// file: $isip/class/numeric/LinearAlgebra/linalg_05.cc// version: $Id: linalg_05.cc,v 1.3 2001/08/27 20:22:06 hamaker Exp $//// isip include files//#include "LinearAlgebra.h"// method: linearSolveTemplate//// arguments://  TVector& x: (output) unknown quantities//  const TMatrix& A: (input) multiplier matrix//  const TVector& b: (input) known quantities//// return: boolean value indicating status//// this method computes the solution to linear equations of the form//     A * x = b// where//     A[i,1] * x[1] + A[i,2] * x[2] + ... + A[i,n] * x[n] = b[i]// for all 0 <= i < n//// this routine finds the x vector which satisfies this set of// equations.  overdetermined, underdetermined, and singular sets use// singular value decomposition. square matrices use LU// decomposition. If the LU decomposition fails, singular value// decomposition is attempted but it is very likely that the results// will be numerically inaccurate.//template <class TMatrix, class TVector>boolean LinearAlgebra::linearSolveTemplate(TVector& x_a,					   const TMatrix& A_a,					   const TVector& b_a) {  // if the matrix is square, we can use LU decomposition  //  if (A_a.isSquare() && ! A_a.isSingular()) {    // create temporary storage for the L and U matrices    //    TMatrix L;    TMatrix U;    VectorLong index;    long sign;        // call the LU decomposition routine and then the lu solver    //    if (A_a.decompositionLU(L, U, index, sign) &&	A_a.luSolve(x_a, L, U, index, b_a)) {      return true;    }    else {      // display warning and use SVD solution      //      Error::handle(name(), L"linearSolveTemplate", ERR_LSOLVE_SINGULAR,		    __FILE__, __LINE__, Error::WARNING);    }  }  // all other cases use SVD for solution  //  // create temporary storage for the V, W, U matrices  //  TMatrix U;  TMatrix W;  TMatrix V;  // decompose the matrix  //  if (!A_a.decompositionSVD(U, W, V)) {    Error::handle(name(), L"linearSolveTemplate", ERR,		  __FILE__, __LINE__);  }  // solve the set and return   //  return (A_a.svdSolve(x_a, U, W, V, b_a, true));}// explicit instantiations//template booleanLinearAlgebra::linearSolveTemplate<MatrixFloat,VectorFloat>(VectorFloat&,						    const MatrixFloat&,						    const VectorFloat&) const;template booleanLinearAlgebra::linearSolveTemplate<MatrixDouble,VectorDouble>(VectorDouble&,						  const MatrixDouble&,						  const VectorDouble&) const;