Function Summary :: Sparse Matrices (MATLAB®)

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Function Summary

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Functions That Support Sparse Matrices Functions That Do Not Support Sparse Matrices Functions with Sparse Alternatives

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Functions That Do Not Support Sparse Matrices

Functions That Support Sparse Matrices

Sparse matrix functions are located in the MATLAB sparfun directory. For a complete list, brief descriptions, and links to reference pages, type:

help sparfun

Sparse matrix functions fall into the following categories:

Elementary Sparse Matrices

Function	Description
`speye`	Sparse identity matrix
`sprand`	Sparse uniformly distributed random matrix
`sprandn`	Sparse normally distributed random matrix
`sprandsym`	Sparse random symmetric matrix
`spdiags`	Sparse matrix formed from diagonals

Full to Sparse Conversion

Function	Description
`sparse`	Create sparse matrix
`full`	Convert sparse matrix to full matrix
`find`	Find indices of nonzero elements
`spconvert`	Import from sparse matrix external format

Working with Sparse Matrices

Function	Description
`nnz`	Number of nonzero matrix elements
`nonzeros`	Nonzero matrix elements
`nzmax`	Amount of storage allocated for nonzero matrix elements
`spones`	Replace nonzero sparse matrix elements with ones
`spalloc`	Allocate space for sparse matrix
`issparse`	True for sparse matrix
`spfun`	Apply function to nonzero matrix elements
`spy`	Visualize sparsity pattern

Graph Theory

Function	Description
`gplot`	Plot graph, as in "graph theory"
`etree`	Elimination tree
`etreeplot`	Plot elimination tree
`treelayout`	Lay out tree or forest
`treeplot`	Plot picture of tree

Reordering Algorithms

Function	Description
`colamd`	Column approximate minimum degree permutation
`symamd`	Symmetric approximate minimum degree permutation
`symrcm`	Symmetric reverse Cuthill-McKee permutation
`colperm`	Column permutation
`randperm`	Random permutation
`dmperm`	Dulmage-Mendelsohn permutation

Linear Algebra

Function	Description
`eigs`	A few eigenvalues
`svds`	A few singular values
`luinc`	Incomplete LU factorization
`ilu`	Incomplete LU factorization
`cholinc`	Incomplete Cholesky factorization
`normest`	Estimate the matrix 2-norm
`condest`	1-norm condition number estimate
`sprank`	Structural rank

Linear Equations (Iterative Methods)

Function	Description
`bicg`	Biconjugate gradients method
`bicgstab`	Biconjugate gradients stabilized method
`bicgstabl`	Biconjugate gradients stabilized(l) method
`cgs`	Conjugate gradients squared method
`gmres`	Generalized minimum residual method
`lsqnonneg`	Solve nonnegative least-squares constraints problem
`lsqr`	LSQR method
`minres`	Minimum residual method
`pcg`	Preconditioned conjugate gradients method
`qmr`	Quasi-minimal residual method
`tfqmr`	Transpose-free quasi-minimal residual method
`symmlq`	Symmetric LQ method

Other Miscellaneous Functions

Function	Description
`spaugment`	Form least squares augmented system
`spparms`	Set parameters for sparse matrix routines
`symbfact`	Symbolic factorization analysis

Functions That Do Not Support Sparse Matrices

These built-in functions do not accept sparse matrices as input. M-file functions that depend on these built-ins do not work with sparse matrices.

Elementary Matrices and Arrays

Function	Description
`rand`	Uniformly distributed pseudorandom numbers

Elementary Math Functions

Complex Functions.

Function	Description
`complex`	Construct complex data from real and imaginary components

Real Array Exponential Functions.

Function	Description
`reallog`	Natural logarithm for nonnegative real arrays
`realpow`	Array power for real-only output
`realsqrt`	Square root for nonnegative real arrays

Bit-Wise Functions

Function	Description
`bitand`	Bitwise AND
`bitcmp`	Bitwise complement
`bitget`	Bit at specified position
`bitmax`	Maximum double-precision floating-point integer
`bitor`	Bitwise OR
`bitset`	Set bit at specified position
`bitshift`	Shift bits specified number of places
`bitxor`	Bitwise XOR

Eigenvalue and Singular Value Functions

Function	Description
`hess`	Hessenberg form of matrix
`ordeig`	Eigenvalues of quasitriangular matrices
`ordqz`	Reorder eigenvalues in QZ factorization
`ordschur`	Reorder eigenvalues in Schur factorization
`schur`	Schur decomposition
`svd`	Singular value decomposition

Matrix Analysis Functions

Function	Description
`cond`	Condition number with respect to inversion
`null`	Null space
`orth`	Range space of matrix
`rcond`	Matrix reciprocal condition number estimate

Factorization Functions

Function	Description
`cholupdate`	Rank 1 update to Cholesky factorization
`gsvd`	Generalized singular value decomposition
`qz`	QZ factorization for generalized eigenvalues

Linear Equation Functions

Function	Description
`linsolve`	Solve linear system of equations
`pinv`	Moore-Penrose pseudoinverse of matrix

Specialized Math Functions

Function	Description
`airy`	Airy functions
`besselh`	Bessel function of third kind (Hankel function)
`besseli`	Modified Bessel function of first kind
`besselj`	Bessel function of first kind
`besselk`	Modified Bessel function of second kind
`bessely`	Bessel function of second kind
`erfc`	Error function
`erf`	Error function
`erfcx`	Error function
`gamma`	Gamma function
`gammaln`	Gamma function
`psi`	Psi (polygamma) function

Filtering and Convolution Functions

Function	Description
`conv2`	2-D convolution
`convn`	N-D convolution
`filter`	1-D digital filter
`filter2`	2-D digital filter

Fourier Transform Functions

Function	Description
`fft`	Discrete Fourier transform
`fftn`	N-D discrete Fourier transform
`ifft`	Inverse discrete Fourier transform
`ifftn`	N-D inverse discrete Fourier transform

Histogram Plotting Functions

Function	Description
`histc`	Histogram count

Functions with Sparse Alternatives

These functions do not accept sparse inputs, but you can use other functions in their place.

Function	Replacement Function Supporting Sparse Inputs
`cond`	Use `condest` instead.
`eig`	Syntax `d = eig(S)` accepts a sparse symmetric matrix `S`. Otherwise, use `eigs` in place of `eig`.
`norm(S,2)`	Use `normest` for the 2-norm of a sparse matrix `S`.
`svd`	Use `svds` instead.

Sparse Matrices

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