| Matrix |
| abstract public class Matrix implements VectorSpace<Matrix<F>, F>,Ring<Matrix<F>>,ValueType,Realtime(Code) |
| This class represents a rectangular table of elements of a ring-like
algebraic structure.
Instances of this class can be used to resolve system of linear equations
involving any kind of
Field Field elements
(e.g.
org.jscience.mathematics.number.Real Real ,
org.jscience.mathematics.number.Complex Complex ,
org.jscience.physics.amount.Amount Amount<?> ,
org.jscience.mathematics.function.Function Function , etc).
For example:[code]
// Creates a dense matrix (2x2) of Rational numbers.
DenseMatrix M = DenseMatrix.valueOf(
{ Rational.valueOf(23, 45), Rational.valueOf(33, 75) },
{ Rational.valueOf(15, 31), Rational.valueOf(-20, 45)});
// Creates a sparse matrix (16x2) of Real numbers.
SparseMatrix M = SparseMatrix.valueOf(
SparseVector.valueOf(16, Real.ZERO, 0, Real.valueOf(5)),
SparseVector.valueOf(16, Real.ZERO, 15, Real.valueOf(-3)));
// Creates a floating-point (64 bits) matrix (3x2).
Float64Matrix M = Float64Matrix.valueOf(
{{ 1.0, 2.0, 3.0}, { 4.0, 5.0, 6.0}});
// Creates a complex single column matrix (1x2).
ComplexMatrix M = ComplexMatrix.valueOf(
{{ Complex.valueOf(1.0, 2.0), Complex.valueOf(4.0, 5.0)}}).transpose();
// Creates an identity matrix (2x2) for modulo integer.
SparseMatrix IDENTITY = SparseMatrix.valueOf(
DenseVector.valueOf(ModuloInteger.ONE, ModuloInteger.ONE), ModuloInteger.ZERO);
[/code]
Non-commutative field multiplication is supported. Invertible square
matrices may form a non-commutative field (also called a division
ring). In which case this class may be used to resolve system of linear
equations with matrix coefficients.
Implementation Note: Matrices may use
javolution.context.StackContext StackContext and
javolution.context.ConcurrentContext ConcurrentContext in order to
minimize heap allocation and accelerate calculations on multi-core
systems.
author:
Jean-Marie Dautelle
version:
3.3, December 24, 2006
See Also:
* Wikipedia: Matrix (mathematics) |
| Method Summary |
|
| abstract public Matrix<F> | adjoint()
Returns the adjoint of this matrix. |
| abstract public F | cofactor(int i, int j)
Returns the cofactor of an element in this matrix. |
| abstract public Matrix<F> | copy()
Returns a copy of this matrix
javolution.context.AllocatorContext allocated
by the calling thread (possibly on the stack). |
| abstract public F | determinant()
Returns the determinant of this matrix. |
| public Matrix<F> | divide(Matrix<F> that)
Returns this matrix divided by the one specified.
Parameters:
that - the matrix divisor. |
| public boolean | equals(Matrix<F> that, Comparator<F> cmp)
Indicates if this matrix can be considered equals to the one
specified using the specified comparator when testing for
element equality. |
| public boolean | equals(Object that)
Indicates if this matrix is strictly equal to the object specified.
Parameters:
that - the object to compare for equality. |
| abstract public F | get(int i, int j)
Returns a single element from this matrix.
Parameters:
i - the row index (range [0..m[).
Parameters:
j - the column index (range [0..n[). |
| abstract public Vector<F> | getColumn(int j)
Returns the column identified by the specified index in this matrix.
Parameters:
j - the column index (range [0..n[). |
| abstract public Vector<F> | getDiagonal()
Returns the diagonal vector. |
| abstract public int | getNumberOfColumns()
Returns the number of columns n for this matrix. |
| abstract public int | getNumberOfRows()
Returns the number of rows m for this matrix. |
| abstract public Vector<F> | getRow(int i)
Returns the row identified by the specified index in this matrix.
Parameters:
i - the row index (range [0..m[). |
| public int | hashCode()
Returns a hash code value for this matrix. |
| abstract public Matrix<F> | inverse()
Returns the inverse of this matrix (must be square). |
| public boolean | isSquare()
Indicates if this matrix is square. |
| public Matrix<F> | minus(Matrix<F> that)
Returns the difference between this matrix and the one specified.
Parameters:
that - the matrix to be subtracted. |
| abstract public Matrix<F> | opposite()
Returns the negation of this matrix. |
| abstract public Matrix<F> | plus(Matrix<F> that)
Returns the sum of this matrix with the one specified.
Parameters:
that - the matrix to be added. |
| public Matrix<F> | pow(int exp)
Returns this matrix raised at the specified exponent.
Parameters:
exp - the exponent. |
| public Matrix<F> | pseudoInverse()
Returns the inverse or pseudo-inverse if this matrix if not square. |
| public Vector<F> | solve(Vector<F> y)
Solves this matrix for the specified vector (returns x
such as this · x = y).
Parameters:
y - the vector for which the solution is calculated. |
| public Matrix<F> | solve(Matrix<F> y)
Solves this matrix for the specified matrix (returns x
such as this · x = y).
Parameters:
y - the matrix for which the solution is calculated. |
| abstract public Matrix<F> | tensor(Matrix<F> that)
Returns the linear algebraic matrix tensor product of this matrix
and another (Kronecker product). |
| abstract public Matrix<F> | times(F k)
Returns the product of this matrix by the specified factor.
Parameters:
k - the coefficient multiplier. |
| abstract public Vector<F> | times(Vector<F> v)
Returns the product of this matrix by the specified vector.
Parameters:
v - the vector. |
| abstract public Matrix<F> | times(Matrix<F> that)
Returns the product of this matrix with the one specified.
Parameters:
that - the matrix multiplier. |
| final public String | toString()
Returns the text representation of this matrix as a
java.lang.String. |
| public Text | toText()
Returns the text representation of this matrix. |
| public F | trace()
Returns the trace of this matrix. |
| abstract public Matrix<F> | transpose()
Returns the transpose of this matrix. |
| abstract public Vector<F> | vectorization()
Returns the vectorization of this matrix. |
