laed4 - laed4: D&C step: secular equation nonlinear solver

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subroutinedlaed4(integern,integeri,doubleprecision,dimension(*)d,doubleprecision,dimension(*)z,doubleprecision,dimension(*)delta,doubleprecisionrho,doubleprecisiondlam,integerinfo)DLAED4 used by DSTEDC. 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. ParametersN 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 DOUBLE PRECISION array, dimension (N) The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J. Z Z is DOUBLE PRECISION array, dimension (N) The components of the updating vector. DELTA DELTA is DOUBLE PRECISION array, dimension (N) If N > 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by DLAED3 and DLAED9. RHO RHO is DOUBLE PRECISION The scalar in the symmetric updating formula. DLAM DLAM is DOUBLE PRECISION The computed lambda_I, the I-th updated eigenvalue. INFO INFO is INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed. InternalParameters: 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. Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA subroutineslaed4(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. ParametersN 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 > 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. InternalParameters: 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. Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

laed4 - laed4: D&C step: secular equation nonlinear solver

Functions subroutine dlaed4 (n, i, d, z, delta, rho, dlam, info) DLAED4 used by DSTEDC. Finds a single root of the secular equation. subroutine slaed4 (n, i, d, z, delta, rho, dlam, info) SLAED4 used by SSTEDC. Finds a single root of the secular equation.