 LAPACK  3.10.1 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.```
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 zlaev2.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  DOUBLE PRECISION CS1, RT1, RT2
128  COMPLEX*16 A, B, C, SN1
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. Parameters ..
134  DOUBLE PRECISION ZERO
135  parameter( zero = 0.0d0 )
136  DOUBLE PRECISION ONE
137  parameter( one = 1.0d0 )
138 * ..
139 * .. Local Scalars ..
140  DOUBLE PRECISION T
141  COMPLEX*16 W
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL dlaev2
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs, dble, dconjg
148 * ..
149 * .. Executable Statements ..
150 *
151  IF( abs( b ).EQ.zero ) THEN
152  w = one
153  ELSE
154  w = dconjg( b ) / abs( b )
155  END IF
156  CALL dlaev2( dble( a ), abs( b ), dble( c ), rt1, rt2, cs1, t )
157  sn1 = w*t
158  RETURN
159 *
160 * End of ZLAEV2
161 *
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:120
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