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man pages->IRIX man pages -> complib/slaed3 (3)
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### Contents

```
SLAED3(3F)							    SLAED3(3F)

```

### NAME[Toc][Back]

```     SLAED3 - find the roots of	the secular equation, as defined by the	values
in	D, W, and RHO, between KSTART and KSTOP
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SLAED3(	K, KSTART, KSTOP, N, D,	Q, LDQ,	RHO, CUTPNT, DLAMDA,
Q2, LDQ2, INDXC, CTOT, W, S, LDS, INFO )

INTEGER	CUTPNT,	INFO, K, KSTART, KSTOP,	LDQ, LDQ2, LDS,	N

REAL		RHO

INTEGER	CTOT( *	), INDXC( * )

REAL		D( * ),	DLAMDA(	* ), Q(	LDQ, * ), Q2( LDQ2, * ), S(
LDS, * ), W( * )
```

### PURPOSE[Toc][Back]

```     SLAED3 finds the roots of the secular equation, as	defined	by the values
in	D, W, and RHO, between KSTART and KSTOP.  It makes the appropriate
calls to SLAED4 and then updates the eigenvectors by multiplying the
matrix of eigenvectors of the pair	of eigensystems	being combined by the
matrix of eigenvectors of the K-by-K system which is solved here.

This code makes very mild assumptions about floating point	arithmetic. It
will work on machines with	a guard	digit in add/subtract, or on those
binary machines without guard digits which	subtract like the Cray X-MP,
Cray Y-MP,	Cray C-90, or Cray-2.  It could	conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.

```

### 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
(deflation	may result in N>K).

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

Q	     (output) REAL array, dimension (LDQ,N)
Initially the first K columns are used as workspace.  On output
the columns KSTART	to KSTOP contain the updated eigenvectors.

Page 1

SLAED3(3F)							    SLAED3(3F)

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.

CUTPNT  (input) INTEGER
The location of the last eigenvalue in the	leading	submatrix.
min(1,N) <= CUTPNT	<= N.

DLAMDA  (input/output) 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. May be changed on output	by having lowest order bit set
to	zero on	Cray X-MP, Cray	Y-MP, Cray-2, or Cray C-90, as
described above.

Q2	     (input) REAL array, dimension (LDQ2, N)
The first K columns of this matrix	contain	the non-deflated
eigenvectors for the split	problem.

LDQ2    (input) INTEGER
The leading dimension of the array	Q2.  LDQ2 >= max(1,N).

INDXC   (input) INTEGER array, dimension (N)
The permutation used to arrange the columns of the	deflated Q
matrix into three groups:	the first group	contains non-zero
elements only at and above	CUTPNT,	the second contains non-zero
elements only below CUTPNT, and the third is dense.  The rows of
the eigenvectors found by SLAED4 must be likewise permuted	before
the matrix	multiply can take place.

CTOT    (input) INTEGER array, dimension (4)
A count of	the total number of the	various	types of columns in Q,
as	described in INDXC.  The fourth	column type is any column
which has been deflated.

W	     (input/output) REAL array,	dimension (K)
The first K elements of this array	contain	the components of the
deflation-adjusted	updating vector. Destroyed on output.

S	     (workspace) REAL array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which	will
be	multiplied by the previously accumulated eigenvectors to
update the	system.

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

Page 2

SLAED3(3F)							    SLAED3(3F)

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
SLAED3(3F)							    SLAED3(3F)

```

### NAME[Toc][Back]

```     SLAED3 - find the roots of	the secular equation, as defined by the	values
in	D, W, and RHO, between KSTART and KSTOP
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SLAED3(	K, KSTART, KSTOP, N, D,	Q, LDQ,	RHO, CUTPNT, DLAMDA,
Q2, LDQ2, INDXC, CTOT, W, S, LDS, INFO )

INTEGER	CUTPNT,	INFO, K, KSTART, KSTOP,	LDQ, LDQ2, LDS,	N

REAL		RHO

INTEGER	CTOT( *	), INDXC( * )

REAL		D( * ),	DLAMDA(	* ), Q(	LDQ, * ), Q2( LDQ2, * ), S(
LDS, * ), W( * )
```

### PURPOSE[Toc][Back]

```     SLAED3 finds the roots of the secular equation, as	defined	by the values
in	D, W, and RHO, between KSTART and KSTOP.  It makes the appropriate
calls to SLAED4 and then updates the eigenvectors by multiplying the
matrix of eigenvectors of the pair	of eigensystems	being combined by the
matrix of eigenvectors of the K-by-K system which is solved here.

This code makes very mild assumptions about floating point	arithmetic. It
will work on machines with	a guard	digit in add/subtract, or on those
binary machines without guard digits which	subtract like the Cray X-MP,
Cray Y-MP,	Cray C-90, or Cray-2.  It could	conceivably fail on
hexadecimal or decimal machines without guard digits, but we know of
none.

```

### 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
(deflation	may result in N>K).

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

Q	     (output) REAL array, dimension (LDQ,N)
Initially the first K columns are used as workspace.  On output
the columns KSTART	to KSTOP contain the updated eigenvectors.

Page 1

SLAED3(3F)							    SLAED3(3F)

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.

CUTPNT  (input) INTEGER
The location of the last eigenvalue in the	leading	submatrix.
min(1,N) <= CUTPNT	<= N.

DLAMDA  (input/output) 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. May be changed on output	by having lowest order bit set
to	zero on	Cray X-MP, Cray	Y-MP, Cray-2, or Cray C-90, as
described above.

Q2	     (input) REAL array, dimension (LDQ2, N)
The first K columns of this matrix	contain	the non-deflated
eigenvectors for the split	problem.

LDQ2    (input) INTEGER
The leading dimension of the array	Q2.  LDQ2 >= max(1,N).

INDXC   (input) INTEGER array, dimension (N)
The permutation used to arrange the columns of the	deflated Q
matrix into three groups:	the first group	contains non-zero
elements only at and above	CUTPNT,	the second contains non-zero
elements only below CUTPNT, and the third is dense.  The rows of
the eigenvectors found by SLAED4 must be likewise permuted	before
the matrix	multiply can take place.

CTOT    (input) INTEGER array, dimension (4)
A count of	the total number of the	various	types of columns in Q,
as	described in INDXC.  The fourth	column type is any column
which has been deflated.

W	     (input/output) REAL array,	dimension (K)
The first K elements of this array	contain	the components of the
deflation-adjusted	updating vector. Destroyed on output.

S	     (workspace) REAL array, dimension (LDS, K)
Will contain the eigenvectors of the repaired matrix which	will
be	multiplied by the previously accumulated eigenvectors to
update the	system.

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

Page 2

SLAED3(3F)							    SLAED3(3F)

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 3333```
[ Back ]
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