Class AbstractCooRingMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

java.lang.Object

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

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

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

Type Parameters:

T - Type of this sparse COO matrix.

U - Type of dense matrix which is similar to T.

V - Type of sparse COO vector which is similar to T.

W - Type of the arrays element in this matrix.

All Implemented Interfaces:

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

Direct Known Subclasses:

AbstractCooFieldMatrix, CooRingMatrix

public abstract class AbstractCooRingMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>
extends AbstractCooSemiringMatrix<T,U,V,W>
implements RingTensorMixin<T,U,W>, MatrixMixin<T,U,V,W>

A sparse matrix stored in coordinate list (COO) format. The AbstractTensor.data of this COO matrix are elements of a Ring.

The non-zero data and non-zero indices of a COO matrix are mutable but the AbstractTensor.shape and total number of non-zero data is fixed.

Sparse matrices allow for the efficient storage of and ops on matrices that contain many zero values.

COO matrices are optimized for hyper-sparse matrices (i.e. matrices which contain almost all zeros relative to the size of the matrix).

COO Representation:

A sparse COO matrix is stored as:

• The full shape of the matrix.
• The non-zero AbstractTensor.data of the matrix. All other data in the matrix are assumed to be zero. Zero values can also explicitly be stored in AbstractTensor.data.
• The row indices of the non-zero values in the sparse matrix.
• The column indices of the non-zero values in the sparse matrix.

Note: many ops assume that the data of the COO matrix are sorted lexicographically by the row and column indices. (i.e.) by row indices first then column indices. However, this is not explicitly verified but any ops implemented in this class will preserve the lexicographical sorting.

If indices need to be sorted, call AbstractCooSemiringMatrix.sortIndices().

See Also:

• Serialized Form

Field Summary

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

colIndices, nnz, numCols, numRows, rowIndices, sparsity, zeroElement

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

data, rank, shape

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	AbstractCooRingMatrix(Shape shape, W[] entries, int[] rowIndices, int[] colIndices)	Creates a sparse coo matrix with the specified non-zero data, non-zero indices, and shape.
protected	AbstractCooRingMatrix(Shape shape, W[] entries, int[] rowIndices, int[] colIndices, Object dummy)	Creates a sparse coo matrix with the specified non-zero data, non-zero indices, and shape.

Method Summary

Modifier and Type	Method	Description
T	H()	Computes the Hermitian transpose of this matrix.
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	isCloseToI()	Checks if the matrix is "close" to an identity matrix.
abstract AbstractCsrRingMatrix<?,U,V,W>	makeLikeCsrMatrix(Shape shape, W[] entries, int[] rowPointers, int[] colIndices)	Constructs a sparse CSR matrix of a similar type to this sparse COO matrix.
T	sub(T b)	Computes the element-wise difference between two tensors of the same shape.
AbstractCsrRingMatrix<?,U,V,W>	toCsr()	Converts this sparse COO matrix to an equivalent sparse CSR matrix.
abstract AbstractCooRingTensor<?,?,W>	toTensor()	Converts this matrix to an equivalent tensor.
abstract AbstractCooRingTensor<?,?,W>	toTensor(Shape newShape)	Converts this matrix to an equivalent tensor with the specified shape.

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

add, argmax, argmin, augment, augment, coalesce, coalesce, copy, dataLength, density, dropZeros, elemMult, flatten, flatten, get, get, getCol, getDiag, getRow, getSlice, getTriL, getTriU, getZeroElement, isHermitian, isI, isOrthogonal, isSymmetric, isTriL, isTriU, makeLikeDenseTensor, makeLikeTensor, makeLikeTensor, makeLikeVector, max, min, mult, multTranspose, numCols, numRows, removeCol, removeCols, removeRow, removeRows, reshape, set, set, setCol, setRow, setSliceCopy, setZeroElement, sortIndices, sparsity, stack, swapCols, swapRows, T, T, T, tensorTr, toDense, toVector, tr

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, isDiag, isHermitian, 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

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

AbstractCooRingMatrix

protected AbstractCooRingMatrix(Shape shape,
 W[] entries,
 int[] rowIndices,
 int[] colIndices)

Creates a sparse coo matrix with the specified non-zero data, non-zero indices, and shape.

Parameters:

shape - Shape of this tensor.

entries - Non-zero data of this sparse matrix.

rowIndices - Non-zero row indices of this sparse matrix.

colIndices - Non-zero column indies of this sparse matrix.

AbstractCooRingMatrix

protected AbstractCooRingMatrix(Shape shape,
 W[] entries,
 int[] rowIndices,
 int[] colIndices,
 Object dummy)

Creates a sparse coo matrix with the specified non-zero data, non-zero indices, and shape.

Parameters:

shape - Shape of this tensor.

entries - Non-zero data of this sparse matrix.

rowIndices - Non-zero row indices of this sparse matrix.

colIndices - Non-zero column indies of this sparse matrix.

dummy - Dummy object to distinguish this constructor from the safe variant.

Method Details

makeLikeCsrMatrix

public abstract AbstractCsrRingMatrix<?,U,V,W> makeLikeCsrMatrix(Shape shape,
 W[] entries,
 int[] rowPointers,
 int[] colIndices)

Constructs a sparse CSR matrix of a similar type to this sparse COO matrix.

Specified by:

makeLikeCsrMatrix in class AbstractCooSemiringMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Parameters:

shape - Shape of the CSR matrix to construct.

entries - Non-zero data of the CSR matrix.

rowPointers - Non-zero row pointers of the CSR matrix.

colIndices - Non-zero column indices of the CSR matrix.

Returns:

A CSR matrix of a similar type to this sparse COO matrix.

toCsr

public AbstractCsrRingMatrix<?,U,V,W> toCsr()

Converts this sparse COO matrix to an equivalent sparse CSR matrix.

Overrides:

toCsr in class AbstractCooSemiringMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Returns:

A sparse CSR matrix equivalent to this sparse COO matrix.

toTensor

public abstract AbstractCooRingTensor<?,?,W> toTensor()

Converts this matrix to an equivalent tensor.

Specified by:

toTensor in class AbstractCooSemiringMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Returns:

A tensor which is equivalent to this matrix.

toTensor

public abstract AbstractCooRingTensor<?,?,W> toTensor(Shape newShape)

Converts this matrix to an equivalent tensor with the specified shape.

Specified by:

toTensor in class AbstractCooSemiringMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Parameters:

newShape - New shape for the tensor. Can be any rank but must be broadcastable to this.shape.

Returns:

A tensor equivalent to this matrix which has been reshaped to newShape

sub

public T sub(T b)

Computes the element-wise difference between two tensors of the same shape.

Specified by:

sub in interface MatrixMixin<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Specified by:

sub in interface TensorOverRing<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Parameters:

b - Second tensor in the element-wise difference.

Returns:

The difference of this tensor with b.

Throws:

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

H

public T H()

Computes the Hermitian transpose of this matrix.

Specified by:

H in interface MatrixMixin<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Specified by:

H in interface TensorOverRing<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Overrides:

H in class AbstractCooSemiringMatrix<T extends AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

Returns:

The Hermitian transpose of this matrix.

See Also:

• TensorOverRing.H(int, int)
• TensorOverRing.H(int...)

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 AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

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:

• 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 AbstractCooRingMatrix<T,U,V,W>,U extends AbstractDenseRingMatrix<U,?,W>,V extends AbstractCooRingVector<V,?,T,U,W>,W extends Ring<W>>

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)
• H()

isCloseToI

public boolean isCloseToI()

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.