Package com.singularsys.extensions.matrix.externalmat

Class ExternalMatrixField<M extends MatrixI,V extends VectorI>

java.lang.Object

com.singularsys.extensions.matrix.externalmat.ExternalMatrixField<M,V>

Type Parameters:

M - type on Matrix used

V - type of Vector used

Implementations should provide implementations of addMM(M l,M r), addVV(V l,V r) etc. It can be assumed that the arguments of these methods are of correct sizes.

All Implemented Interfaces:

FieldI, IntegerConvertor, MatrixFieldI, JepComponent, Serializable

public abstract class ExternalMatrixField<M extends MatrixI,V extends VectorI>
extends Object
implements MatrixFieldI

Base class for MatrixField implementations with external matrix libraries.

See Also:

• Serialized Form

Constructor Summary

Constructors

Constructor	Description
ExternalMatrixField(ExternalMatrixFactory<M,V> mf, FieldI baseField)	Constructor.

Method Summary

Modifier and Type	Method	Description
Object	add(Object l, Object r)	Adds two matrices or vectors.
protected Object	addEle(Object l, Object r)	Adds two elements which are not vectors or matrices.
protected abstract M	addMM(M l, M r)	Add two matrices.
protected abstract V	addVV(V lv, V rv)	Add two vectors.
Boolean	and(Object l, Object r)	Logical and.
protected Boolean	andEle(Object l, Object r)
protected M	castM(Object m)	Given that the argument is of type MatrixI cast to the type M.
protected V	castV(Object v)	Given that the argument is of type VectorI cast to the type V.
Object	cross(Object l, Object r)	Cross product of two vectors
protected abstract V	crossVV(V lv, V rv)	Cross product of two 3D vectors
Object	det(Object m)	Determinant of a matrix
protected abstract Object	detM(M mat)	Return the determinant of a matrix.
Object	div(Object l, Object r)	Divides two members of the field.
protected Object	divEle(Object l, Object r)
protected abstract M	divMO(M l, Object r)	Divide a matrix by a scalar
protected abstract V	divVO(V l, Object r)	Divide a vector by a scalar
Object	dot(Object l, Object r)	The dot product of two vectors
protected abstract Object	dotVV(V lv, V rv)	Dot or inner product of two vectors
Object	elementValue(Object o)	Try to convert argument to base type of elements of Vector/Matrix.
Boolean	eq(Object l, Object r)	Equals
protected Boolean	eqEle(Object l, Object r)
protected abstract Boolean	eqMM(M l, M r)	Test if two matrices are equal.
protected abstract Boolean	eqVV(V l, V r)	Test if two vectors are equal.
Boolean	ge(Object l, Object r)	Greater or equal to
protected Boolean	geEle(Object l, Object r)
Boolean	gt(Object l, Object r)	Greater than
protected Boolean	gtEle(Object l, Object r)
Object	inv(Object l)	Returns the inverse of a square matrix.
protected abstract M	invM(M mat)	Finds the inverse of a matrix.
Boolean	le(Object l, Object r)	Less than or equals to
protected Boolean	leEle(Object l, Object r)
Boolean	lt(Object l, Object r)	Less than
protected Boolean	ltEle(Object l, Object r)
Object	mod(Object l, Object r)	The modulus of two members of the field.
protected Object	modEle(Object l, Object r)
Object	mul(Object l, Object r)	Multiplies two members of the field.
protected Object	mulEle(Object l, Object r)
protected abstract M	mulMM(M l, M r)	Multiply matrix by matrix
protected abstract M	mulMO(M l, Object r)	Multiply matrix by scalar
protected abstract V	mulMV(M l, V r)	Multiply matrix by column-vector
protected abstract V	mulVM(V l, M r)	Multiply row-vector by matrix
protected abstract V	mulVO(V l, Object r)	Multiply a vector by a scalar
protected abstract M	mulVV(V l, V r)	Outer product of two vectors
Boolean	ne(Object l, Object r)	Not Equals
protected Boolean	neEle(Object l, Object r)
Object	neg(Object l)	The negation -x of an element.
protected Object	negEle(Object l)
protected abstract M	negM(M l)
protected abstract V	negV(V lv)
protected abstract Boolean	neMM(M l, M r)	Test if two matrices are not equal.
protected abstract Boolean	neVV(V l, V r)	Test if two vectors are not-equal.
Boolean	not(Object l)	Logical not.
protected Boolean	notEle(Object l)
Boolean	or(Object l, Object r)	Logical or.
protected Boolean	orEle(Object l, Object r)
Object	pow(Object l, Object r)	Default power method only works for scalars.
protected Object	powEle(Object l, Object r)
Object	solve(Object A, Object B)	Solve equation A * X = B
protected abstract M	solveMM(M A, M B)	Solve the matrix equation A * M = B
protected abstract V	solveMV(M A, V b)	Solve the matrix equation A * v = B
Object	sub(Object l, Object r)	Subtract two members of the field.
protected Object	subEle(Object l, Object r)
protected abstract M	subMM(M l, M r)
protected abstract V	subVV(V lv, V rv)
Object	trace(Object l)	Returns the trace of a matrix.
abstract Object	traceM(M m)	Trace of a matrix
Object	trans(Object l)	Transpose of a matrix
protected abstract Object	transM(M mat)	Transpose of a matrix
Object	transV(V l)	Transpose of a vector.

Methods inherited from class java.lang.Object

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

Methods inherited from interface com.singularsys.extensions.field.FieldI

getOne, getZero

Methods inherited from interface com.singularsys.extensions.field.IntegerConvertor

convertFromInt, convertToInt

Methods inherited from interface com.singularsys.jep.JepComponent

getLightWeightInstance, init

Constructor Details

ExternalMatrixField

public ExternalMatrixField(ExternalMatrixFactory<M,V> mf,
 FieldI baseField)

Constructor.

Parameters:

mf - corresponding MatrixField

baseField - field used to compute operations of the base field

Method Details

castM

protected M castM(Object m)

Given that the argument is of type MatrixI cast to the type M.

Parameters:

m - the argument

Returns:

argument cast to desired type

castV

protected V castV(Object v)

Given that the argument is of type VectorI cast to the type V.

Parameters:

v - the argument

Returns:

argument cast to desired type

addEle

protected Object addEle(Object l,
 Object r)
                 throws EvaluationException

Adds two elements which are not vectors or matrices. By default the base field is used to implement this method, but it could be overwritten.

Parameters:

l - lhs

r - rhs

Returns:

the sum

Throws:

EvaluationException - where necessary

addVV

protected abstract V addVV(V lv,
 V rv)
                    throws EvaluationException

Add two vectors. Arguments are guaranteed to be the same size.

Parameters:

lv - lhs vector

rv - rhs vector

Returns:

the sum of the vectors

Throws:

EvaluationException

addMM

protected abstract M addMM(M l,
 M r)
                    throws EvaluationException

Add two matrices. Arguments are guaranteed to be the same size.

Parameters:

l - lhs matrix

r - rhs matrix

Returns:

the sum of the matrices

Throws:

EvaluationException

add

public Object add(Object l,
 Object r)
           throws EvaluationException

Adds two matrices or vectors. Calls either addVV(VectorI, VectorI), addMM(MatrixI, MatrixI) or addEle(Object, Object) depending on the arguments.

Specified by:

add in interface FieldI

Parameters:

l - lhs

r - rhs

Returns:

the sum of the arguments if l and r are of both of type VectorI or both of type MatrixI or null otherwise.

Throws:

EvaluationException - if sizes do not match or attempts to add object of other types

elementValue

public Object elementValue(Object o)
                    throws EvaluationException

Try to convert argument to base type of elements of Vector/Matrix. Calls MatrixFactoryI.elementValue(Object) to check base value is correct type.

Parameters:

o - item to convert

Returns:

o

Throws:

EvaluationException - if the argument is a vector or matrix

subEle

protected Object subEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

subVV

protected abstract V subVV(V lv,
 V rv)
                    throws EvaluationException

Throws:

EvaluationException

subMM

protected abstract M subMM(M l,
 M r)
                    throws EvaluationException

Throws:

EvaluationException

sub

public Object sub(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Subtract two members of the field.

Specified by:

sub in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

negEle

protected Object negEle(Object l)
                 throws EvaluationException

Throws:

EvaluationException

negV

protected abstract V negV(V lv)
                   throws EvaluationException

Throws:

EvaluationException

negM

protected abstract M negM(M l)
                   throws EvaluationException

Throws:

EvaluationException

neg

public Object neg(Object l)
           throws EvaluationException

Description copied from interface: FieldI

The negation -x of an element.

Specified by:

neg in interface FieldI

Parameters:

l - the argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

mulEle

protected Object mulEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

mulVO

protected abstract V mulVO(V l,
 Object r)
                    throws EvaluationException

Multiply a vector by a scalar

Parameters:

l - vector

r - scalar

Returns:

produce

Throws:

EvaluationException

mulMO

protected abstract M mulMO(M l,
 Object r)
                    throws EvaluationException

Multiply matrix by scalar

Parameters:

l - matrix

r - scalar

Returns:

product

Throws:

EvaluationException

mulVV

protected abstract M mulVV(V l,
 V r)
                    throws EvaluationException

Outer product of two vectors

Parameters:

l - column-vector

r - row-vector

Returns:

matrix whose size if size(l) x size(r)

Throws:

EvaluationException

mulVM

protected abstract V mulVM(V l,
 M r)
                    throws EvaluationException

Multiply row-vector by matrix

Parameters:

l - lhs row vector

r - rhs matrix

Returns:

a vector

Throws:

EvaluationException

mulMV

protected abstract V mulMV(M l,
 V r)
                    throws EvaluationException

Multiply matrix by column-vector

Parameters:

l - lhs matrix

r - rhs column-vector

Returns:

a vector

Throws:

EvaluationException

mulMM

protected abstract M mulMM(M l,
 M r)
                    throws EvaluationException

Multiply matrix by matrix

Parameters:

l - lhs matrix

r - rhs matrix

Returns:

a matrix

Throws:

EvaluationException

mul

public Object mul(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Multiplies two members of the field.

Specified by:

mul in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

divEle

protected Object divEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

divVO

protected abstract V divVO(V l,
 Object r)
                    throws EvaluationException

Divide a vector by a scalar

Parameters:

l - vector

r - scalar

Returns:

product

Throws:

EvaluationException

divMO

protected abstract M divMO(M l,
 Object r)
                    throws EvaluationException

Divide a matrix by a scalar

Parameters:

l - matrix

r - scalar

Returns:

product

Throws:

EvaluationException

div

public Object div(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Divides two members of the field.

Specified by:

div in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

modEle

protected Object modEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

mod

public Object mod(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

The modulus of two members of the field.

Specified by:

mod in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

powEle

protected Object powEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

pow

public Object pow(Object l,
 Object r)
           throws EvaluationException

Default power method only works for scalars. Can be overwritten for other behaviour.

Specified by:

pow in interface FieldI

Parameters:

l - lhs

r - rhs

Returns:

l^r

Throws:

EvaluationException - By default throw if either argument is a matrix or vector

eqEle

protected Boolean eqEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

eqVV

protected abstract Boolean eqVV(V l,
 V r)
                         throws EvaluationException

Test if two vectors are equal. It can be assumed the sizes are equal.

Parameters:

l - lhs

r - rhs

Returns:

True or False

Throws:

EvaluationException

eqMM

protected abstract Boolean eqMM(M l,
 M r)
                         throws EvaluationException

Test if two matrices are equal. It can be assumed the sizes are equal.

Parameters:

l - lhs

r - rhs

Returns:

True or False

Throws:

EvaluationException

eq

public Boolean eq(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Equals

Specified by:

eq in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

neEle

protected Boolean neEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

neVV

protected abstract Boolean neVV(V l,
 V r)
                         throws EvaluationException

Test if two vectors are not-equal. It can be assumed the sizes are equal.

Parameters:

l - lhs

r - rhs

Returns:

True or False

Throws:

EvaluationException

neMM

protected abstract Boolean neMM(M l,
 M r)
                         throws EvaluationException

Test if two matrices are not equal. It can be assumed the sizes are equal.

Parameters:

l - lhs

r - rhs

Returns:

True or False

Throws:

EvaluationException

ne

public Boolean ne(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Not Equals

Specified by:

ne in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

andEle

protected Boolean andEle(Object l,
 Object r)
                  throws EvaluationException

Throws:

EvaluationException

and

public Boolean and(Object l,
 Object r)
            throws EvaluationException

Description copied from interface: FieldI

Logical and.

Specified by:

and in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

orEle

protected Boolean orEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

or

public Boolean or(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Logical or.

Specified by:

or in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

notEle

protected Boolean notEle(Object l)
                  throws EvaluationException

Throws:

EvaluationException

not

public Boolean not(Object l)
            throws EvaluationException

Description copied from interface: FieldI

Logical not.

Specified by:

not in interface FieldI

Parameters:

l - argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

gtEle

protected Boolean gtEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

gt

public Boolean gt(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Greater than

Specified by:

gt in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

geEle

protected Boolean geEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

ge

public Boolean ge(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Greater or equal to

Specified by:

ge in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

ltEle

protected Boolean ltEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

lt

public Boolean lt(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Less than

Specified by:

lt in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

leEle

protected Boolean leEle(Object l,
 Object r)
                 throws EvaluationException

Throws:

EvaluationException

le

public Boolean le(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: FieldI

Less than or equals to

Specified by:

le in interface FieldI

Parameters:

l - left-hand argument

r - right-hand argument

Returns:

an object representing the result or null if it can not be evaluated.

Throws:

EvaluationException - on error

trans

public Object trans(Object l)
             throws EvaluationException

Description copied from interface: MatrixFieldI

Transpose of a matrix

Specified by:

trans in interface MatrixFieldI

Parameters:

l - the matrix

Returns:

a matrix containing the transpose

Throws:

EvaluationException

transV

public Object transV(V l)
              throws EvaluationException

Transpose of a vector. Default implementation is just to inefficiently return a copy of the vector.

Parameters:

l - a vector

Returns:

a new vector

Throws:

EvaluationException - if necessary

transM

protected abstract Object transM(M mat)
                          throws EvaluationException

Transpose of a matrix

Parameters:

mat - a matrix

Returns:

it transpose

Throws:

EvaluationException

dot

public Object dot(Object l,
 Object r)
           throws EvaluationException

Description copied from interface: MatrixFieldI

The dot product of two vectors

Specified by:

dot in interface MatrixFieldI

Parameters:

l -

r -

Returns:

the dot product if both arguments are vectors, null otherwise.

Throws:

EvaluationException

dotVV

protected abstract Object dotVV(V lv,
 V rv)
                         throws EvaluationException

Dot or inner product of two vectors

Parameters:

lv - lhs vector

rv - rhs vector

Returns:

value of scalar product

Throws:

EvaluationException

cross

public Object cross(Object l,
 Object r)
             throws EvaluationException

Cross product of two vectors

Specified by:

cross in interface MatrixFieldI

Parameters:

l - lhs vector

r - rhs vector

Returns:

value of scalar product

Throws:

EvaluationException - if either argument is not a 3D vector

crossVV

protected abstract V crossVV(V lv,
 V rv)
                      throws EvaluationException

Cross product of two 3D vectors

Parameters:

lv - left-hand side vector

rv - right-hand side vector

Returns:

their cross product

Throws:

EvaluationException - if necessary

traceM

public abstract Object traceM(M m)
                       throws EvaluationException

Trace of a matrix

Parameters:

m - the matrix

Returns:

the trace

Throws:

EvaluationException

trace

public Object trace(Object l)
             throws EvaluationException

Description copied from interface: MatrixFieldI

Returns the trace of a matrix.

Specified by:

trace in interface MatrixFieldI

Parameters:

l - the matrix

Returns:

the trace

Throws:

EvaluationException

det

public Object det(Object m)
           throws EvaluationException

Determinant of a matrix

Specified by:

det in interface MatrixFieldI

Parameters:

m - the matrix

Returns:

the determinant

Throws:

EvaluationException - if matrix is not square.

detM

protected abstract Object detM(M mat)
                        throws EvaluationException

Return the determinant of a matrix.

Parameters:

mat - the matrix

Returns:

the determinant

Throws:

EvaluationException - on error

invM

protected abstract M invM(M mat)
                   throws EvaluationException

Finds the inverse of a matrix. Default implementation uses Gauss-Jordan with partial pivoting

Parameters:

mat - the matrix

Returns:

its inverse

Throws:

EvaluationException - if matrix is singular

inv

public Object inv(Object l)
           throws EvaluationException

Description copied from interface: MatrixFieldI

Returns the inverse of a square matrix.

Specified by:

inv in interface MatrixFieldI

Parameters:

l - the matrix

Returns:

the trace

Throws:

EvaluationException - if matrix is not square or is singular

solveMM

protected abstract M solveMM(M A,
 M B)
                      throws EvaluationException

Solve the matrix equation A * M = B

Parameters:

A - matrix

B - matrix

Returns:

matrix M

Throws:

EvaluationException

solveMV

protected abstract V solveMV(M A,
 V b)
                      throws EvaluationException

Solve the matrix equation A * v = B

Parameters:

A - matrix

b - vector

Returns:

vector v

Throws:

EvaluationException

solve

public Object solve(Object A,
 Object B)
             throws EvaluationException

Description copied from interface: MatrixFieldI

Solve equation A * X = B

Specified by:

solve in interface MatrixFieldI

Parameters:

A - a square matrix

B - either a vector or matrix with same number of rows as A

Returns:

a vector or matrix solving equations

Throws:

EvaluationException - if matrix is not square or is singular