jmathlib.toolbox.jmathlib.matrix._private.Jampack
Class Solve

java.lang.Object
  extended by jmathlib.toolbox.jmathlib.matrix._private.Jampack.Solve

public class Solve
extends java.lang.Object

Solve solves linear systems of the form

      A*X = B
      AH*X = B
      X*A = B
      X*AH = B
where A is a nonsingular Zmat, B is a Zmat, and '^H' denotes the conjugate transpose. Appropriate action is taken for Zmats that are Zltmats, Zutmats, and Zpsdmats. If a decomposition is computed and the History parameter is set, then the decomposition is saved for reuse.

Comments: For triangular matrices only the systems AX=B and A^HX=B are solved by hard code, the other two being solved by wizardry involving transposed systems. This requires the generation of new Zmats of the same size as B, which is inefficient if B is, say, square. Later these methods will be implemented with hard code.

Version:
Pre-alpha
Author:
G. W. Stewart

Constructor Summary
Solve()
           
 
Method Summary
static Zmat ahib(Zltmat L, Zmat B)
          Solves LHX = B, where L is a Zltmat and B is a Zmat.
static Zmat ahib(Zmat A, Zmat B)
          Solve AHX = B, where A is a Zmat and B is a Zmat.
static Zmat ahib(Zutmat U, Zmat B)
          Solves UHX = B, where U is a Zutmat and B is a Zmat.
static Zmat aib(Zltmat L, Zmat B)
          Solves LX = B, where L is a Zltmat and B is a Zmat.
static Zmat aib(Zmat A, Zmat B)
          Solves AX = B, where A is a Zmat and B is a Zmat.
static Zmat aib(Zpsdmat A, Zmat B)
          Solves AX = B, where A is a Zpsdmat and B is a Zmat.
static Zmat aib(Zutmat U, Zmat B)
          Solves UX = B, where U is a Zutmat and B is a Zmat.
static Zmat bahi(Zmat B, Zltmat L)
          Solves XLH = B, where L is a Zltmat and B is a Zmat.
static Zmat bahi(Zmat B, Zmat A)
          Solve XA^H = B, where A is a Zmat and B is a Zmat.
static Zmat bahi(Zmat B, Zutmat U)
          Solves XUH = B, where U is a Zutmat and B is a Zmat.
static Zmat bai(Zmat B, Zltmat L)
          Solves XL = B, where L is a Zltmat and B is a Zmat.
static Zmat bai(Zmat B, Zmat A)
          Solve XA = B, where A is a Zmat and B is a Zmat.
static Zmat bai(Zmat B, Zpsdmat A)
          Solves XA = B, where A is a Zpsdmat and B is a Zmat.
static Zmat bai(Zmat B, Zutmat U)
          Solves XU = B, where U is a Zutmat and B is a Zmat.
 
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

aib

public static Zmat aib(Zltmat L,
                       Zmat B)
                throws JampackException
Solves LX = B, where L is a Zltmat and B is a Zmat.

Parameters:
L - The matrix of the sysem
B - The right-hand side
Returns:
L-1B
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Thrown for singular L.

ahib

public static Zmat ahib(Zltmat L,
                        Zmat B)
                 throws JampackException
Solves LHX = B, where L is a Zltmat and B is a Zmat.

Parameters:
L - The matrix of the sysem
B - The right-hand side
Returns:
L-HB
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Thrown for singular L.

bai

public static Zmat bai(Zmat B,
                       Zltmat L)
                throws JampackException
Solves XL = B, where L is a Zltmat and B is a Zmat.

Parameters:
B - The right-hand side
L - The matrix of the system
Returns:
BL-1
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

bahi

public static Zmat bahi(Zmat B,
                        Zltmat L)
                 throws JampackException
Solves XLH = B, where L is a Zltmat and B is a Zmat.

Parameters:
B - The right-hand side
L - The matrix of the system
Returns:
BL-H
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

aib

public static Zmat aib(Zutmat U,
                       Zmat B)
                throws JampackException
Solves UX = B, where U is a Zutmat and B is a Zmat.

Parameters:
U - The matrix of the system
B - The right-hand side
Returns:
U-1B
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Thrown for singular U.

ahib

public static Zmat ahib(Zutmat U,
                        Zmat B)
                 throws JampackException
Solves UHX = B, where U is a Zutmat and B is a Zmat.

Parameters:
U - The matrix of the system
B - The right-hand side
Returns:
U-HB
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Thrown for singular U.

bai

public static Zmat bai(Zmat B,
                       Zutmat U)
                throws JampackException
Solves XU = B, where U is a Zutmat and B is a Zmat.

Parameters:
B - The right-hand side
U - The matrix of the system
Returns:
BU-1
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

bahi

public static Zmat bahi(Zmat B,
                        Zutmat U)
                 throws JampackException
Solves XUH = B, where U is a Zutmat and B is a Zmat.

Parameters:
B - The right-hand side
U - The matrix of the system
Returns:
BU-H
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

aib

public static Zmat aib(Zmat A,
                       Zmat B)
                throws JampackException
Solves AX = B, where A is a Zmat and B is a Zmat.

Parameters:
A - The matrix of the sysem
B - The right-hand side
Returns:
A-1B
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

ahib

public static Zmat ahib(Zmat A,
                        Zmat B)
                 throws JampackException
Solve AHX = B, where A is a Zmat and B is a Zmat.

Parameters:
A - The matrix of the sysem
B - The right-hand side
Returns:
A-HB
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

bai

public static Zmat bai(Zmat B,
                       Zmat A)
                throws JampackException
Solve XA = B, where A is a Zmat and B is a Zmat.

Parameters:
B - The right-hand side
A - The matrix of the sysem
Returns:
BA-1
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

bahi

public static Zmat bahi(Zmat B,
                        Zmat A)
                 throws JampackException
Solve XA^H = B, where A is a Zmat and B is a Zmat.

Parameters:
B - The right-hand side
A - The matrix of the sysem
Returns:
BA-H
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

aib

public static Zmat aib(Zpsdmat A,
                       Zmat B)
                throws JampackException
Solves AX = B, where A is a Zpsdmat and B is a Zmat.

Parameters:
A - The matrix of the sysem
B - The right-hand side
Returns:
A-1B
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

bai

public static Zmat bai(Zmat B,
                       Zpsdmat A)
                throws JampackException
Solves XA = B, where A is a Zpsdmat and B is a Zmat.

Parameters:
B - The right-hand side
A - The matrix of the sysem
Returns:
BA-1
Throws:
JampackException - Thrown for nonsquare matrix or nonconformity.
Passed from below.

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