# slarrk(3) [centos man page]

slarrk.f(3) LAPACK slarrk.f(3)NAME

slarrk.f-SYNOPSIS

Functions/Subroutines 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.Function/Subroutine Documentation subroutine slarrk (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. 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 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 Internal Parameters: 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. Date: September 2012 Definition at line 145 of file slarrk.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 slarrk.f(3)

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slarrk.f(3) LAPACK slarrk.f(3)NAME

slarrk.f-SYNOPSIS

Functions/Subroutines subroutine slarrk (N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO) SLARRKFunction/Subroutine Documentation subroutine slarrk (integerN, integerIW, realGL, realGU, real, dimension( * )D, real, dimension( * )E2, realPIVMIN, realRELTOL, realW, realWERR, integerINFO) SLARRK 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. 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 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 Internal Parameters: 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. Date: November 2011 Definition at line 145 of file slarrk.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.1Sun May 26 2013 slarrk.f(3)