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Class JSci.maths.LinearMath 

java.lang.Object
   |
   +----JSci.maths.AbstractMath
           |
           +----JSci.maths.LinearMath
public final class LinearMath
extends AbstractMath
The linear math library. This class cannot be subclassed or instantiated because all methods are static.

Method Index

o eigenSolveHermitian(ComplexSquareMatrix, ComplexVector[])
This method finds the eigenvalues and eigenvectors of a Hermitian matrix.
o eigenSolveSymmetric(DoubleSquareMatrix, DoubleVector[])
This method finds the eigenvalues and eigenvectors of a symmetric square matrix.
o eigenSolveSymmetric(DoubleTridiagonalMatrix, DoubleVector[])
This method finds the eigenvalues and eigenvectors of a symmetric tridiagonal matrix by the QL method.
o eigenvalueSolveHermitian(ComplexSquareMatrix)
This method finds the eigenvalues of a Hermitian matrix.
o eigenvalueSolveSymmetric(DoubleSquareMatrix)
This method finds the eigenvalues of a symmetric square matrix.
o eigenvalueSolveSymmetric(DoubleTridiagonalMatrix)
This method finds the eigenvalues of a symmetric tridiagonal matrix by the QL method.
o leastSquaresFit(int, double[][])
Fits an nth degree polynomial to data using the method of least squares.
o linearRegression(double[][])
Fits a line to multi-dimensional data using the method of least squares.
o solve(DoubleSquareMatrix[], DoubleVector)
Solves the linear system Mx=v.
o solveGMRes(DoubleMatrix, DoubleVector, int, double)
Solves the unsymmetric linear system Ax=b using the Generalized Minimum Residual method (doesn't require A to be nonsingular).

Methods

o solve 
 public static DoubleVector solve(DoubleSquareMatrix lu[],
                                  DoubleVector v)
Solves the linear system Mx=v.

Parameters:
lu - the decomposed matrix M
v - a double vector
Returns:
the double vector x
See Also:
luDecompose, choleskyDecompose
o solveGMRes 
 public static DoubleVector solveGMRes(DoubleMatrix A,
                                       DoubleVector b,
                                       int max_iter,
                                       double tol) throws MaximumIterationsExceededException
Solves the unsymmetric linear system Ax=b using the Generalized Minimum Residual method (doesn't require A to be nonsingular). While slower than LU decomposition, it is more robust and should be used with large matrices. It is guaranted to converge exactly in N iterations for an N by N matrix (minus some numerical errors).

Parameters:
max_iter - maximum number of iterations
tol - tolerance
Throws: IllegalArgumentException
if either the tolerance or the number of iterations is not positive. Also, if an unexpected error occurs.
Throws: MaximumIterationsExceededException
if it cannot converge according to the given parameters.
o leastSquaresFit 
 public static DoubleVector leastSquaresFit(int n,
                                            double data[][])
Fits an nth degree polynomial to data using the method of least squares.

Parameters:
n - the degree of the polynomial
data - [0][] contains the x-series, [1][] contains the y-series
Returns:
a vector containing the polynomial's coefficients (in ascending degree order)
o linearRegression 
 public static DoubleVector linearRegression(double data[][])
Fits a line to multi-dimensional data using the method of least squares.

Parameters:
data - [0...n-1][] contains the x-series' (they must be linearly uncorrelated), [n][] contains the y-series
Returns:
a vector containing the coefficients
o eigenvalueSolveHermitian 
 public static double[] eigenvalueSolveHermitian(ComplexSquareMatrix matrix) throws MaximumIterationsExceededException
This method finds the eigenvalues of a Hermitian matrix.

Parameters:
matrix - a Hermitian matrix
Returns:
an array containing the eigenvalues
Throws: MaximumIterationsExceededException
If it takes more than 50 iterations to determine an eigenvalue.
o eigenSolveHermitian 
 public static double[] eigenSolveHermitian(ComplexSquareMatrix matrix,
                                            ComplexVector eigenvector[]) throws MaximumIterationsExceededException
This method finds the eigenvalues and eigenvectors of a Hermitian matrix.

Parameters:
matrix - a Hermitian matrix
eigenvector - an empty array of complex vectors to hold the eigenvectors. All eigenvectors will be orthogonal.
Returns:
an array containing the eigenvalues
Throws: MaximumIterationsExceededException
If it takes more than 50 iterations to determine an eigenvalue.
o eigenvalueSolveSymmetric 
 public static double[] eigenvalueSolveSymmetric(DoubleTridiagonalMatrix matrix) throws MaximumIterationsExceededException
This method finds the eigenvalues of a symmetric tridiagonal matrix by the QL method. It is based on the NETLIB algol/fortran procedure tql1 by Bowdler, Martin, Reinsch and Wilkinson.

Parameters:
matrix - a double symmetric tridiagonal matrix
Returns:
an array containing the eigenvalues
Throws: MaximumIterationsExceededException
If it takes more than 50 iterations to determine an eigenvalue.
o eigenSolveSymmetric 
 public static double[] eigenSolveSymmetric(DoubleTridiagonalMatrix matrix,
                                            DoubleVector eigenvector[]) throws MaximumIterationsExceededException
This method finds the eigenvalues and eigenvectors of a symmetric tridiagonal matrix by the QL method. It is based on the NETLIB algol/fortran procedure tql2 by Bowdler, Martin, Reinsch and Wilkinson.

Parameters:
matrix - a double symmetric tridiagonal matrix
eigenvector - an empty array of double vectors to hold the eigenvectors. All eigenvectors will be orthogonal.
Returns:
an array containing the eigenvalues
Throws: MaximumIterationsExceededException
If it takes more than 50 iterations to determine an eigenvalue.
o eigenvalueSolveSymmetric 
 public static double[] eigenvalueSolveSymmetric(DoubleSquareMatrix matrix) throws MaximumIterationsExceededException
This method finds the eigenvalues of a symmetric square matrix. The matrix is reduced to tridiagonal form and then the QL method is applied. It is based on the NETLIB algol/fortran procedure tred1/tql1 by Bowdler, Martin, Reinsch and Wilkinson.

Parameters:
matrix - a double symmetric square matrix
Returns:
an array containing the eigenvalues
Throws: MaximumIterationsExceededException
If it takes more than 50 iterations to determine an eigenvalue.
o eigenSolveSymmetric 
 public static double[] eigenSolveSymmetric(DoubleSquareMatrix matrix,
                                            DoubleVector eigenvector[]) throws MaximumIterationsExceededException
This method finds the eigenvalues and eigenvectors of a symmetric square matrix. The matrix is reduced to tridiagonal form and then the QL method is applied. It is based on the NETLIB algol/fortran procedure tred2/tql2 by Bowdler, Martin, Reinsch and Wilkinson.

Parameters:
matrix - a double symmetric square matrix
eigenvector - an empty array of double vectors to hold the eigenvectors. All eigenvectors will be orthogonal.
Returns:
an array containing the eigenvalues
Throws: MaximumIterationsExceededException
If it takes more than 50 iterations to determine an eigenvalue. 
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