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

All Methods Instance Methods Concrete Methods
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 diagonal 1.
`int`	`hashCode()`	Hash code for this GenMatrix.
`GenMatrix<C>`	`inverse()`	Inverse of this.
`boolean`	`isDiagonal()`	Test if this is a non-zero diagonal matrix.
`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.
`C`	`trace()`	Trace.
`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.
  - trace
```
public C trace()
```
    Trace.
    
    Returns:
    
    sum of diagonal elements.
  - 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 diagonal 1.
    
    Returns:
    
    U as matrix with equal length rows and diagonal 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.
  - isDiagonal
```
public boolean isDiagonal()
```
    Test if this is a non-zero diagonal matrix.
    
    Returns:
    
    true if this is non-zero diagonal, 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).

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

Class GenMatrix<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.jas.structure.MonoidElem

Methods inherited from interface edu.jas.structure.RingElem

Field Detail

ring

matrix

Constructor Detail

GenMatrix

GenMatrix

GenMatrix

GenMatrix

Method Detail

get

setMutate

set

getColumn

getRow

getDiagonal

trace

getUpper

getUpperScaled

getLower

toString

toScript

toScriptFactory

factory

copy

stack

concat

isZERO

isONE

isDiagonal

equals

hashCode

compareTo

isUnit

signum

sum

subtract

negate

abs

multiply

scalarMultiply

leftScalarMultiply

linearCombination

linearCombination

linearCombination

leftLinearCombination

transpose

transpose

multiply

multiplySimple

divide

divideLeft

remainder

quotientRemainder

inverse

gcd

egcd