Lines Matching full:matrix
32 * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
34 * \param MatrixType the type of the matrix of which we are computing the QR decomposition
36 * This class performs a rank-revealing QR decomposition of a matrix \b A into matrices \b P, \b Q and \b R
41 * by using Householder transformations. Here, \b P is a permutation matrix, \b Q a unitary matrix and \b R an
42 * upper triangular matrix.
66 typedef Matrix<Index, 1, ColsAtCompileTime, RowMajor, 1, MaxColsAtCompileTime> IntRowVectorType;
103 FullPivHouseholderQR(const MatrixType& matrix)
104 : m_qr(matrix.rows(), matrix.cols()),
105 m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
106 m_rows_transpositions(matrix.rows()),
107 m_cols_transpositions(matrix.cols()),
108 m_cols_permutation(matrix.cols()),
109 m_temp((std::min)(matrix.rows(), matrix.cols())),
113 compute(matrix);
116 /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
123 * \note The case where b is a matrix is not yet implemented. Also, this
141 /** \returns Expression object representing the matrix Q
145 /** \returns a reference to the matrix where the Householder QR decomposition is stored
153 FullPivHouseholderQR& compute(const MatrixType& matrix);
167 /** \returns the absolute value of the determinant of the matrix of which
169 * (that is, O(n) where n is the dimension of the square matrix)
182 /** \returns the natural log of the absolute value of the determinant of the matrix of which
184 * (that is, O(n) where n is the dimension of the square matrix)
196 /** \returns the rank of the matrix of which *this is the QR decomposition.
212 /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
224 /** \returns true if the matrix of which *this is the QR decomposition represents an injective
237 /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
250 /** \returns true if the matrix of which *this is the QR decomposition is invertible.
262 /** \returns the inverse of the matrix of which *this is the QR decomposition.
264 * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
265 * Use isInvertible() to first determine whether this matrix is invertible.
366 eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
374 eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
379 FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
381 Index rows = matrix.rows();
382 Index cols = matrix.cols();
385 m_qr = matrix;
392 m_rows_transpositions.resize(matrix.rows());
393 m_cols_transpositions.resize(matrix.cols());
481 Matrix<Scalar,1,Rhs::ColsAtCompileTime> temp(rhs().cols());
516 * \tparam MatrixType type of underlying dense matrix
525 typedef Matrix<typename MatrixType::Scalar, 1, MatrixType::RowsAtCompileTime, RowMajor, 1,
