edu.jas.vector

Class GenMatrix<C extends RingElem<C>>

java.lang.Object

edu.jas.vector.GenMatrix<C>

All Implemented Interfaces:

AbelianGroupElem<GenMatrix<C>>, AlgebraElem<GenMatrix<C>,C>, Element<GenMatrix<C>>, MonoidElem<GenMatrix<C>>, RingElem<GenMatrix<C>>, java.io.Serializable, java.lang.Comparable<GenMatrix<C>>

public class GenMatrix<C extends RingElem<C>>
extends java.lang.Object
implements AlgebraElem<GenMatrix<C>,C>

GenMatrix implements a generic matrix algebra over RingElem entries. Matrix has n columns and m rows over C.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
java.util.ArrayList<java.util.ArrayList<C>>	matrix
GenMatrixRing<C>	ring

Constructor Summary

Constructors

Constructor and Description
GenMatrix(GenMatrixRing<C> r) Constructor for zero GenMatrix.
GenMatrix(GenMatrixRing<C> r, java.util.ArrayList<java.util.ArrayList<C>> m) Constructor for GenMatrix.
GenMatrix(GenMatrixRing<C> r, java.util.List<java.util.List<C>> m) Constructor for GenMatrix.

Method Summary

Modifier and Type	Method and Description
GenMatrix<C>	abs() Absolute value of this matrix.
int	compareTo(GenMatrix<C> b) compareTo, lexicogaphical comparison.
GenMatrix<C>	copy() clone method.
GenMatrix<C>	divide(GenMatrix<C> S) Divide this by S.
GenMatrix<C>[]	egcd(GenMatrix<C> b) Extended greatest common divisor.
boolean	equals(java.lang.Object other) Comparison with any other object.
GenMatrixRing<C>	factory() Get the corresponding element factory.
GenMatrix<C>	gcd(GenMatrix<C> b) Greatest common divisor.
C	get(int i, int j) Get element at row i, column j.
int	hashCode() Hash code for this GenMatrix.
GenMatrix<C>	inverse() Inverse of this.
boolean	isONE() Test if this is one.
boolean	isUnit() Test if this is a unit.
boolean	isZERO() Test if this is equal to a zero matrix.
GenMatrix<C>	leftLinearCombination(C s, C t, GenMatrix<C> b) left linear compination of this matrix with scalar multiple of other matrix.
GenMatrix<C>	leftScalarMultiply(C s) Left product of this matrix with scalar.
GenMatrix<C>	linearCombination(C t, GenMatrix<C> b) Left linear combination of this matrix with scalar multiple of other matrix.
GenMatrix<C>	linearCombination(C s, GenMatrix<C> b, C t) Linear compination of this matrix with scalar multiple of other matrix.
GenMatrix<C>	linearCombination(GenMatrix<C> b, C t) Linear combination of this matrix with scalar multiple of other matrix.
GenMatrix<C>	multiply(GenMatrix<C> S) Multiply this with S.
GenMatrix<C>	multiplySimple(GenMatrix<C> S) Multiply this with S.
GenMatrix<C>	negate() Negative of this matrix.
GenMatrix<C>[]	quotientRemainder(GenMatrix<C> S) Quotient and remainder by division of this by S.
GenMatrix<C>	remainder(GenMatrix<C> S) Remainder after division of this by S.
GenMatrix<C>	scalarMultiply(C s) Product of this matrix with scalar.
GenMatrix<C>	set(int i, int j, C el) Set element at row i, column j.
void	setMutate(int i, int j, C el) Set element at row i, column j.
int	signum() sign of matrix.
GenMatrix<C>	subtract(GenMatrix<C> b) Difference of matrices.
GenMatrix<C>	sum(GenMatrix<C> b) Sum of matrices.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toScriptFactory() Get a scripting compatible string representation of the factory.
java.lang.String	toString() Get the String representation as RingElem.
GenMatrix<C>	transpose(GenMatrixRing<C> tr) Transposed matrix.

Methods inherited from class java.lang.Object

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

Field Detail

ring

public final GenMatrixRing<C extends RingElem<C>> ring

matrix

public final java.util.ArrayList<java.util.ArrayList<C extends RingElem<C>>> matrix

Constructor Detail

GenMatrix

public GenMatrix(GenMatrixRing<C> r)

Constructor for zero GenMatrix.

Parameters:

r - matrix ring

GenMatrix

public GenMatrix(GenMatrixRing<C> r,
                 java.util.List<java.util.List<C>> m)

Constructor for GenMatrix.

Parameters:

r - matrix ring

m - matrix

GenMatrix

public GenMatrix(GenMatrixRing<C> r,
                 java.util.ArrayList<java.util.ArrayList<C>> m)

Constructor for GenMatrix.

Parameters:

r - matrix ring

m - matrix

Method Detail

get

public C get(int i,
             int j)

Get element at row i, column j.

Parameters:

i - row index.

j - column index.

Returns:

this(i,j).

setMutate

public void setMutate(int i,
                      int j,
                      C el)

Set element at row i, column j. Mutates this matrix.

Parameters:

i - row index.

j - column index.

el - element to set.

set

public GenMatrix<C> set(int i,
                        int j,
                        C el)

Set element at row i, column j.

Parameters:

i - row index.

j - column index.

el - element to set.

Returns:

new matrix m, with m(i,j) == el.

toString

public java.lang.String toString()

Get the String representation as RingElem.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface Element<GenMatrix<C extends RingElem<C>>>

Returns:

script compatible representation for this Element.

See Also:

Element.toScript()

toScriptFactory

public java.lang.String toScriptFactory()

Get a scripting compatible string representation of the factory.

Specified by:

toScriptFactory in interface Element<GenMatrix<C extends RingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

factory

public GenMatrixRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<GenMatrix<C extends RingElem<C>>>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public GenMatrix<C> copy()

clone method.

Specified by:

copy in interface Element<GenMatrix<C extends RingElem<C>>>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Test if this is equal to a zero matrix.

Specified by:

isZERO in interface AbelianGroupElem<GenMatrix<C extends RingElem<C>>>

Returns:

true if this is 0, else false.

isONE

public boolean isONE()

Test if this is one.

Specified by:

isONE in interface MonoidElem<GenMatrix<C extends RingElem<C>>>

Returns:

true if this is 1, else false.

equals

public boolean equals(java.lang.Object other)

Comparison with any other object.

Specified by:

equals in interface Element<GenMatrix<C extends RingElem<C>>>

Overrides:

equals in class java.lang.Object

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this GenMatrix.

Specified by:

hashCode in interface Element<GenMatrix<C extends RingElem<C>>>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

compareTo

public int compareTo(GenMatrix<C> b)

compareTo, lexicogaphical comparison.

Specified by:

compareTo in interface Element<GenMatrix<C extends RingElem<C>>>

Specified by:

compareTo in interface java.lang.Comparable<GenMatrix<C extends RingElem<C>>>

Parameters:

b - other

Returns:

1 if (this < b), 0 if (this == b) or -1 if (this > b).

isUnit

public boolean isUnit()

Test if this is a unit. I.e. there exists x with this.multiply(x).isONE() == true. Tests if all diagonal elements are units and all other elements are zero.

Specified by:

isUnit in interface MonoidElem<GenMatrix<C extends RingElem<C>>>

Returns:

true if this is a unit, else false.

signum

public int signum()

sign of matrix.

Specified by:

signum in interface AbelianGroupElem<GenMatrix<C extends RingElem<C>>>

Returns:

1 if (this < 0), 0 if (this == 0) or -1 if (this > 0).

sum

public GenMatrix<C> sum(GenMatrix<C> b)

Sum of matrices.

Specified by:

sum in interface AbelianGroupElem<GenMatrix<C extends RingElem<C>>>

Returns:

this+b

subtract

public GenMatrix<C> subtract(GenMatrix<C> b)

Difference of matrices.

Specified by:

subtract in interface AbelianGroupElem<GenMatrix<C extends RingElem<C>>>

Returns:

this-b

negate

public GenMatrix<C> negate()

Negative of this matrix.

Specified by:

negate in interface AbelianGroupElem<GenMatrix<C extends RingElem<C>>>

Returns:

-this

abs

public GenMatrix<C> abs()

Absolute value of this matrix.

Specified by:

abs in interface AbelianGroupElem<GenMatrix<C extends RingElem<C>>>

Returns:

abs(this)

scalarMultiply

public GenMatrix<C> scalarMultiply(C s)

Product of this matrix with scalar.

Specified by:

scalarMultiply in interface AlgebraElem<GenMatrix<C extends RingElem<C>>,C extends RingElem<C>>

Parameters:

s - scalar

Returns:

this*s

leftScalarMultiply

public GenMatrix<C> leftScalarMultiply(C s)

Left product of this matrix with scalar.

Returns:

s*this

linearCombination

public GenMatrix<C> linearCombination(C s,
                                      GenMatrix<C> b,
                                      C t)

Linear compination of this matrix with scalar multiple of other matrix.

Specified by:

linearCombination in interface AlgebraElem<GenMatrix<C extends RingElem<C>>,C extends RingElem<C>>

Parameters:

s - scalar

b - algebra element

t - scalar

Returns:

this*s+b*t

linearCombination

public GenMatrix<C> linearCombination(GenMatrix<C> b,
                                      C t)

Linear combination of this matrix with scalar multiple of other matrix.

Specified by:

linearCombination in interface AlgebraElem<GenMatrix<C extends RingElem<C>>,C extends RingElem<C>>

Parameters:

b - algebra element

t - scalar

Returns:

this+b*t

linearCombination

public GenMatrix<C> linearCombination(C t,
                                      GenMatrix<C> b)

Left linear combination of this matrix with scalar multiple of other matrix.

Returns:

this+t*b

leftLinearCombination

public GenMatrix<C> leftLinearCombination(C s,
                                          C t,
                                          GenMatrix<C> b)

left linear compination of this matrix with scalar multiple of other matrix.

Returns:

s*this+t*b

transpose

public GenMatrix<C> transpose(GenMatrixRing<C> tr)

Transposed matrix.

Returns:

transpose(this)

multiply

public GenMatrix<C> multiply(GenMatrix<C> S)

Multiply this with S.

Specified by:

multiply in interface MonoidElem<GenMatrix<C extends RingElem<C>>>

Parameters:

S -

Returns:

this * S.

multiplySimple

public GenMatrix<C> multiplySimple(GenMatrix<C> S)

Multiply this with S. Simple unblocked algorithm.

Parameters:

S -

Returns:

this * S.

divide

public GenMatrix<C> divide(GenMatrix<C> S)

Divide this by S.

Specified by:

divide in interface MonoidElem<GenMatrix<C extends RingElem<C>>>

Parameters:

S -

Returns:

this / S.

remainder

public GenMatrix<C> remainder(GenMatrix<C> S)

Remainder after division of this by S.

Specified by:

remainder in interface MonoidElem<GenMatrix<C extends RingElem<C>>>

Parameters:

S -

Returns:

this - (this / S) * S.

quotientRemainder

public GenMatrix<C>[] quotientRemainder(GenMatrix<C> S)

Quotient and remainder by division of this by S.

Parameters:

S - a GenMatrix

Returns:

[this/S, this - (this/S)*S].

inverse

public GenMatrix<C> inverse()

Inverse of this.

Specified by:

inverse in interface MonoidElem<GenMatrix<C extends RingElem<C>>>

Returns:

x with this * x = 1, if it exists.

gcd

public GenMatrix<C> gcd(GenMatrix<C> b)

Greatest common divisor.

Specified by:

gcd in interface RingElem<GenMatrix<C extends RingElem<C>>>

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

public GenMatrix<C>[] egcd(GenMatrix<C> b)

Extended greatest common divisor.

Specified by:

egcd in interface RingElem<GenMatrix<C extends RingElem<C>>>

Parameters:

b - other element.

Returns:

[ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).