Module flag4j

Package org.flag4j.arrays.backend

Class FieldTensorBase<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,V extends Field<V>>

java.lang.Object

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

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

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

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

org.flag4j.arrays.backend.FieldTensorBase<T,U,V>

Type Parameters:

T - The type of this tensor.

U - Type of dense tensor equivalent to T. If T is dense, then this should be the same type as T. This parameter is required because some operations (e.g. TensorOverSemiRing.tensorDot(TensorOverSemiRing, int)) between two sparse tensors result in a dense tensor.

V - The type of the Field for this tensor's entries.

All Implemented Interfaces:

Serializable, TensorBinaryOpsMixin<T,T>, TensorMixin<T,Field<V>[],V>

Direct Known Subclasses:

CooFieldMatrixBase, CooFieldTensorBase, CooFieldVectorBase, CsrFieldMatrixBase, DenseFieldMatrixBase, DenseFieldTensorBase, DenseFieldVectorBase

public abstract class FieldTensorBase<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,V extends Field<V>>
extends TensorOverField<T,U,Field<V>[],V>

The base class for all tensors whose entries are elements of a Field.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private V	zeroElement	Stores the zero element of the field for this tensor.

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

entries, rank, shape

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	FieldTensorBase(Shape shape, Field<V>[] entries)	Creates a tensor with the specified entries and shape.

Method Summary

Modifier and Type	Method	Description
T	add(double b)	Adds a real value to each entry of this tensor.
T	add(T b)	Computes the element-wise sum between two tensors of the same shape.
T	add(V b)	Adds a scalar field value to each entry of this tensor.
void	addEq(V b)	Adds a scalar value to each entry of this tensor and stores the result in this tensor.
T	conj()	Computes the element-wise conjugation of this tensor.
T	copy()	Creates a copy of this tensor.
T	div(double b)	Divides each entry of this tensor by a real value.
T	div(V b)	Divides each entry of this tensor by a scalar field element.
void	divEq(V b)	Divides each entry of this tensor by s scalar field element and stores the result in this tensor.
T	elemMult(T b)	Computes the element-wise multiplication of two tensors of the same shape.
T	flatten()	Flattens tensor to single dimension while preserving order of entries.
T	flatten(int axis)	Flattens a tensor along the specified axis.
V	get(int... indices)	Gets the element of this tensor at the specified indices.
V	getZeroElement()	Gets the zero element for the field of this tensor.
T	H()	Computes the Hermitian transpose of a tensor by exchanging and conjugating the first and last axes of this tensor.
boolean	isOnes()	Checks if this tensor only contains ones.
boolean	isZeros()	Checks if this tensor only contains zeros.
T	mult(double b)	Multiplies a real value to each entry of this tensor.
T	mult(V b)	Multiplies a scalar field value to each entry of this tensor.
void	multEq(V b)	Multiplies a scalar value to each entry of this tensor and stores the result in this tensor.
V	prod()	Computes the product of all values in this tensor.
T	recip()	Computes the element-wise reciprocals of this tensor.
T	reshape(Shape newShape)	Copies and reshapes this tensor.
protected void	setZeroElement(V zeroElement)	Sets the zero element for the field of this tensor.
T	sqrt()	Computes the element-wise square root of a tensor.
T	sub(double b)	Subtracts a real value from each entry of this tensor.
T	sub(T b)	Computes the element-wise difference between two tensors of the same shape.
T	sub(V b)	Subtracts a scalar field value from each entry of this tensor.
void	subEq(V b)	Subtracts a scalar value from each entry of this tensor and stores the result in this tensor.
V	sum()	Computes the sum of all values in this tensor.
T	T()	Computes the transpose of a tensor by exchanging the first and last axes of this tensor.
T	tensorTr(int axis1, int axis2)	Computes the generalized trace of this tensor along the specified axes.

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

abs, H, H

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

tensorDot, tensorDot, tensorDot, tensorDot, tensorTr

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

getEntries, getRank, getShape, makeLikeTensor, reshape, sameShape, set, 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.TensorMixin

T, T

Field Details

zeroElement

private V extends Field<V> zeroElement

Stores the zero element of the field for this tensor.

Constructor Details

FieldTensorBase

protected FieldTensorBase(Shape shape,
 Field<V>[] 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.

Method Details

setZeroElement

protected void setZeroElement(V zeroElement)

Sets the zero element for the field of this tensor. This is useful in some operations for cases where the total number of entries or total number of non-zero entries is zero. In such cases, the zero element cannot be determined for a generic field so null is used. When

Parameters:

zeroElement - Zero element for the field of this tensor.

getZeroElement

public V getZeroElement()

Gets the zero element for the field of this tensor.

Returns:

The zero element for the field of this tensor. If it could not be determined during construction of this object and has not been set explicitly by setZeroElement(Field) then null will be returned.

get

public V get(int... indices)

Gets the element of this tensor at the specified indices.

Specified by:

get in interface TensorMixin<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,V extends Field<V>>

Specified by:

get in class AbstractTensor<T extends FieldTensorBase<T,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

indices - Indices of the element to get.

Returns:

The element of this tensor at the specified indices.

Throws:

ArrayIndexOutOfBoundsException - If any indices are not within this matrix.

flatten

public T flatten()

Flattens tensor to single dimension while preserving order of entries.

Specified by:

flatten in class AbstractTensor<T extends FieldTensorBase<T,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

The flattened tensor.

See Also:

• flatten(int)

flatten

public T flatten(int axis)

Flattens a tensor along the specified axis.

Specified by:

flatten in class AbstractTensor<T extends FieldTensorBase<T,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

axis - Axis along which to flatten tensor.

Throws:

ArrayIndexOutOfBoundsException - If the axis is not positive or larger than this.AbstractTensor.getRank()-1.

See Also:

• flatten()

reshape

public T reshape(Shape newShape)

Copies and reshapes this tensor.

Specified by:

reshape in class AbstractTensor<T extends FieldTensorBase<T,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

newShape - New shape for the tensor.

Returns:

A copy of this tensor with the new shape.

Throws:

TensorShapeException - If newShape is not broadcastable to this.shape.

sum

public V sum()

Computes the sum of all values in this tensor.

Specified by:

sum in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

The sum of all values in this tensor.

prod

public V prod()

Computes the product of all values in this tensor.

Specified by:

prod in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

The product of all values in this tensor.

add

public T add(T b)

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

Specified by:

add in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Second tensor in the element-wise sum.

Returns:

The sum of this tensor with b.

Throws:

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

sub

public T sub(T b)

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

Specified by:

sub in class TensorOverRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Second tensor in the element-wise difference.

Returns:

The difference of this tensor with the scalar b.

Throws:

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

add

public T add(double b)

Adds a real value to each entry of this tensor.

Specified by:

add in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Value to add to each value of this tensor.

Returns:

Sum of this tensor with b.

sub

public T sub(double b)

Subtracts a real value from each entry of this tensor.

Specified by:

sub in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Value to subtract from each value of this tensor.

Returns:

Difference of this tensor with b.

mult

public T mult(double b)

Multiplies a real value to each entry of this tensor.

Specified by:

mult in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Value to multiply to each value of this tensor.

Returns:

Product of this tensor with b.

div

public T div(double b)

Divides each entry of this tensor by a real value.

Specified by:

div in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Value to divide each value of this tensor by.

Returns:

Quotient of this tensor with b.

conj

public T conj()

Computes the element-wise conjugation of this tensor.

Specified by:

conj in class TensorOverRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

The element-wise conjugation of this tensor.

elemMult

public T elemMult(T b)

Computes the element-wise multiplication of two tensors of the same shape.

Specified by:

elemMult in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Second tensor in the element-wise product.

Returns:

The element-wise product between this tensor and b.

Throws:

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

tensorTr

public T tensorTr(int axis1,
 int axis2)

Computes the generalized trace of this tensor along the specified axes.

The generalized tensor trace is the sum along the diagonal values of the 2D sub-arrays_old of this tensor specified by axis1 and axis2. The shape of the resulting tensor is equal to this tensor with the axis1 and axis2 removed.

Specified by:

tensorTr in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

axis1 - First axis for 2D sub-array.

axis2 - Second axis for 2D sub-array.

Returns:

The generalized trace of this tensor along axis1 and axis2.

Throws:

IndexOutOfBoundsException - If the two axes are not both larger than zero and less than this tensors rank.

IllegalArgumentException - If axis1 == @code axis2 or this.shape.get(axis1) != this.shape.get(axis1) (i.e. the axes are equal or the tensor does not have the same length along the two axes.)

isZeros

public boolean isZeros()

Checks if this tensor only contains zeros.

Specified by:

isZeros in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

True if this tensor only contains zeros. Otherwise, returns false.

isOnes

public boolean isOnes()

Checks if this tensor only contains ones. If this tensor is sparse, only the non-zero entries are considered.

Specified by:

isOnes in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

True if this tensor only contains ones. Otherwise, returns false.

add

public T add(V b)

Adds a scalar field value to each entry of this tensor.

Specified by:

add in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar field value in sum.

Returns:

The sum of this tensor with the scalar b.

addEq

public void addEq(V b)

Adds a scalar value to each entry of this tensor and stores the result in this tensor.

Specified by:

addEq in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar field value in sum.

sub

public T sub(V b)

Subtracts a scalar field value from each entry of this tensor.

Specified by:

sub in class TensorOverRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar field value in difference.

Returns:

The difference of this tensor and the scalar b.

subEq

public void subEq(V b)

Subtracts a scalar value from each entry of this tensor and stores the result in this tensor.

Specified by:

subEq in class TensorOverRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar value in difference.

mult

public T mult(V b)

Multiplies a scalar field value to each entry of this tensor.

Specified by:

mult in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar field value in product.

Returns:

The product of this tensor with b.

multEq

public void multEq(V b)

Multiplies a scalar value to each entry of this tensor and stores the result in this tensor.

Specified by:

multEq in class TensorOverSemiRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar value in product.

div

public T div(V b)

Divides each entry of this tensor by a scalar field element.

Specified by:

div in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar field value in quotient.

Returns:

The quotient of this tensor with b.

divEq

public void divEq(V b)

Divides each entry of this tensor by s scalar field element and stores the result in this tensor.

Specified by:

divEq in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Parameters:

b - Scalar field value in quotient.

sqrt

public T sqrt()

Computes the element-wise square root of a tensor.

Specified by:

sqrt in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

The result of applying an element-wise square root to this tensor. Note, this method will compute the principle square root i.e. the square root with positive real part.

T

public T T()

Computes the transpose of a tensor by exchanging the first and last axes of this tensor.

Returns:

The transpose of this tensor.

See Also:

• TensorMixin.T(int, int)
• TensorMixin.T(int...)

H

public T H()

Computes the Hermitian transpose of a tensor by exchanging and conjugating the first and last axes of this tensor.

Specified by:

H in class TensorOverRing<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

The Hermitian transpose of this tensor.

See Also:

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

recip

public T recip()

Computes the element-wise reciprocals of this tensor.

Specified by:

recip in class TensorOverField<T extends FieldTensorBase<T,U,V>,U extends FieldTensorBase<U,U,V>,Field<V extends Field<V>>[],V extends Field<V>>

Returns:

A tensor containing the reciprocal elements of this tensor.

copy

public T copy()

Creates a copy of this tensor.

Returns:

A copy of this tensor.