slasd5(3) [centos man page]
slasd5.f(3) LAPACK slasd5.f(3) NAME
slasd5.f - SYNOPSIS
Functions/Subroutines subroutine slasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK) SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd5 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDSIGMA, real, dimension( 2 )WORK) SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. Purpose: This subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO * Z * transpose(Z) . The diagonal entries in the array D are assumed to satisfy 0 <= D(i) < D(j) for i < j . We also assume RHO > 0 and that the Euclidean norm of the vector Z is one. Parameters: I I is INTEGER The index of the eigenvalue to be computed. I = 1 or I = 2. D D is REAL array, dimension (2) The original eigenvalues. We assume 0 <= D(1) < D(2). Z Z is REAL array, dimension (2) The components of the updating vector. DELTA DELTA is REAL array, dimension (2) Contains (D(j) - sigma_I) in its j-th component. The vector DELTA contains the information necessary to construct the eigenvectors. RHO RHO is REAL The scalar in the symmetric updating formula. DSIGMA DSIGMA is REAL The computed sigma_I, the I-th updated eigenvalue. WORK WORK is REAL array, dimension (2) WORK contains (D(j) + sigma_I) in its j-th component. 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 117 of file slasd5.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slasd5.f(3)
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slasd4.f(3) LAPACK slasd4.f(3) NAME
slasd4.f - SYNOPSIS
Functions/Subroutines subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO) SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc. Function/Subroutine Documentation subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realSIGMA, real, dimension( * )WORK, integerINFO) SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc. 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: September 2012 Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA Definition at line 154 of file slasd4.f. Author Generated automatically by Doxygen for LAPACK from the source code. Version 3.4.2 Tue Sep 25 2012 slasd4.f(3)