 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zlaev2()

 subroutine zlaev2 ( complex*16 A, complex*16 B, complex*16 C, double precision RT1, double precision RT2, double precision CS1, complex*16 SN1 )

ZLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.

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Purpose:
``` ZLAEV2 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*16 The (1,1) element of the 2-by-2 matrix.``` [in] B ``` B is COMPLEX*16 The (1,2) element and the conjugate of the (2,1) element of the 2-by-2 matrix.``` [in] C ``` C is COMPLEX*16 The (2,2) element of the 2-by-2 matrix.``` [out] RT1 ``` RT1 is DOUBLE PRECISION The eigenvalue of larger absolute value.``` [out] RT2 ``` RT2 is DOUBLE PRECISION The eigenvalue of smaller absolute value.``` [out] CS1 ` CS1 is DOUBLE PRECISION` [out] SN1 ``` SN1 is COMPLEX*16 The vector (CS1, SN1) is a unit right eigenvector for RT1.```
Date
December 2016
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 123 of file zlaev2.f.

123 *
124 * -- LAPACK auxiliary routine (version 3.7.0) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * December 2016
128 *
129 * .. Scalar Arguments ..
130  DOUBLE PRECISION cs1, rt1, rt2
131  COMPLEX*16 a, b, c, sn1
132 * ..
133 *
134 * =====================================================================
135 *
136 * .. Parameters ..
137  DOUBLE PRECISION zero
138  parameter( zero = 0.0d0 )
139  DOUBLE PRECISION one
140  parameter( one = 1.0d0 )
141 * ..
142 * .. Local Scalars ..
143  DOUBLE PRECISION t
144  COMPLEX*16 w
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL dlaev2
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC abs, dble, dconjg
151 * ..
152 * .. Executable Statements ..
153 *
154  IF( abs( b ).EQ.zero ) THEN
155  w = one
156  ELSE
157  w = dconjg( b ) / abs( b )
158  END IF
159  CALL dlaev2( dble( a ), abs( b ), dble( c ), rt1, rt2, cs1, t )
160  sn1 = w*t
161  RETURN
162 *
163 * End of ZLAEV2
164 *
subroutine dlaev2(A, B, C, RT1, RT2, CS1, SN1)
DLAEV2 computes the eigenvalues and eigenvectors of a 2-by-2 symmetric/Hermitian matrix.
Definition: dlaev2.f:122
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