Ejemplo n.º 1
0
// DPOSV uses Cholesky factorization A=U^T*U, A=L*L^T 
// to compute the solution to a real system of linear 
// equations A*X=B, where A is a square, (N,N) symmetric 
// positive definite matrix and X and B are (N,NRHS).
//
// If the system is over or under-determined, 
// (i.e. A is not square), then pass the problem
// to the Least-squares solver (DGELSS) below.
//---------------------------------------------------------
void umSOLVE_CH(const DMat& mat, const DMat& B, DMat& X)
//---------------------------------------------------------
{
  if (!mat.ok()) {umWARNING("umSOLVE_CH()", "system is empty"); return;}
  if (!mat.is_square()) {
    umSOLVE_LS(mat, B, X);    // return a least-squares solution.
    return;
  }
  
  DMat A(mat);    // Work with a copy of input array.
  X = B;          // initialize solution with rhs

  int rows=A.num_rows(), LDA=A.num_rows(), cols=A.num_cols();
  int LDB=X.num_rows(), NRHS=X.num_cols(), info=0;
  assert(LDB >= rows);  // enough space for solutions?

  // Solve the system.
  POSV('U', rows, NRHS, A.data(), LDA, X.data(), LDB, info);

  if (info < 0) { 
    X = 0.0;
    umERROR("umSOLVE_CH(A,B, X)", 
            "Error in input argument (%d)\nNo solution computed.", -info);
  } else if (info > 0) {
    X = 0.0;
    umERROR("umSOLVE_CH(A,B, X)", 
            "\nINFO = %d.  The leading minor of order %d of A"
            "\nis not positive definite, so the factorization" 
            "\ncould not be completed. No solution computed.", 
              info, info);
  }
}
Ejemplo n.º 2
0
// DGESV uses the LU factorization to compute solution 
// to a real system of linear equations, A * X = B, 
// where A is square (N,N) and X, B are (N,NRHS).
//
// If the system is over or under-determined, 
// (i.e. A is not square), then pass the problem
// to the Least-squares solver (DGELSS) below.
//---------------------------------------------------------
void umSOLVE(const DMat& mat, const DMat& B, DMat& X)
//---------------------------------------------------------
{
  if (!mat.ok()) {umWARNING("umSOLVE()", "system is empty"); return;}
  if (!mat.is_square()) {
    umSOLVE_LS(mat, B, X);    // return a least-squares solution.
    return;
  }

  DMat A(mat);    // work with copy of input
  X = B;          // initialize result with RHS

  int rows=A.num_rows(), LDA=A.num_rows(), cols=A.num_cols();
  int LDB=B.num_rows(), NRHS=B.num_cols(), info=0;
  if (rows<1) {umWARNING("umSOLVE()", "system is empty"); return;}
  IVec ipiv(rows);

  // Solve the system.
  GESV(rows, NRHS, A.data(), LDA, ipiv.data(), X.data(), LDB, info);

  if (info < 0) { 
    X = 0.0;
    umERROR("umSOLVE(A,B, X)", 
            "Error in input argument (%d)\nNo solution computed.", -info);
  } else if (info > 0) {
    X = 0.0;
    umERROR("umSOLVE(A,B, X)", 
            "\nINFO = %d.  U(%d,%d) was exactly zero."
            "\nThe factorization has been completed, but the factor U is "
            "\nexactly singular, so the solution could not be computed.", 
              info, info, info);
  }
}
Ejemplo n.º 3
0
// DGELSS computes minimum norm solution to a real linear 
// least squares problem:   Minimize 2-norm(| b - A*x |).   
// using the singular value decomposition (SVD) of A. 
// A is an M-by-N matrix which may be rank-deficient.   
//---------------------------------------------------------
void umSOLVE_LS(const DMat& mat, const DMat& B, DMat& X)
//---------------------------------------------------------
{
  if (!mat.ok()) {umWARNING("umSOLVE_LS()", "system is empty"); return;}

  DMat A(mat);    // work with copy of input.

  int rows=A.num_rows(), cols=A.num_cols(), mmn=A.min_mn();
  int LDB=A.max_mn(), NRHS=B.num_cols();
  if (rows!=B.num_rows()) {umERROR("umSOLVE_LS(A,B)", "Inconsistant matrix sizes.");}

  DVec s(mmn);    // allocate array for singular values

  // X must be big enough to store various results.
  // Resize X so that its leading dimension = max(M,N), 
  // then load the set of right hand sides.

  X.resize(LDB,NRHS, true, 0.0);

  for (int j=1; j<=NRHS; ++j)     // loop across colums
    for (int i=1; i<=rows; ++i)   // loop down rows
      X(i,j) = B(i,j);

  // RCOND is used to determine the effective rank of A.   
  // Singular values S(i) <= RCOND*S(1) are treated as zero.   
  // If RCOND < 0, machine precision is used instead.   

//double rcond =  1.0 / 1.0e16;
  double rcond = -1.0;

  // NBN: ACML does not use the work vector.
  int mnLo=A.min_mn(), mnHi=A.max_mn(), rank=1, info=1;
  int lwork = 10*mnLo + std::max(2*mnLo, std::max(mnHi, NRHS));
  DVec work(lwork); 

  // Solve the system
  GELSS (rows, cols, NRHS, A.data(), rows, X.data(), LDB, s.data(), rcond, rank, work.data(), lwork, info);

  //---------------------------------------------
  // Report:
  //---------------------------------------------

  if (info == 0) {
    umLOG(1, "umSOLVE_LS reports successful LS-solution."
             "\nRCOND = %0.6e, "
             "\nOptimal length of work array was %d\n", rcond, lwork);
  } 
  else 
  {
    if (info < 0) { 
      X = 0.0;
      umERROR("umSOLVE_LS(DMat&, DMat&)", 
              "Error in input argument (%d)\nNo solution or error bounds computed.", -info);

    } else if (info > 0) {
      X = 0.0;
      umERROR("umSOLVE_LS(DMat&, DMat&)", 
          "\nThe algorithm for computing the SVD failed to converge.\n"
          "\n%d off-diagonal elements of an intermediate "
          "\nbidiagonal form did not converge to zero.\n "
          "\nRCOND = %0.6e, "
          "\nOptimal length of work array was %d.\n", info, rcond, lwork);
    }
  }
}