Module flag4j

Package org.flag4j.arrays.dense

Class FieldTensor<T extends Field<T>>

java.lang.Object

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

org.flag4j.arrays.backend.TensorOverSemiRing<FieldTensor<T>,FieldTensor<T>,Field<T>[],T>

org.flag4j.arrays.backend.TensorOverRing<FieldTensor<T>,FieldTensor<T>,Field<T>[],T>

org.flag4j.arrays.backend.TensorOverField<FieldTensor<T>,FieldTensor<T>,Field<T>[],T>

org.flag4j.arrays.backend.FieldTensorBase<FieldTensor<T>,FieldTensor<T>,T>

org.flag4j.arrays.backend.DenseFieldTensorBase<FieldTensor<T>,CooFieldTensor<T>,T>

org.flag4j.arrays.dense.FieldTensor<T>

Type Parameters:

T - Type of the field element for the tensor.

All Implemented Interfaces:

Serializable, DenseTensorMixin<FieldTensor<T>,CooFieldTensor<T>>, TensorBinaryOpsMixin<FieldTensor<T>,FieldTensor<T>>, TensorMixin<FieldTensor<T>,Field<T>[],T>

public class FieldTensor<T extends Field<T>>
extends DenseFieldTensorBase<FieldTensor<T>,CooFieldTensor<T>,T>

A dense tensor whose entries are Field elements.

The AbstractTensor.entries of a field tensor are mutable but the AbstractTensor.shape is fixed.

See Also:

• Serialized Form

Field Summary

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

entries, rank, shape

Constructor Summary

Constructors

Constructor	Description
FieldTensor(Shape shape, Field<T>[] entries)	Creates a tensor with the specified entries and shape.
FieldTensor(Shape shape, T fillValue)	Creates a tensor with the specified shape filled with fillValue.

Method Summary

Modifier and Type	Method	Description
boolean	equals(Object object)	Checks if an object is equal to this tensor object.
FieldTensor<T>	H(int... axes)	Computes the conjugate transpose of this tensor.
FieldTensor<T>	H(int axis1, int axis2)	Computes the conjugate transpose of a tensor by conjugating and exchanging axis1 and axis2.
int	hashCode()
FieldTensor<T>	makeLikeTensor(Shape shape, Field<T>[] entries)	Constructs a tensor of the same type as this tensor with the given the shape and entries.
FieldTensor<T>	T(int... axes)	Computes the transpose of this tensor.
FieldTensor<T>	T(int axis1, int axis2)	Computes the transpose of a tensor by exchanging axis1 and axis2.
FieldTensor<T>	tensorDot(FieldTensor<T> src2)	Computes the tensor dot product of this tensor with a second tensor.
FieldTensor<T>	tensorDot(FieldTensor<T> src2, int[] aAxes, int[] bAxes)	Computes the tensor contraction of this tensor with a specified tensor over the specified set of axes.
CooFieldTensor<T>	toCoo()	Converts this dense tensor to an equivalent sparse tensor.
FieldMatrix<T>	toMatrix()	Converts this tensor to an equivalent matrix.
FieldMatrix<T>	toMatrix(Shape matShape)	Converts this tensor to a matrix with the specified shape.
FieldVector<T>	toVector()	Converts this tensor to an equivalent vector.

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

abs, addEq, allClose, div, divEq, elemMultEq, set, subEq

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

add, add, add, addEq, conj, copy, div, div, divEq, elemMult, flatten, flatten, get, getZeroElement, H, isOnes, isZeros, mult, mult, multEq, prod, recip, reshape, setZeroElement, sqrt, sub, sub, sub, subEq, sum, T, tensorTr

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

tensorDot, tensorDot, tensorTr

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

getEntries, getRank, getShape, reshape, sameShape, totalEntries

Methods inherited from class java.lang.Object

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

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

allClose

Constructor Details

FieldTensor

public FieldTensor(Shape shape,
 Field<T>[] entries)

Creates a tensor with the specified entries and shape.

Parameters:

shape - Shape of this tensor.

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

FieldTensor

public FieldTensor(Shape shape,
 T fillValue)

Creates a tensor with the specified shape filled with fillValue.

Parameters:

shape - Shape of this tensor.

fillValue - Value to fill tensor with.

Method Details

tensorDot

public FieldTensor<T> tensorDot(FieldTensor<T> src2,
 int[] aAxes,
 int[] bAxes)

Computes the tensor contraction of this tensor with a specified tensor over the specified set of axes. That is, computes the sum of products between the two tensors along the specified set of axes.

Overrides:

tensorDot in class DenseFieldTensorBase<FieldTensor<T extends Field<T>>,CooFieldTensor<T extends Field<T>>,T extends Field<T>>

Parameters:

src2 - TensorOld to contract with this tensor.

aAxes - Axes along which to compute products for this tensor.

bAxes - Axes along which to compute products for src2 tensor.

Returns:

The tensor dot product over the specified axes.

Throws:

IllegalArgumentException - If the two tensors shapes do not match along the specified axes pairwise in aAxes and bAxes.

IllegalArgumentException - If aAxes and bAxes do not match in length, or if any of the axes are out of bounds for the corresponding tensor.

tensorDot

public FieldTensor<T> tensorDot(FieldTensor<T> src2)

Computes the tensor dot product of this tensor with a second tensor. That is, sums the product of two tensor elements over the last axis of this tensor and the second-to-last axis of src2. If both tensors are rank 2, this is equivalent to matrix multiplication.

Overrides:

tensorDot in class TensorOverSemiRing<FieldTensor<T extends Field<T>>,FieldTensor<T extends Field<T>>,Field<T extends Field<T>>[],T extends Field<T>>

Parameters:

src2 - TensorOld to compute dot product with this tensor.

Returns:

The tensor dot product over the last axis of this tensor and the second to last axis of src2.

Throws:

IllegalArgumentException - If this tensors shape along the last axis does not match src2 shape along the second-to-last axis.

H

public FieldTensor<T> H(int axis1,
 int axis2)

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

Overrides:

H in class DenseFieldTensorBase<FieldTensor<T extends Field<T>>,CooFieldTensor<T extends Field<T>>,T extends Field<T>>

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:

• FieldTensorBase.H()
• H(int...)

H

public FieldTensor<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.

Overrides:

H in class DenseFieldTensorBase<FieldTensor<T extends Field<T>>,CooFieldTensor<T extends Field<T>>,T extends Field<T>>

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)
• FieldTensorBase.H()

makeLikeTensor

public FieldTensor<T> makeLikeTensor(Shape shape,
 Field<T>[] entries)

Constructs a tensor of the same type as this tensor with the given the shape and entries.

Specified by:

makeLikeTensor in interface TensorMixin<FieldTensor<T extends Field<T>>,Field<T extends Field<T>>[],T extends Field<T>>

Specified by:

makeLikeTensor in class AbstractTensor<FieldTensor<T extends Field<T>>,Field<T extends Field<T>>[],T extends Field<T>>

Parameters:

shape - Shape of the tensor to construct.

entries - Entries of the tensor to construct.

Returns:

A tensor of the same type as this tensor with the given the shape and entries.

T

public FieldTensor<T> T(int axis1,
 int axis2)

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

Specified by:

T in interface TensorMixin<FieldTensor<T extends Field<T>>,Field<T extends Field<T>>[],T extends Field<T>>

Overrides:

T in class DenseFieldTensorBase<FieldTensor<T extends Field<T>>,CooFieldTensor<T extends Field<T>>,T extends Field<T>>

Parameters:

axis1 - First axis to exchange.

axis2 - Second axis to exchange.

Returns:

The 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:

• FieldTensorBase.T()
• T(int...)

T

public FieldTensor<T> T(int... axes)

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

Specified by:

T in interface TensorMixin<FieldTensor<T extends Field<T>>,Field<T extends Field<T>>[],T extends Field<T>>

Overrides:

T in class DenseFieldTensorBase<FieldTensor<T extends Field<T>>,CooFieldTensor<T extends Field<T>>,T extends Field<T>>

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 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:

• T(int, int)
• FieldTensorBase.T()

toCoo

public CooFieldTensor<T> toCoo()

Converts this dense tensor to an equivalent sparse tensor.

Returns:

A sparse tensor equivalent to this dense tensor.

toVector

public FieldVector<T> toVector()

Converts this tensor to an equivalent vector. If this tensor is not rank 1, then it will be flattened.

Returns:

A vector equivalent of this tensor.

toMatrix

public FieldMatrix<T> toMatrix(Shape matShape)

Converts this tensor to a matrix with the specified shape.

Parameters:

matShape - Shape of the resulting matrix. Must be broadcastable with the shape of this tensor.

Returns:

A matrix of shape matShape with the values of this tensor.

Throws:

LinearAlgebraException - If matShape is not of rank 2.

toMatrix

public FieldMatrix<T> toMatrix()

Converts this tensor to an equivalent matrix.

Returns:

If this tensor is rank 2, then the equivalent matrix will be returned. If the tensor is rank 1, then a matrix with a single row will be returned. If the rank of this tensor is larger than 2, it will be flattened to a single row.

equals

public boolean equals(Object object)

Checks if an object is equal to this tensor object.

Overrides:

equals in class Object

Parameters:

object - Object to check equality with this tensor.

Returns:

True if the two tensors have the same shape, are numerically equivalent, and are of type FieldTensor. False otherwise.

hashCode

public int hashCode()

Overrides:

hashCode in class Object