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"SparseArray" (Compiled Type)

"SparseArray"::[type,rank]

represents a sparse array composite type with elements of specified type and rank.

Details

  • "SparseArray" can be used in Typed and related constructs to specify a type.
  • "SparseArray" objects are automatically memory managed.

Properties

  • With "SparseArray"::[type, rank], unspecified values are always taken to be zero and rank can only be 1 or 2.

Expression Conversions

    From Expressions

  • SparseArray expressions can be converted into compiled code elements with types created with "SparseArray".

    • To Expressions

  • Compiled code elements with types created with "SparseArray" can be converted into SparseArray expressions.

Examples

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

"SparseArray" can be used as an input and output from a CompiledCodeFunction:

In[1]:=1
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-ck3oom
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-fgxe20
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-b7fs2j

Scope  (1)Survey of the scope of standard use cases

SparseArray properties may be used within CompiledCodeFunction:

In[1]:=1
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-fyv32h
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-dr9s82
Out[2]=2

This is equivalent to the "Density" property:

In[3]:=3
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-dp96x
Out[3]=3

The function uses real arithmetic so that it works even when the total number of elements is too large for a machine-sized integer:

In[4]:=4
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-fydpro
Out[4]=4

Neat Examples  (1)Surprising or curious use cases

Compute a power series of a sparse matrix:

In[1]:=1
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-ctj6i5
Out[1]=1

This is equivalent to computing the square of a matrix:

In[2]:=2
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-dn18yk
Out[2]=2

Generate coefficients of the exponential function and use them to compute a matrix exponential:

In[3]:=3
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-mxskj3
Out[3]=3

The MatrixExp function is a better way to compute the exponential, but the power series result was close:

In[4]:=4
✖
https://wolfram.com/xid/0kxwryfilf5dyctojyjol8sgq-025noh
Out[4]=4