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man pages->IRIX man pages -> complib/slaed9 (3)
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### Contents

```
SLAED9(3F)							    SLAED9(3F)

```

### NAME[Toc][Back]

```     SLAED9 - 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	SLAED9(	K, KSTART, KSTOP, N, D,	Q, LDQ,	RHO, DLAMDA, W,	S,
LDS, INFO )

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

REAL		RHO

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

### PURPOSE[Toc][Back]

```     SLAED9 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 SLAED4 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
SLAED4.  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) REAL array, dimension (N)
D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.

Q	     (workspace) REAL array, dimension (LDQ,N)

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

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

DLAMDA  (input) REAL 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

SLAED9(3F)							    SLAED9(3F)

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

S	     (output) REAL 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
SLAED9(3F)							    SLAED9(3F)

```

### NAME[Toc][Back]

```     SLAED9 - 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	SLAED9(	K, KSTART, KSTOP, N, D,	Q, LDQ,	RHO, DLAMDA, W,	S,
LDS, INFO )

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

REAL		RHO

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

### PURPOSE[Toc][Back]

```     SLAED9 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 SLAED4 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
SLAED4.  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) REAL array, dimension (N)
D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.

Q	     (workspace) REAL array, dimension (LDQ,N)

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

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

DLAMDA  (input) REAL 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

SLAED9(3F)							    SLAED9(3F)

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

S	     (output) REAL 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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