https://reference.wolfram.com/language/ref/Partition.en.md" - title: "RandomSample" link: "https://reference.wolfram.com/language/ref/RandomSample.en.md" - title: "StringTake" link: "https://reference.wolfram.com/language/ref/StringTake.en.md" - title: "ImageTake" link: "https://reference.wolfram.com/language/ref/ImageTake.en.md" - title: "ImageSize" link: "https://reference.wolfram.com/language/ref/ImageSize.en.md" - title: "Eigenvalues" link: "https://reference.wolfram.com/language/ref/Eigenvalues.en.md" - title: "Min" link: "https://reference.wolfram.com/language/ref/Min.en.md" --- # UpTo UpTo[n] represents up to n objects or positions. If n objects or positions are available, all are used. If fewer are available, only those available are used. ## Details * ``UpTo`` is used in functions such as ``Take``, ``Partition`` and ``Eigenvalues`` that require or allow requesting a specific number of elements to use or return. ## Examples (16) ### Basic Examples (7) Take up to the number of elements available: ```wl In[1]:= Take[{a, b, c, d}, UpTo[6]] Out[1]= {a, b, c, d} In[2]:= Take[{a, b, c, d}, UpTo[2]] Out[2]= {a, b} ``` --- Drop up to the number of elements available: ```wl In[1]:= Drop[{a, b, c, d}, UpTo[6]] Out[1]= {} ``` --- Take up to the number of elements available, dropping what remains, if anything: ```wl In[1]:= TakeDrop[{a, b, c, d}, UpTo[6]] Out[1]= {{a, b, c, d}, {}} ``` --- Partition into blocks that are up to 3 elements long; the last block is shorter: ```wl In[1]:= Partition[Range[10], UpTo[3]] Out[1]= {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10}} ``` --- Give the 10 most common elements, or as many as are available: ```wl In[1]:= Commonest[RandomInteger[{0, 5}, 15], UpTo[10]] Out[1]= {5, 4, 0, 1, 2, 3} ``` --- Give the order of the 10 smallest elements, or as many as are available: ```wl In[1]:= Ordering[RandomInteger[{0, 5}, 5], UpTo[10]] Out[1]= {2, 5, 1, 3, 4} ``` --- Give the maximum height and width of a graphic: ```wl In[1]:= Table[Graphics[Circle[], Background -> LightGreen, ImageSize -> UpTo[100], AspectRatio -> n], {n, {0.5, 1, 2}}] Out[1]= {[image], [image], [image]} ``` ### Scope (7) Take up to 20 characters from a string: ```wl In[1]:= StringTake["abcdefghijklm", UpTo[20]] Out[1]= "abcdefghijklm" ``` --- Find the 4 largest eigenvalues in a matrix, or as many as there are if fewer: ```wl In[1]:= Eigenvalues[Table[N[1 / (i + j + 1)], {i, 3}, {j, 3}], UpTo[4]] Out[1]= {0.657051, 0.0189263, 0.000212737} ``` --- Create a "ragged" partition where last elements can be shorter: ```wl In[1]:= Partition[{a, b, c, d, e, f, g}, UpTo[3]] Out[1]= {{a, b, c}, {d, e, f}, {g}} In[2]:= Partition[{a, b, c, d, e, f, g}, UpTo[3], 1] Out[2]= {{a, b, c}, {b, c, d}, {c, d, e}, {d, e, f}, {e, f, g}, {f, g}, {g}} ``` --- Obtain the 6 most common elements, or as many as there are if fewer: ```wl In[1]:= Commonest[{b, a, c, 2, a, b, 1, 2}, UpTo[6]] Out[1]= {b, a, c, 2, 1} ``` --- Generate a random sample of up to 6 elements, or as many as there are if fewer: ```wl In[1]:= RandomSample[Range[5], UpTo[6]] Out[1]= {4, 5, 3, 2, 1} ``` --- Obtain the first 4 minimal elements, or as many as are available: ```wl In[1]:= MinimalBy[{{a, 1}, {b, 1}, {b, 3}}, First, UpTo[4]] Out[1]= {{a, 1}, {b, 1}, {b, 3}} ``` --- Partition an image so that lengths are up to 36 pixels and heights are up to 28 pixels: ```wl In[1]:= Grid[ImagePartition[[image], {UpTo[36], UpTo[28]}]] Out[1]= | | | | | | | ------- | ------- | ------- | ------- | ------- | | [image] | [image] | [image] | [image] | [image] | | [image] | [image] | [image] | [image] | [image] | | [image] | [image] | [image] | [image] | [image] | | [image] | [image] | [image] | [image] | [image] | | [image] | [image] | [image] | [image] | [image] | ``` ### Properties & Relations (2) ``Cases`` behaves as though it implicitly uses ``UpTo`` : ```wl In[1]:= Cases[{1, "f", g, "h", "j"}, _ ? StringQ, 1, 4] Out[1]= {"f", "h", "j"} ``` You can give an explicit ``UpTo`` specification to ``Cases`` : ```wl In[2]:= Cases[{1, "f", g, "h", "j"}, _ ? StringQ, 1, UpTo[4]] Out[2]= {"f", "h", "j"} ``` --- ``ImageTake`` behaves as though it implicitly uses ``UpTo`` : ```wl In[1]:= i1 = ImageTake[[image], 200] Out[1]= [image] ``` You can give an explicit ``UpTo`` specification to ``ImageTake`` : ```wl In[2]:= i2 = ImageTake[[image], UpTo[200]] Out[2]= [image] In[3]:= i1 === i2 Out[3]= True ``` ## See Also * [`Take`](https://reference.wolfram.com/language/ref/Take.en.md) * [`Drop`](https://reference.wolfram.com/language/ref/Drop.en.md) * [`Partition`](https://reference.wolfram.com/language/ref/Partition.en.md) * [`RandomSample`](https://reference.wolfram.com/language/ref/RandomSample.en.md) * [`StringTake`](https://reference.wolfram.com/language/ref/StringTake.en.md) * [`ImageTake`](https://reference.wolfram.com/language/ref/ImageTake.en.md) * [`ImageSize`](https://reference.wolfram.com/language/ref/ImageSize.en.md) * [`Eigenvalues`](https://reference.wolfram.com/language/ref/Eigenvalues.en.md) * [`Min`](https://reference.wolfram.com/language/ref/Min.en.md) ## Related Guides * [Graphics Shape & Size](https://reference.wolfram.com/language/guide/GraphicsShapeAndSize.en.md) * [Elements of Lists](https://reference.wolfram.com/language/guide/ElementsOfLists.en.md) ## History * [Introduced in 2015 (10.3)](https://reference.wolfram.com/language/guide/SummaryOfNewFeaturesIn103.en.md)