TargetStructure

TargetStructure

is an option for linear algebra functions that specifies the representation of the result produced by the function.

Details

Examples

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Basic Examples  (3)

An identity matrix:

Return the identity matrix as a structured array instead:

Return the identity matrix as a sparse array:

For IdentityMatrix, the setting Automatic determines the structure based on matrix size:

Scope  (8)

Matrix Constructors  (4)

A rectangular diagonal matrix:

This is equivalent to the explicit setting TargetStructure"Dense":

Return the diagonal matrix as a sparse array:

Return the diagonal matrix as a structured array:

A Hankel matrix:

Return a Hankel matrix as a structured array:

A Cauchy matrix:

Return a Cauchy matrix as a dense matrix:

A Hilbert matrix:

Return the Hilbert matrix as a Cauchy matrix instead:

Return the Hilbert matrix as a Hankel matrix instead:

Matrix Decompositions  (2)

Cholesky decomposition of a Hilbert matrix:

Represent the Cholesky triangle as an UpperTriangularMatrix:

Core-nilpotent decomposition of a matrix, with the core and nilpotent parts in a single matrix:

With TargetStructure"Structured", the core and nilpotent parts are brought together in a BlockDiagonalMatrix:

Other Functions  (2)

A Hilbert matrix:

With TargetStructure"Dense", the function UpperTriangularize returns a dense matrix:

With TargetStructure"Sparse", a sparse array is returned:

With TargetStructure"Structured", a structured array is returned:

With the setting TargetStructureAutomatic, the function LowerTriangularize gives a dense matrix if the input is a dense matrix:

If the input is a sparse array, the result is also a sparse array:

Applications  (3)

Generate a large identity matrix as a dense matrix:

Computing its determinant takes some time:

Generate the identity matrix as a structured matrix:

Computing the determinant of the structured version is faster:

Generate a Fourier matrix as a dense matrix:

Generate a random complex vector:

This multiplies the Fourier matrix and the vector:

Generate the Fourier matrix as a structured matrix:

Multiplication using the structured version is faster:

The results are equivalent:

Generate a Hilbert matrix as a dense matrix:

Generate a random real vector:

Solve a linear system with the Hilbert matrix:

Generate the Hilbert matrix as a Cauchy matrix:

Solving the linear system using the Cauchy version is faster:

Properties & Relations  (4)

The setting TargetStructureAutomatic produces a dense matrix for small dimensions:

A structured array is returned for large dimensions:

The setting TargetStructure"Dense" produces a dense matrix:

The setting TargetStructureNone does the same thing:

The setting TargetStructure"Sparse" produces a sparse array, whenever possible:

The setting TargetStructure"Structured" produces a structured array, whenever possible:

Wolfram Research (2023), TargetStructure, Wolfram Language function, https://reference.wolfram.com/language/ref/TargetStructure.html.

Text

Wolfram Research (2023), TargetStructure, Wolfram Language function, https://reference.wolfram.com/language/ref/TargetStructure.html.

CMS

Wolfram Language. 2023. "TargetStructure." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TargetStructure.html.

APA

Wolfram Language. (2023). TargetStructure. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TargetStructure.html

BibTeX

@misc{reference.wolfram_2024_targetstructure, author="Wolfram Research", title="{TargetStructure}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/TargetStructure.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_targetstructure, organization={Wolfram Research}, title={TargetStructure}, year={2023}, url={https://reference.wolfram.com/language/ref/TargetStructure.html}, note=[Accessed: 21-November-2024 ]}