C++ GMatrix::GetNumColumns方法代码示例

bool LinearSystem<Real>::SolveSymmetricCG (const GMatrix<Real>& A,
    const Real* B, Real* X)
{
    // Based on the algorithm in "Matrix Computations" by Golum and Van Loan.
    assertion(A.GetNumRows() == A.GetNumColumns(), "Matrix must be square\n");
    int size = A.GetNumRows();
    Real* R = new1<Real>(size);
    Real* P = new1<Real>(size);
    Real* W = new1<Real>(size);

    // The first iteration.
    size_t numBytes = size*sizeof(Real);
    memset(X, 0, numBytes);
    memcpy(R, B, numBytes);
    Real rho0 = Dot(size, R, R);
    memcpy(P, R, numBytes);
    Multiply(A, P, W);
    Real alpha = rho0/Dot(size, P, W);
    UpdateX(size, X, alpha, P);
    UpdateR(size, R, alpha, W);
    Real rho1 = Dot(size, R, R);

    // The remaining iterations.
    const int imax = 1024;
    int i;
    for (i = 1; i < imax; ++i)
    {
        Real root0 = Math<Real>::Sqrt(rho1);
        Real norm = Dot(size, B, B);
        Real root1 = Math<Real>::Sqrt(norm);
        if (root0 <= ZeroTolerance*root1)
        {
            break;
        }

        Real beta = rho1/rho0;
        UpdateP(size, P, beta, R);
        Multiply(A, P, W);
        alpha = rho1/Dot(size, P, W);
        UpdateX(size, X, alpha, P);
        UpdateR(size, R, alpha, W);
        rho0 = rho1;
        rho1 = Dot(size, R, R);
    }

    delete1(W);
    delete1(P);
    delete1(R);

    return i < imax;
}

void SingularValueDecomposition<Real>::HouseholderPostmultiply (
    const GVector<Real>& V, GMatrix<Real>& A)
{
	GVector<Real> W = (((Real)-2)/V.SquaredLength())*(A*V);
	int numRows = A.GetNumRows();
	int numCols = A.GetNumColumns();
	for (int row = 0; row < numRows; ++row)
	{
		for (int col = 0; col < numCols; ++col)
		{
			A[row][col] += W[row]*V[col];
		}
	}
}

void LinearSystem<Real>::BackwardEliminate (int reduceRow,
    BandedMatrix<Real>& A, GMatrix<Real>& B)
{
    int rowMax = reduceRow - 1;
    int rowMin = reduceRow - A.GetNumUBands();
    if (rowMin < 0)
    {
        rowMin = 0;
    }

    for (int row = rowMax; row >= rowMin; --row)
    {
        Real mult = A(row,reduceRow);
        A(row,reduceRow) = (Real)0;
        for (int col = 0; col < B.GetNumColumns(); ++col)
        {
            B(row,col) -= mult*B(reduceRow,col);
        }
    }
}

SingularValueDecomposition<Real>::SingularValueDecomposition (
    const GMatrix<Real>& M, GMatrix<Real>& L, GMatrix<Real>& D,
    GMatrix<Real>& RTranspose)
{
	// TODO.  Implement other QR factorizations and SVD code from "Matrix
	// Computations", and then give the user the ability to specify which
	// methods are used here.

	int numRows = M.GetNumRows();
	int numCols = M.GetNumColumns();
	L.SetSize(numRows, numRows);
	D.SetSize(numRows, numCols);
	RTranspose.SetSize(numCols, numCols);

	GMatrix<Real> kMTM = M.TransposeTimes(M);
	EigenDecomposition<Real> es(kMTM);
	es.Solve(false);
	GMatrix<Real> V = es.GetEigenvectors();
	GMatrix<Real> MV = M*V;
	HouseholderQR(MV, L, D);
	RTranspose = V.Transpose();
}

void SingularValueDecomposition<Real>::HouseholderQR (
    const GMatrix<Real>& A, GMatrix<Real>& Q, GMatrix<Real>& R)
{
	// The matrix R gets a copy of A, and is then overwritten during the
	// algorithm with the correct entries to be upper triangular.
	R = A;
	int numRows = R.GetNumRows();
	int numCols = R.GetNumColumns();
	assertion(numRows >= numCols, "Too many columns (use transpose)\n");
	int row, col;
	GVector<Real> V(numRows);
	std::vector<GVector<Real> > VSave;
	for (col = 0; col < numCols; ++col)
	{
		// Create the Householder vector for the partial column of A.
		for (row = 0; row < col; ++row)
		{
			V[row] = (Real)0;
		}
		Real length = (Real)0;
		for (row = col; row < numRows; ++row)
		{
			V[row] = R[row][col];
			length += V[row]*V[row];
		}
		length = Math<Real>::Sqrt(length);
		Real beta = V[col] + Math<Real>::Sign(V[col])*length;
		if (beta != (Real)0)
		{
			Real invBeta = ((Real)1)/beta;
			for (int i = col + 1; i < numRows; ++i)
			{
				V[i] *= invBeta;
			}
		}
		V[col] = (Real)1;

		// Premultiply A by the V-reflection matrix.
		HouseholderPremultiply(V, R);

		// Save the Householder vectors.
		VSave.push_back(V);
	}

	// First, make Q the identity.  Second, extract the Householder vectors
	// and premultiply by the V-reflections to build Q.
	memset(Q.GetElements(), 0, Q.GetNumElements()*sizeof(Real));
	for (row = 0; row < numRows; ++row)
	{
		Q[row][row] = (Real)1;
	}

	for (col = numCols - 1; col >= 0; --col)
	{
		// Get the Householder vector.
		V = VSave[col];

		// Premultiply Q by the V-reflection matrix.
		HouseholderPremultiply(V, Q);
	}
}