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

```
DSTEVD(3F)							    DSTEVD(3F)

```

### NAME[Toc][Back]

```     DSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real
symmetric tridiagonal matrix
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DSTEVD(	JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
INFO )

CHARACTER	JOBZ

INTEGER	INFO, LDZ, LIWORK, LWORK, N

INTEGER	IWORK( * )

DOUBLE		PRECISION D( * ), E( * ), WORK(	* ), Z(	LDZ, * )
```

### PURPOSE[Toc][Back]

```     DSTEVD computes all eigenvalues and, optionally, eigenvectors of a	real
symmetric tridiagonal matrix. If eigenvectors are desired,	it uses	a
divide and	conquer	algorithm.

The divide	and conquer algorithm 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]

```     JOBZ    (input) CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

N	     (input) INTEGER
The order of the matrix.  N >= 0.

D	     (input/output) DOUBLE PRECISION array, dimension (N)
On	entry, the n diagonal elements of the tridiagonal matrix A.
On	exit, if INFO =	0, the eigenvalues in ascending	order.

E	     (input/output) DOUBLE PRECISION array, dimension (N)
On	entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A, stored in elements 1 to N-1 of E; E(N) need not be set,
but is used by the	routine.  On exit, the contents	of E are
destroyed.

Z	     (output) DOUBLE PRECISION array, dimension	(LDZ, N)
If	JOBZ = 'V', then if INFO = 0, Z	contains the orthonormal
eigenvectors of the matrix	A, with	the i-th column	of Z holding
the eigenvector associated	with D(i).  If JOBZ = 'N', then	Z is
not referenced.

Page 1

DSTEVD(3F)							    DSTEVD(3F)

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1, and if JOBZ =
'V', LDZ >= max(1,N).

WORK    (workspace/output)	DOUBLE PRECISION array,
dimension (LWORK) On exit,	if LWORK > 0, WORK(1) returns the
optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  If JOBZ	= 'N' or N <= 1	then
LWORK must	be at least 1.	If JOBZ	 = 'V' and N > 1 then LWORK
must be at	least (	1 + 3*N	+ 2*N*lg N + 2*N**2 ), where lg( N ) =
smallest integer k	such that 2**k >= N.

IWORK   (workspace/output)	INTEGER	array, dimension (LIWORK)
On	exit, if LIWORK	> 0, IWORK(1) returns the optimal LIWORK.

LIWORK  (input) INTEGER
The dimension of the array	IWORK.	If JOBZ	 = 'N' or N <= 1 then
LIWORK must be at least 1.	 If JOBZ  = 'V'	and N >	1 then LIWORK
must be at	least 2+5*N.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i,	the algorithm failed to	converge; i offdiagonal
elements of E did	not converge to	zero.
DSTEVD(3F)							    DSTEVD(3F)

```

### NAME[Toc][Back]

```     DSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real
symmetric tridiagonal matrix
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DSTEVD(	JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
INFO )

CHARACTER	JOBZ

INTEGER	INFO, LDZ, LIWORK, LWORK, N

INTEGER	IWORK( * )

DOUBLE		PRECISION D( * ), E( * ), WORK(	* ), Z(	LDZ, * )
```

### PURPOSE[Toc][Back]

```     DSTEVD computes all eigenvalues and, optionally, eigenvectors of a	real
symmetric tridiagonal matrix. If eigenvectors are desired,	it uses	a
divide and	conquer	algorithm.

The divide	and conquer algorithm 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]

```     JOBZ    (input) CHARACTER*1
= 'N':  Compute eigenvalues only;
= 'V':  Compute eigenvalues and eigenvectors.

N	     (input) INTEGER
The order of the matrix.  N >= 0.

D	     (input/output) DOUBLE PRECISION array, dimension (N)
On	entry, the n diagonal elements of the tridiagonal matrix A.
On	exit, if INFO =	0, the eigenvalues in ascending	order.

E	     (input/output) DOUBLE PRECISION array, dimension (N)
On	entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A, stored in elements 1 to N-1 of E; E(N) need not be set,
but is used by the	routine.  On exit, the contents	of E are
destroyed.

Z	     (output) DOUBLE PRECISION array, dimension	(LDZ, N)
If	JOBZ = 'V', then if INFO = 0, Z	contains the orthonormal
eigenvectors of the matrix	A, with	the i-th column	of Z holding
the eigenvector associated	with D(i).  If JOBZ = 'N', then	Z is
not referenced.

Page 1

DSTEVD(3F)							    DSTEVD(3F)

LDZ     (input) INTEGER
The leading dimension of the array	Z.  LDZ	>= 1, and if JOBZ =
'V', LDZ >= max(1,N).

WORK    (workspace/output)	DOUBLE PRECISION array,
dimension (LWORK) On exit,	if LWORK > 0, WORK(1) returns the
optimal LWORK.

LWORK   (input) INTEGER
The dimension of the array	WORK.  If JOBZ	= 'N' or N <= 1	then
LWORK must	be at least 1.	If JOBZ	 = 'V' and N > 1 then LWORK
must be at	least (	1 + 3*N	+ 2*N*lg N + 2*N**2 ), where lg( N ) =
smallest integer k	such that 2**k >= N.

IWORK   (workspace/output)	INTEGER	array, dimension (LIWORK)
On	exit, if LIWORK	> 0, IWORK(1) returns the optimal LIWORK.

LIWORK  (input) INTEGER
The dimension of the array	IWORK.	If JOBZ	 = 'N' or N <= 1 then
LIWORK must be at least 1.	 If JOBZ  = 'V'	and N >	1 then LIWORK
must be at	least 2+5*N.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i,	the algorithm failed to	converge; i offdiagonal
elements of E did	not converge to	zero.

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