Package org.flag4j.arrays.dense

Class Tensor

java.lang.Object

org.flag4j.core.TensorBase<Tensor,Tensor,CTensor,CTensor,Tensor,double[],Double>

org.flag4j.core.dense_base.DenseTensorBase<Tensor,CTensor,Tensor,double[],Double>

org.flag4j.core.dense_base.RealDenseTensorBase<Tensor,CTensor>

org.flag4j.arrays.dense.Tensor

All Implemented Interfaces:

Serializable, DenseMixin<Double>, RealTensorMixin<Tensor,CTensor>, TensorComparisonsMixin, TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>, TensorManipulationsMixin<Tensor>, TensorOperationsMixin<Tensor,Tensor,CTensor,CTensor,Tensor,Double>, TensorPropertiesMixin

public class Tensor
extends RealDenseTensorBase<Tensor,CTensor>
implements TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Real Dense Tensor. May have any rank (that is, may have any number of unique axes/dimensions).

See Also:

• Serialized Form

Field Summary

Fields inherited from class org.flag4j.core.TensorBase

DEFAULT_ROUND_TO_ZERO_THRESHOLD, entries, shape

Constructor Summary

Constructors

Constructor	Description
Tensor(Matrix A)	Constructs a tensor whose shape and entries are specified by a matrix.
Tensor(Tensor A)	Constructs a tensor from another tensor.
Tensor(Vector A)	Constructs a tensor whose shape and entries are specified by a vector.
Tensor(Shape shape)	Constructs a tensor with given shape filled with zeros.
Tensor(Shape shape, double fillValue)	Constructs a tensor with given shape filled with specified values.
Tensor(Shape shape, double[] entries)	Constructs a tensor with given shape filled with specified values.
Tensor(Shape shape, int[] entries)	Constructs a tensor with given shape filled with specified values.
Tensor(Shape shape, Double[] entries)	Constructs a tensor with given shape filled with specified values.
Tensor(Shape shape, Integer[] entries)	Constructs a tensor with given shape filled with specified values.

Method Summary

Modifier and Type	Method	Description
CTensor	add(CTensor B)	Computes the element-wise addition between two tensors of the same rank.
CTensor	add(CooCTensor B)	Computes the element-wise addition between two tensors of the same rank.
Tensor	add(CooTensor B)	Computes the element-wise addition between two tensors of the same rank.
void	addEq(CooTensor B)	Computes the element-wise addition of two tensors of the same rank and stores the result in this tensor.
CTensor	elemDiv(CTensor B)	Computes the element-wise division between two tensors.
CTensor	elemMult(CTensor B)	Computes the element-wise multiplication between two tensors.
CooCTensor	elemMult(CooCTensor B)	Computes the element-wise multiplication between two tensors.
CooTensor	elemMult(CooTensor B)	Computes the element-wise multiplication between two tensors.
boolean	equals(Object object)	Checks if an object is equal to this tensor object.
Tensor	flatten()	Flattens tensor to single dimension.
Tensor	flatten(int axis)	Flattens a tensor along the specified axis.
protected Tensor	getSelf()	Simply returns this tensor.
protected CTensor	makeComplexTensor(Shape shape, double[] entries)	Factory to create a complex tensor with the specified shape and size.
protected CTensor	makeComplexTensor(Shape shape, CNumber[] entries)	Factory to create a complex tensor with the specified shape and size.
protected Tensor	makeTensor(Shape shape, double[] entries)	Factory to create a tensor with the specified shape and size.
CTensor	sub(CTensor B)	Computes the element-wise subtraction between two tensors of the same rank.
CTensor	sub(CooCTensor B)	Computes the element-wise subtraction between two tensors of the same rank.
Tensor	sub(CooTensor B)	Computes the element-wise subtraction between two tensors of the same rank.
void	subEq(CooTensor B)	Computes the element-wise subtraction of two tensors of the same rank and stores the result in this tensor.
Tensor	T()	Computes the transpose of a tensor.
Tensor	T(int... axes)	Computes the transpose of this tensor.
Tensor	T(int axis1, int axis2)	Computes the transpose of a tensor.
Tensor	tensorDot(Tensor src2)	Computes the tensor dot product of this tensor with a second tensor.
Tensor	tensorDot(Tensor src2, int[] aAxes, int[] bAxes)	Computes the tensor contraction of this tensor with a specified tensor over the specified set of axes.
Tensor	tensorInv(int numIndices)	Computes the 'inverse' of this tensor.
CooTensor	toCoo()	Converts this dense tensor to an equivalent sparse COO tensor.
Matrix	toMatrix()	Converts this tensor to an equivalent matrix.
Matrix	toMatrix(Shape matShape)	Converts this tensor to a matrix with the specified shape.
String	toString()	Formats this tensor as a human-readable string.
Vector	toVector()	Converts this tensor to an equivalent vector.

Methods inherited from class org.flag4j.core.dense_base.RealDenseTensorBase

abs, add, add, add, addEq, addEq, allClose, argMax, argMin, copy, div, div, elemDiv, elemMult, get, hashCode, isNeg, isOnes, isPos, isZeros, max, maxAbs, min, minAbs, mult, mult, recip, reshape, reshape, round, round, roundToZero, roundToZero, set, sqrt, sub, sub, sub, subEq, subEq, sum, toComplex

Methods inherited from class org.flag4j.core.TensorBase

allClose, getEntries, getRank, getShape, sameLength, sameShape, tensorEquals, totalEntries

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.flag4j.core.TensorExclusiveMixin

add, elemDiv, elemMult, getRank, sub, tensorDot, tensorDot, tensorInv, transpose, transpose

Methods inherited from interface org.flag4j.core.TensorOperationsMixin

transpose

Constructor Details

Tensor

public Tensor(Shape shape)

Constructs a tensor with given shape filled with zeros.

Parameters:

shape - Shape of the tensor.

Tensor

public Tensor(Shape shape,
 double fillValue)

Constructs a tensor with given shape filled with specified values.

Parameters:

shape - Shape of the tensor.

fillValue - Value to fill tensor with.

Tensor

public Tensor(Shape shape,
 double[] entries)

Constructs a tensor with given shape filled with specified values.

Parameters:

shape - Shape of the tensor.

entries - Entries of the vector.

Throws:

IllegalArgumentException - If the shape does not match the number of entries.

Tensor

public Tensor(Shape shape,
 int[] entries)

Constructs a tensor with given shape filled with specified values.

Parameters:

shape - Shape of the tensor.

entries - Entries of the vector.

Throws:

IllegalArgumentException - If the shape does not match the number of entries.

Tensor

public Tensor(Shape shape,
 Double[] entries)

Constructs a tensor with given shape filled with specified values.

Parameters:

shape - Shape of the tensor.

entries - Entries of the vector.

Throws:

IllegalArgumentException - If the shape does not match the number of entries.

Tensor

public Tensor(Shape shape,
 Integer[] entries)

Constructs a tensor with given shape filled with specified values.

Parameters:

shape - Shape of the tensor.

entries - Entries of the vector.

Throws:

IllegalArgumentException - If the shape does not match the number of entries.

Tensor

public Tensor(Tensor A)

Constructs a tensor from another tensor. This effectively copies the tensor.

Parameters:

A - tensor to copy.

Tensor

public Tensor(Matrix A)

Constructs a tensor whose shape and entries are specified by a matrix.

Parameters:

A - Matrix to copy to tensor.

Tensor

public Tensor(Vector A)

Constructs a tensor whose shape and entries are specified by a vector.

Parameters:

A - Vector to copy to tensor.

Method Details

makeTensor

protected Tensor makeTensor(Shape shape,
 double[] entries)

Factory to create a tensor with the specified shape and size.

Specified by:

makeTensor in class DenseTensorBase<Tensor,CTensor,Tensor,double[],Double>

Parameters:

shape - Shape of the tensor to make.

entries - Entries of the tensor to make.

Returns:

A new tensor with the specified shape and entries.

makeComplexTensor

protected CTensor makeComplexTensor(Shape shape,
 double[] entries)

Factory to create a complex tensor with the specified shape and size.

Specified by:

makeComplexTensor in class RealDenseTensorBase<Tensor,CTensor>

Parameters:

shape - Shape of the tensor to make.

entries - Entries of the tensor to make.

Returns:

A new tensor with the specified shape and entries.

makeComplexTensor

protected CTensor makeComplexTensor(Shape shape,
 CNumber[] entries)

Factory to create a complex tensor with the specified shape and size.

Specified by:

makeComplexTensor in class RealDenseTensorBase<Tensor,CTensor>

Parameters:

shape - Shape of the tensor to make.

entries - Entries of the tensor to make.

Returns:

A new tensor with the specified shape and entries.

getSelf

protected Tensor getSelf()

Simply returns this tensor.

Specified by:

getSelf in class TensorBase<Tensor,Tensor,CTensor,CTensor,Tensor,double[],Double>

Returns:

A reference to this tensor.

flatten

public Tensor flatten(int axis)

Flattens a tensor along the specified axis.

Specified by:

flatten in interface TensorManipulationsMixin<Tensor>

Parameters:

axis - Axis along which to flatten tensor.

Throws:

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

equals

public boolean equals(Object object)

Checks if an object is equal to this tensor object.

Specified by:

equals in interface TensorComparisonsMixin

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 Tensor. False otherwise.

toCoo

public CooTensor toCoo()

Converts this dense tensor to an equivalent sparse COO tensor.

Specified by:

toCoo in class DenseTensorBase<Tensor,CTensor,Tensor,double[],Double>

Returns:

A sparse COO tensor which is equivalent to this dense tensor.

flatten

public Tensor flatten()

Flattens tensor to single dimension.

Specified by:

flatten in interface TensorManipulationsMixin<Tensor>

Returns:

The flattened tensor.

addEq

public void addEq(CooTensor B)

Computes the element-wise addition of two tensors of the same rank and stores the result in this tensor.

Parameters:

B - Second tensor in the addition.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

T

public Tensor T()

Computes the transpose of a tensor. Same as TensorOperationsMixin.transpose(). In the context of a tensor, this exchanges the first and last axis of the tensor. Also see TensorExclusiveMixin.transpose(int, int) and T(int, int).

Specified by:

T in interface TensorOperationsMixin<Tensor,Tensor,CTensor,CTensor,Tensor,Double>

Returns:

The transpose of this tensor.

tensorDot

public Tensor tensorDot(Tensor 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.

Specified by:

tensorDot in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

src2 - Tensor 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 Tensor tensorDot(Tensor 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.

Specified by:

tensorDot in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

src2 - Tensor 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.

See Also:

• tensorDot(Tensor, int[], int[])

T

public Tensor T(int axis1,
 int axis2)

Computes the transpose of a tensor. Same as TensorExclusiveMixin.transpose(int, int). In the context of a tensor, this exchanges the specified axes. Also see TensorOperationsMixin.transpose() and T() to exchange first and last axes.

Specified by:

T in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

axis1 - First axis to exchange.

axis2 - Second axis to exchange.

Returns:

The transpose of this tensor.

T

public Tensor T(int... axes)

Computes the transpose of this tensor. That is, interchanges the axes of this tensor so that it matches the specified axes permutation. Same as TensorExclusiveMixin.transpose(int[]).

Specified by:

T in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

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:

IllegalArgumentException - If axes is not a permutation of {1, 2, 3, ... N-1}.

add

public Tensor add(CooTensor B)

Computes the element-wise addition between two tensors of the same rank.

Specified by:

add in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Second tensor in the addition.

Returns:

The result of adding the tensor B to this tensor element-wise.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

add

public CTensor add(CTensor B)

Computes the element-wise addition between two tensors of the same rank.

Specified by:

add in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Second tensor in the addition.

Returns:

The result of adding the tensor B to this tensor element-wise.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

add

public CTensor add(CooCTensor B)

Computes the element-wise addition between two tensors of the same rank.

Specified by:

add in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Second tensor in the addition.

Returns:

The result of adding the tensor B to this tensor element-wise.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

sub

public Tensor sub(CooTensor B)

Computes the element-wise subtraction between two tensors of the same rank.

Specified by:

sub in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Second tensor in element-wise subtraction.

Returns:

The result of subtracting the tensor B from this tensor element-wise.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

sub

public CTensor sub(CTensor B)

Computes the element-wise subtraction between two tensors of the same rank.

Specified by:

sub in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Second tensor in element-wise subtraction.

Returns:

The result of subtracting the tensor B from this tensor element-wise.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

sub

public CTensor sub(CooCTensor B)

Computes the element-wise subtraction between two tensors of the same rank.

Specified by:

sub in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Second tensor in element-wise subtraction.

Returns:

The result of subtracting the tensor B from this tensor element-wise.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

subEq

public void subEq(CooTensor B)

Computes the element-wise subtraction of two tensors of the same rank and stores the result in this tensor.

Parameters:

B - Second tensor in the subtraction.

Throws:

IllegalArgumentException - If this tensor and B have different shapes.

elemMult

public CooTensor elemMult(CooTensor B)

Computes the element-wise multiplication between two tensors.

Specified by:

elemMult in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Tensor to element-wise multiply to this tensor.

Returns:

The result of the element-wise tensor multiplication.

Throws:

IllegalArgumentException - If the tensors do not have the same shape.

elemMult

public CTensor elemMult(CTensor B)

Computes the element-wise multiplication between two tensors.

Specified by:

elemMult in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Tensor to element-wise multiply to this tensor.

Returns:

The result of the element-wise tensor multiplication.

Throws:

IllegalArgumentException - If the tensors do not have the same shape.

elemMult

public CooCTensor elemMult(CooCTensor B)

Computes the element-wise multiplication between two tensors.

Specified by:

elemMult in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Tensor to element-wise multiply to this tensor.

Returns:

The result of the element-wise tensor multiplication.

Throws:

IllegalArgumentException - If the tensors do not have the same shape.

elemDiv

public CTensor elemDiv(CTensor B)

Computes the element-wise division between two tensors.

Specified by:

elemDiv in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

B - Tensor to element-wise divide with this tensor.

Returns:

The result of the element-wise tensor division.

Throws:

IllegalArgumentException - If the tensors do not have the same shape.

tensorInv

public Tensor tensorInv(int numIndices)

Computes the 'inverse' of this tensor. That is, computes the tensor X=this.tensorInv() such that this.tensorDot(X, numIndices) is the 'identity' tensor for the tensor dot product operation. A tensor I is the identity for a tensor dot product if this.tensorDot(I, numIndices).equals(this).

Specified by:

tensorInv in interface TensorExclusiveMixin<Tensor,Tensor,CooTensor,CTensor>

Parameters:

numIndices - The number of first numIndices which are involved in the inverse sum.

Returns:

The 'inverse' of this tensor as defined in the above sense.

See Also:

• TensorExclusiveMixin.tensorInv()

toVector

public Vector 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 Matrix 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.

toMatrix

public Matrix 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 is larger than 2, it will be flattened to a single row.

toString

public String toString()

Formats this tensor as a human-readable string. Specifically, a string containing the shape and flattened entries of this tensor.

Overrides:

toString in class Object

Returns:

A human-readable string representing this tensor.