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man pages->IRIX man pages -> complib/dlaed9 (3)
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### Contents

```
DLAED9(3F)							    DLAED9(3F)

```

### NAME[Toc][Back]

```     DLAED9 - find the roots of	the secular equation, as defined by the	values
in	D, Z, and RHO, between KSTART and KSTOP
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DLAED9(	K, KSTART, KSTOP, N, D,	Q, LDQ,	RHO, DLAMDA, W,	S,
LDS, INFO )

INTEGER	INFO, K, KSTART, KSTOP,	LDQ, LDS, N

DOUBLE		PRECISION RHO

DOUBLE		PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, *
), W( *	)
```

### PURPOSE[Toc][Back]

```     DLAED9 finds the roots of the secular equation, as	defined	by the values
in	D, Z, and RHO, between KSTART and KSTOP.  It makes the appropriate
calls to DLAED4 and then stores the new matrix of eigenvectors for	use in
calculating the next level	of Z vectors.

```

### ARGUMENTS[Toc][Back]

```     K	     (input) INTEGER
The number	of terms in the	rational function to be	solved by
DLAED4.  K	>= 0.

KSTART  (input) INTEGER
KSTOP   (input) INTEGER The updated eigenvalues Lambda(I),	KSTART
<=	I <= KSTOP are to be computed.	1 <= KSTART <= KSTOP <=	K.

N	     (input) INTEGER
The number	of rows	and columns in the Q matrix.  N	>= K (delation
may result	in N > K).

D	     (output) DOUBLE PRECISION array, dimension	(N)
D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.

Q	     (workspace) DOUBLE	PRECISION array, dimension (LDQ,N)

LDQ     (input) INTEGER
The leading dimension of the array	Q.  LDQ	>= max(	1, N ).

RHO     (input) DOUBLE PRECISION
The value of the parameter	in the rank one	update equation.  RHO
>=	0 required.

DLAMDA  (input) DOUBLE PRECISION array, dimension (K)
The first K elements of this array	contain	the old	roots of the
deflated updating problem.	 These are the poles of	the secular
equation.

Page 1

DLAED9(3F)							    DLAED9(3F)

W	     (input) DOUBLE PRECISION array, dimension (K)
The first K elements of this array	contain	the components of the

S	     (output) DOUBLE PRECISION array, dimension	(LDS, K)
Will contain the eigenvectors of the repaired matrix which	will
be	stored for subsequent Z	vector calculation and multiplied by
the previously accumulated	eigenvectors to	update the system.

LDS     (input) INTEGER
The leading dimension of S.  LDS >= max( 1, K ).

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = 1,	an eigenvalue did not converge
DLAED9(3F)							    DLAED9(3F)

```

### NAME[Toc][Back]

```     DLAED9 - find the roots of	the secular equation, as defined by the	values
in	D, Z, and RHO, between KSTART and KSTOP
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DLAED9(	K, KSTART, KSTOP, N, D,	Q, LDQ,	RHO, DLAMDA, W,	S,
LDS, INFO )

INTEGER	INFO, K, KSTART, KSTOP,	LDQ, LDS, N

DOUBLE		PRECISION RHO

DOUBLE		PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, *
), W( *	)
```

### PURPOSE[Toc][Back]

```     DLAED9 finds the roots of the secular equation, as	defined	by the values
in	D, Z, and RHO, between KSTART and KSTOP.  It makes the appropriate
calls to DLAED4 and then stores the new matrix of eigenvectors for	use in
calculating the next level	of Z vectors.

```

### ARGUMENTS[Toc][Back]

```     K	     (input) INTEGER
The number	of terms in the	rational function to be	solved by
DLAED4.  K	>= 0.

KSTART  (input) INTEGER
KSTOP   (input) INTEGER The updated eigenvalues Lambda(I),	KSTART
<=	I <= KSTOP are to be computed.	1 <= KSTART <= KSTOP <=	K.

N	     (input) INTEGER
The number	of rows	and columns in the Q matrix.  N	>= K (delation
may result	in N > K).

D	     (output) DOUBLE PRECISION array, dimension	(N)
D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.

Q	     (workspace) DOUBLE	PRECISION array, dimension (LDQ,N)

LDQ     (input) INTEGER
The leading dimension of the array	Q.  LDQ	>= max(	1, N ).

RHO     (input) DOUBLE PRECISION
The value of the parameter	in the rank one	update equation.  RHO
>=	0 required.

DLAMDA  (input) DOUBLE PRECISION array, dimension (K)
The first K elements of this array	contain	the old	roots of the
deflated updating problem.	 These are the poles of	the secular
equation.

Page 1

DLAED9(3F)							    DLAED9(3F)

W	     (input) DOUBLE PRECISION array, dimension (K)
The first K elements of this array	contain	the components of the

S	     (output) DOUBLE PRECISION array, dimension	(LDS, K)
Will contain the eigenvectors of the repaired matrix which	will
be	stored for subsequent Z	vector calculation and multiplied by
the previously accumulated	eigenvectors to	update the system.

LDS     (input) INTEGER
The leading dimension of S.  LDS >= max( 1, K ).

INFO    (output) INTEGER
= 0:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  if INFO = 1,	an eigenvalue did not converge

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