Package 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	Description
java.util.ArrayList<java.util.ArrayList<C>>	matrix
GenMatrixRing<C>	ring

Constructor Summary

Constructors

Constructor	Description
GenMatrix(GenMatrixRing<C> r)	Constructor for zero GenMatrix.
GenMatrix(GenMatrixRing<C> r, C[][] m)	Constructor for 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	Description
GenMatrix<C>	abs()	Absolute value of this matrix.
int	compareTo(GenMatrix<C> b)	compareTo, lexicogaphical comparison.
GenMatrix<C>	concat(GenMatrixRing<C> cc, GenMatrix<C> b)	Concat method.
GenMatrix<C>	copy()	Copy method.
GenMatrix<C>	divide(GenMatrix<C> S)	Divide this by S.
GenMatrix<C>	divideLeft(GenMatrix<C> S)	Divide left 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.
GenVector<C>	getColumn(int i)	Get column i.
GenVector<C>	getDiagonal()	Get diagonal.
GenMatrix<C>	getLower()	Get lower triangular L matrix.
GenVector<C>	getRow(int i)	Get row i.
GenMatrix<C>	getUpper()	Get upper triangular U matrix.
GenMatrix<C>	getUpperScaled()	Get upper triangular U matrix with diagonale 1.
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(C s)	Product of this matrix with scalar.
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>	stack(GenMatrixRing<C> st, GenMatrix<C> b)	Stack method.
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()	Transposed matrix.
GenMatrix<C>	transpose(GenMatrixRing<C> tr)	Transposed matrix.

Methods inherited from class java.lang.Object

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

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

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

GenMatrix

public GenMatrix(GenMatrixRing<C> r,
                 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.

getColumn

public GenVector<C> getColumn(int i)

Get column i.

Parameters:

i - column index.

Returns:

this(*,i) as vector.

getRow

public GenVector<C> getRow(int i)

Get row i.

Parameters:

i - row index.

Returns:

this(i,*) as vector.

getDiagonal

public GenVector<C> getDiagonal()

Get diagonal.

Returns:

diagonal(this) as vector.

getUpper

public GenMatrix<C> getUpper()

Get upper triangular U matrix.

Returns:

U as matrix with equal length rows.

getUpperScaled

public GenMatrix<C> getUpperScaled()

Get upper triangular U matrix with diagonale 1.

Returns:

U as matrix with equal length rows and diagonale 1.

getLower

public GenMatrix<C> getLower()

Get lower triangular L matrix.

Returns:

L as matrix with equal length rows.

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<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<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<C extends RingElem<C>>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public GenMatrix<C> copy()

Copy method.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

Element.copy()

stack

public GenMatrix<C> stack(GenMatrixRing<C> st,
                          GenMatrix<C> b)

Stack method.

Parameters:

st - stacked matrix ring.

b - other matrix.

Returns:

stacked matrix, this on top of other.

concat

public GenMatrix<C> concat(GenMatrixRing<C> cc,
                           GenMatrix<C> b)

Concat method.

Parameters:

cc - concated matrix ring.

b - other matrix.

Returns:

concated matrix, this before of other.

isZERO

public boolean isZERO()

Test if this is equal to a zero matrix.

Specified by:

isZERO in interface AbelianGroupElem<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<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<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<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 java.lang.Comparable<C extends RingElem<C>>

Specified by:

compareTo in interface Element<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 matrix is not singular. Was previously a test if all diagonal elements are units and all other elements are zero.

Specified by:

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

Parameters:

b - other matrix.

Returns:

this+b

subtract

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

Difference of matrices.

Specified by:

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

Parameters:

b - other matrix.

Returns:

this-b

negate

public GenMatrix<C> negate()

Negative of this matrix.

Specified by:

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

Returns:

-this

abs

public GenMatrix<C> abs()

Absolute value of this matrix.

Specified by:

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

Returns:

abs(this)

multiply

public GenMatrix<C> multiply(C s)

Product of this matrix with scalar.

Parameters:

s - scalar.

Returns:

this*s

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.

Parameters:

s - 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

t - scalar

b - other matrix.

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:

t - scalar

b - other matrix.

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.

Parameters:

t - scalar

b - 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.

Parameters:

s - scalar

t - scalar

b - other matrix.

Returns:

s*this+t*b

transpose

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

Transposed matrix.

Parameters:

tr - transposed matrix ring.

Returns:

transpose(this)

transpose

public GenMatrix<C> transpose()

Transposed matrix.

Returns:

transpose(this)

multiply

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

Multiply this with S.

Specified by:

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

Parameters:

S - other matrix.

Returns:

this * S.

multiplySimple

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

Multiply this with S. Simple unblocked algorithm.

Parameters:

S - other matrix.

Returns:

this * S.

divide

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

Divide this by S.

Specified by:

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

Parameters:

S - other matrix.

Returns:

this * S^{-1}.

divideLeft

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

Divide left this by S.

Parameters:

S - other matrix.

Returns:

S^{-1} * this.

remainder

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

Remainder after division of this by S.

Specified by:

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

Parameters:

S - other matrix.

Returns:

this - (this / S) * S.

quotientRemainder

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

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<C extends RingElem<C>>

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<C extends RingElem<C>>

Returns:

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

See Also:

LinAlg.inverseLU(edu.jas.vector.GenMatrix,java.util.List)

gcd

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

Greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

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