org.ojalgo.matrix
Class ComplexMatrix

java.lang.Object
  org.ojalgo.matrix.ComplexMatrix

All Implemented Interfaces:

Serializable, Access2D<ComplexNumber>, Basic2D, BasicMatrix

public final class ComplexMatrix
extends Object

ComplexMatrix

Author:

apete

See Also:

Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface org.ojalgo.matrix.BasicMatrix

BasicMatrix.Factory<I extends BasicMatrix>

Field Summary

static MatrixFactory<ComplexNumber>

FACTORY

Constructor Summary

ComplexMatrix(MatrixStore<ComplexNumber> aStore)

Method Summary

BasicMatrix	add(BasicMatrix aMtrx) Adds the elements of aMtrx to the elements of this matrix.
BasicMatrix	add(int aRow, int aCol, Number aNmbr) Do not use this method to populate large dense matrices! Only use it to change a few (a small number) of elements.
BasicMatrix	add(Number aNmbr) Adds aNmbr to the elements of this.
BasicMatrix	conjugate() For real matrices conjugate() and transpose() are identical.
BasicMatrix	divide(Number aNmbr) Divides the elements of this with aNmbr.
BasicMatrix	divideElements(BasicMatrix aMtrx) Divides the elements of this with the elements of aMtrx.
double	doubleValue(int i, int j) Extracts one element of this matrix as a double.
BasicMatrix	enforce(NumberContext aContext)
boolean	equals(BasicMatrix aMtrx, NumberContext aCntxt)
boolean	equals(Object obj)
void	flushCache() BasicMatrix instances are intended to be immutable.
N	get(int aRow, int aColumn)
static MatrixBuilder<ComplexNumber>	getBuilder(int aRowDim, int aColDim)
int	getColDim() The size of this structure in the column-direction/dimension
BasicMatrix	getColumns(int... someCols)
Scalar<N>	getCondition()
Scalar<N>	getDeterminant()
List<ComplexNumber>	getEigenvalues()
Scalar<N>	getFrobeniusNorm() The Frobenius norm is the square root of the sum of the squares of each element, or the square root of the sum of the square of the singular values.
Scalar<?>	getInfinityNorm()
Scalar<N>	getKyFanNorm(int k)
int	getMinDim()
Scalar<?>	getOneNorm()
Scalar<N>	getOperatorNorm() 2-norm, max singular value
int	getRank() The rank of a matrix is the (maximum) number of linearly independent rows or columns it contains.
int	getRowDim() The size of this structure in the row-direction/dimension
BasicMatrix	getRows(int... someRows)
List<Double>	getSingularValues()
Scalar<N>	getTrace() The sum of the diagonal elements.
Scalar<N>	getTraceNorm()
Scalar<N>	getVectorNorm(int aDegree) Treats [this] as if it is one dimensional (a vector) and calculates the vector norm.
int	hashCode()
BasicMatrix	invert() About inverting matrices:
boolean	isEmpty() Matrices are either square, tall, fat or empty.
boolean	isFat() Matrices are either square, tall, fat or empty.
boolean	isFullRank()
boolean	isHermitian()
boolean	isScalar()
boolean	isSquare() Matrices are either square, tall, fat or empty.
boolean	isSymmetric()
boolean	isTall() Matrices are either square, tall, fat or empty.
boolean	isVector()
BasicMatrix	mergeColumns(BasicMatrix aMtrx) [aMtrx] is appended to the bottom of [this].
BasicMatrix	mergeRows(BasicMatrix aMtrx) [aMtrx] is appended to the right side of [this].
BasicMatrix	multiply(Number aNmbr) Multiplies the elements of this matrix with aNmbr.
BasicMatrix	multiplyElements(BasicMatrix aMtrx) Multiplies the elements of this matrix with the elements of aMtrx.
BasicMatrix	multiplyLeft(BasicMatrix aMtrx) Matrix multiplication: [aMtrx][this] The column dimension of the left matrix must equal the row dimension of the right matrix.
BasicMatrix	multiplyRight(BasicMatrix aMtrx) Matrix multiplication: [this][aMtrx] The column dimension of the left matrix must equal the row dimension of the right matrix.
Scalar<N>	multiplyVectors(BasicMatrix aVctr) Assumes that both [this] and [aVctr] have row or column dimension, doesn't matter which, equal to 1.
BasicMatrix	negate()
BasicMatrix	replace(int aRow, int aCol, Number aNmbr) Do not use this method to populate large dense matrices! Only use it to change a few (a small number) of elements.
BasicMatrix	round(NumberContext aContext)
int	size()
BasicMatrix	solve(BasicMatrix aRHS) This method solves a system of linear equations: [this][X]=[aRHS].
BasicMatrix	subtract(BasicMatrix aMtrx) Subtracts the elements of aMtrx from the elements of this matrix.
BasicMatrix	subtract(Number aNmbr) Subtracts aNmbr from the elements of this matrix.
BigDecimal	toBigDecimal(int aRow, int aCol) Extracts one element of this matrix as a BigDecimal.
PhysicalStore<BigDecimal>	toBigStore() Must be a copy that is safe to modify.
ComplexNumber	toComplexNumber(int aRow, int aCol) Extracts one element of this matrix as a ComplexNumber.
PhysicalStore<ComplexNumber>	toComplexStore() Must be a copy that is safe to modify.
List<BasicMatrix>	toListOfColumns()
List<N>	toListOfElements() It is also possible to call BasicMatrix.toBigStore(), BasicMatrix.toComplexStore() or BasicMatrix.toPrimitiveStore() and then PhysicalStore.asList().
List<BasicMatrix>	toListOfRows()
PhysicalStore<Double>	toPrimitiveStore() Must be a copy that is safe to modify.
Scalar<N>	toScalar(int aRow, int aCol) Extracts one element of this matrix as a Scalar.
String	toString()
String	toString(int aRow, int aCol)
BasicMatrix	transpose() Transposes this matrix.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Field Detail

FACTORY

public static final MatrixFactory<ComplexNumber> FACTORY

Constructor Detail

ComplexMatrix

public ComplexMatrix(MatrixStore<ComplexNumber> aStore)

Method Detail

getBuilder

public static MatrixBuilder<ComplexNumber> getBuilder(int aRowDim,
                                                      int aColDim)

enforce

public BasicMatrix enforce(NumberContext aContext)

round

public BasicMatrix round(NumberContext aContext)

toBigDecimal

public BigDecimal toBigDecimal(int aRow,
                               int aCol)

Description copied from interface: BasicMatrix

Extracts one element of this matrix as a BigDecimal.

Parameters:

aRow - A row index.

aCol - A column index.

Returns:

One matrix element

toComplexNumber

public ComplexNumber toComplexNumber(int aRow,
                                     int aCol)

Description copied from interface: BasicMatrix

Extracts one element of this matrix as a ComplexNumber.

Parameters:

aRow - A row index.

aCol - A column index.

Returns:

One matrix element

toComplexStore

public PhysicalStore<ComplexNumber> toComplexStore()

Description copied from interface: BasicMatrix

Must be a copy that is safe to modify.

Specified by:

toComplexStore in interface BasicMatrix

See Also:

BasicMatrix.toBigStore(), BasicMatrix.toPrimitiveStore()

toString

public String toString(int aRow,
                       int aCol)

add

public BasicMatrix add(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

Adds the elements of aMtrx to the elements of this matrix. The matrices must have equal dimensions.

Specified by:

add in interface BasicMatrix

Parameters:

aMtrx - What to add.

Returns:

A new matrix whos elements are the sum of this' and aMtrx'.

add

public BasicMatrix add(int aRow,
                       int aCol,
                       Number aNmbr)

Description copied from interface: BasicMatrix

Do not use this method to populate large dense matrices! Only use it to change a few (a small number) of elements.

Specified by:

add in interface BasicMatrix

add

public BasicMatrix add(Number aNmbr)

Description copied from interface: BasicMatrix

Adds aNmbr to the elements of this.

Specified by:

add in interface BasicMatrix

Parameters:

aNmbr - What to add

Returns:

A new matrix whos elements are the sum of this' elements and aNmbr.

conjugate

public BasicMatrix conjugate()

Description copied from interface: BasicMatrix

For real matrices conjugate() and transpose() are identical. For complex matrices they're not.

Specified by:

conjugate in interface BasicMatrix

Returns:

The conjugate transpose of this.

See Also:

BasicMatrix.transpose()

divide

public BasicMatrix divide(Number aNmbr)

Description copied from interface: BasicMatrix

Divides the elements of this with aNmbr.

Specified by:

divide in interface BasicMatrix

Parameters:

aNmbr - The denominator.

Returns:

A new matrix whos elements are the elements of this divided with aNmbr.

divideElements

public BasicMatrix divideElements(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

Divides the elements of this with the elements of aMtrx. The matrices must have equal dimensions.

Specified by:

divideElements in interface BasicMatrix

Parameters:

aMtrx - The denominator elements.

Returns:

A new matrix whos elements are the elements of this divided with the elements of aMtrx.

doubleValue

public double doubleValue(int i,
                          int j)

Extracts one element of this matrix as a double.

Parameters:

i - A row index.

j - A column index.

Returns:

One matrix element

equals

public final boolean equals(BasicMatrix aMtrx,
                            NumberContext aCntxt)

Specified by:

equals in interface BasicMatrix

Returns:

true if the frobenius norm of the difference between [this] and [aStore] is zero within the limits of aCntxt.

equals

public final boolean equals(Object obj)

Overrides:

equals in class Object

flushCache

public void flushCache()

Description copied from interface: BasicMatrix

BasicMatrix instances are intended to be immutable. If they are it is possible to cache (partial) calculation results. Calling this method should flush any cached calculation results.

Specified by:

flushCache in interface BasicMatrix

get

public N get(int aRow,
             int aColumn)

getColDim

public int getColDim()

The size of this structure in the column-direction/dimension

Returns:

The number of columns

getColumns

public BasicMatrix getColumns(int... someCols)

Specified by:

getColumns in interface BasicMatrix

Parameters:

someCols - An ordered array of column indeces.

Returns:

A matrix with a subset of, reordered, columns.

getCondition

public Scalar<N> getCondition()

Specified by:

getCondition in interface BasicMatrix

getDeterminant

public Scalar<N> getDeterminant()

Specified by:

getDeterminant in interface BasicMatrix

Returns:

The matrix' determinant.

getEigenvalues

public List<ComplexNumber> getEigenvalues()

Specified by:

getEigenvalues in interface BasicMatrix

getFrobeniusNorm

public Scalar<N> getFrobeniusNorm()

Description copied from interface: BasicMatrix

The Frobenius norm is the square root of the sum of the squares of each element, or the square root of the sum of the square of the singular values.

Specified by:

getFrobeniusNorm in interface BasicMatrix

Returns:

The matrix' Frobenius norm

See Also:

BasicMatrix.getFrobeniusNorm()

getInfinityNorm

public Scalar<?> getInfinityNorm()

Specified by:

getInfinityNorm in interface BasicMatrix

Returns:

Max row sum

See Also:

BasicMatrix.getFrobeniusNorm(), BasicMatrix.getInfinityNorm(), BasicMatrix.getKyFanNorm(int), BasicMatrix.getOneNorm(), BasicMatrix.getOperatorNorm(), BasicMatrix.getTraceNorm(), BasicMatrix.getVectorNorm(int)

getKyFanNorm

public Scalar<N> getKyFanNorm(int k)

Specified by:

getKyFanNorm in interface BasicMatrix

See Also:

BasicMatrix.getFrobeniusNorm(), BasicMatrix.getInfinityNorm(), BasicMatrix.getKyFanNorm(int), BasicMatrix.getOneNorm(), BasicMatrix.getOperatorNorm(), BasicMatrix.getTraceNorm(), BasicMatrix.getVectorNorm(int)

getMinDim

public int getMinDim()

getOneNorm

public Scalar<?> getOneNorm()

Specified by:

getOneNorm in interface BasicMatrix

Returns:

Max col sum

See Also:

BasicMatrix.getFrobeniusNorm(), BasicMatrix.getInfinityNorm(), BasicMatrix.getKyFanNorm(int), BasicMatrix.getOneNorm(), BasicMatrix.getOperatorNorm(), BasicMatrix.getTraceNorm(), BasicMatrix.getVectorNorm(int)

getOperatorNorm

public Scalar<N> getOperatorNorm()

Description copied from interface: BasicMatrix

2-norm, max singular value

Specified by:

getOperatorNorm in interface BasicMatrix

See Also:

BasicMatrix.getFrobeniusNorm(), BasicMatrix.getInfinityNorm(), BasicMatrix.getKyFanNorm(int), BasicMatrix.getOneNorm(), BasicMatrix.getOperatorNorm(), BasicMatrix.getTraceNorm(), BasicMatrix.getVectorNorm(int)

getRank

public int getRank()

Description copied from interface: BasicMatrix

The rank of a matrix is the (maximum) number of linearly independent rows or columns it contains. It is also equal to the number of nonzero singular values of the matrix.

Specified by:

getRank in interface BasicMatrix

Returns:

The matrix' rank.

getRowDim

public int getRowDim()

The size of this structure in the row-direction/dimension

Returns:

The number of rows

getRows

public BasicMatrix getRows(int... someRows)

Specified by:

getRows in interface BasicMatrix

Parameters:

someRows - An ordered array of row indeces.

Returns:

A matrix with a subset of, reordered, rows.

getSingularValues

public List<Double> getSingularValues()

Specified by:

getSingularValues in interface BasicMatrix

getTrace

public Scalar<N> getTrace()

Description copied from interface: BasicMatrix

The sum of the diagonal elements.

Specified by:

getTrace in interface BasicMatrix

Returns:

The matrix' trace.

getTraceNorm

public Scalar<N> getTraceNorm()

Specified by:

getTraceNorm in interface BasicMatrix

See Also:

BasicMatrix.getFrobeniusNorm(), BasicMatrix.getInfinityNorm(), BasicMatrix.getKyFanNorm(int), BasicMatrix.getOneNorm(), BasicMatrix.getOperatorNorm(), BasicMatrix.getTraceNorm(), BasicMatrix.getVectorNorm(int)

getVectorNorm

public Scalar<N> getVectorNorm(int aDegree)

Description copied from interface: BasicMatrix

Treats [this] as if it is one dimensional (a vector) and calculates the vector norm. The interface only requires that implementations can handle arguments 0, 1, 2 and Integer.MAX_VALUE.

Specified by:

getVectorNorm in interface BasicMatrix

See Also:

BasicMatrix.getFrobeniusNorm(), BasicMatrix.getInfinityNorm(), BasicMatrix.getKyFanNorm(int), BasicMatrix.getOneNorm(), BasicMatrix.getOperatorNorm(), BasicMatrix.getTraceNorm(), BasicMatrix.getVectorNorm(int)

hashCode

public final int hashCode()

Overrides:

hashCode in class Object

invert

public BasicMatrix invert()

Description copied from interface: BasicMatrix

About inverting matrices:

• "right inverse": [this][right inverse]=[I]. You may calculate it using BasicMatrix.solve(BasicMatrix).
• "left inverse": [left inverse][this]=[I]. You may calculate it using BasicMatrix.solve(BasicMatrix) and transposing.
• "generalised inverse": [this][generalised inverse][this]=[this]. Note that if [this] is singular or non-square, then [generalised inverse] is not unique.
• "pseudoinverse": The generalised inverse (there are typically/possibly many) with the smallest frobenius norm is called the pseudoinverse. You may calculate it using the QR or SingularValue decompositions.
• "inverse":
  • If [left inverse]=[right inverse] then it is also [inverse].
  • If [this] is square and has full rank then the [generalised inverse] is unique, with the [pseudoinverse] given, and equal to [inverse].

Specified by:

invert in interface BasicMatrix

Returns:

The "best possible" inverse....

isEmpty

public boolean isEmpty()

Description copied from interface: BasicMatrix

Matrices are either square, tall, fat or empty. m <= 0 or n <= 0

Specified by:

isEmpty in interface BasicMatrix

Returns:

true if matrix is empty

isFat

public boolean isFat()

Description copied from interface: BasicMatrix

Matrices are either square, tall, fat or empty. 1 <= m < n

Specified by:

isFat in interface BasicMatrix

Returns:

true if matrix is fat

isFullRank

public final boolean isFullRank()

Specified by:

isFullRank in interface BasicMatrix

Returns:

true if BasicMatrix.getRank() == min(getRowDim(),getColDim())

isHermitian

public boolean isHermitian()

Specified by:

isHermitian in interface BasicMatrix

isScalar

public boolean isScalar()

Specified by:

isScalar in interface BasicMatrix

Returns:

true if this is a 1x1 matrix

isSquare

public boolean isSquare()

Description copied from interface: BasicMatrix

Matrices are either square, tall, fat or empty. m = n <> 0

Specified by:

isSquare in interface BasicMatrix

Returns:

true if matrix is square

isSymmetric

public boolean isSymmetric()

Specified by:

isSymmetric in interface BasicMatrix

isTall

public boolean isTall()

Description copied from interface: BasicMatrix

Matrices are either square, tall, fat or empty. m > n >= 1

Specified by:

isTall in interface BasicMatrix

Returns:

true if matrix is tall

isVector

public boolean isVector()

Specified by:

isVector in interface BasicMatrix

Returns:

true if the row or column dimensions are equal to 1.

mergeColumns

public BasicMatrix mergeColumns(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

[aMtrx] is appended to the bottom of [this]. The two matrices must have the same number of columns.

Specified by:

mergeColumns in interface BasicMatrix

Parameters:

aMtrx - The matrix to merge.

Returns:

A new matrix with more rows.

mergeRows

public BasicMatrix mergeRows(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

[aMtrx] is appended to the right side of [this]. The two matrices must have the same number of rows.

Specified by:

mergeRows in interface BasicMatrix

Parameters:

aMtrx - The matrix to merge.

Returns:

A new matrix with more columns.

multiply

public BasicMatrix multiply(Number aNmbr)

Description copied from interface: BasicMatrix

Multiplies the elements of this matrix with aNmbr.

Specified by:

multiply in interface BasicMatrix

Parameters:

aNmbr - What to multiply with.

Returns:

A new matrix whos elements are the elements of this multiplied with aNmbr.

multiplyElements

public BasicMatrix multiplyElements(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

Multiplies the elements of this matrix with the elements of aMtrx. The matrices must have equal dimensions.

Specified by:

multiplyElements in interface BasicMatrix

Parameters:

aMtrx - The elements to multiply by.

Returns:

A new matrix whos elements are the elements of this multiplied with the elements of aMtrx.

multiplyLeft

public BasicMatrix multiplyLeft(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

Matrix multiplication: [aMtrx][this]
The column dimension of the left matrix must equal the row dimension of the right matrix.

Specified by:

multiplyLeft in interface BasicMatrix

Parameters:

aMtrx - The left matrix.

Returns:

The product.

See Also:

BasicMatrix.multiplyRight(BasicMatrix)

multiplyRight

public BasicMatrix multiplyRight(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

Matrix multiplication: [this][aMtrx]
The column dimension of the left matrix must equal the row dimension of the right matrix.

Specified by:

multiplyRight in interface BasicMatrix

Parameters:

aMtrx - The right matrix.

Returns:

The product.

See Also:

BasicMatrix.multiplyLeft(BasicMatrix)

multiplyVectors

public Scalar<N> multiplyVectors(BasicMatrix aVctr)

Description copied from interface: BasicMatrix

Assumes that both [this] and [aVctr] have row or column dimension, doesn't matter which, equal to 1. The two vectors must have the same number of elements.

Specified by:

multiplyVectors in interface BasicMatrix

negate

public BasicMatrix negate()

Specified by:

negate in interface BasicMatrix

Returns:

A new matrix with negated elements.

replace

public BasicMatrix replace(int aRow,
                           int aCol,
                           Number aNmbr)

Description copied from interface: BasicMatrix

Do not use this method to populate large dense matrices! Only use it to change a few (a small number) of elements.

Specified by:

replace in interface BasicMatrix

size

public int size()

Returns:

The total number of elements contained in this structure

solve

public BasicMatrix solve(BasicMatrix aRHS)

Description copied from interface: BasicMatrix

This method solves a system of linear equations: [this][X]=[aRHS]. A combination of columns in [this] should produce a column in [aRHS]. It is ok for [aRHS] to have more than 1 column.

• If the problem is over-qualified an approximate solution is returned.
• If the problem is under-qualified one possible solution is returned.

Remember that: [X][this]=[aRHS] is equivalent to [this]^T[X]^T=[aRHS]^T

Specified by:

solve in interface BasicMatrix

Parameters:

aRHS - The right hand side of the equation.

Returns:

The solution, [X].

subtract

public BasicMatrix subtract(BasicMatrix aMtrx)

Description copied from interface: BasicMatrix

Subtracts the elements of aMtrx from the elements of this matrix. The matrices must have equal dimensions.

Specified by:

subtract in interface BasicMatrix

Parameters:

aMtrx - What to subtract.

Returns:

A new matrix whos elements are the difference of this' and aMtrx'.

subtract

public BasicMatrix subtract(Number aNmbr)

Description copied from interface: BasicMatrix

Subtracts aNmbr from the elements of this matrix.

Specified by:

subtract in interface BasicMatrix

Parameters:

aNmbr - What to subtract.

Returns:

A new matrix whos elements are the differences between this' elements and aNmbr.

toBigStore

public PhysicalStore<BigDecimal> toBigStore()

Description copied from interface: BasicMatrix

Must be a copy that is safe to modify.

Specified by:

toBigStore in interface BasicMatrix

See Also:

BasicMatrix.toComplexStore(), BasicMatrix.toPrimitiveStore()

toListOfColumns

public List<BasicMatrix> toListOfColumns()

Specified by:

toListOfColumns in interface BasicMatrix

toListOfElements

public List<N> toListOfElements()

Description copied from interface: BasicMatrix

It is also possible to call BasicMatrix.toBigStore(), BasicMatrix.toComplexStore() or BasicMatrix.toPrimitiveStore() and then PhysicalStore.asList().

Specified by:

toListOfElements in interface BasicMatrix

toListOfRows

public List<BasicMatrix> toListOfRows()

Specified by:

toListOfRows in interface BasicMatrix

toPrimitiveStore

public PhysicalStore<Double> toPrimitiveStore()

Description copied from interface: BasicMatrix

Must be a copy that is safe to modify.

Specified by:

toPrimitiveStore in interface BasicMatrix

See Also:

BasicMatrix.toBigStore(), BasicMatrix.toComplexStore()

toScalar

public Scalar<N> toScalar(int aRow,
                          int aCol)

Description copied from interface: Basic2D

Extracts one element of this matrix as a Scalar.

Specified by:

toScalar in interface Basic2D

Parameters:

aRow - A row index.

aCol - A column index.

Returns:

One matrix element

toString

public String toString()

Overrides:

toString in class Object

transpose

public BasicMatrix transpose()

Description copied from interface: BasicMatrix

Transposes this matrix. For complex matrices conjugate() and transpose() are NOT EQUAL.

Specified by:

transpose in interface BasicMatrix

Returns:

A matrix that is the transpose of this matrix.

See Also:

BasicMatrix.conjugate()