MatrixMathLA.h

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// # MatrixMath.h: The Casacore linear algebra functions
// # Copyright (C) 1994,1995,1996,1999,2000,2002
// # Associated Universities, Inc. Washington DC, USA.
// #
// # This library is free software; you can redistribute it and/or modify it
// # under the terms of the GNU Library General Public License as published by
// # the Free Software Foundation; either version 2 of the License, 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 Library General Public
// # License for more details.
// #
// # You should have received a copy of the GNU Library General Public License
// # along with this library; if not, write to the Free Software Foundation,
// # Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
// #
// # Correspondence concerning AIPS++ should be addressed as follows:
// #        Internet email: casa-feedback@nrao.edu.
// #        Postal address: AIPS++ Project Office
// #                        National Radio Astronomy Observatory
// #                        520 Edgemont Road
// #                        Charlottesville, VA 22903-2475 USA
 
#ifndef SCIMATH_MATRIXMATHLA_H
#define SCIMATH_MATRIXMATHLA_H
 
#include <casacore/casa/aips.h>
#include <casacore/casa/Arrays/Vector.h>
#include <casacore/casa/Arrays/Matrix.h>
#include <casacore/casa/BasicSL/Complex.h>
 
namespace casacore {  // # NAMESPACE CASACORE - BEGIN
 
//<summary>
//    Linear algebra functions on Vectors and Matrices.
// </summary>
//
// <reviewed reviewer="UNKNOWN" date="before2004/08/25" tests="tLinAlgebra">
//
// <linkfrom anchor="Linear Algebra" classes="Vector Matrix">
//    <here>Linear Algebra</here> -- Linear algebra functions
//     on Vectors and Matrices.
// </linkfrom>
//
//<group name="Linear Algebra">
 
// Routines which calculate the inverse of a matrix.  The inverse is very
// often the worst way to do a calculation.  Nevertheless it is often
// convenient. The present implementation uses LU decomposition implemented
// by LAPACK. The determinate can be calculated "for free" as it is the
// product of the diagonal terms after decomposition.  If the input matrix is
// singular, a matrix with no rows or columns is returned.  <src>in</src>
// must be a square matrix.
// <note role="warning">This function will only work for complex types if
// Complex and DComplex map onto their FORTRAN counterparts.</note>
// # We could special case small matrices for efficiency.
//<group>
template <class T>
void invert(Matrix<T> &out, T &determinate, const Matrix<T> &in);
template <class T>
Matrix<T> invert(const Matrix<T> &in);
template <class T>
T determinate(const Matrix<T> &in);
//</group>
 
// This function inverts a symmetric positive definite matrix.  It is
// written in C++, so it should work with any data type for which
// operators +, -, *, /, =, and sqrt are defined.  The function uses
// the Cholesky decomposition method to invert the matrix.  Cholesky
// decomposition is about a factor of 2 better than LU decomposition
// where symmetry is ignored.
template <class T>
void invertSymPosDef(Matrix<T> &out, T &determinate, const Matrix<T> &in);
template <class T>
Matrix<T> invertSymPosDef(const Matrix<T> &in);
 
//</group>
 
// # These are actually used by invertSymPosDef. They will not
// # normally be called by the end user.
 
// # This function performs Cholesky decomposition.
// # A is a positive-definite symmetric matrix. Only the upper triangle of
// # A is needed on input. On output, the lower triangle of A contains the
// # Cholesky factor L.  The diagonal elements of L are returned in vector
// # diag.
template <class T>
void CholeskyDecomp(Matrix<T> &A, Vector<T> &diag);
 
// # Solve linear equation A*x = b, where A positive-definite symmetric.
// # On input, A contains Cholesky factor L in its low triangle except the
// # diagonal elements which are in vector diag.  On return x contains the
// # solution.  b and x can be the same vector to save memory space.
template <class T>
void CholeskySolve(Matrix<T> &A, Vector<T> &diag, Vector<T> &b, Vector<T> &x);
 
// # These are the LAPACK routines actually used by invert. They will not
// # normally be called by the end user.
 
#if !defined(NEED_FORTRAN_UNDERSCORES)
#define NEED_FORTRAN_UNDERSCORES 1
#endif
 
#if NEED_FORTRAN_UNDERSCORES
#define sgetrf sgetrf_
#define dgetrf dgetrf_
#define cgetrf cgetrf_
#define zgetrf zgetrf_
#define sgetri sgetri_
#define dgetri dgetri_
#define cgetri cgetri_
#define zgetri zgetri_
#define sposv sposv_
#define dposv dposv_
#define cposv cposv_
#define zposv zposv_
#define spotri spotri_
#define dpotri dpotri_
#define cpotri cpotri_
#define zpotri zpotri_
#endif
 
extern "C" {
void sgetrf(const int *m, const int *n, float *a, const int *lda, int *ipiv, int *info);
void dgetrf(const int *m, const int *n, double *a, const int *lda, int *ipiv, int *info);
void cgetrf(const int *m, const int *n, Complex *a, const int *lda, int *ipiv, int *info);
void zgetrf(const int *m, const int *n, DComplex *a, const int *lda, int *ipiv, int *info);
void sgetri(const int *m, float *a, const int *lda, const int *ipiv, float *work, const int *lwork,
            int *info);
void dgetri(const int *m, double *a, const int *lda, const int *ipiv, double *work,
            const int *lwork, int *info);
void cgetri(const int *m, Complex *a, const int *lda, const int *ipiv, Complex *work,
            const int *lwork, int *info);
void zgetri(const int *m, DComplex *a, const int *lda, const int *ipiv, DComplex *work,
            const int *lwork, int *info);
 
void sposv(const char *uplo, const int *n, const int *nrhs, float *a, const int *lda, float *b,
           const int *ldb, int *info);
void dposv(const char *uplo, const int *n, const int *nrhs, double *a, const int *lda, double *b,
           const int *ldb, int *info);
void cposv(const char *uplo, const int *n, const int *nrhs, Complex *a, const int *lda, Complex *b,
           const int *ldb, int *info);
void zposv(const char *uplo, const int *n, const int *nrhs, DComplex *a, const int *lda,
           DComplex *b, const int *ldb, int *info);
 
void spotri(const char *uplo, const int *n, float *a, const int *lda, int *info);
void dpotri(const char *uplo, const int *n, double *a, const int *lda, int *info);
void cpotri(const char *uplo, const int *n, Complex *a, const int *lda, int *info);
void zpotri(const char *uplo, const int *n, DComplex *a, const int *lda, int *info);
}
 
// # Overloaded versions of the above to make templating work more easily
inline void getrf(const int *m, const int *n, float *a, const int *lda, int *ipiv, int *info) {
  sgetrf(m, n, a, lda, ipiv, info);
}
inline void getrf(const int *m, const int *n, double *a, const int *lda, int *ipiv, int *info) {
  dgetrf(m, n, a, lda, ipiv, info);
}
inline void getrf(const int *m, const int *n, Complex *a, const int *lda, int *ipiv, int *info) {
  cgetrf(m, n, a, lda, ipiv, info);
}
inline void getrf(const int *m, const int *n, DComplex *a, const int *lda, int *ipiv, int *info) {
  zgetrf(m, n, a, lda, ipiv, info);
}
inline void getri(const int *m, float *a, const int *lda, const int *ipiv, float *work,
                  const int *lwork, int *info) {
  sgetri(m, a, lda, ipiv, work, lwork, info);
}
inline void getri(const int *m, double *a, const int *lda, const int *ipiv, double *work,
                  const int *lwork, int *info) {
  dgetri(m, a, lda, ipiv, work, lwork, info);
}
inline void getri(const int *m, Complex *a, const int *lda, const int *ipiv, Complex *work,
                  const int *lwork, int *info) {
  cgetri(m, a, lda, ipiv, work, lwork, info);
}
inline void getri(const int *m, DComplex *a, const int *lda, const int *ipiv, DComplex *work,
                  const int *lwork, int *info) {
  zgetri(m, a, lda, ipiv, work, lwork, info);
}
 
inline void posv(const char *uplo, const int *n, const int *nrhs, float *a, const int *lda,
                 float *b, const int *ldb, int *info) {
  sposv(uplo, n, nrhs, a, lda, b, ldb, info);
}
inline void posv(const char *uplo, const int *n, const int *nrhs, double *a, const int *lda,
                 double *b, const int *ldb, int *info) {
  dposv(uplo, n, nrhs, a, lda, b, ldb, info);
}
inline void posv(const char *uplo, const int *n, const int *nrhs, Complex *a, const int *lda,
                 Complex *b, const int *ldb, int *info) {
  cposv(uplo, n, nrhs, a, lda, b, ldb, info);
}
inline void posv(const char *uplo, const int *n, const int *nrhs, DComplex *a, const int *lda,
                 DComplex *b, const int *ldb, int *info) {
  zposv(uplo, n, nrhs, a, lda, b, ldb, info);
}
 
inline void potri(const char *uplo, const int *n, float *a, const int *lda, int *info) {
  spotri(uplo, n, a, lda, info);
}
inline void potri(const char *uplo, const int *n, double *a, const int *lda, int *info) {
  dpotri(uplo, n, a, lda, info);
}
inline void potri(const char *uplo, const int *n, Complex *a, const int *lda, int *info) {
  cpotri(uplo, n, a, lda, info);
}
inline void potri(const char *uplo, const int *n, DComplex *a, const int *lda, int *info) {
  zpotri(uplo, n, a, lda, info);
}
 
}  // namespace casacore
 
#ifndef CASACORE_NO_AUTO_TEMPLATES
#include <casacore/scimath/Mathematics/MatrixMathLA.tcc>
#endif  // # CASACORE_NO_AUTO_TEMPLATES
#endif