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---
:name: dlasd5
:md5sum: a3ba28af47ea722e3d88224bb102319d
:category: :subroutine
:arguments:
- i:
:type: integer
:intent: input
- d:
:type: doublereal
:intent: input
:dims:
- "2"
- z:
:type: doublereal
:intent: input
:dims:
- "2"
- delta:
:type: doublereal
:intent: output
:dims:
- "2"
- rho:
:type: doublereal
:intent: input
- dsigma:
:type: doublereal
:intent: output
- work:
:type: doublereal
:intent: workspace
:dims:
- "2"
:substitutions: {}
:fortran_help: " SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )\n\n\
* Purpose\n\
* =======\n\
*\n\
* This subroutine computes the square root of the I-th eigenvalue\n\
* of a positive symmetric rank-one modification of a 2-by-2 diagonal\n\
* matrix\n\
*\n\
* diag( D ) * diag( D ) + RHO * Z * transpose(Z) .\n\
*\n\
* The diagonal entries in the array D are assumed to satisfy\n\
*\n\
* 0 <= 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) DOUBLE PRECISION array, dimension ( 2 )\n\
* The original eigenvalues. We assume 0 <= D(1) < D(2).\n\
*\n\
* Z (input) DOUBLE PRECISION array, dimension ( 2 )\n\
* The components of the updating vector.\n\
*\n\
* DELTA (output) DOUBLE PRECISION array, dimension ( 2 )\n\
* Contains (D(j) - sigma_I) in its j-th component.\n\
* The vector DELTA contains the information necessary\n\
* to construct the eigenvectors.\n\
*\n\
* RHO (input) DOUBLE PRECISION\n\
* The scalar in the symmetric updating formula.\n\
*\n\
* DSIGMA (output) DOUBLE PRECISION\n\
* The computed sigma_I, the I-th updated eigenvalue.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension ( 2 )\n\
* WORK contains (D(j) + sigma_I) in its j-th component.\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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