laslv.h

LAPACK++ (Linear Algebra PACKage in C++) is a software library for numerical linear algebra that sol

// -*-C++-*- 

// Copyright (C) 2004 
// Christian Stimming <[e-mail]>

// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2, or (at
// your option) any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU Lesser General Public License for more details.

// You should have received a copy of the GNU Lesser General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
// USA.

//      LAPACK++ (V. 1.1)
//      (C) 1992-1996 All Rights Reserved.

/** @file
 * @brief Functions for solving linear equations
 */

#ifndef _LASLV_H
#define _LASLV_H

#include "lafnames.h"
#include LA_GEN_MAT_DOUBLE_H
#include LA_VECTOR_DOUBLE_H
#ifdef LA_COMPLEX_SUPPORT
# include LA_GEN_MAT_COMPLEX_H
# include LA_VECTOR_COMPLEX_H
#endif
#include LA_VECTOR_LONG_INT_H


/** @name Real-valued matrices */
//@{
 /** Compute the solution to a real system of linear equations A*X=B
 *
 * Depending on the dimensions of A, either a LU or a QR decomposition
 * is used.
 *
 * @note This function was broken with non-square matrices and QR
 * decomposition for a long time. It is fixed and verified only
 * since lapackpp-2.4.11.
 */
DLLIMPORT
void LaLinearSolve( const LaGenMatDouble& A, LaGenMatDouble& X, 
		    const LaGenMatDouble& B );

/** Compute the solution to a real system of linear equations A*X=B
 * in-place.
 *
 * Depending on the dimensions of A, either a LU or a QR decomposition
 * is used.
 *
 * In-place means: The contents of A are overwritten during the
 * calculation. B is not overwritten but always copied during this
 * operation.
 *
 * @note This function was broken with non-square matrices and QR
 * decomposition for a long time. It is fixed and verified only
 * since lapackpp-2.4.11.
 */
DLLIMPORT
void LaLinearSolveIP( LaGenMatDouble& A, LaGenMatDouble& X, 
		      const LaGenMatDouble& B );


/** Compute the solution to a real system of linear equations A*X=B by
 * using the LU decomposition. This only works for a squares matrix A.
 */
DLLIMPORT
void LaLULinearSolve( const LaGenMatDouble& A, LaGenMatDouble& X, 
		      const LaGenMatDouble& B );

/** Compute the solution to a real system of linear equations A*X=B by
 * using the LU decomposition in-place. This only works for a squares
 * matrix A.
 *
 * In-place means: The contents of A are overwritten during the
 * calculation. B is not overwritten but always copied during this
 * operation.
 */
DLLIMPORT
void LaLULinearSolveIP( LaGenMatDouble& A, LaGenMatDouble& X, 
			const LaGenMatDouble& B );

/** Compute the solution to a real system of linear equations A*X=B by
 * using QR decomposition, which works for any rectangular matrix A.
 *
 * @note This function was broken for a long time. It is fixed and
 * verified only since lapackpp-2.4.11.
 */
DLLIMPORT
void LaQRLinearSolve( const LaGenMatDouble& A, LaGenMatDouble& X, 
		      const LaGenMatDouble& B );

/** Compute the solution to a real system of linear equations A*X=B by
 * using the QR decomposition in-place. This works for any rectangular 
 * matrix A.
 *
 * In-place means: The contents of A are overwritten during the
 * calculation. B is not overwritten but always copied during this
 * operation.
 *
 * @note This function was broken for a long time. It is fixed and
 * verified only since lapackpp-2.4.11.
 */
DLLIMPORT
void LaQRLinearSolveIP( LaGenMatDouble& A, LaGenMatDouble& X, 
			const LaGenMatDouble& B );

/** @brief Compute the LU factorization
 *
 * Compute the LU factorization (in-place) of a general M-by-N
 * matrix A.
 *
 * More info: See man @c dgetrf. 
 *
 * In-place means: The contents of GM are overwritten during the
 * calculation.
 *
 * @param GM Matrix to be factorized in-place.
 *
 * @param PIV Vector to return the pivoting indices. This vector
 * *has* to be at least as long as min(M,N).
 */
DLLIMPORT
void LUFactorizeIP(LaGenMatDouble &GM, LaVectorLongInt &PIV);
//@}



#ifdef LA_COMPLEX_SUPPORT
/** @name Complex-valued matrices */
//@{
 /** Compute the solution to a complex-valued system of linear
 * equations A*X=B
 *
 * Depending on the dimensions of A, either a LU or a QR decomposition
 * is used.
 *
 * @note This function was broken with non-square matrices and QR
 * decomposition for a long time. It is fixed and verified only
 * since lapackpp-2.4.11.
 */
DLLIMPORT
void LaLinearSolve( const LaGenMatComplex& A, LaGenMatComplex& X, 
		    const LaGenMatComplex& B );

/** Compute the solution to a complex-valued system of linear
 * equations A*X=B in-place.
 *
 * Depending on the dimensions of A, either a LU or a QR decomposition
 * is used.
 *
 * In-place means: The contents of A are overwritten during the
 * calculation. B is not overwritten but always copied during this
 * operation.
 *
 * @note This function was broken with non-square matrices and QR
 * decomposition for a long time. It is fixed and verified only
 * since lapackpp-2.4.11.
 */
DLLIMPORT
void LaLinearSolveIP( LaGenMatComplex& A, LaGenMatComplex& X, 
		      const LaGenMatComplex& B );


/** Compute the solution to a complex-valued system of linear
 * equations A*X=B by using the LU decomposition. This only works for
 * a squares matrix A.
 */
DLLIMPORT
void LaLULinearSolve( const LaGenMatComplex& A, LaGenMatComplex& X, 
		      const LaGenMatComplex& B );

/** Compute the solution to a complex-valued system of linear
 * equations A*X=B by using the LU decomposition in-place. This only
 * works for a squares matrix A.
 *
 * In-place means: The contents of A are overwritten during the
 * calculation. B is not overwritten but always copied during this
 * operation.
 */
DLLIMPORT
void LaLULinearSolveIP( LaGenMatComplex& A, LaGenMatComplex& X, 
			const LaGenMatComplex& B );

/** Compute the solution to a complex-valued system of linear
 * equations A*X=B by using QR decomposition, which works for any
 * rectangular matrix A.
 *
 * @note This function was broken for a long time. It is fixed and
 * verified only since lapackpp-2.4.11.
 */
DLLIMPORT
void LaQRLinearSolve( const LaGenMatComplex& A, LaGenMatComplex& X, 
		      const LaGenMatComplex& B );

/** Compute the solution to a complex-valued system of linear
 * equations A*X=B by using the QR decomposition in-place. This works
 * for any rectangular matrix A.
 *
 * In-place means: The contents of A are overwritten during the
 * calculation. B is not overwritten but always copied during this
 * operation.
 *
 * @note This function was broken for a long time. It is fixed and
 * verified only since lapackpp-2.4.11.
 */
DLLIMPORT
void LaQRLinearSolveIP( LaGenMatComplex& A, LaGenMatComplex& X, 
			const LaGenMatComplex& B );

/** @brief Compute the LU factorization
 *
 * Compute the LU factorization (in-place) of a general M-by-N
 * matrix A.
 *
 * In-place means: The contents of GM are overwritten during the
 * calculation.
 *
 * More info: See man @c zgetrf. 
 *
 * @param GM Matrix to be factorized in-place.
 * @param PIV Vector to return the pivoting indices. 
 * This vector *has* to be at least as long as min(M,N).
 */
DLLIMPORT
void LUFactorizeIP(LaGenMatComplex &GM, LaVectorLongInt &PIV);
//@}

/** @brief Compute the inverse of a matrix from LU factorization