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Sparse Matrices

Elementary sparse matrices, reordering algorithms, iterative methods, sparse linear algebra

Sparse matrices provide efficient storage of double or logical data that has a large percentage of zeros. While full (or dense) matrices store every single element in memory regardless of value, sparse matrices store only the nonzero elements and their row indices. For this reason, using sparse matrices can significantly reduce the amount of memory required for data storage.

All MATLAB® built-in arithmetic, logical, and indexing operations can be applied to sparse matrices, or to mixtures of sparse and full matrices. Operations on sparse matrices return sparse matrices and operations on full matrices return full matrices. For more information, see Ventajas computacionales de matrices escasas and Construyendo matrices escasas.

Funciones

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spallocAllocate space for sparse matrix
spdiagsExtract and create sparse band and diagonal matrices
speyeSparse identity matrix
sprandSparse uniformly distributed random matrix
sprandnSparse normally distributed random matrix
sprandsymSparse symmetric random matrix
sparseCreate sparse matrix
spconvertImport from sparse matrix external format
issparseDetermine whether input is sparse
nnzNumber of nonzero matrix elements
nonzerosNonzero matrix elements
nzmaxAmount of storage allocated for nonzero matrix elements
spfunApply function to nonzero sparse matrix elements
sponesReplace nonzero sparse matrix elements with ones
spparmsSet parameters for sparse matrix routines
spyVisualize sparsity pattern
findBuscar índices y valores de elementos no nulos
fullConvert sparse matrix to full storage
dissectNested dissection permutation
amdApproximate minimum degree permutation
colamdColumn approximate minimum degree permutation
colpermSparse column permutation based on nonzero count
dmpermDulmage-Mendelsohn decomposition
randpermRandom permutation
symamdSymmetric approximate minimum degree permutation
symrcmSparse reverse Cuthill-McKee ordering
pcgPreconditioned conjugate gradients method
minresMinimum residual method
symmlqSymmetric LQ method
gmresGeneralized minimum residual method (with restarts)
bicgBiconjugate gradients method
bicgstabBiconjugate gradients stabilized method
bicgstablBiconjugate gradients stabilized (l) method
cgsConjugate gradients squared method
qmrQuasi-minimal residual method
tfqmrTranspose-free quasi-minimal residual method
lsqrLSQR method
ichol Incomplete Cholesky factorization
iluIncomplete LU factorization
eigsSubset of eigenvalues and eigenvectors
svdsSubset of singular values and vectors
normest2-norm estimate
condest1-norm condition number estimate
sprankStructural rank
etreeElimination tree
symbfactSymbolic factorization analysis
spaugmentForm least-squares augmented system
dmpermDulmage-Mendelsohn decomposition
etreeplotPlot elimination tree
treelayoutLay out tree or forest
treeplotPlot picture of tree
gplotPlot nodes and links representing adjacency matrix
unmeshConvert edge matrix to coordinate and Laplacian matrices

Temas

Construyendo matrices escasas

Almacenando datos dispersos como una matriz.

Ventajas computacionales de matrices escasas

Ventajas de las matrices escasas sobre matrices completas.

Acceso a matrices escasas

Indexación y visualización de datos dispersos.

Operaciones de matriz dispersa

Reordenando, Factorizando y comparando con matrices escasas.

Sparse Matrix Reordering

This example shows how reordering the rows and columns of a sparse matrix can influence the speed and storage requirements of a matrix operation.

Graphs and Matrices

This example shows an application of sparse matrices and explains the relationship between graphs and matrices.

Ejemplos destacados