org.ojalgo.matrix

Interface BasicMatrix

All Superinterfaces:

Access1D<Number>, Access1D.Aggregatable<Number>, Access1D.Elements, Access2D<Number>, Access2D.Aggregatable<Number>, Access2D.Elements, Group, Group.Additive<BasicMatrix>, Iterable<Number>, NormedVectorSpace<BasicMatrix,Number>, Operation, Operation.Addition<BasicMatrix>, Operation.Multiplication<BasicMatrix>, Operation.Subtraction<BasicMatrix>, ScalarOperation, ScalarOperation.Addition<BasicMatrix,Number>, ScalarOperation.Division<BasicMatrix,Number>, ScalarOperation.Multiplication<BasicMatrix,Number>, ScalarOperation.Subtraction<BasicMatrix,Number>, Structure1D, Structure2D, Structure2D.ReducibleTo1D<BasicMatrix>, VectorSpace<BasicMatrix,Number>

All Known Implementing Classes:

BigMatrix, ComplexMatrix, PrimitiveMatrix, QuaternionMatrix, RationalMatrix

public interface BasicMatrix
extends Access2D<Number>, Access2D.Elements, Access2D.Aggregatable<Number>, Structure2D.ReducibleTo1D<BasicMatrix>, NormedVectorSpace<BasicMatrix,Number>, Operation.Subtraction<BasicMatrix>, Operation.Multiplication<BasicMatrix>, ScalarOperation.Addition<BasicMatrix,Number>, ScalarOperation.Division<BasicMatrix,Number>, ScalarOperation.Subtraction<BasicMatrix,Number>

This interface declares a set of high level methods for linear algebra. Only the most basic set of matrix functionality is defined here. Various matrix decompositions may be used to do some of the more advanced tasks.

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	BasicMatrix.Builder<I extends BasicMatrix>
static interface	BasicMatrix.Factory<I extends BasicMatrix>

Nested classes/interfaces inherited from interface org.ojalgo.access.Access2D

Access2D.Aggregatable<N extends Number>, Access2D.Collectable<N extends Number,R extends Mutate2D.Receiver<N>>, Access2D.Elements, Access2D.ElementView<N extends Number>, Access2D.IndexOf, Access2D.Sliceable<N extends Number>, Access2D.Visitable<N extends Number>

Nested classes/interfaces inherited from interface org.ojalgo.access.Structure2D

Structure2D.IntRowColumn, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.RowColumnCallback, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Nested classes/interfaces inherited from interface org.ojalgo.access.Structure1D

Structure1D.BasicMapper<T>, Structure1D.IndexCallback, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback

Nested classes/interfaces inherited from interface org.ojalgo.algebra.Group

Group.Additive<S>, Group.Multiplicative<S>

Nested classes/interfaces inherited from interface org.ojalgo.algebra.Operation

Operation.Addition<T>, Operation.Division<T>, Operation.Multiplication<T>, Operation.Subtraction<T>

Nested classes/interfaces inherited from interface org.ojalgo.algebra.ScalarOperation

ScalarOperation.Addition<T,N extends Number>, ScalarOperation.Division<T,N extends Number>, ScalarOperation.Multiplication<T,N extends Number>, ScalarOperation.Subtraction<T,N extends Number>

Method Summary

Modifier and Type	Method and Description
BasicMatrix	add(int row, int col, Access2D<?> addend)
static double	calculateFrobeniusNorm(BasicMatrix matrix) 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.
static double	calculateInfinityNorm(BasicMatrix matrix)
static double	calculateOneNorm(BasicMatrix matrix)
BasicMatrix.Builder<? extends BasicMatrix>	copy()
BasicMatrix	divideElements(Access2D<?> aMtrx) Divides the elements of this with the elements of aMtrx.
BasicMatrix	enforce(NumberContext context) Will enforce this number context on the elements
boolean	equals(Access2D<?> aMtrx, NumberContext aCntxt)
void	flushCache() BasicMatrix instances are intended to be immutable.
BasicMatrix	getColumnsRange(int first, int limit)
Scalar<?>	getCondition() Deprecated. v40 Use SingularValue
Scalar<?>	getDeterminant()
List<ComplexNumber>	getEigenvalues() Deprecated. v40 Use SingularValue
int	getRank() Deprecated. v40 Use SingularValue
BasicMatrix	getRowsRange(int first, int kimit)
List<? extends Number>	getSingularValues() Deprecated. v40 Use SingularValue
Scalar<?>	getTrace() The sum of the diagonal elements.
BasicMatrix	invert() About inverting matrices:
boolean	isFullRank() Deprecated. v40
boolean	isHermitian()
boolean	isSymmetric()
BasicMatrix	mergeColumns(Access2D<?> belowRows) [belowRows] is appended below [this].
BasicMatrix	mergeRows(Access2D<?> rightColumns) [rightColumns] is appended to the right of [this].
BasicMatrix	modify(UnaryFunction<? extends Number> aFunc) Deprecated. v42
BasicMatrix	multiplyElements(Access2D<?> aMtrx) Multiplies the elements of this matrix with the elements of aMtrx.
BasicMatrix	selectColumns(int... someCols)
BasicMatrix	selectRows(int... someRows)
BasicMatrix	solve(Access2D<?> aRHS) This method solves a system of linear equations: [this][X]=[aRHS].
Scalar<?>	toScalar(long row, long col) Extracts one element of this matrix as a Scalar.
default String	toString(int row, int col) Deprecated. v42
BasicMatrix	transpose() Transposes this matrix.

Methods inherited from interface org.ojalgo.access.Access2D

asCollectable2D, asPrimitive2D, columns, doubleValue, doubleValue, elements, equals, get, get, newPrimitiveColumnCollectable, newPrimitiveRowCollectable, rows, toRawCopy2D, toString, wrap, wrap, wrapAccess2D, wrapAccess2D

Methods inherited from interface org.ojalgo.access.Access1D

asCollectable1D, asPrimitive1D, axpy, dot, equals, hashCode, iterator, nonzeros, stream, supplyTo, toRawCopy1D, wrap, wrap, wrap, wrapAccess1D, wrapAccess1D, wrapAccess1D

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Methods inherited from interface org.ojalgo.access.Access2D.Elements

isAbsolute, isAbsolute, isColumnSmall, isColumnSmall, isRowSmall, isRowSmall, isSmall, isSmall

Methods inherited from interface org.ojalgo.access.Access1D.Elements

isAllSmall

Methods inherited from interface org.ojalgo.access.Access2D.Aggregatable

aggregateColumn, aggregateColumn, aggregateDiagonal, aggregateRow, aggregateRow, reduceColumns, reduceRows

Methods inherited from interface org.ojalgo.access.Access1D.Aggregatable

aggregateAll, aggregateRange

Methods inherited from interface org.ojalgo.access.Structure2D.ReducibleTo1D

reduceColumns, reduceRows

Methods inherited from interface org.ojalgo.access.Structure2D

column, column, column, column, column, count, countColumns, countRows, index, index, isEmpty, isFat, isScalar, isSquare, isTall, isVector, loopAll, loopColumn, loopColumn, loopDiagonal, loopMatching, loopRow, loopRow, mapperOf, row, row, row, row, row

Methods inherited from interface org.ojalgo.access.Structure1D

loopAll, loopMatching, loopRange, mapper

Methods inherited from interface org.ojalgo.algebra.NormedVectorSpace

isSmall, norm, signum

Methods inherited from interface org.ojalgo.algebra.VectorSpace

conjugate

Methods inherited from interface org.ojalgo.algebra.Group.Additive

negate

Methods inherited from interface org.ojalgo.algebra.Operation.Addition

add

Methods inherited from interface org.ojalgo.algebra.ScalarOperation.Multiplication

multiply, multiply

Methods inherited from interface org.ojalgo.algebra.Operation.Subtraction

subtract

Methods inherited from interface org.ojalgo.algebra.Operation.Multiplication

multiply

Methods inherited from interface org.ojalgo.algebra.ScalarOperation.Addition

add, add

Methods inherited from interface org.ojalgo.algebra.ScalarOperation.Division

divide, divide

Methods inherited from interface org.ojalgo.algebra.ScalarOperation.Subtraction

subtract, subtract

Method Detail

calculateFrobeniusNorm

static double calculateFrobeniusNorm(BasicMatrix matrix)

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.

Returns:

The matrix' Frobenius norm

calculateInfinityNorm

static double calculateInfinityNorm(BasicMatrix matrix)

Returns:

The inf-norm or maximum row sum

calculateOneNorm

static double calculateOneNorm(BasicMatrix matrix)

Returns:

The 1-norm or maximum column sum

add

BasicMatrix add(int row,
                int col,
                Access2D<?> addend)

Parameters:

row - The row index of where to superimpose the top left element of the addend

col - The column index of where to superimpose the top left element of the addend

addend - A matrix to superimpose

Returns:

A new matrix

copy

BasicMatrix.Builder<? extends BasicMatrix> copy()

Returns:

A fully mutable matrix builder with the elements initially set to a copy of this matrix.

divideElements

BasicMatrix divideElements(Access2D<?> aMtrx)

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

Parameters:

aMtrx - The denominator elements.

Returns:

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

enforce

BasicMatrix enforce(NumberContext context)

Will enforce this number context on the elements

Parameters:

context - The context

Returns:

A new matrix with the elements enforced

equals

boolean equals(Access2D<?> aMtrx,
               NumberContext aCntxt)

Returns:

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

flushCache

void flushCache()

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.

getColumnsRange

BasicMatrix getColumnsRange(int first,
                            int limit)

Parameters:

first - The first column to include.

limit - The limit (exclusive) - the first column not to include.

Returns:

A new matrix with only the specified range of columns

getCondition

@Deprecated
Scalar<?> getCondition()

Deprecated. v40 Use SingularValue

Matrix condition (2-norm)

Returns:

ratio of largest to smallest singular value.

getDeterminant

Scalar<?> getDeterminant()

Returns:

The matrix' determinant.

getEigenvalues

@Deprecated
List<ComplexNumber> getEigenvalues()

Deprecated. v40 Use SingularValue

getRank

@Deprecated
int getRank()

Deprecated. v40 Use SingularValue

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.

Returns:

The matrix' rank.

getRowsRange

BasicMatrix getRowsRange(int first,
                         int kimit)

Parameters:

first - The first row to include.

kimit - The limit (exclusive) - the first row not to include.

Returns:

A new matrix with only the specified range of rows

getSingularValues

@Deprecated
List<? extends Number> getSingularValues()

Deprecated. v40 Use SingularValue

getTrace

Scalar<?> getTrace()

The sum of the diagonal elements.

Returns:

The matrix' trace.

invert

BasicMatrix invert()

About inverting matrices:

• "right inverse": [this][right inverse]=[I]. You may calculate it using solve(Access2D).
• "left inverse": [left inverse][this]=[I]. You may calculate it using solve(Access2D) 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].

Returns:

The "best possible" inverse....

isFullRank

@Deprecated
boolean isFullRank()

Deprecated. v40

Returns:

true if getRank() == min(Structure2D.countRows(), Structure2D.countColumns())

isHermitian

boolean isHermitian()

isSymmetric

boolean isSymmetric()

mergeColumns

BasicMatrix mergeColumns(Access2D<?> belowRows)

[belowRows] is appended below [this]. The two matrices must have the same number of columns.

Parameters:

belowRows - The matrix to merge.

Returns:

A new matrix with more rows.

mergeRows

BasicMatrix mergeRows(Access2D<?> rightColumns)

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

Parameters:

rightColumns - The matrix to merge.

Returns:

A new matrix with more columns.

modify

@Deprecated
BasicMatrix modify(UnaryFunction<? extends Number> aFunc)

Deprecated. v42

multiplyElements

BasicMatrix multiplyElements(Access2D<?> aMtrx)

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

Parameters:

aMtrx - The elements to multiply by.

Returns:

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

selectColumns

BasicMatrix selectColumns(int... someCols)

Parameters:

someCols - An ordered array of column indeces.

Returns:

A matrix with a subset of, reordered, columns.

selectRows

BasicMatrix selectRows(int... someRows)

Parameters:

someRows - An ordered array of row indeces.

Returns:

A matrix with a subset of, reordered, rows.

solve

BasicMatrix solve(Access2D<?> aRHS)

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

Parameters:

aRHS - The right hand side of the equation.

Returns:

The solution, [X].

toScalar

Scalar<?> toScalar(long row,
                   long col)

Extracts one element of this matrix as a Scalar.

Parameters:

row - A row index.

col - A column index.

Returns:

One matrix element

toString

@Deprecated
default String toString(int row,
                                    int col)

Deprecated. v42

transpose

BasicMatrix transpose()

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

Returns:

A matrix that is the transpose of this matrix.

See Also:

VectorSpace.conjugate()