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---
:name: claesy
:md5sum: cda88734cca22f111cf3994c8552cfb4
:category: :subroutine
:arguments:
- a:
:type: complex
:intent: input
- b:
:type: complex
:intent: input
- c:
:type: complex
:intent: input
- rt1:
:type: complex
:intent: output
- rt2:
:type: complex
:intent: output
- evscal:
:type: complex
:intent: output
- cs1:
:type: complex
:intent: output
- sn1:
:type: complex
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CLAESY( A, B, C, RT1, RT2, EVSCAL, CS1, SN1 )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CLAESY computes the eigendecomposition of a 2-by-2 symmetric matrix\n\
* ( ( A, B );( B, C ) )\n\
* provided the norm of the matrix of eigenvectors is larger than\n\
* some threshold value.\n\
*\n\
* RT1 is the eigenvalue of larger absolute value, and RT2 of\n\
* smaller absolute value. If the eigenvectors are computed, then\n\
* on return ( CS1, SN1 ) is the unit eigenvector for RT1, hence\n\
*\n\
* [ CS1 SN1 ] . [ A B ] . [ CS1 -SN1 ] = [ RT1 0 ]\n\
* [ -SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* A (input) COMPLEX\n\
* The ( 1, 1 ) element of input matrix.\n\
*\n\
* B (input) COMPLEX\n\
* The ( 1, 2 ) element of input matrix. The ( 2, 1 ) element\n\
* is also given by B, since the 2-by-2 matrix is symmetric.\n\
*\n\
* C (input) COMPLEX\n\
* The ( 2, 2 ) element of input matrix.\n\
*\n\
* RT1 (output) COMPLEX\n\
* The eigenvalue of larger modulus.\n\
*\n\
* RT2 (output) COMPLEX\n\
* The eigenvalue of smaller modulus.\n\
*\n\
* EVSCAL (output) COMPLEX\n\
* The complex value by which the eigenvector matrix was scaled\n\
* to make it orthonormal. If EVSCAL is zero, the eigenvectors\n\
* were not computed. This means one of two things: the 2-by-2\n\
* matrix could not be diagonalized, or the norm of the matrix\n\
* of eigenvectors before scaling was larger than the threshold\n\
* value THRESH (set below).\n\
*\n\
* CS1 (output) COMPLEX\n\
* SN1 (output) COMPLEX\n\
* If EVSCAL .NE. 0, ( CS1, SN1 ) is the unit right eigenvector\n\
* for RT1.\n\
*\n\n\
* =====================================================================\n\
*\n"
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