Class AbstractDenseRingMatrix<T extends AbstractDenseRingMatrix<T,U,V>,U extends AbstractDenseRingVector<U,T,V>,V extends Ring<V>>

java.lang.Object

org.flag4j.arrays.backend.AbstractTensor<T,V[],V>

org.flag4j.arrays.backend.semiring_arrays.AbstractDenseSemiringTensor<T,V>

org.flag4j.arrays.backend.semiring_arrays.AbstractDenseSemiringMatrix<T,U,V>

org.flag4j.arrays.backend.ring_arrays.AbstractDenseRingMatrix<T,U,V>

Type Parameters:

T - The type of this matrix.

U - The type of the vector which is of similar type to <T>.

V - The type of the arrays the data of the matrix belong to.

All Implemented Interfaces:

Serializable, MatrixMixin<T,T,U,V>, RingTensorMixin<T,T,V>, TensorOverRing<T,T,V[],V>, SemiringTensorMixin<T,T,V>, TensorOverSemiring<T,T,V[],V>

Direct Known Subclasses:

AbstractDenseFieldMatrix, RingMatrix

public abstract class AbstractDenseRingMatrix<T extends AbstractDenseRingMatrix<T,U,V>,U extends AbstractDenseRingVector<U,T,V>,V extends Ring<V>>
extends AbstractDenseSemiringMatrix<T,U,V>
implements RingTensorMixin<T,T,V>, MatrixMixin<T,T,U,V>

The base class for all dense matrices whose elements are members of a Ring.

See Also:

• Serialized Form

Field Summary

Fields inherited from class org.flag4j.arrays.backend.semiring_arrays.AbstractDenseSemiringMatrix

numCols, numRows

Fields inherited from class org.flag4j.arrays.backend.semiring_arrays.AbstractDenseSemiringTensor

zeroElement

Fields inherited from class org.flag4j.arrays.backend.AbstractTensor

data, rank, shape

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	AbstractDenseRingMatrix(Shape shape, V[] data)	Creates a tensor with the specified data and shape.

Method Summary

Modifier and Type	Method	Description
boolean	allClose(T b)	Checks if two sparse CSR ring matrices are element-wise equal within the following tolerance for two entries x and y:
boolean	allClose(T b, double relRol, double absTol)	Checks if two matrices are element-wise equal within the tolerance specified by relTol and absTol.
T	H(int... axes)	Computes the conjugate transpose of this tensor.
T	H(int axis1, int axis2)	Computes the conjugate transpose of a tensor by conjugating and exchanging axis1 and axis2.
boolean	isCloseToIdentity()	Checks if the matrix is "close" to an identity matrix.
boolean	isHermitian()	Checks if a matrix is Hermitian.
double	norm(int p, int q)	Computes the p-norm of this vector.
T	sub(T b)	Computes the element-wise difference of two matrices.
void	subEq(T b)	Computes the element-wise difference between two matrices of the same shape and stores the result in this matrix.

Methods inherited from class org.flag4j.arrays.backend.semiring_arrays.AbstractDenseSemiringMatrix

augment, augment, dataLength, flatten, flatten, get, getCol, getDiag, getRow, getSlice, getTriL, getTriU, H, isI, isOrthogonal, isSymmetric, isTriL, isTriU, makeLikeCooMatrix, makeLikeCsrMatrix, makeLikeVector, makeLikeVector, mult, mult, multTranspose, numCols, numRows, removeCol, removeCols, removeRow, removeRows, set, setCol, setCol, setRow, setRow, setSlice, setSliceCopy, setValues, stack, swapCols, swapRows, T, toCoo, toCoo, toCsr, toCsr, toTensor, toTensor, toVector, tr

Methods inherited from class org.flag4j.arrays.backend.semiring_arrays.AbstractDenseSemiringTensor

add, addEq, argmax, argmin, copy, elemMult, get, getZeroElement, makeLikeCooTensor, max, min, reshape, set, setZeroElement, T, T, tensorDot, tensorTr

Methods inherited from class org.flag4j.arrays.backend.AbstractTensor

getData, getRank, getShape, makeLikeTensor, reshape, sameShape, totalEntries

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.flag4j.arrays.backend.MatrixMixin

accept, add, augment, augment, copy, dataLength, div, elemMult, fib, get, getCol, getCol, getDiag, getDiag, getRow, getRow, getShape, getSlice, getTriL, getTriL, getTriU, getTriU, H, isDiag, isI, isOrthogonal, isSquare, isSymmetric, isTri, isTriL, isTriU, isVector, mult, mult, multTranspose, numCols, numRows, removeCol, removeCols, removeRow, removeRows, set, setCol, setRow, setSliceCopy, stack, stack, swapCols, swapRows, T, toVector, tr, trace, vectorType

Methods inherited from interface org.flag4j.arrays.backend.ring_arrays.RingTensorMixin

add, addEq, argmax, argmaxAbs, argmin, argminAbs, conj, isOnes, isZeros, makeEmptyDataArray, max, maxAbs, min, minAbs, mult, multEq, norm, norm, prod, sub, subEq, sum

Methods inherited from interface org.flag4j.arrays.backend.ring_arrays.TensorOverRing

abs, H

Methods inherited from interface org.flag4j.arrays.backend.semiring_arrays.TensorOverSemiring

add, elemMult, getData, getRank, getShape, makeLikeTensor, tensorDot, tensorDot, tensorDot, tensorDot, tensorTr, tensorTr

Constructor Details

AbstractDenseRingMatrix

protected AbstractDenseRingMatrix(Shape shape,
 V[] data)

Creates a tensor with the specified data and shape.

Parameters:

shape - Shape of this tensor.

data - Entries of this tensor. If this tensor is dense, this specifies all data within the tensor. If this tensor is sparse, this specifies only the non-zero data of the tensor.

Method Details

sub

public T sub(T b)

Computes the element-wise difference of two matrices.

Specified by:

sub in interface MatrixMixin<T extends AbstractDenseRingMatrix<T,U,V>,T extends AbstractDenseRingMatrix<T,U,V>,U extends AbstractDenseRingVector<U,T,V>,V extends Ring<V>>

Specified by:

sub in interface TensorOverRing<T extends AbstractDenseRingMatrix<T,U,V>,T extends AbstractDenseRingMatrix<T,U,V>,V extends Ring<V>[],V extends Ring<V>>

Parameters:

b - Second matrix in the element-wise difference.

Returns:

The element-wise difference of this matrix and b.

subEq

public void subEq(T b)

Computes the element-wise difference between two matrices of the same shape and stores the result in this matrix.

Parameters:

b - Second matrix in the element-wise difference.

Throws:

TensorShapeException - If this matrix and b do not have the same shape.

H

public T H(int axis1,
 int axis2)

Computes the conjugate transpose of a tensor by conjugating and exchanging axis1 and axis2.

Specified by:

H in interface TensorOverRing<T extends AbstractDenseRingMatrix<T,U,V>,T extends AbstractDenseRingMatrix<T,U,V>,V extends Ring<V>[],V extends Ring<V>>

Parameters:

axis1 - First axis to exchange and conjugate.

axis2 - Second axis to exchange and conjugate.

Returns:

The conjugate transpose of this tensor according to the specified axes.

Throws:

IndexOutOfBoundsException - If either axis1 or axis2 are out of bounds for the rank of this tensor.

See Also:

• AbstractDenseSemiringMatrix.H()
• H(int...)

H

public T H(int... axes)

Computes the conjugate transpose of this tensor. That is, conjugates and permutes the axes of this tensor so that it matches the permutation specified by axes.

Specified by:

H in interface TensorOverRing<T extends AbstractDenseRingMatrix<T,U,V>,T extends AbstractDenseRingMatrix<T,U,V>,V extends Ring<V>[],V extends Ring<V>>

Parameters:

axes - Permutation of tensor axis. If the tensor has rank N, then this must be an array of length N which is a permutation of {0, 1, 2, ..., N-1}.

Returns:

The conjugate transpose of this tensor with its axes permuted by the axes array.

Throws:

IndexOutOfBoundsException - If any element of axes is out of bounds for the rank of this tensor.

IllegalArgumentException - If axes is not a permutation of {1, 2, 3, ... N-1}.

See Also:

• H(int, int)
• AbstractDenseSemiringMatrix.H()

isHermitian

public boolean isHermitian()

Checks if a matrix is Hermitian. That is, if the matrix is square and equal to its conjugate transpose.

Specified by:

isHermitian in interface MatrixMixin<T extends AbstractDenseRingMatrix<T,U,V>,T extends AbstractDenseRingMatrix<T,U,V>,U extends AbstractDenseRingVector<U,T,V>,V extends Ring<V>>

Overrides:

isHermitian in class AbstractDenseSemiringMatrix<T extends AbstractDenseRingMatrix<T,U,V>,U extends AbstractDenseRingVector<U,T,V>,V extends Ring<V>>

Returns:

true if this matrix is Hermitian; false otherwise.

isCloseToIdentity

public boolean isCloseToIdentity()

Checks if the matrix is "close" to an identity matrix. Two entries x and y are considered "close" if they satisfy the following:

      |x-y| <= (1E-08 + 1E-05*|y|)
 

Returns:

true if the matrix is approximately an identity matrix, otherwise false.

allClose

public boolean allClose(T b)

Checks if two sparse CSR ring matrices are element-wise equal within the following tolerance for two entries x and y:

  |x-y| <= (1e-08 + 1e-05*|y|)
 

To specify the relative and absolute tolerances use allClose(AbstractDenseRingMatrix, double, double)

Returns:

true if this matrix and b element-wise equal within the tolerance |x-y| <= (1e-08 + 1e-05*|y|).

See Also:

• allClose(AbstractDenseRingMatrix, double, double)

allClose

public boolean allClose(T b,
 double relRol,
 double absTol)

Checks if two matrices are element-wise equal within the tolerance specified by relTol and absTol. Two elements x and y are considered "close" if they satisfy the following:

  |x-y| <= (absTol + relTol*|y|)
 

Parameters:

b - Matrix to compare to this matrix.

absTol - Absolute tolerance.

relTol - Relative tolerance.

Returns:

true if the src1 matrix is the same shape as the src2 matrix and all data are 'close', i.e. elements a and b at the same positions in the two matrices respectively satisfy |a-b| <= (absTol + relTol*|b|). Otherwise, returns false.

See Also:

• allClose(AbstractDenseRingMatrix)

norm

public double norm(int p,
 int q)

Computes the p-norm of this vector.

Parameters:

p - p value in the p-norm.

Returns:

The Euclidean norm of this vector.