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man pages->IRIX man pages -> complib/dlaed4 (3)
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### Contents

```
DLAED4(3F)							    DLAED4(3F)

```

### NAME[Toc][Back]

```     DLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric
rank-one modification to a	diagonal matrix	whose elements are given in
the array d, and that   D(i) < D(j) for i < j  and	that RHO > 0
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DLAED4(	N, I, D, Z, DELTA, RHO,	DLAM, INFO )

INTEGER	I, INFO, N

DOUBLE		PRECISION DLAM,	RHO

DOUBLE		PRECISION D( * ), DELTA( * ), Z( * )
```

### PURPOSE[Toc][Back]

```     This subroutine computes the I-th updated eigenvalue of a symmetric
rank-one modification to a	diagonal matrix	whose elements are given in
the array d, and that no loss in generality.  The rank-one	modified
system is thus

diag( D	)  +  RHO *  Z * Z_transpose.

where we assume the Euclidean norm	of Z is	1.

The method	consists of approximating the rational functions in the
secular equation by simpler interpolating rational	functions.

```

### ARGUMENTS[Toc][Back]

```     N	    (input) INTEGER
The	length of all arrays.

I	    (input) INTEGER
The	index of the eigenvalue	to be computed.	 1 <= I	<= N.

D	    (input) DOUBLE PRECISION array, dimension (N)
The	original eigenvalues.  It is assumed that they are in order,
D(I) < D(J)	 for I < J.

Z	    (input) DOUBLE PRECISION array, dimension (N)
The	components of the updating vector.

DELTA  (output) DOUBLE PRECISION array, dimension (N)
If N .ne. 1, DELTA contains	(D(j) -	lambda_I) in its  j-th
component.	If N = 1, then DELTA(1)	= 1.  The vector DELTA
contains the information necessary to construct the	eigenvectors.

RHO    (input) DOUBLE PRECISION
The	scalar in the symmetric	updating formula.

Page 1

DLAED4(3F)							    DLAED4(3F)

DLAM   (output) DOUBLE PRECISION
The	computed lambda_I, the I-th updated eigenvalue.

INFO   (output) INTEGER
= 0:  successful exit
> 0:  if INFO = 1, the updating process failed.
```

### PARAMETERS[Toc][Back]

```     Logical variable ORGATI (origin-at-i?) is used for	distinguishing whether
D(i) or D(i+1) is treated as the origin.

ORGATI = .true.	origin at i ORGATI = .false.   origin at i+1

Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are
working with THREE	poles!

MAXIT is the maximum number of iterations allowed for each	eigenvalue.
DLAED4(3F)							    DLAED4(3F)

```

### NAME[Toc][Back]

```     DLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric
rank-one modification to a	diagonal matrix	whose elements are given in
the array d, and that   D(i) < D(j) for i < j  and	that RHO > 0
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DLAED4(	N, I, D, Z, DELTA, RHO,	DLAM, INFO )

INTEGER	I, INFO, N

DOUBLE		PRECISION DLAM,	RHO

DOUBLE		PRECISION D( * ), DELTA( * ), Z( * )
```

### PURPOSE[Toc][Back]

```     This subroutine computes the I-th updated eigenvalue of a symmetric
rank-one modification to a	diagonal matrix	whose elements are given in
the array d, and that no loss in generality.  The rank-one	modified
system is thus

diag( D	)  +  RHO *  Z * Z_transpose.

where we assume the Euclidean norm	of Z is	1.

The method	consists of approximating the rational functions in the
secular equation by simpler interpolating rational	functions.

```

### ARGUMENTS[Toc][Back]

```     N	    (input) INTEGER
The	length of all arrays.

I	    (input) INTEGER
The	index of the eigenvalue	to be computed.	 1 <= I	<= N.

D	    (input) DOUBLE PRECISION array, dimension (N)
The	original eigenvalues.  It is assumed that they are in order,
D(I) < D(J)	 for I < J.

Z	    (input) DOUBLE PRECISION array, dimension (N)
The	components of the updating vector.

DELTA  (output) DOUBLE PRECISION array, dimension (N)
If N .ne. 1, DELTA contains	(D(j) -	lambda_I) in its  j-th
component.	If N = 1, then DELTA(1)	= 1.  The vector DELTA
contains the information necessary to construct the	eigenvectors.

RHO    (input) DOUBLE PRECISION
The	scalar in the symmetric	updating formula.

Page 1

DLAED4(3F)							    DLAED4(3F)

DLAM   (output) DOUBLE PRECISION
The	computed lambda_I, the I-th updated eigenvalue.

INFO   (output) INTEGER
= 0:  successful exit
> 0:  if INFO = 1, the updating process failed.
```

### PARAMETERS[Toc][Back]

```     Logical variable ORGATI (origin-at-i?) is used for	distinguishing whether
D(i) or D(i+1) is treated as the origin.

ORGATI = .true.	origin at i ORGATI = .false.   origin at i+1

Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are
working with THREE	poles!

MAXIT is the maximum number of iterations allowed for each	eigenvalue.

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