dlarrk.f(3) [debian man page]
dlarrk.f(3) LAPACK dlarrk.f(3) NAME
dlarrk.f - SYNOPSIS
Functions/Subroutines subroutine dlarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO) DLARRK Function/Subroutine Documentation subroutine dlarrk (integerN, integerIW, double precisionGL, double precisionGU, double precision, dimension( * )D, double precision, dimension( * )E2, double precisionPIVMIN, double precisionRELTOL, double precisionW, double precisionWERR, integerINFO) DLARRK 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. Parameters: N 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 Internal Parameters: 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. Date: November 2011 Definition at line 145 of file dlarrk.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.1 Sun May 26 2013 dlarrk.f(3)
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dlarrk.f(3) LAPACK dlarrk.f(3) NAME
dlarrk.f - SYNOPSIS
Functions/Subroutines 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. Function/Subroutine Documentation subroutine dlarrk (integerN, integerIW, double precisionGL, double precisionGU, double precision, dimension( * )D, double precision, dimension( * )E2, double precisionPIVMIN, double precisionRELTOL, double precisionW, double precisionWERR, 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. Parameters: N 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 Internal Parameters: 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. Date: September 2012 Definition at line 145 of file dlarrk.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 dlarrk.f(3)