larrk - larrk: step in stemr, compute one eigval

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subroutinedlarrk(integern,integeriw,doubleprecisiongl,doubleprecisiongu,doubleprecision,dimension(*)d,doubleprecision,dimension(*)e2,doubleprecisionpivmin,doubleprecisionreltol,doubleprecisionw,doubleprecisionwerr,integerinfo)DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. Purpose: DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. This is an auxiliary code to be called from DSTEMR. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that. See W. Kahan 'Accurate Eigenvalues of a Symmetric Tridiagonal Matrix', Report CS41, Computer Science Dept., Stanford University, July 21, 1966. ParametersN N is INTEGER The order of the tridiagonal matrix T. N >= 0. IW IW is INTEGER The index of the eigenvalues to be returned. GL GL is DOUBLE PRECISION GU GU is DOUBLE PRECISION An upper and a lower bound on the eigenvalue. D D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix T. E2 E2 is DOUBLE PRECISION array, dimension (N-1) The (n-1) squared off-diagonal elements of the tridiagonal matrix T. PIVMIN PIVMIN is DOUBLE PRECISION The minimum pivot allowed in the Sturm sequence for T. RELTOL RELTOL is DOUBLE PRECISION The minimum relative width of an interval. When an interval is narrower than RELTOL times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, i.e., converged. Note: this should always be at least radix*machine epsilon. W W is DOUBLE PRECISION WERR WERR is DOUBLE PRECISION The error bound on the corresponding eigenvalue approximation in W. INFO INFO is INTEGER = 0: Eigenvalue converged = -1: Eigenvalue did NOT converge InternalParameters: FUDGE DOUBLE PRECISION, default = 2 A 'fudge factor' to widen the Gershgorin intervals. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutineslarrk(integern,integeriw,realgl,realgu,real,dimension(*)d,real,dimension(*)e2,realpivmin,realreltol,realw,realwerr,integerinfo)SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. Purpose: SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. This is an auxiliary code to be called from SSTEMR. To avoid overflow, the matrix must be scaled so that its largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest accuracy, it should not be much smaller than that. See W. Kahan 'Accurate Eigenvalues of a Symmetric Tridiagonal Matrix', Report CS41, Computer Science Dept., Stanford University, July 21, 1966. ParametersN N is INTEGER The order of the tridiagonal matrix T. N >= 0. IW IW is INTEGER The index of the eigenvalues to be returned. GL GL is REAL GU GU is REAL An upper and a lower bound on the eigenvalue. D D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix T. E2 E2 is REAL array, dimension (N-1) The (n-1) squared off-diagonal elements of the tridiagonal matrix T. PIVMIN PIVMIN is REAL The minimum pivot allowed in the Sturm sequence for T. RELTOL RELTOL is REAL The minimum relative width of an interval. When an interval is narrower than RELTOL times the larger (in magnitude) endpoint, then it is considered to be sufficiently small, i.e., converged. Note: this should always be at least radix*machine epsilon. W W is REAL WERR WERR is REAL The error bound on the corresponding eigenvalue approximation in W. INFO INFO is INTEGER = 0: Eigenvalue converged = -1: Eigenvalue did NOT converge InternalParameters: FUDGE REAL , default = 2 A 'fudge factor' to widen the Gershgorin intervals. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

larrk - larrk: step in stemr, compute one eigval

Functions subroutine dlarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info) DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy. subroutine slarrk (n, iw, gl, gu, d, e2, pivmin, reltol, w, werr, info) SLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.