Forms the triangular factor T of a block reflector H = I - V*T*V**H.
Performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive computations which guarantee high relative accuracy in the eigenvalues.
Computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by ?bdsdc.
Applies a sequence of plane rotations to a general rectangular matrix.
Returns set entry of a random matrix.
Orthogonalizes a column vector with respect to the orthonormal basis matrix.
Applies an elementary permutation on the rows and columns of a symmetric matrix.
Scans a matrix for its last non-zero column.
Copies a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF).
Improves the computed solution to a system of linear equations for general matrices by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution.