org.ojalgo.matrix.decomposition
Interface MatrixDecomposition<N extends Number>

All Known Subinterfaces:

Bidiagonal<N>, Cholesky<N>, Eigenvalue<N>, Hessenberg<N>, LU<N>, QR<N>, Schur<N>, SingularValue<N>, Tridiagonal<N>

All Known Implementing Classes:

BidiagonalDecomposition, CholeskyDecomposition, EigenvalueDecomposition, HessenbergDecomposition, JamaCholesky, JamaEigenvalue, JamaEigenvalue.General, JamaEigenvalue.Nonsymmetric, JamaEigenvalue.Symmetric, JamaLU, JamaQR, JamaSingularValue, LUDecomposition, QRDecomposition, SchurDecomposition, SingularValueDecomposition, TridiagonalDecomposition

public interface MatrixDecomposition<N extends Number>

Some standard matrix names:

• [A] could be any matrix.
• [D] is a diagonal matrix. Possibly bi-, tri- or block-diagonal.
• [H] is an, upper or lower, Hessenberg matrix.
• [I] is an identity matrix.
• [L] is a lower (left) triangular matrix.
• [P] is a permutation matrix - an identity matrix with interchanged rows or columns. [P]^-1=[P]^T
• [Q] is an orthogonal, or unitary, matrix. [Q]^-1=[Q]^T.
• [R] is a right (upper) tringular matrix. It is equivalent to [U].
• [U] is an upper (right) triangular matrix. It is equivalent to [R].
• [V] is an eigenvector matrix.

With the above definitions we can express various decompositions as:

• Bidiagonal: [A] = [Q1][D][Q2]^T
• Cholesky: [A] = [L][L]^T
• Eigenvalue: [A] = [V][D][V]^-1
• Hessenberg: [A] = [Q][H][Q]^T
• LU: [A] = [L][U]
• QR: [A] = [Q][R]
• Schur: [A] = [Q][U][Q]^-1
• Singular Value: [A] = [Q1][D][Q2]^T
• Tridiagonal: [A] = [Q][D][Q]^T

Author:

apete

Method Summary

boolean	compute(Access2D<?> aMtrx)
boolean	equals(MatrixDecomposition<N> aDecomp, NumberContext aCntxt)
boolean	equals(MatrixStore<N> aMtrx, NumberContext aCntxt)
MatrixStore<N>	getInverse() The output must be a "right inverse" and a "generalised inverse".
MatrixStore<N>	getInverse(DecompositionStore<N> preallocated) Implementiong this method is optional.
boolean	isComputed()
boolean	isFullSize()
boolean	isSolvable()
MatrixStore<N>	reconstruct()
void	reset() Delete computed results, and resets attributes to default values
MatrixStore<N>	solve(MatrixStore<N> aRHS) [A][X]=[B] or [this][return]=[aRHS]
MatrixStore<N>	solve(MatrixStore<N> aRHS, DecompositionStore<N> preallocated) Implementiong this method is optional.

Method Detail

compute

boolean compute(Access2D<?> aMtrx)

Parameters:

aMtrx - A matrix to decompose

Returns:

true if the computation suceeded; false if not

equals

boolean equals(MatrixDecomposition<N> aDecomp,
               NumberContext aCntxt)

equals

boolean equals(MatrixStore<N> aMtrx,
               NumberContext aCntxt)

getInverse

MatrixStore<N> getInverse()

The output must be a "right inverse" and a "generalised inverse".

See Also:

BasicMatrix.invert()

getInverse

MatrixStore<N> getInverse(DecompositionStore<N> preallocated)

Implementiong this method is optional.

Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling getInverse().

Parameters:

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution.

Returns:

The inverse

isComputed

boolean isComputed()

Returns:

true if computation has been attemped; false if not.

See Also:

compute(Access2D), isSolvable()

isFullSize

boolean isFullSize()

Returns:

True if the implementation generates a full sized decomposition.

isSolvable

boolean isSolvable()

Returns:

true if it is ok to call solve(MatrixStore) (computation was successful); false if not

See Also:

solve(MatrixStore), isComputed()

reconstruct

MatrixStore<N> reconstruct()

reset

void reset()

Delete computed results, and resets attributes to default values

solve

MatrixStore<N> solve(MatrixStore<N> aRHS)

[A][X]=[B] or [this][return]=[aRHS]

solve

MatrixStore<N> solve(MatrixStore<N> aRHS,
                     DecompositionStore<N> preallocated)

Implementiong this method is optional.

Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling solve(MatrixStore).

Parameters:

aRHS - The Right Hand Side, wont be modfied

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution.

Returns:

The solution