slaed6.f(3) [centos man page]
slaed6.f(3) LAPACK slaed6.f(3) NAME
slaed6.f - SYNOPSIS
Functions/Subroutines subroutine slaed6 (KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO) SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. Function/Subroutine Documentation subroutine slaed6 (integerKNITER, logicalORGATI, realRHO, real, dimension( 3 )D, real, dimension( 3 )Z, realFINIT, realTAU, integerINFO) SLAED6 used by sstedc. Computes one Newton step in solution of the secular equation. Purpose: SLAED6 computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true. the root is between d(2) and d(3); otherwise it is between d(1) and d(2) This routine will be called by SLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations. Parameters: KNITER KNITER is INTEGER Refer to SLAED4 for its significance. ORGATI ORGATI is LOGICAL If ORGATI is true, the needed root is between d(2) and d(3); otherwise it is between d(1) and d(2). See SLAED4 for further details. RHO RHO is REAL Refer to the equation f(x) above. D D is REAL array, dimension (3) D satisfies d(1) < d(2) < d(3). Z Z is REAL array, dimension (3) Each of the elements in z must be positive. FINIT FINIT is REAL The value of f at 0. It is more accurate than the one evaluated inside this routine (if someone wants to do so). TAU TAU is REAL The root of the equation f(x). INFO INFO is INTEGER = 0: successful exit > 0: if INFO = 1, failure to converge Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Further Details: 10/02/03: This version has a few statements commented out for thread safety (machine parameters are computed on each entry). SJH. 05/10/06: Modified from a new version of Ren-Cang Li, use Gragg-Thornton-Warner cubic convergent scheme for better stability. Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 141 of file slaed6.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slaed6.f(3)
Check Out this Related Man Page
slaed4.f(3) LAPACK slaed4.f(3) NAME
slaed4.f - SYNOPSIS
Functions/Subroutines subroutine slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) SLAED4 used by sstedc. Finds a single root of the secular equation. Function/Subroutine Documentation subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO) SLAED4 used by sstedc. Finds a single root of the secular equation. Purpose: This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus diag( D ) + RHO * Z * Z_transpose. where we assume the Euclidean norm of Z is 1. The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions. Parameters: N N is INTEGER The length of all arrays. I I is INTEGER The index of the eigenvalue to be computed. 1 <= I <= N. D D is REAL array, dimension (N) The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J. Z Z is REAL array, dimension (N) The components of the updating vector. DELTA DELTA is REAL array, dimension (N) If N .GT. 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by SLAED3 and SLAED9. RHO RHO is REAL The scalar in the symmetric updating formula. DLAM DLAM is REAL The computed lambda_I, the I-th updated eigenvalue. INFO INFO is INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed. Internal Parameters: Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin. ORGATI = .true. origin at i ORGATI = .false. origin at i+1 Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles! MAXIT is the maximum number of iterations allowed for each eigenvalue. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: September 2012 Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 146 of file slaed4.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slaed4.f(3)