org.ojalgo.matrix
Class BigMatrix

java.lang.Object
  org.ojalgo.matrix.BigMatrix

All Implemented Interfaces:

Serializable, BasicMatrix

public final class BigMatrix
extends Object
implements Serializable

BigMatrix

Author:

apete

See Also:

Serialized Form

Field Summary

static MatrixFactory

FACTORY

Constructor Summary

BigMatrix(MatrixStore<BigDecimal> aStore)

Method Summary

BasicMatrix	add(BasicMatrix aMtrx) Adds the elements of aMtrx to the elements of this matrix.
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(BigMatrix aMtrx) The matrices, each element, have to be exactly equal as in BigDecimal.equals(Object).
boolean	equals(Object anObject)
int	getColDim()
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<N>	getInfinityNorm() Deprecated. Since Version 25. Use getVectorInfinityNorm() instead
Scalar<N>	getKyFanNorm(int k)
Scalar<N>	getOperatorNorm()
int	getRank() The rank of a matrix is the maximum number of linearly independent rows or columns it contains.
int	getRowDim()
BasicMatrix	getRows(int[] someRows)
List<N>	getSingularValues()
Scalar<N>	getTrace() The sum of the diagonal elements.
Scalar<N>	getVectorInfinityNorm() The largest, absolute, element value.
Scalar<N>	getVectorNorm(int aDegree) Treats [this] as if it is one dimensional (a vector) and calculates the vector norm.
Scalar<N>	getVectorProduct(BasicMatrix aVctr) Treats [this] and [aVctr] as if they are one dimensional (vectors) and calculates the vector (dot) product.
Scalar<N>	getVectorZeroNorm()
Scalar<N>	getZeroNorm() Deprecated. Since Version 25. Use getVectorZeroNorm() instead
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	isHermitian()
boolean	isSquare() Matrices are either square, tall, fat or empty.
boolean	isSymmetric()
boolean	isTall() Matrices are either square, tall, fat or empty.
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.
BasicMatrix	negate()
BasicMatrix	set(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.
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()
ComplexNumber	toComplexNumber(int aRow, int aCol) Extracts one element of this matrix as a ComplexNumber.
PhysicalStore<ComplexNumber>	toComplexStore()
List<BasicMatrix>	toListOfColumns()
List<BigDecimal>	toListOfElements()
List<BasicMatrix>	toListOfRows()
PhysicalStore<Double>	toPrimitiveStore()
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 FACTORY

Constructor Detail

BigMatrix

public BigMatrix(MatrixStore<BigDecimal> aStore)

Method Detail

equals

public boolean equals(BigMatrix aMtrx)

The matrices, each element, have to be exactly equal as in BigDecimal.equals(Object).

toBigStore

public PhysicalStore<BigDecimal> toBigStore()

Specified by:

toBigStore in interface BasicMatrix

See Also:

BasicMatrix.toComplexStore(), BasicMatrix.toPrimitiveStore()

toString

public String toString(int aRow,
                       int aCol)

Specified by:

toString in interface BasicMatrix

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(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)

Description copied from interface: BasicMatrix

Extracts one element of this matrix as a double.

Specified by:

doubleValue in interface BasicMatrix

Parameters:

i - A row index.

j - A column index.

Returns:

One matrix element

enforce

public BasicMatrix enforce(NumberContext aContext)

Specified by:

enforce in interface BasicMatrix

equals

public final boolean equals(BasicMatrix aMtrx,
                            NumberContext aCntxt)

Specified by:

equals in interface BasicMatrix

equals

public final boolean equals(Object anObject)

Overrides:

equals in class Object

getColDim

public int getColDim()

Specified by:

getColDim in interface BasicMatrix

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

getInfinityNorm

@Deprecated
public Scalar<N> getInfinityNorm()

Deprecated. Since Version 25. Use getVectorInfinityNorm() instead

Description copied from interface: BasicMatrix

The largest, absolute, element value.

Specified by:

getInfinityNorm in interface BasicMatrix

getKyFanNorm

public Scalar<N> getKyFanNorm(int k)

Specified by:

getKyFanNorm in interface BasicMatrix

getOperatorNorm

public Scalar<N> getOperatorNorm()

Specified by:

getOperatorNorm in interface BasicMatrix

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()

Specified by:

getRowDim in interface BasicMatrix

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<N> 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.

getVectorInfinityNorm

public Scalar<N> getVectorInfinityNorm()

Description copied from interface: BasicMatrix

The largest, absolute, element value.

Specified by:

getVectorInfinityNorm in interface BasicMatrix

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.

Specified by:

getVectorNorm in interface BasicMatrix

See Also:

BasicMatrix.toListOfRows(), BasicMatrix.toListOfColumns(), BasicMatrix.toListOfElements()

getVectorProduct

public Scalar<N> getVectorProduct(BasicMatrix aVctr)

Description copied from interface: BasicMatrix

Treats [this] and [aVctr] as if they are one dimensional (vectors) and calculates the vector (dot) product. The two vectors must have the same number of elements.

Specified by:

getVectorProduct in interface BasicMatrix

getVectorZeroNorm

public Scalar<N> getVectorZeroNorm()

Specified by:

getVectorZeroNorm in interface BasicMatrix

Returns:

The number of non-zero elements

getZeroNorm

@Deprecated
public Scalar<N> getZeroNorm()

Deprecated. Since Version 25. Use getVectorZeroNorm() instead

Description copied from interface: BasicMatrix

Unfortunate method name. Will perhaps be renamed getVectorZeroNorm.

Specified by:

getZeroNorm in interface BasicMatrix

Returns:

The vector zero-norm

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

isHermitian

public boolean isHermitian()

Specified by:

isHermitian in interface BasicMatrix

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

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)

negate

public BasicMatrix negate()

Specified by:

negate in interface BasicMatrix

Returns:

A new matrix with negated elements.

set

public BasicMatrix set(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:

set in interface BasicMatrix

size

public int size()

Specified by:

size in interface BasicMatrix

Returns:

The number of elements.

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.

toBigDecimal

public BigDecimal toBigDecimal(int aRow,
                               int aCol)

Description copied from interface: BasicMatrix

Extracts one element of this matrix as a BigDecimal.

Specified by:

toBigDecimal in interface BasicMatrix

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.

Specified by:

toComplexNumber in interface BasicMatrix

Parameters:

aRow - A row index.

aCol - A column index.

Returns:

One matrix element

toComplexStore

public PhysicalStore<ComplexNumber> toComplexStore()

Specified by:

toComplexStore in interface BasicMatrix

See Also:

BasicMatrix.toBigStore(), BasicMatrix.toPrimitiveStore()

toListOfColumns

public List<BasicMatrix> toListOfColumns()

Specified by:

toListOfColumns in interface BasicMatrix

toListOfElements

public List<BigDecimal> toListOfElements()

Specified by:

toListOfElements in interface BasicMatrix

toListOfRows

public List<BasicMatrix> toListOfRows()

Specified by:

toListOfRows in interface BasicMatrix

toPrimitiveStore

public PhysicalStore<Double> toPrimitiveStore()

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: BasicMatrix

Extracts one element of this matrix as a Scalar.

Specified by:

toScalar in interface BasicMatrix

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()