drasys.or.linear.algebra
Interface SVDecompositionI

All Known Implementing Classes:

QRIteration

public interface SVDecompositionI

extends DecompositionI

The interface used by all algorithms to access singular value decomposition algorithms.

See Also:

References:

Linear Algebra and Its Applications
    Gilbert Strang / Hardcover / Published 1988
Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences)
    Gene H. Golub, Charles F. Van Loan (Contributor) / Paperback / Published 1996
Numerical Recipes in C : The Art of Scientific Computing
    William H. Press, et al / Hardcover / Published 1993
Parallel Algorithms for Matrix Computations
    K.A. Gallivan / Paperback / Published 1990


Method Summary
double	computeConditionNumber()           Computes the condition number of the matrix.
DenseMatrix	computeInverse()           Computes the inverse of the decomposed matrix from the components.
MatrixI	computeInverse(MatrixI results)           Computes the inverse of the decomposed matrix from the components.
void	decompose(MatrixI matrix)           Decompose matrix A into U, W and V matrices.
DenseMatrix	getU()           Get the U matrix.
MatrixI	getU(MatrixI results)           Get the U matrix.
DenseMatrix	getV()           Get the V matrix.
MatrixI	getV(MatrixI results)           Get the V matrix.
SparseMatrix	getW()           Get the W matrix.
MatrixI	getW(MatrixI results)           Get the W matrix.
boolean	isIllConditioned()           Returns true if the decomposed matrix is ill-conditioned.
boolean	isSingular()           Returns true if the decomposed matrix is singular.
DenseVector	solveEquations(VectorI rightHandSides)           Uses backsubstitution to solve the simultaneous equations.
VectorI	solveEquations(VectorI rightHandSides, VectorI results)           Uses backsubstitution to solve the simultaneous equations.

 

Method Detail

getU

public DenseMatrix getU()

Get the U matrix.

Returns:

null if no matrix has been decomposed.

getU

public MatrixI getU(MatrixI results)

Get the U matrix.

Returns:

null if no matrix has been decomposed.

getV

public DenseMatrix getV()

Get the V matrix.

Returns:

null if no matrix has been decomposed.

getV

public MatrixI getV(MatrixI results)

Get the V matrix.

Returns:

null if no matrix has been decomposed.

getW

public SparseMatrix getW()

Get the W matrix.

Returns:

null if no matrix has been decomposed.

getW

public MatrixI getW(MatrixI results)

Get the W matrix.

Returns:

null if no matrix has been decomposed.

decompose

public void decompose(MatrixI matrix)
               throws AlgebraException

Decompose matrix A into U, W and V matrices. Where: A[r][c] = U[r][c] * W[c][c] * transpose(V[c][c]) and W is a diagonal matrix of the singular values.

Specified by:

decompose in interface DecompositionI

solveEquations

public DenseVector solveEquations(VectorI rightHandSides)
                           throws AlgebraException

Uses backsubstitution to solve the simultaneous equations.

Specified by:

solveEquations in interface DecompositionI

Returns:

the results.

Throws:

AlgebraError - if no matrix has been decomposed

solveEquations

public VectorI solveEquations(VectorI rightHandSides,
                              VectorI results)
                       throws AlgebraException

Uses backsubstitution to solve the simultaneous equations.

Specified by:

solveEquations in interface DecompositionI

Returns:

the results.

Throws:

AlgebraError - if no matrix has been decomposed

computeInverse

public DenseMatrix computeInverse()
                           throws AlgebraException

Computes the inverse of the decomposed matrix from the components. Where: inverse(A) = V * diagonal(1/w[i][i]) * transpose(U).

Specified by:

computeInverse in interface DecompositionI

Returns:

the results.

Throws:

AlgebraError - if no matrix has been decomposed

computeInverse

public MatrixI computeInverse(MatrixI results)
                       throws AlgebraException

Computes the inverse of the decomposed matrix from the components. Where: inverse(A) = V * diagonal(1/w[i][i]) * transpose(U).

Specified by:

computeInverse in interface DecompositionI

Returns:

the results.

Throws:

AlgebraError - if no matrix has been decomposed

computeConditionNumber

public double computeConditionNumber()

Computes the condition number of the matrix. The condition number is a measure of the singularity of the matrix.

Returns:

NaN is the matrix is singular.

Throws:

AlgebraError - if no matrix has been decomposed

isIllConditioned

public boolean isIllConditioned()

Returns true if the decomposed matrix is ill-conditioned.

Throws:

AlgebraError - if no matrix has been decomposed

isSingular

public boolean isSingular()

Returns true if the decomposed matrix is singular.

Throws:

AlgebraError - if no matrix has been decomposed