Package org.djunits.vecmat.d3

Class Matrix3x3<Q extends Quantity<Q>>

java.lang.Object

org.djunits.vecmat.def.VectorMatrix<Q,T,SI,H,TT>

org.djunits.vecmat.def.Table<Q,M,SI,H,MT>

org.djunits.vecmat.def.Matrix<Q,M,SI,H,M>

org.djunits.vecmat.def.SquareMatrix<Q,M,SI,H>

org.djunits.vecmat.def.SquareDenseMatrix<Q,Matrix3x3<Q>,Matrix3x3<SIQuantity>,Matrix3x3<?>>

org.djunits.vecmat.d3.Matrix3x3<Q>

Type Parameters:

Q - the quantity type

All Implemented Interfaces:

Serializable, Additive<Matrix3x3<Q>>, Scalable<Matrix3x3<Q>>, Value<Matrix3x3<Q>,Q>, Hadamard<Matrix3x3<?>,Matrix3x3<SIQuantity>>

public class Matrix3x3<Q extends Quantity<Q>>
extends SquareDenseMatrix<Q,Matrix3x3<Q>,Matrix3x3<SIQuantity>,Matrix3x3<?>>

Matrix3x3 implements a matrix with 3x3 real-valued entries. The matrix is immutable, except for the display unit, which can be changed.

Copyright (c) 2025-2026 Delft University of Technology, Jaffalaan 5, 2628 BX Delft, the Netherlands. All rights reserved. See for project information https://djunits.org. The DJUNITS project is distributed under a three-clause BSD-style license.

Author:

Alexander Verbraeck

See Also:

• Serialized Form

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	Matrix3x3(double[] dataSi, Unit<?,Q> displayUnit)	Create a new Matrix3x3 with a unit.

Method Summary

Modifier and Type	Method	Description
Matrix3x3<SIQuantity>	adjugate()	Return the adjugate (classical adjoint) matrix for this matrix, often denoted as adj(M).
<TQ extends Quantity<TQ>> Matrix3x3<TQ>	as(Unit<?,TQ> targetUnit)	Return the matrix 'as' a matrix with a known quantity, using a unit to express the result in.
Matrix3x3<SIQuantity>	divideEntries(Matrix3x3<?> other)	Divide the entries of this vector, matrix or table on an entry-by-entry basis with those of another collection of the same type (but possibly representing another quantity).
Vector3.Col<Q>	getColumnVector(int col)	Return a quantity column (0-based) from the table or matrix.
Vector3.Col<Q>	getDiagonalVector()	Retrieve the main diagonal of the matrix as a column vector.
Vector3.Row<Q>	getRowVector(int row)	Return a quantity row (0-based) from the table or matrix.
Matrix3x3<Q>	instantiateSi(double[] siNew)	Return a new vector or matrix with the given SI or BASE values.
Matrix3x3<SIQuantity>	instantiateSi(double[] siNew, SIUnit siUnit)	Return a new vector or matrix in SI-units with the given SI or BASE values.
Matrix3x3<SIQuantity>	inverse()	Return the inverse of the square matrix, if the matrix is non-singular.
Matrix3x3<SIQuantity>	invertEntries()	Invert the vector, matrix or table on an entry-by-entry basis.
Vector3.Col<Q>	mgetColumnVector(int mCol)	Return a quantity column (1-based) from the table or matrix.
Vector3.Row<Q>	mgetRowVector(int mRow)	Return a quantity row (1-based) from the table or matrix.
Matrix3x3<SIQuantity>	multiply(Matrix3x3<?> otherMat)	Multiply this matrix with another matrix using matrix multiplication and return the result.
Vector3.Col<SIQuantity>	multiply(Vector3.Col<?> otherVec)	Multiply this matrix with a column vector, resulting in a column vector.
Matrix3x3<SIQuantity>	multiplyEntries(Quantity<?> quantity)	Multiply the entries of this vector, matrix or table by the given quantity.
Matrix3x3<SIQuantity>	multiplyEntries(Matrix3x3<?> other)	Multiply the entries of this vector, matrix or table on an entry-by-entry basis with those of another collection of the same type (but possibly representing another quantity).
static <Q extends Quantity<Q>> Matrix3x3<Q>	of(double[][] gridInUnit, Unit<?,Q> unit)	Create a new Matrix3x3 with a unit, based on a 2-dimensional grid with values in the given unit.
static <Q extends Quantity<Q>> Matrix3x3<Q>	of(double[] dataInUnit, Unit<?,Q> unit)	Create a new Matrix3x3 with a unit, based on a row-major array with values in the given unit.
static <Q extends Quantity<Q>> Matrix3x3<Q>	of(Q[] data)	Create a Matrix3x3 without needing generics, based on a row-major array of quantities.
static <Q extends Quantity<Q>> Matrix3x3<Q>	of(Q[][] grid)	Create a Matrix3x3 without needing generics, based on a 2-dimensional grid of quantities.
static <Q extends Quantity<Q>> Matrix3x3<Q>	ofSi(double[][] gridSi, Unit<?,Q> displayUnit)	Create a new Matrix3x3 with a unit, based on a 2-dimensional grid with SI-values.
static <Q extends Quantity<Q>> Matrix3x3<Q>	ofSi(double[] dataSi, Unit<?,Q> displayUnit)	Create a Matrix3x3 without needing generics, based on a row-major array with SI-values.

Methods inherited from class org.djunits.vecmat.def.SquareDenseMatrix

cols, equals, getColumnSi, getRowSi, getSiArray, hashCode, nonZeroCount, rows, si, unsafeSiArray

Methods inherited from class org.djunits.vecmat.def.SquareMatrix

determinant, determinantSi, getDiagonalScalars, getDiagonalSi, isSkewSymmetric, isSkewSymmetric, isSymmetric, isSymmetric, normFrobenius, order, trace, transpose

Methods inherited from class org.djunits.vecmat.def.Matrix

format, format, format, multiply

Methods inherited from class org.djunits.vecmat.def.Table

checkCol, checkRow, get, getColumnScalars, getRowScalars, getScalarArray, getScalarGrid, getSiGrid, mcheckCol, mcheckRow, mget, mgetColumnScalars, mgetColumnSi, mgetRowScalars, mgetRowSi, msi

Methods inherited from class org.djunits.vecmat.def.VectorMatrix

abs, add, add, asMatrix1x1, asMatrix2x2, asMatrix3x3, asMatrixNxM, asMatrixNxN, asQuantityTable, asVector1, asVector2Col, asVector2Row, asVector3Col, asVector3Row, asVectorNCol, asVectorNRow, checkMultiply, checkMultiply, divideElements, getDisplayUnit, isRelative, max, mean, median, min, multiplyElements, negate, nnz, scaleBy, setDisplayUnit, subtract, subtract, sum, toString

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.djunits.vecmat.operations.Hadamard

divideEntries

Methods inherited from interface org.djunits.value.Scalable

divideBy

Methods inherited from interface org.djunits.value.Value

isAbsolute, setDisplayUnit

Constructor Details

Matrix3x3

protected Matrix3x3(double[] dataSi,
 Unit<?,Q> displayUnit)

Create a new Matrix3x3 with a unit.

Parameters:

dataSi - the matrix values [a11, a12, a13, a21, a22, a23, a31, a32, a33] expressed in the SI-unit

displayUnit - the display unit for the matrix

Method Details

instantiateSi

public Matrix3x3<Q> instantiateSi(double[] siNew)

Description copied from class: VectorMatrix

Return a new vector or matrix with the given SI or BASE values.

Specified by:

instantiateSi in class VectorMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

siNew - the values for the new vector or matrix in row-major format

Returns:

a new matrix with the provided SI or BASE values

instantiateSi

public Matrix3x3<SIQuantity> instantiateSi(double[] siNew,
 SIUnit siUnit)

Description copied from class: VectorMatrix

Return a new vector or matrix in SI-units with the given SI or BASE values.

Specified by:

instantiateSi in class VectorMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

siNew - the values for the new vector or matrix in row-major format

siUnit - the new unit for the new vector or matrix

Returns:

a new matrix with the provided SI or BASE values

getRowVector

public Vector3.Row<Q> getRowVector(int row)

Description copied from class: Table

Return a quantity row (0-based) from the table or matrix. Note that the specific vector to return can be tightened by the implementing class.

Specified by:

getRowVector in class Table<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

row - the row number to retrieve (0-based)

Returns:

a row vector with the data at the given row

mgetRowVector

public Vector3.Row<Q> mgetRowVector(int mRow)

Description copied from class: Table

Return a quantity row (1-based) from the table or matrix. Note that the specific vector to return can be tightened by the implementing class.

Specified by:

mgetRowVector in class Table<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

mRow - the row number to retrieve (1-based)

Returns:

a row vector with the data at the given row

getColumnVector

public Vector3.Col<Q> getColumnVector(int col)

Description copied from class: Table

Return a quantity column (0-based) from the table or matrix. Note that the specific vector to return can be tightened by the implementing class.

Specified by:

getColumnVector in class Table<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

col - the column number to retrieve (0-based)

Returns:

a column vector with the data at the given column

mgetColumnVector

public Vector3.Col<Q> mgetColumnVector(int mCol)

Description copied from class: Table

Return a quantity column (1-based) from the table or matrix. Note that the specific vector to return can be tightened by the implementing class.

Specified by:

mgetColumnVector in class Table<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

mCol - the column number to retrieve (1-based)

Returns:

a column vector with the data at the given column

getDiagonalVector

public Vector3.Col<Q> getDiagonalVector()
                                 throws IllegalStateException

Description copied from class: SquareMatrix

Retrieve the main diagonal of the matrix as a column vector.

Specified by:

getDiagonalVector in class SquareMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>>

Returns:

the main diagonal as a Vector

Throws:

IllegalStateException

inverse

public Matrix3x3<SIQuantity> inverse()
                              throws NonInvertibleMatrixException

Description copied from class: SquareMatrix

Return the inverse of the square matrix, if the matrix is non-singular. The unit of the matrix is U^(-1).

Specified by:

inverse in class SquareMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>>

Returns:

the inverse of the square matrix, if the matrix is non-singular

Throws:

NonInvertibleMatrixException - when the matrix is singular or cannot be inverted

adjugate

public Matrix3x3<SIQuantity> adjugate()

Description copied from class: SquareMatrix

Return the adjugate (classical adjoint) matrix for this matrix, often denoted as adj(M). The unit of adj(M) is U^(n-1) where n is the order of the matrix.

Specified by:

adjugate in class SquareMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>>

Returns:

the adjugate (classical adjoint) matrix

invertEntries

public Matrix3x3<SIQuantity> invertEntries()

Description copied from interface: Hadamard

Invert the vector, matrix or table on an entry-by-entry basis.

Specified by:

invertEntries in interface Hadamard<Matrix3x3<?>,Matrix3x3<SIQuantity>>

Overrides:

invertEntries in class VectorMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Returns:

a new vector, matrix or table with an entry-by-entry inversion (1/value) of the entries

multiplyEntries

public Matrix3x3<SIQuantity> multiplyEntries(Matrix3x3<?> other)

Description copied from interface: Hadamard

Multiply the entries of this vector, matrix or table on an entry-by-entry basis with those of another collection of the same type (but possibly representing another quantity).

Specified by:

multiplyEntries in interface Hadamard<Matrix3x3<?>,Matrix3x3<SIQuantity>>

Overrides:

multiplyEntries in class VectorMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

other - the other collection of the same type

Returns:

a new vector, matrix or table with an entry-by-entry multiplication of its entries

divideEntries

public Matrix3x3<SIQuantity> divideEntries(Matrix3x3<?> other)

Description copied from interface: Hadamard

Divide the entries of this vector, matrix or table on an entry-by-entry basis with those of another collection of the same type (but possibly representing another quantity).

Specified by:

divideEntries in interface Hadamard<Matrix3x3<?>,Matrix3x3<SIQuantity>>

Overrides:

divideEntries in class VectorMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

other - the other collection of the same type

Returns:

a new vector, matrix or table with an entry-by-entry division of this collection's entries and other's entries

multiply

public Matrix3x3<SIQuantity> multiply(Matrix3x3<?> otherMat)

Multiply this matrix with another matrix using matrix multiplication and return the result.

Parameters:

otherMat - the matrix to multiply with.

Returns:

the matrix from the multiplication with the correct unit

multiply

public Vector3.Col<SIQuantity> multiply(Vector3.Col<?> otherVec)

Multiply this matrix with a column vector, resulting in a column vector.

Parameters:

otherVec - the column vector to multiply with

Returns:

the resulting vector from the multiplication

multiplyEntries

public Matrix3x3<SIQuantity> multiplyEntries(Quantity<?> quantity)

Description copied from interface: Hadamard

Multiply the entries of this vector, matrix or table by the given quantity.

Specified by:

multiplyEntries in interface Hadamard<Matrix3x3<?>,Matrix3x3<SIQuantity>>

Overrides:

multiplyEntries in class VectorMatrix<Q extends Quantity<Q>,Matrix3x3<Q extends Quantity<Q>>,Matrix3x3<SIQuantity>,Matrix3x3<?>,Matrix3x3<Q extends Quantity<Q>>>

Parameters:

quantity - the scalar quantity to multiply by

Returns:

a new vector, matrix or table where the entries have been multiplied by the given quantity

of

public static <Q extends Quantity<Q>> Matrix3x3<Q> of(double[] dataInUnit,
 Unit<?,Q> unit)

Create a new Matrix3x3 with a unit, based on a row-major array with values in the given unit.

Type Parameters:

Q - the quantity type

Parameters:

dataInUnit - the matrix values {a11, a12, 13, ..., a31, a32, a33} expressed in the unit

unit - the unit of the data, also used as the display unit

Returns:

a new Matrix3x3 with a unit

Throws:

IllegalArgumentException - when dataInUnit does not contain 3x3 = 9 values

ofSi

public static <Q extends Quantity<Q>> Matrix3x3<Q> ofSi(double[] dataSi,
 Unit<?,Q> displayUnit)

Create a Matrix3x3 without needing generics, based on a row-major array with SI-values.

Type Parameters:

Q - the quantity type

Parameters:

dataSi - the matrix values {a11, a12, 13, ..., a31, a32, a33} as an array using SI units

displayUnit - the display unit to use

Returns:

a new Matrix3x3 with a unit

Throws:

IllegalArgumentException - when dataSi does not contain 3x3 = 9 values

of

public static <Q extends Quantity<Q>> Matrix3x3<Q> of(Q[] data)

Create a Matrix3x3 without needing generics, based on a row-major array of quantities. The unit is taken from the first quantity in the array.

Type Parameters:

Q - the quantity type

Parameters:

data - the matrix values {a11, a12, 13, ..., a31, a32, a33} expressed as an array of quantities

Returns:

a new Matrix3x3 with a unit

Throws:

IllegalArgumentException - when data does not contain 3x3 = 9 quantities

ofSi

public static <Q extends Quantity<Q>> Matrix3x3<Q> ofSi(double[][] gridSi,
 Unit<?,Q> displayUnit)

Create a new Matrix3x3 with a unit, based on a 2-dimensional grid with SI-values.

Type Parameters:

Q - the quantity type

Parameters:

gridSi - the matrix values {{a11, a12, 13}, ..., {a31, a32, a33}} expressed in the SI or base unit

displayUnit - the unit of the data, which will also be used as the display unit

Returns:

a new Matrix3x3 with a unit

Throws:

IllegalArgumentException - when dataInUnit does not contain 3x3 = 9 values

of

public static <Q extends Quantity<Q>> Matrix3x3<Q> of(double[][] gridInUnit,
 Unit<?,Q> unit)

Create a new Matrix3x3 with a unit, based on a 2-dimensional grid with values in the given unit.

Type Parameters:

Q - the quantity type

Parameters:

gridInUnit - the matrix values {{a11, a12, 13}, ..., {a31, a32, a33}} expressed in the unit

unit - the unit of the values, also used as the display unit

Returns:

a new Matrix3x3 with a unit

Throws:

IllegalArgumentException - when dataInUnit does not contain 3x3 = 9 values

of

public static <Q extends Quantity<Q>> Matrix3x3<Q> of(Q[][] grid)

Create a Matrix3x3 without needing generics, based on a 2-dimensional grid of quantities. The unit is taken from the first quantity in the grid.

Type Parameters:

Q - the quantity type

Parameters:

grid - the matrix values {{a11, a12, 13}, ..., {a31, a32, a33}} expressed as a 2-dimensional array of quantities

Returns:

a new Matrix3x3 with a unit

Throws:

IllegalArgumentException - when dataInUnit does not contain 3x3 = 9 quantities

as

public <TQ extends Quantity<TQ>> Matrix3x3<TQ> as(Unit<?,TQ> targetUnit)
                                           throws IllegalArgumentException

Return the matrix 'as' a matrix with a known quantity, using a unit to express the result in. Throw a Runtime exception when the SI units of this vector and the target vector do not match.

Type Parameters:

TQ - target quantity type

Parameters:

targetUnit - the unit to convert the matrix to

Returns:

a matrix typed in the target matrix class

Throws:

IllegalArgumentException - when the units do not match