org.jblas

Class Solve

java.lang.Object

org.jblas.Solve

public class Solve
extends Object

Solving linear equations.

Constructor Summary

Constructors

Constructor and Description
Solve()

Method Summary

Modifier and Type	Method and Description
static DoubleMatrix	pinv(DoubleMatrix A) Computes the pseudo-inverse.
static FloatMatrix	pinv(FloatMatrix A) Computes the pseudo-inverse.
static DoubleMatrix	solve(DoubleMatrix A, DoubleMatrix B) Solves the linear equation A*X = B.
static FloatMatrix	solve(FloatMatrix A, FloatMatrix B) Solves the linear equation A*X = B.
static DoubleMatrix	solveLeastSquares(DoubleMatrix A, DoubleMatrix B) Computes the Least Squares solution for over or underdetermined linear equations A*X = B In the overdetermined case, when m > n, that is, there are more equations than variables, it computes the least squares solution of X -> ||A*X - B ||_2.
static FloatMatrix	solveLeastSquares(FloatMatrix A, FloatMatrix B) Computes the Least Squares solution for over or underdetermined linear equations A*X = B In the overdetermined case, when m > n, that is, there are more equations than variables, it computes the least squares solution of X -> ||A*X - B ||_2.
static DoubleMatrix	solvePositive(DoubleMatrix A, DoubleMatrix B) Solves the linear equation A*X = B for symmetric and positive definite A.
static FloatMatrix	solvePositive(FloatMatrix A, FloatMatrix B) Solves the linear equation A*X = B for symmetric and positive definite A.
static DoubleMatrix	solveSymmetric(DoubleMatrix A, DoubleMatrix B) Solves the linear equation A*X = B for symmetric A.
static FloatMatrix	solveSymmetric(FloatMatrix A, FloatMatrix B) Solves the linear equation A*X = B for symmetric A.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Solve

public Solve()

Method Detail

solve

public static DoubleMatrix solve(DoubleMatrix A,
                                 DoubleMatrix B)

Solves the linear equation A*X = B.

solveSymmetric

public static DoubleMatrix solveSymmetric(DoubleMatrix A,
                                          DoubleMatrix B)

Solves the linear equation A*X = B for symmetric A.

solvePositive

public static DoubleMatrix solvePositive(DoubleMatrix A,
                                         DoubleMatrix B)

Solves the linear equation A*X = B for symmetric and positive definite A.

solveLeastSquares

public static DoubleMatrix solveLeastSquares(DoubleMatrix A,
                                             DoubleMatrix B)

Computes the Least Squares solution for over or underdetermined linear equations A*X = B In the overdetermined case, when m > n, that is, there are more equations than variables, it computes the least squares solution of X -> ||A*X - B ||_2. In the underdetermined case, when m < n (less equations than variables), there are infinitely many solutions and it computes the minimum norm solution.

Parameters:

A - an (m,n) matrix

B - a (m,k) matrix

Returns:

either the minimum norm or least squares solution.

pinv

public static DoubleMatrix pinv(DoubleMatrix A)

Computes the pseudo-inverse. Note, this function uses the solveLeastSquares and might produce different numerical solutions for the underdetermined case than matlab.

Parameters:

A - rectangular matrix

Returns:

matrix P such that A*P*A = A and P*A*P = P.

solve

public static FloatMatrix solve(FloatMatrix A,
                                FloatMatrix B)

Solves the linear equation A*X = B.

solveSymmetric

public static FloatMatrix solveSymmetric(FloatMatrix A,
                                         FloatMatrix B)

Solves the linear equation A*X = B for symmetric A.

solvePositive

public static FloatMatrix solvePositive(FloatMatrix A,
                                        FloatMatrix B)

Solves the linear equation A*X = B for symmetric and positive definite A.

solveLeastSquares

public static FloatMatrix solveLeastSquares(FloatMatrix A,
                                            FloatMatrix B)

Computes the Least Squares solution for over or underdetermined linear equations A*X = B In the overdetermined case, when m > n, that is, there are more equations than variables, it computes the least squares solution of X -> ||A*X - B ||_2. In the underdetermined case, when m < n (less equations than variables), there are infinitely many solutions and it computes the minimum norm solution.

Parameters:

A - an (m,n) matrix

B - a (m,k) matrix

Returns:

either the minimum norm or least squares solution.

pinv

public static FloatMatrix pinv(FloatMatrix A)

Computes the pseudo-inverse. Note, this function uses the solveLeastSquares and might produce different numerical solutions for the underdetermined case than matlab.

Parameters:

A - rectangular matrix

Returns:

matrix P such that A*P*A = A and P*A*P = P.