Package etomica.space2d

Class Tensor2D

java.lang.Object

etomica.space2d.Tensor2D

All Implemented Interfaces:

Tensor, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

RotationTensor2D

public class Tensor2D
extends java.lang.Object
implements Tensor, java.io.Serializable

Implementation of a tensor for a 2-dimensional space. Tensor is formed from four elements.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
Tensor2D()	Default constructor sets all tensor elements to zero.
Tensor2D(double[][] d)	Constructs tensor with elements set by the given array.

Method Summary

Modifier and Type	Method	Description
void	assignTo(double[] d)	Fills the given array with the elements of this tensor.
void	assignTo(double[][] d)	Fills the given 2-dimensional array with the elements of this tensor.
void	assignTo(Vector[] v)	Assigns the tensor elements column-wise to the given vectors.
java.lang.Object	clone()	Support of implementation of Cloneable interface.
double	component(int i, int j)
int	D()
void	DE(Tensor t)	"Divide equals" (/=) operation, element-by-element.
double	determinant()	Computes the determinant of the matrix represented by this tensor
void	diagE(Vector v)	Makes this a diagonal tensor with elements set by the given vector.
void	E(double a)	"Equals" operation, setting all elements of this tensor to the given value
void	E(double[] d)
void	E(double[][] d)	Sets the tensor elements using the elements of the array.
void	E(Tensor t)	"Equals" operation.
void	E(Vector[] v)	Fills the tensor column-wise with the given vectors.
boolean	equals(Tensor t)	Element-by-element comparison of tensors
void	Ev1v2(Vector u1, Vector u2)	Sets this tensor equal to the dyadic or outer product of the given vectors.
void	invert()	Replaces this tensor with its inverse.
boolean	isNaN()
void	map(IFunction f)	Applies given function to each element of this tensor.
void	ME(Tensor t)	"Minus equals" (-=) operation, subtracting the elements of the given tensor from the respective elements of this tensor.
void	MEv1v2(Vector v1, Vector v2)	"Minus equals" (-=) operation with a dyad argument.
void	PE(double a)	"Plus equals" (+=) operation, adding the given value to each element of this tensor
void	PE(int i, int j, double a)	"Plus equals" (+=) operation, performed on a single element of this tensor.
void	PE(Tensor t)	"Plus equals" (+=) operation, adding the elements of the given tensor to the respective elements of this tensor
void	PEa1Tt1(double a1, Tensor t1)	"Plus equals" (+=) operation based on a scalar and tensor.
void	PEv1v2(Vector v1, Vector v2)	"Plus equals" (+=) operation with a dyad argument.
void	setComponent(int i, int j, double d)
void	TE(double a)	"Times equals" (*=) operation, replaces each element of this tensor by its current value times the given scalar
void	TE(Tensor t)	"Times equals" (*=) operation, as matrix multiplication.
double[]	toArray()	Returns tensor in an array, writing rowwise, i.e., in order xx, xy, yx, yy.
java.lang.String	toString()
double	trace()
void	transform(Vector v)	Applies the given tensor transformation to this vector, replacing its elements with the transformed values.
void	transpose()	Performs a transpose operation on this tensor, replacing each element ab by its counterpart element ba

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Tensor2D

public Tensor2D()

Default constructor sets all tensor elements to zero.

Tensor2D

public Tensor2D(double[][] d)

Constructs tensor with elements set by the given array. Elements are interpreted in order as xx, xy, yx, yy.

Method Detail

D

public int D()

Specified by:

D in interface Tensor

Returns:

the dimension of the space in which this tensor is defined

toArray

public double[] toArray()

Returns tensor in an array, writing rowwise, i.e., in order xx, xy, yx, yy.

Specified by:

toArray in interface Tensor

Returns:

a new array containing the tensor elements

clone

public java.lang.Object clone()

Support of implementation of Cloneable interface. Returns a new Tensor with elements equal to this one.

Specified by:

clone in interface Tensor

Overrides:

clone in class java.lang.Object

Returns:

a new tensor that is a copy of this one

component

public double component(int i,
                        int j)

Specified by:

component in interface Tensor

Parameters:

i - "row" index of the requested component

j - "column" index of the requested component

Returns:

the component a_i,j of this tensor

setComponent

public void setComponent(int i,
                         int j,
                         double d)

Specified by:

setComponent in interface Tensor

Parameters:

i - "row" index of the component being set

j - "column" index of the component being set

d - value to which the component a_i,j of this tensor is set

E

public void E(Tensor t)

Description copied from interface: Tensor

"Equals" operation. Sets all components of this tensor equal to those of the given tensor.

Specified by:

E in interface Tensor

Parameters:

t - the given tensor used to set this tensor's values

E

public void E(Vector[] v)

Description copied from interface: Tensor

Fills the tensor column-wise with the given vectors. The number of vectors must equal the dimension of the tensor, and the vector dimensions must equal the tensor dimension. Each vector forms a column of the tensor, so for D = 3, xx = v[0].x, xy = v[1].x, xz = v[2].x,...,yx = v[0].y, etc.

Specified by:

E in interface Tensor

Parameters:

v - the given vectors used to set this tensor's values

diagE

public void diagE(Vector v)

Description copied from interface: Tensor

Makes this a diagonal tensor with elements set by the given vector. All other elements of this tensor are set to zero.

Specified by:

diagE in interface Tensor

Parameters:

v - the given vector

assignTo

public void assignTo(Vector[] v)

Description copied from interface: Tensor

Assigns the tensor elements column-wise to the given vectors. The number of vectors must equal the dimension of the tensor, and the vector dimensions must equal the tensor dimension.

Specified by:

assignTo in interface Tensor

Ev1v2

public void Ev1v2(Vector u1,
                  Vector u2)

Description copied from interface: Tensor

Sets this tensor equal to the dyadic or outer product of the given vectors. Element ab is given by v1.a * v2.b

Specified by:

Ev1v2 in interface Tensor

Parameters:

u1 - first vector of the dyad

u2 - second vector of the dyad

E

public void E(double a)

Description copied from interface: Tensor

"Equals" operation, setting all elements of this tensor to the given value

Specified by:

E in interface Tensor

Parameters:

a - the given value used to set this tensor's elements

PE

public void PE(double a)

Description copied from interface: Tensor

"Plus equals" (+=) operation, adding the given value to each element of this tensor

Specified by:

PE in interface Tensor

Parameters:

a - the value added to each element

PE

public void PE(Tensor t)

Description copied from interface: Tensor

"Plus equals" (+=) operation, adding the elements of the given tensor to the respective elements of this tensor

Specified by:

PE in interface Tensor

Parameters:

t - the given tensor added to this tensor

PE

public void PE(int i,
               int j,
               double a)

Description copied from interface: Tensor

"Plus equals" (+=) operation, performed on a single element of this tensor.

Specified by:

PE in interface Tensor

Parameters:

i - "row" index of the modified element

j - "column" index of the modified element

a - value to be added to the element a_i,j

PEv1v2

public void PEv1v2(Vector v1,
                   Vector v2)

Description copied from interface: Tensor

"Plus equals" (+=) operation with a dyad argument. Increments this tensor by the dyadic or outer product of the given vectors. Element ab of this tensor is replaced by (ab + v1.a * v2.b)

Specified by:

PEv1v2 in interface Tensor

PEa1Tt1

public void PEa1Tt1(double a1,
                    Tensor t1)

Description copied from interface: Tensor

"Plus equals" (+=) operation based on a scalar and tensor. Each element ab of this tensor is replaced by a1 * t1.ab.

Specified by:

PEa1Tt1 in interface Tensor

Parameters:

a1 - the scalar multiplier

t1 - the given tensor

MEv1v2

public void MEv1v2(Vector v1,
                   Vector v2)

Description copied from interface: Tensor

"Minus equals" (-=) operation with a dyad argument. Decrements this tensor by the dyadic or outer product of the given vectors. Element ab of this tensor is replaced by (ab - v1.a * v2.b)

Specified by:

MEv1v2 in interface Tensor

ME

public void ME(Tensor t)

Description copied from interface: Tensor

"Minus equals" (-=) operation, subtracting the elements of the given tensor from the respective elements of this tensor. This tensor's values are replaced by the so-computed difference.

Specified by:

ME in interface Tensor

Parameters:

t - the given tensor subtracted from this tensor

trace

public double trace()

Specified by:

trace in interface Tensor

Returns:

the sum of the diagonal elements of this tensor

transpose

public void transpose()

Description copied from interface: Tensor

Performs a transpose operation on this tensor, replacing each element ab by its counterpart element ba

Specified by:

transpose in interface Tensor

determinant

public double determinant()

Description copied from interface: Tensor

Computes the determinant of the matrix represented by this tensor

Specified by:

determinant in interface Tensor

Returns:

the determinant of this tensor

invert

public void invert()

Description copied from interface: Tensor

Replaces this tensor with its inverse. The inverse is defined such that the tensor multiplied by its inverse gives the identity tensor.

Specified by:

invert in interface Tensor

TE

public void TE(double a)

Description copied from interface: Tensor

"Times equals" (*=) operation, replaces each element of this tensor by its current value times the given scalar

Specified by:

TE in interface Tensor

Parameters:

a - the given scalar multiplier

TE

public void TE(Tensor t)

Description copied from interface: Tensor

"Times equals" (*=) operation, as matrix multiplication. Replaces each element of this tensor by the value given by result of (this)*t, where multiplication is treated as if multiplying matrices.

Specified by:

TE in interface Tensor

Parameters:

t - the tensor this is multiplying

DE

public void DE(Tensor t)

Description copied from interface: Tensor

"Divide equals" (/=) operation, element-by-element. Replaces each element of this tensor by its current value divided by the corresponding element in the given tensor. Element ab is replated by ab / t.ab.

Specified by:

DE in interface Tensor

Parameters:

t - the given tensor

E

public void E(double[] d)

E

public void E(double[][] d)

Description copied from interface: Tensor

Sets the tensor elements using the elements of the array. Tensor values are filled row-wise, so array values [0][0], [0][1], [0][2],...[1][0]... are assigned to xx, xy, xz, yx, etc. respectively.

Specified by:

E in interface Tensor

assignTo

public void assignTo(double[] d)

Description copied from interface: Tensor

Fills the given array with the elements of this tensor. Array values 0, 1, 2,... are assigned from xx, xy, xz, yx, etc. respectively, filling in a row-wise fashion.

Specified by:

assignTo in interface Tensor

Parameters:

d - an array of length D², containing the tensor elements upon return

assignTo

public void assignTo(double[][] d)

Description copied from interface: Tensor

Fills the given 2-dimensional array with the elements of this tensor. Array values [0][0], [0][1] are assigned from xx, xy, xz, yx, etc. respectively, such that d[i] contains the i^th row of the tensor.

Specified by:

assignTo in interface Tensor

Parameters:

d - a D-by-D array, containing the tensor elements upon return

isNaN

public boolean isNaN()

Specified by:

isNaN in interface Tensor

Returns:

true if any element of this tensor is NaN (not a number)

map

public void map(IFunction f)

Description copied from interface: Tensor

Applies given function to each element of this tensor. Replaces element with the resulting value.

Specified by:

map in interface Tensor

Parameters:

f - the function applied to each element

transform

public void transform(Vector v)

Description copied from interface: Tensor

Applies the given tensor transformation to this vector, replacing its elements with the transformed values. This operation is equivalent to a matrix multiplication.

Specified by:

transform in interface Tensor

equals

public boolean equals(Tensor t)

Description copied from interface: Tensor

Element-by-element comparison of tensors

Specified by:

equals in interface Tensor

Parameters:

t - the given tensor

Returns:

true if every element of given tensor equals the corresponding element of this tensor

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object