smile.math.matrix

Interface ARPACK

public interface ARPACK

ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems.

The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse or structured matrices A where structured means that a matrix-vector product requires order n rather than the usual order n^2 floating point operations. This software is based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM). These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems. For many standard problems, a matrix factorization is not required. Only the action of the matrix on a vector is needed.

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static class	ARPACK.AsymmOption Which eigenvalues of asymmetric matrix to compute.
static class	ARPACK.SymmOption Which eigenvalues of symmetric matrix to compute.

Field Summary

Fields

Modifier and Type	Field and Description
static org.slf4j.Logger	logger

Method Summary

Modifier and Type	Method and Description
static Matrix.EVD	eigen(DMatrix A, ARPACK.AsymmOption which, int nev) Computes NEV eigenvalues of an asymmetric double precision matrix.
static Matrix.EVD	eigen(DMatrix A, ARPACK.AsymmOption which, int nev, int ncv, double tol) Computes NEV eigenvalues of an asymmetric double precision matrix.
static FloatMatrix.EVD	eigen(SMatrix A, ARPACK.AsymmOption which, int nev) Computes NEV eigenvalues of an asymmetric single precision matrix.
static FloatMatrix.EVD	eigen(SMatrix A, ARPACK.AsymmOption which, int nev, int ncv, float tol) Computes NEV eigenvalues of an asymmetric single precision matrix.
static Matrix.SVD	svd(DMatrix A, int k) Computes k largest approximate singular triples of a matrix.
static Matrix.SVD	svd(DMatrix A, int k, int ncv, double tol) Computes k largest approximate singular triples of a matrix.
static FloatMatrix.SVD	svd(SMatrix A, int k) Computes k largest approximate singular triples of a matrix.
static FloatMatrix.SVD	svd(SMatrix A, int k, int ncv, float tol) Computes k largest approximate singular triples of a matrix.
static Matrix.EVD	syev(DMatrix A, ARPACK.SymmOption which, int nev) Computes NEV eigenvalues of a symmetric double precision matrix.
static Matrix.EVD	syev(DMatrix A, ARPACK.SymmOption which, int nev, int ncv, double tol) Computes NEV eigenvalues of a symmetric double precision matrix.
static FloatMatrix.EVD	syev(SMatrix A, ARPACK.SymmOption which, int nev) Computes NEV eigenvalues of a symmetric single precision matrix.
static FloatMatrix.EVD	syev(SMatrix A, ARPACK.SymmOption which, int nev, int ncv, float tol) Computes NEV eigenvalues of a symmetric single precision matrix.

Field Detail

logger

static final org.slf4j.Logger logger

Method Detail

syev

static Matrix.EVD syev(DMatrix A,
                       ARPACK.SymmOption which,
                       int nev)

Computes NEV eigenvalues of a symmetric double precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

syev

static Matrix.EVD syev(DMatrix A,
                       ARPACK.SymmOption which,
                       int nev,
                       int ncv,
                       double tol)

Computes NEV eigenvalues of a symmetric double precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

ncv - the number of Arnoldi vectors.

tol - the stopping criterion.

syev

static FloatMatrix.EVD syev(SMatrix A,
                            ARPACK.SymmOption which,
                            int nev)

Computes NEV eigenvalues of a symmetric single precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

syev

static FloatMatrix.EVD syev(SMatrix A,
                            ARPACK.SymmOption which,
                            int nev,
                            int ncv,
                            float tol)

Computes NEV eigenvalues of a symmetric single precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

ncv - the number of Arnoldi vectors.

tol - the stopping criterion.

eigen

static Matrix.EVD eigen(DMatrix A,
                        ARPACK.AsymmOption which,
                        int nev)

Computes NEV eigenvalues of an asymmetric double precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

eigen

static Matrix.EVD eigen(DMatrix A,
                        ARPACK.AsymmOption which,
                        int nev,
                        int ncv,
                        double tol)

Computes NEV eigenvalues of an asymmetric double precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

ncv - the number of Arnoldi vectors.

tol - the stopping criterion.

eigen

static FloatMatrix.EVD eigen(SMatrix A,
                             ARPACK.AsymmOption which,
                             int nev)

Computes NEV eigenvalues of an asymmetric single precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

eigen

static FloatMatrix.EVD eigen(SMatrix A,
                             ARPACK.AsymmOption which,
                             int nev,
                             int ncv,
                             float tol)

Computes NEV eigenvalues of an asymmetric single precision matrix.

Parameters:

A - the matrix to decompose.

which - which eigenvalues to compute.

nev - the number of eigenvalues of OP to be computed. 0 < k < n.

ncv - the number of Arnoldi vectors.

tol - the stopping criterion.

svd

static Matrix.SVD svd(DMatrix A,
                      int k)

Computes k largest approximate singular triples of a matrix.

Parameters:

A - the matrix to decompose.

k - the number of singular triples to compute.

svd

static Matrix.SVD svd(DMatrix A,
                      int k,
                      int ncv,
                      double tol)

Computes k largest approximate singular triples of a matrix.

Parameters:

A - the matrix to decompose.

k - the number of singular triples to compute.

ncv - the number of Arnoldi vectors.

tol - the stopping criterion.

svd

static FloatMatrix.SVD svd(SMatrix A,
                           int k)

Computes k largest approximate singular triples of a matrix.

Parameters:

A - the matrix to decompose.

k - the number of singular triples to compute.

svd

static FloatMatrix.SVD svd(SMatrix A,
                           int k,
                           int ncv,
                           float tol)

Computes k largest approximate singular triples of a matrix.

Parameters:

A - the matrix to decompose.

k - the number of singular triples to compute.

ncv - the number of Arnoldi vectors.

tol - the stopping criterion.