Jampack

Class Solve

java.lang.Object

Jampack.Solve

public class Solve
extends 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

Constructors

Constructor and Description
Solve()

Method Summary

Methods

Modifier and Type	Method and Description
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 L^HX = 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 XL^H = 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 U^HX = 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 XU^H = 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 A^HX = 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.