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---
:name: slaed4
:md5sum: d6ca8d8edb3a5f41edc126568787c862
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- i:
:type: integer
:intent: input
- d:
:type: real
:intent: input
:dims:
- n
- z:
:type: real
:intent: input
:dims:
- n
- delta:
:type: real
:intent: output
:dims:
- n
- rho:
:type: real
:intent: input
- dlam:
:type: real
:intent: output
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This subroutine computes the I-th updated eigenvalue of a symmetric\n\
* rank-one modification to a diagonal matrix whose elements are\n\
* given in the array d, and that\n\
*\n\
* D(i) < D(j) for i < j\n\
*\n\
* and that RHO > 0. This is arranged by the calling routine, and is\n\
* no loss in generality. The rank-one modified system is thus\n\
*\n\
* diag( D ) + RHO * Z * Z_transpose.\n\
*\n\
* where we assume the Euclidean norm of Z is 1.\n\
*\n\
* The method consists of approximating the rational functions in the\n\
* secular equation by simpler interpolating rational functions.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The length of all arrays.\n\
*\n\
* I (input) INTEGER\n\
* The index of the eigenvalue to be computed. 1 <= I <= N.\n\
*\n\
* D (input) REAL array, dimension (N)\n\
* The original eigenvalues. It is assumed that they are in\n\
* order, D(I) < D(J) for I < J.\n\
*\n\
* Z (input) REAL array, dimension (N)\n\
* The components of the updating vector.\n\
*\n\
* DELTA (output) REAL array, dimension (N)\n\
* If N .GT. 2, DELTA contains (D(j) - lambda_I) in its j-th\n\
* component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5\n\
* for detail. The vector DELTA contains the information necessary\n\
* to construct the eigenvectors by SLAED3 and SLAED9.\n\
*\n\
* RHO (input) REAL\n\
* The scalar in the symmetric updating formula.\n\
*\n\
* DLAM (output) REAL\n\
* The computed lambda_I, the I-th updated eigenvalue.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* > 0: if INFO = 1, the updating process failed.\n\
*\n\
* Internal Parameters\n\
* ===================\n\
*\n\
* Logical variable ORGATI (origin-at-i?) is used for distinguishing\n\
* whether D(i) or D(i+1) is treated as the origin.\n\
*\n\
* ORGATI = .true. origin at i\n\
* ORGATI = .false. origin at i+1\n\
*\n\
* Logical variable SWTCH3 (switch-for-3-poles?) is for noting\n\
* if we are working with THREE poles!\n\
*\n\
* MAXIT is the maximum number of iterations allowed for each\n\
* eigenvalue.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* Ren-Cang Li, Computer Science Division, University of California\n\
* at Berkeley, USA\n\
*\n\
* =====================================================================\n\
*\n"
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