Class Summary Class Description ComplexMatrix ComplexVector DenseMatrix<F extends Field<F>> This class represents a matrix made of`dense vectors`

(as rows).DenseVector<F extends Field<F>> This class represents a dense vector.Float64Matrix This class represents an optimized`matrix`

implementation for`64 bits floating-point`

numbers.Float64Vector This class represents an optimized`vector`

implementation for 64 bits floating point elements.LUDecomposition<F extends Field<F>> This class represents the decomposition of a`matrix`

`A`

into a product of a`lower`

and`upper`

triangular matrices,`L`

and`U`

respectively, such as`A = P\xc2\xb7L\xc2\xb7U`

`with`

`P`

`a`

`permutation`

matrix.Matrix<F extends Field<F>> This class represents a rectangular table of elements of a ring-like algebraic structure.SparseMatrix<F extends Field<F>> This class represents a matrix made of`sparse vectors`

(as rows).SparseVector<F extends Field<F>> This class represents a sparse vector.Vector<F extends Field<F>> This class represents an immutable element of a vector space.Exception Summary Exception Description DimensionException Signals that an operation is performed upon vectors or matrices whose dimensions disagree.

## Package org.jscience.mathematics.vector Description

Provides support for linear algebra in the form of `matrices`

and `vectors`

.

With the `Matrix`

class, you should be able to resolve linear systems of equations involving any kind of elements such as `Rational`

, `ModuloInteger`

(modulo operations), `Complex`

, `RationalFunction`

, etc. The main requirement being that your element class implements the mathematical `Field`

interface.

Most `numbers`

and even invertible matrices themselves may implement this interface. Non-commutative multiplication is supported which allows for the resolution of systems of equations with invertible matrix coefficients (matrices of matrices).

For classes embedding automatic error calculation (e.g. `Real`

or `Amount`

), the error on the solution obtained tells you if can trust that solution or not (e.g. system close to singularity). The following example illustrates this point.

Let\'s say you have a simple electric circuit composed of 2 resistors in series with a battery. You want to know the voltage (U1, U2) at the nodes of the resistors and the current (I) traversing the circuit.

` `**import** **static** org.jscience.physics.units.SI.*; Amount<ElectricResistance> R1 = Amount.valueOf(100, 1, OHM); // 1% precision. Amount<ElectricResistance> R2 = Amount.valueOf(300, 3, OHM); // 1% precision. Amount<ElectricPotential> U0 = Amount.valueOf(28, 0.01, VOLT); // \xc2\xb10.01 V fluctuation. // Equations: U0 = U1 + U2 |1 1 0 | |U1| |U0| // U1 = R1 * I => |-1 0 R1| * |U2| = |0 | // U2 = R2 * I |0 -1 R2| |I | |0 | // // A * X = B // DenseMatrix<Amount<?>> A = DenseMatrix.valueOf(**new** Amount<?>[][] { { Amount.ONE, Amount.ONE, Amount.valueOf(0, OHM) }, { Amount.ONE.opposite(), Amount.ZERO, R1 }, { Amount.ZERO, Amount.ONE.opposite(), R2 } }); DenseVector<Amount<?>> B = DenseVector.valueOf(**new** Amount<?>[] { U0, Amount.valueOf(0, VOLT), Amount.valueOf(0, VOLT) }); Vector<Amount<?>> X = A.solve(B); System.out.println(X); System.out.println(X.get(2).to(MILLI(AMPERE))); > {(7.0 \xc2\xb1 1.6E-1) V, (21.0 \xc2\xb1 1.5E-1) V, (7.0E-2 \xc2\xb1 7.3E-4) V/\xce\xa9} > (70.0 \xc2\xb1 7.3E-1) mA

Because the `Amount`

class guarantees the accuracy/precision of its calculations. As long as the input resistances, voltage stay within their specification range then the current **is guaranteed**to be

`(70.0 \xc2\xb1 7.3E-1) mA`

. When the inputs have no error specified, the error on the result corresponds to calculations numeric errors only (which might increase significantly if the matrix is close to singularity).**SCaVis 2.1 © jWork.ORG**