# slasd4.f(3) [debian man page]

slasd4.f(3) LAPACK slasd4.f(3)NAME

slasd4.f-SYNOPSIS

Functions/Subroutines subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO) SLASD4Function/Subroutine Documentation subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realSIGMA, real, dimension( * )WORK, integerINFO) SLASD4 Purpose: This subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= 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 ) * 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, 0 <= 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 .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors. RHO RHO is REAL The scalar in the symmetric updating formula. SIGMA SIGMA is REAL The computed sigma_I, the I-th updated eigenvalue. WORK WORK is REAL array, dimension (N) If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th component. If N = 1, then WORK( 1 ) = 1. 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: November 2011 Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 154 of file slasd4.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.1Sun May 26 2013 slasd4.f(3)

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slaed4.f(3) LAPACK slaed4.f(3)NAME

slaed4.f-SYNOPSIS

Functions/Subroutines subroutine slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO) SLAED4Function/Subroutine Documentation subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO) SLAED4 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: November 2011 Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 146 of file slaed4.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.1Sun May 26 2013 slaed4.f(3)