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man pages->IRIX man pages -> complib/zlaev2 (3)
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### Contents

```
ZLAEV2(3F)							    ZLAEV2(3F)

```

### NAME[Toc][Back]

```     ZLAEV2 - compute the eigendecomposition of	a 2-by-2 Hermitian matrix  [ A
B ]  [ CONJG(B) C ]
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZLAEV2(	A, B, C, RT1, RT2, CS1,	SN1 )

DOUBLE		PRECISION CS1, RT1, RT2

COMPLEX*16	A, B, C, SN1
```

### PURPOSE[Toc][Back]

```     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 ].

```

### ARGUMENTS[Toc][Back]

```     A	    (input) COMPLEX*16
The	(1,1) element of the 2-by-2 matrix.

B	    (input) COMPLEX*16
The	(1,2) element and the conjugate	of the (2,1) element of	the
2-by-2 matrix.

C	    (input) COMPLEX*16
The	(2,2) element of the 2-by-2 matrix.

RT1    (output) DOUBLE PRECISION
The	eigenvalue of larger absolute value.

RT2    (output) DOUBLE PRECISION
The	eigenvalue of smaller absolute value.

CS1    (output) DOUBLE PRECISION
SN1	   (output) 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.

Page 1

ZLAEV2(3F)							    ZLAEV2(3F)

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.
ZLAEV2(3F)							    ZLAEV2(3F)

```

### NAME[Toc][Back]

```     ZLAEV2 - compute the eigendecomposition of	a 2-by-2 Hermitian matrix  [ A
B ]  [ CONJG(B) C ]
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZLAEV2(	A, B, C, RT1, RT2, CS1,	SN1 )

DOUBLE		PRECISION CS1, RT1, RT2

COMPLEX*16	A, B, C, SN1
```

### PURPOSE[Toc][Back]

```     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 ].

```

### ARGUMENTS[Toc][Back]

```     A	    (input) COMPLEX*16
The	(1,1) element of the 2-by-2 matrix.

B	    (input) COMPLEX*16
The	(1,2) element and the conjugate	of the (2,1) element of	the
2-by-2 matrix.

C	    (input) COMPLEX*16
The	(2,2) element of the 2-by-2 matrix.

RT1    (output) DOUBLE PRECISION
The	eigenvalue of larger absolute value.

RT2    (output) DOUBLE PRECISION
The	eigenvalue of smaller absolute value.

CS1    (output) DOUBLE PRECISION
SN1	   (output) 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.

Page 1

ZLAEV2(3F)							    ZLAEV2(3F)

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.

PPPPaaaaggggeeee 2222```
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