 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ claev2()

 subroutine claev2 ( complex A, complex B, complex C, real RT1, real RT2, real CS1, complex SN1 )

CLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

Purpose:
``` CLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix
[  A         B  ]
[  CONJG(B)  C  ].
On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
eigenvector for RT1, giving the decomposition

[ CS1  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ]
[-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ].```
Parameters
 [in] A ``` A is COMPLEX The (1,1) element of the 2-by-2 matrix.``` [in] B ``` B is COMPLEX The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.``` [in] C ``` C is COMPLEX The (2,2) element of the 2-by-2 matrix.``` [out] RT1 ``` RT1 is REAL The eigenvalue of larger absolute value.``` [out] RT2 ``` RT2 is REAL The eigenvalue of smaller absolute value.``` [out] CS1 ` CS1 is REAL` [out] SN1 ``` SN1 is COMPLEX The vector (CS1, SN1) is a unit right eigenvector for RT1.```
Further Details:
```  RT1 is accurate to a few ulps barring over/underflow.

RT2 may be inaccurate if there is massive cancellation in the
determinant A*C-B*B; higher precision or correctly rounded or
correctly truncated arithmetic would be needed to compute RT2
accurately in all cases.

CS1 and SN1 are accurate to a few ulps barring over/underflow.

Overflow is possible only if RT1 is within a factor of 5 of overflow.
Underflow is harmless if the input data is 0 or exceeds
underflow_threshold / macheps.```

Definition at line 120 of file claev2.f.

121*
122* -- LAPACK auxiliary routine --
123* -- LAPACK is a software package provided by Univ. of Tennessee, --
124* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125*
126* .. Scalar Arguments ..
127 REAL CS1, RT1, RT2
128 COMPLEX A, B, C, SN1
129* ..
130*
131* =====================================================================
132*
133* .. Parameters ..
134 REAL ZERO
135 parameter( zero = 0.0e0 )
136 REAL ONE
137 parameter( one = 1.0e0 )
138* ..
139* .. Local Scalars ..
140 REAL T
141 COMPLEX W
142* ..
143* .. External Subroutines ..
144 EXTERNAL slaev2
145* ..
146* .. Intrinsic Functions ..
147 INTRINSIC abs, conjg, real
148* ..
149* .. Executable Statements ..
150*
151 IF( abs( b ).EQ.zero ) THEN
152 w = one
153 ELSE
154 w = conjg( b ) / abs( b )
155 END IF
156 CALL slaev2( real( a ), abs( b ), real( c ), rt1, rt2, cs1, t )
157 sn1 = w*t
158 RETURN
159*
160* End of CLAEV2
161*
subroutine slaev2(A, B, C, RT1, RT2, CS1, SN1)
SLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Definition: slaev2.f:120
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