22.6 Function Reference

22.6.1 Functions by Category

22.6.1.1 Generate sparse matrix

spdiags

A generalization of the function `spdiag'.

speye

Returns a sparse identity matrix.

sprand

Generate a random sparse matrix.

sprandn

Generate a random sparse matrix.

sprandsym

Generate a symmetric random sparse matrix.

22.6.1.2 Sparse matrix conversion

full

returns a full storage matrix from a sparse one See also: sparse

sparse

SPARSE: create a sparse matrix

spconvert

This function converts for a simple sparse matrix format easily produced by other programs into Octave's internal sparse format.

spfind

SPFIND: a sparse version of the find operator 1.

22.6.1.3 Manipulate sparse matrices

issparse

Return 1 if the value of the expression EXPR is a sparse matrix.

nnz

returns number of non zero elements in SM See also: sparse

nonzeros

Returns a vector of the non-zero values of the sparse matrix S

nzmax

Returns the amount of storage allocated to the sparse matrix SM.

spalloc

Returns an empty sparse matrix of size R-by-C.

spfun

Compute `f(X)' for the non-zero values of X This results in a sparse matrix with the same structure as X.

spones

Replace the non-zero entries of X with ones.

spy

Plot the sparsity pattern of the sparse matrix X

22.6.1.4 Graph Theory

etree

Returns the elimination tree for the matrix S.

etreeplot

Plots the elimination tree of the matrix s or s+s' if s in non-symmetric.

gplot

Plots a graph defined by A and xy in the graph theory sense.

treelayout

Not implemented

treeplot

Produces a graph of a tree or forest.

22.6.1.5 Sparse matrix reordering

ccolamd

Constrained column approximate minimum degree permutation.

colamd

Column approximate minimum degree permutation.

colperm

Returns the column permutations such that the columns of `S (:, P)' are ordered in terms of increase number of non-zero elements.

csymamd

For a symmetric positive definite matrix S, returns the permutation vector p such that `S (P, P)' tends to have a sparser Cholesky factor than S.

dmperm

Perform a Deulmage-Mendelsohn permutation on the sparse matrix S.

symamd

For a symmetric positive definite matrix S, returns the permutation vector p such that `S (P, P)' tends to have a sparser Cholesky factor than S.

symrcm

Not implemented

22.6.1.6 Linear algebra

cholinc

Not implemented

condest

Not implemented

eigs

Not implemented

matrix_type

Identify the matrix type or mark a matrix as a particular type.

normest

Not implemented

spchol

Compute the Cholesky factor, R, of the symmetric positive definite.

spcholinv

Use the Cholesky factorization to compute the inverse of the sparse symmetric positive definite matrix A.

spchol2inv

Invert a sparse symmetric, positive definite square matrix from its Cholesky decomposition, U.

spdet

Compute the determinant of sparse matrix A using UMFPACK.

spinv

Compute the inverse of the square matrix A.

spkron

Form the kronecker product of two sparse matrices.

splchol

Compute the Cholesky factor, L, of the symmetric positive definite.

splu

Compute the LU decomposition of the sparse matrix A, using subroutines from UMFPACK.

spqr

Compute the sparse QR factorization of a, using CSPARSE.

sprank

Not implemented

svds

Not implemented

22.6.1.7 Iterative techniques

bicg

Not implemented

bicgstab

Not implemented

cgs

Not implemented

gmres

Not implemented

luinc

Produce the incomplete LU factorization of the sparse matrix A.

lsqr

Not implemented

minres

Not implemented

pcg

Solves the linear system of equations A * x = b by means of the Preconditioned Conjugate Gradient iterative method.

pcr

Solves the linear system of equations A * x = b by means of the Preconditioned Conjugate Residual iterative method.

qmr

Not implemented

symmlq

Not implemented

22.6.1.8 Miscellaneous

spaugment

Not implemented

spparms

Sets or displays the parameters used by the sparse solvers and factorization functions.

symbfact

Performs a symbolic factorization analysis on the sparse matrix S.

spstats

Return the stats for the non-zero elements of the sparse matrix S COUNT is the number of non-zeros in each column, MEAN is the mean of the non-zeros in each column, and VAR is the variance of the non-zeros in each column

spprod

Product of elements along dimension DIM.

spcumprod

Cumulative product of elements along dimension DIM.

spcumsum

Cumulative sum of elements along dimension DIM.

spsum

Sum of elements along dimension DIM.

spsumsq

Sum of squares of elements along dimension DIM.

spmin

For a vector argument, return the minimum value.

spmax

For a vector argument, return the maximum value.

spatan2

Compute atan (Y / X) for corresponding sparse matrix elements of Y and X.

spdiag

Return a diagonal matrix with the sparse vector V on diagonal K.

22.6.2 Functions Alphabetically

• ccolamd: Constrained column approximate minimum degree permutation.
• colamd: Column approximate minimum degree permutation.
• colperm: Returns the column permutations such that the columns of `S (:, P)' are ordered in terms of increase number of non-zero elements.
• csymamd: For a symmetric positive definite matrix S, returns the permutation vector p such that `S (P, P)' tends to have a sparser Cholesky factor than S.
• dmperm: Perfrom a Deulmage-Mendelsohn permutation on the sparse matrix S.
• etree: Returns the elimination tree for the matrix S.
• etreeplot: Plots the elimination tree of the matrix s or s+s' if s in non-symmetric.
• full: returns a full storage matrix from a sparse one See also: sparse
• gplot: Plots a graph defined by A and xy in the graph theory sense.
• issparse: Return 1 if the value of the expression EXPR is a sparse matrix.
• luinc: Produce the incomplete LU factorization of the sparse A.
• matrix_type: Identify the matrix type or mark a matrix as a particular type.
• nnz: returns number of non zero elements in SM See also: sparse
• nonzeros: Returns a vector of the non-zero values of the sparse matrix S
• nzmax: Returns the amount of storage allocated to the sparse matrix SM.
• pcg: Solves linear system of equations by means of the Preconditioned Conjugate Gradient iterative method.
• pcr: Solves linear system of equations by means of the Preconditioned Conjugate Residual iterative method.
• spalloc: Returns an empty sparse matrix of size R-by-C.
• sparse: SPARSE: create a sparse matrix
• spatan2: Compute atan (Y / X) for corresponding sparse matrix elements of Y and X.
• spchol: Compute the Cholesky factor, R, of the symmetric positive definite.
• spcholinv: Use the Cholesky factorization to compute the inverse of the sparse symmetric positive definite matrix A.
• spchol2inv: Invert a sparse symmetric, positive definite square matrix from its Cholesky decomposition, U.
• spconvert: This function converts for a simple sparse matrix format easily produced by other programs into Octave's internal sparse format.
• spcumprod: Cumulative product of elements along dimension DIM.
• spcumsum: Cumulative sum of elements along dimension DIM.
• spdet: Compute the determinant of sparse matrix A using UMFPACK.
• spdiag: Return a diagonal matrix with the sparse vector V on diagonal K.
• spdiags: A generalization of the function `spdiag'.
• speye: Returns a sparse identity matrix.
• spfind: SPFIND: a sparse version of the find operator 1.
• spfun: Compute `f(X)' for the non-zero values of X This results in a sparse matrix with the same structure as X.
• spinv: Compute the inverse of the square matrix A.
• spkron: Form the kronecker product of two sparse matrices.
• splchol: Compute the Cholesky factor, L, of the symmetric positive definite.
• splu: Compute the LU decomposition of the sparse matrix A, using subroutines from UMFPACK.
• spmax: For a vector argument, return the maximum value.
• spmin: For a vector argument, return the minimum value.
• spones: Replace the non-zero entries of X with ones.
• spparms: Sets or displays the parameters used by the sparse solvers and factorization functions.
• spprod: Product of elements along dimension DIM.
• spqr: Compute the sparse QR factorization of a, using CSPARSE.
• sprand: Generate a random sparse matrix.
• sprandn: Generate a random sparse matrix.
• sprandsym: Generate a symmetric random sparse matrix.
• spstats: Return the stats for the non-zero elements of the sparse matrix S COUNT is the number of non-zeros in each column, MEAN is the mean of the non-zeros in each column, and VAR is the variance of the non-zeros in each column
• spsum: Sum of elements along dimension DIM.
• spsumsq: Sum of squares of elements along dimension DIM.
• spy: Plot the sparsity pattern of the sparse matrix X
• symamd: For a symmetric positive definite matrix S, returns the permutation vector p such that `S (P, P)' tends to have a sparser Cholesky factor than S.
• symbfact: Performs a symbolic factorization analysis on the sparse matrix S.
• treeplot: Produces a graph of a tree or forest.