Package org.flag4j.linalg.solvers.exact

Class ExactTensorSolver<T extends TensorBase<T,?,?,?,?,?,?>,U extends MatrixMixin<U,?,?,?,?,?,V,?>,V extends VectorMixin<V,?,?,?,?,U,?,?>>

java.lang.Object

org.flag4j.linalg.solvers.exact.ExactTensorSolver<T,U,V>

Type Parameters:

T - Type of tensor in equation to solve.

U - Matrix type equivalent of tensor to solve.

V - Vector type equivalent of tensor to solve.

All Implemented Interfaces:

LinearTensorSolver<T>

Direct Known Subclasses:

ComplexExactTensorSolver, RealExactTensorSolver

public abstract class ExactTensorSolver<T extends TensorBase<T,?,?,?,?,?,?>,U extends MatrixMixin<U,?,?,?,?,?,V,?>,V extends VectorMixin<V,?,?,?,?,U,?,?>>
extends Object
implements LinearTensorSolver<T>

Solves a well determined system of equations A*X=B in an exact sense where A, X, and B are tensors.

If the system is not well determined, i.e. A is 'square' and full rank, then use a least-squares solver.

Field Summary

Fields

Modifier and Type	Field	Description
private final LinearSolver<U,V>	matrixSolver	Solver to solve a linear matrix equation C*X=d for X where C and X are matrices and d is a vector.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	ExactTensorSolver(LinearSolver<U,V> matrixSolver)	Creates an exact tensor solver which will use reform the problem as a matrix linear system and use the provided solver to solve the tensor system.

Method Summary

Modifier and Type	Method	Description
protected void	checkSize(int aNumEntries, int prod)	Ensures that aNumEntries==prod.
protected Shape	getOutputShape(T A, T B, int aRankOriginal)	Constructs the shape of the output.
protected abstract U	initMatrix(T A, int prod)	Initializes matrix for equivalent linear matrix equation.
protected abstract V	initVector(T B)	Initializes vector for equivalent linear matrix equation.
T	solve(T A, T B)	Solves the linear tensor equation given by A*X=B for the tensor X.
protected abstract T	wrap(V x, Shape outputShape)	Wraps solution as a tensor and reshapes to the proper shape.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

matrixSolver

private final LinearSolver<U extends MatrixMixin<U,?,?,?,?,?,V,?>,V extends VectorMixin<V,?,?,?,?,U,?,?>> matrixSolver

Solver to solve a linear matrix equation C*X=d for X where C and X are matrices and d is a vector.

Constructor Details

ExactTensorSolver

protected ExactTensorSolver(LinearSolver<U,V> matrixSolver)

Creates an exact tensor solver which will use reform the problem as a matrix linear system and use the provided solver to solve the tensor system.

Parameters:

matrixSolver - Matrix solver to use as the solver for the equivalent matrix system.

Method Details

solve

public T solve(T A,
 T B)

Solves the linear tensor equation given by A*X=B for the tensor X. All indices of X are summed over in the tensor product with the rightmost indices of A as if by A.tensorDot(X, M, N) where M = new int[]{X.rank()-1, X.rank(), X.rank()+1, ..., A.rank()-1} and N = new int[]{0, 1, ..., X.rank()-1}

Specified by:

solve in interface LinearTensorSolver<T extends TensorBase<T,?,?,?,?,?,?>>

Parameters:

A - Coefficient tensor in the linear system.

B - Tensor of constants in the linear system.

Returns:

The solution to x in the linear system A*X=B.

getOutputShape

protected Shape getOutputShape(T A,
 T B,
 int aRankOriginal)

Constructs the shape of the output.

Parameters:

A - Tensor corresponding to A in A*X=B.

B - Tensor corresponding to B in A*X=B.

aRankOriginal - Original rank of A before any reshaping.

Returns:

The shape of X in A*X=B.

checkSize

protected void checkSize(int aNumEntries,
 int prod)

Ensures that aNumEntries==prod.

Parameters:

aNumEntries - The total number of entries in the A tensor.

prod - Product of all axis lengths in the output shape.

initMatrix

protected abstract U initMatrix(T A,
 int prod)

Initializes matrix for equivalent linear matrix equation.

Parameters:

A - Tensor to convert to matrix.

prod - Product of all axis lengths in A.

Returns:

A matrix with the same entries as tensor A with shape (prod, prod).

initVector

protected abstract V initVector(T B)

Initializes vector for equivalent linear matrix equation.

Parameters:

B - Tensor to convert to vector.

Returns:

Flattens tensor B and converts to a vector.

wrap

protected abstract T wrap(V x,
 Shape outputShape)

Wraps solution as a tensor and reshapes to the proper shape.

Parameters:

x - Vector solution to matrix linear equation which is equivalent to the tensor equation A*X=B.

outputShape - Shape for the solution tensor X.

Returns:

The solution X to the linear tensor equation A*X=B.