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

java.lang.Object

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

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

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

Type Parameters:

T - Type of this vector.

U - Type of equivalent dense vector.

V - Type of matrix equivalent to T.

Y - Type of dense matrix equivalent to U.

Y - Type of the arrays element in this vector.

All Implemented Interfaces:

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

Direct Known Subclasses:

AbstractCooFieldVector, CooRingVector

public abstract class AbstractCooRingVector<T extends AbstractCooRingVector<T,U,V,W,Y>,U extends AbstractDenseRingVector<U,W,Y>,V extends AbstractCooRingMatrix<V,W,T,Y>,W extends AbstractDenseRingMatrix<W,U,Y>,Y extends Ring<Y>>
extends AbstractCooSemiringVector<T,U,V,W,Y>
implements RingTensorMixin<T,U,Y>, VectorMixin<T,V,W,Y>

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

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

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

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

A sparse COO vector is stored as:

• The full AbstractTensor.shape/VectorMixin.size() of the vector.
• The non-zero AbstractTensor.data of the vector. All other data in the vector are assumed to be zero. Zero values can also explicitly be stored in AbstractTensor.data.
• The AbstractCooSemiringVector.indices of the non-zero values in the sparse vector.

Note: many ops assume that the data of the COO vector are sorted lexicographically. However, this is not explicitly verified. Every operation implemented in this class will preserve the lexicographical sorting.

If indices need to be sorted for any reason, call AbstractCooSemiringVector.sortIndices().

See Also:

• Serialized Form

Field Summary

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

indices, nnz, size, sparsity

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

data, rank, shape

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	AbstractCooRingVector(Shape shape, Y[] entries, int[] indices)	Creates a COO vector with the specified data and shape.

Method Summary

Modifier and Type	Method	Description
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.
Y	inner(T b)	Computes the inner product between two vectors.
T	sub(T b)	Computes the element-wise difference between two tensors of the same shape.

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

add, coalesce, coalesce, copy, density, dot, dropZeros, elemMult, flatten, flatten, get, get, getZeroElement, join, length, mag, makeLikeDenseMatrix, makeLikeDenseTensor, makeLikeMatrix, makeLikeTensor, makeLikeTensor, normalize, outer, repeat, reshape, set, setZeroElement, sortIndices, sparsity, stack, T, T, tensorDot, tensorTr, toDense, toMatrix, toTensor, toTensor

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

getData, getRank, getShape, makeLikeTensor, reshape, sameShape, T, 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.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.semiring_arrays.SemiringTensorMixin

argmax, argmin, max, min

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

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

dot, get, join, length, mag, normalize, outer, repeat, size, stack, stack, toMatrix, toMatrix

Constructor Details

AbstractCooRingVector

protected AbstractCooRingVector(Shape shape,
 Y[] entries,
 int[] indices)

Creates a COO vector with the specified data and shape.

Parameters:

shape - Shape of the vector.

entries - The non-zero entries of the vector.

indices - The If this tensor is sparse, this specifies only the non-zero data of the tensor.

Method Details

inner

public Y inner(T b)

Computes the inner product between two vectors.

Note: this method is distinct from AbstractCooSemiringVector.dot(AbstractCooSemiringVector). The inner product is equivalent to the dot product of this tensor with the conjugation of b.

Specified by:

inner in interface VectorMixin<T extends AbstractCooRingVector<T,U,V,W,Y>,U extends AbstractDenseRingVector<U,W,Y>,V extends AbstractCooRingMatrix<V,W,T,Y>,W extends AbstractDenseRingMatrix<W,U,Y>>

Overrides:

inner in class AbstractCooSemiringVector<T extends AbstractCooRingVector<T,U,V,W,Y>,U extends AbstractDenseRingVector<U,W,Y>,V extends AbstractCooRingMatrix<V,W,T,Y>,W extends AbstractDenseRingMatrix<W,U,Y>,Y extends Ring<Y>>

Parameters:

b - Second vector in the inner product.

Returns:

The inner product between this vector and the vector b.

Throws:

IllegalArgumentException - If this vector and vector b do not have the same number of data.

See Also:

• AbstractCooSemiringVector.dot(AbstractCooSemiringVector)

sub

public T sub(T b)

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

Specified by:

sub in interface TensorOverRing<T extends AbstractCooRingVector<T,U,V,W,Y>,U extends AbstractDenseRingVector<U,W,Y>,V extends AbstractCooRingMatrix<V,W,T,Y>,W extends AbstractDenseRingMatrix<W,U,Y>>

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(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 AbstractCooRingVector<T,U,V,W,Y>,U extends AbstractDenseRingVector<U,W,Y>,V extends AbstractCooRingMatrix<V,W,T,Y>,W extends AbstractDenseRingMatrix<W,U,Y>>

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:

• TensorOverRing.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 AbstractCooRingVector<T,U,V,W,Y>,U extends AbstractDenseRingVector<U,W,Y>,V extends AbstractCooRingMatrix<V,W,T,Y>,W extends AbstractDenseRingMatrix<W,U,Y>>

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)
• TensorOverRing.H()