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---
:name: slaed5
:md5sum: 1e0d84a3982b12261a34f11249234b49
:category: :subroutine
:arguments:
- i:
:type: integer
:intent: input
- d:
:type: real
:intent: input
:dims:
- "2"
- z:
:type: real
:intent: input
:dims:
- "2"
- delta:
:type: real
:intent: output
:dims:
- "2"
- rho:
:type: real
:intent: input
- dlam:
:type: real
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SLAED5( I, D, Z, DELTA, RHO, DLAM )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This subroutine computes the I-th eigenvalue of a symmetric rank-one\n\
* modification of a 2-by-2 diagonal matrix\n\
*\n\
* diag( D ) + RHO * Z * transpose(Z) .\n\
*\n\
* The diagonal elements in the array D are assumed to satisfy\n\
*\n\
* D(i) < D(j) for i < j .\n\
*\n\
* We also assume RHO > 0 and that the Euclidean norm of the vector\n\
* Z is one.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* I (input) INTEGER\n\
* The index of the eigenvalue to be computed. I = 1 or I = 2.\n\
*\n\
* D (input) REAL array, dimension (2)\n\
* The original eigenvalues. We assume D(1) < D(2).\n\
*\n\
* Z (input) REAL array, dimension (2)\n\
* The components of the updating vector.\n\
*\n\
* DELTA (output) REAL array, dimension (2)\n\
* The vector DELTA contains the information necessary\n\
* to construct the eigenvectors.\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\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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