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---
:name: slaev2
:md5sum: b2933ce4bc39bd2862647978c0b49408
:category: :subroutine
:arguments:
- a:
:type: real
:intent: input
- b:
:type: real
:intent: input
- c:
:type: real
:intent: input
- rt1:
:type: real
:intent: output
- rt2:
:type: real
:intent: output
- cs1:
:type: real
:intent: output
- sn1:
:type: real
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )\n\n\
* Purpose\n\
* =======\n\
*\n\
* SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix\n\
* [ A B ]\n\
* [ B C ].\n\
* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the\n\
* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right\n\
* eigenvector for RT1, giving the decomposition\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) REAL\n\
* The (1,1) element of the 2-by-2 matrix.\n\
*\n\
* B (input) REAL\n\
* The (1,2) element and the conjugate of the (2,1) element of\n\
* the 2-by-2 matrix.\n\
*\n\
* C (input) REAL\n\
* The (2,2) element of the 2-by-2 matrix.\n\
*\n\
* RT1 (output) REAL\n\
* The eigenvalue of larger absolute value.\n\
*\n\
* RT2 (output) REAL\n\
* The eigenvalue of smaller absolute value.\n\
*\n\
* CS1 (output) REAL\n\
* SN1 (output) REAL\n\
* The vector (CS1, SN1) is a unit right eigenvector for RT1.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* RT1 is accurate to a few ulps barring over/underflow.\n\
*\n\
* RT2 may be inaccurate if there is massive cancellation in the\n\
* determinant A*C-B*B; higher precision or correctly rounded or\n\
* correctly truncated arithmetic would be needed to compute RT2\n\
* accurately in all cases.\n\
*\n\
* CS1 and SN1 are accurate to a few ulps barring over/underflow.\n\
*\n\
* Overflow is possible only if RT1 is within a factor of 5 of overflow.\n\
* Underflow is harmless if the input data is 0 or exceeds\n\
* underflow_threshold / macheps.\n\
*\n\
* =====================================================================\n\
*\n"
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