Class AbstractCooFieldMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<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>

org.flag4j.arrays.backend.field_arrays.AbstractCooFieldMatrix<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 field element in this matrix.

All Implemented Interfaces:

Serializable, FieldTensorMixin<T,U,W>, TensorOverField<T,U,W[],W>, 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:

CooCMatrix, CooFieldMatrix

public abstract class AbstractCooFieldMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>
extends AbstractCooRingMatrix<T,U,V,W>
implements FieldTensorMixin<T,U,W>, MatrixMixin<T,U,V,W>

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

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	AbstractCooFieldMatrix(Shape shape, W[] entries, int[] rowIndices, int[] colIndices)	Creates a sparse coo matrix with the specified non-zero data, non-zero indices, and shape.

Method Summary

Modifier and Type	Method	Description
CooMatrix	abs()	Computes the element-wise absolute value of this tensor.
T	div(T b)	Computes the element-wise quotient between two tensors.
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	isFinite()	Checks if this tensor only contains finite values.
boolean	isInfinite()	Checks if this tensor contains at least one infinite value.
boolean	isNaN()	Checks if this tensor contains at least one NaN value.
abstract AbstractCsrFieldMatrix<?,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.
U	multTranspose(T b)	Multiplies this matrix with the transpose of the b tensor as if by this.mult(b.H()).
T	sqrt()	Computes the element-wise square root of this tensor.
AbstractCsrFieldMatrix<?,U,V,W>	toCsr()	Converts this sparse COO matrix to an equivalent sparse CSR matrix.

Methods inherited from class org.flag4j.arrays.backend.ring_arrays.AbstractCooRingMatrix

isCloseToI, sub, toTensor, toTensor

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, 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.field_arrays.FieldTensorMixin

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

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

accept, add, augment, augment, copy, dataLength, 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, numCols, numRows, removeCol, removeCols, removeRow, removeRows, set, setCol, setRow, setSliceCopy, stack, stack, sub, swapCols, swapRows, T, toVector, tr, trace, vectorType

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

sub

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

AbstractCooFieldMatrix

protected AbstractCooFieldMatrix(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.

Method Details

makeLikeCsrMatrix

public abstract AbstractCsrFieldMatrix<?,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 AbstractCooRingMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<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.

multTranspose

public U multTranspose(T b)

Multiplies this matrix with the transpose of the b tensor as if by this.mult(b.H()). For large matrices, this method may be significantly faster than directly computing the Hermitian transpose followed by the multiplication as this.mult(b.H()).

Specified by:

multTranspose in interface MatrixMixin<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Overrides:

multTranspose in class AbstractCooSemiringMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Parameters:

b - The second matrix in the multiplication and the matrix to transpose.

Returns:

The result of multiplying this matrix with the Hermitian transpose of b.

abs

public CooMatrix abs()

Computes the element-wise absolute value of this tensor.

Specified by:

abs in interface TensorOverRing<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Returns:

The element-wise absolute value of this tensor.

H

public T H()

Computes the Hermitian transpose of this matrix.

Specified by:

H in interface MatrixMixin<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Specified by:

H in interface TensorOverRing<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Overrides:

H in class AbstractCooRingMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<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 AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Overrides:

H in class AbstractCooRingMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<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 AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Overrides:

H in class AbstractCooRingMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<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()

toCsr

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

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

Overrides:

toCsr in class AbstractCooRingMatrix<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Returns:

A sparse CSR matrix equivalent to this sparse COO matrix.

div

public T div(T b)

Computes the element-wise quotient between two tensors.

WARNING: This method is not supported for sparse tensors. If called on a sparse tensor, an UnsupportedOperationException will be thrown. Element-wise division is undefined for sparse matrices as it would almost certainly result in a division by zero.

Specified by:

div in interface MatrixMixin<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Specified by:

div in interface TensorOverField<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Parameters:

b - Second tensor in the element-wise quotient.

Returns:

The element-wise quotient of this tensor with b.

Throws:

UnsupportedOperationException - if this method is ever invoked on a sparse tensor.

sqrt

public T sqrt()

Computes the element-wise square root of this tensor.

Specified by:

sqrt in interface TensorOverField<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Returns:

The element-wise square root of this tensor.

isFinite

public boolean isFinite()

Checks if this tensor only contains finite values.

Specified by:

isFinite in interface TensorOverField<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Returns:

true if this tensor only contains finite values; false otherwise.

See Also:

• isInfinite()
• isNaN()

isInfinite

public boolean isInfinite()

Checks if this tensor contains at least one infinite value.

Specified by:

isInfinite in interface TensorOverField<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Returns:

true if this tensor contains at least one infinite value; false otherwise.

See Also:

• isFinite()
• isNaN()

isNaN

public boolean isNaN()

Checks if this tensor contains at least one NaN value.

Specified by:

isNaN in interface TensorOverField<T extends AbstractCooFieldMatrix<T,U,V,W>,U extends AbstractDenseFieldMatrix<U,?,W>,V extends AbstractCooFieldVector<V,?,T,U,W>,W extends Field<W>>

Returns:

true if this tensor contains at least one NaN value; false otherwise.

See Also:

• isFinite()
• isInfinite()