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

```
SSBGV(3F)							     SSBGV(3F)

```

### NAME[Toc][Back]

```     SSBGV - compute all the eigenvalues, and optionally, the eigenvectors of
a real generalized	symmetric-definite banded eigenproblem,	of the form
A*x=(lambda)*B*x
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB,	BB, LDBB, W, Z,	LDZ,
WORK, INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, KA, KB, LDAB, LDBB, LDZ, N

REAL	       AB( LDAB, * ), BB( LDBB,	* ), W(	* ), WORK( * ),	Z(
LDZ, * )
```

### PURPOSE[Toc][Back]

```     SSBGV computes all	the eigenvalues, and optionally, the eigenvectors of a
real generalized symmetric-definite banded	eigenproblem, of the form
A*x=(lambda)*B*x. Here A and B are	assumed	to be symmetric	and banded,
and B is also positive definite.

```

### ARGUMENTS[Toc][Back]

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

UPLO    (input) CHARACTER*1
= 'U':  Upper triangles of	A and B	are stored;
= 'L':  Lower triangles of	A and B	are stored.

N	     (input) INTEGER
The order of the matrices A and B.	 N >= 0.

KA	     (input) INTEGER
The number	of superdiagonals of the matrix	A if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'. KA >= 0.

KB	     (input) INTEGER
The number	of superdiagonals of the matrix	B if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'. KB >= 0.

AB	     (input/output) REAL array,	dimension (LDAB, N)
On	entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+1	rows of	the array.  The	j-th
column of A is stored in the j-th column of the array AB as
follows:  if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,jka)<=i<=j;
if UPLO	= 'L', AB(1+i-j,j)    =	A(i,j) for
j<=i<=min(n,j+ka).

On	exit, the contents of AB are destroyed.

Page 1

SSBGV(3F)							     SSBGV(3F)

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KA+1.

BB	     (input/output) REAL array,	dimension (LDBB, N)
On	entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1	rows of	the array.  The	j-th
column of B is stored in the j-th column of the array BB as
follows:  if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,jkb)<=i<=j;
if UPLO	= 'L', BB(1+i-j,j)    =	B(i,j) for
j<=i<=min(n,j+kb).

On	exit, the factor S from	the split Cholesky factorization B =
S**T*S, as	returned by SPBSTF.

LDBB    (input) INTEGER
The leading dimension of the array	BB.  LDBB >= KB+1.

W	     (output) REAL array, dimension (N)
If	INFO = 0, the eigenvalues in ascending order.

Z	     (output) REAL array, dimension (LDZ, N)
If	JOBZ = 'V', then if INFO = 0, Z	contains the matrix Z of
eigenvectors, with	the i-th column	of Z holding the eigenvector
associated	with W(i). The eigenvectors are	normalized so that
Z**T*B*Z =	I.  If JOBZ = 'N', then	Z is not referenced.

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

WORK    (workspace) REAL array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i,	and i is:
<=	N:  the	algorithm failed to converge:  i off-diagonal elements
of	an intermediate	tridiagonal form did not converge to zero; >
N:	  if INFO = N +	i, for 1 <= i <= N, then SPBSTF
returned INFO = i:	B is not positive definite.  The factorization
of	B could	not be completed and no	eigenvalues or eigenvectors
were computed.
SSBGV(3F)							     SSBGV(3F)

```

### NAME[Toc][Back]

```     SSBGV - compute all the eigenvalues, and optionally, the eigenvectors of
a real generalized	symmetric-definite banded eigenproblem,	of the form
A*x=(lambda)*B*x
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB,	BB, LDBB, W, Z,	LDZ,
WORK, INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, KA, KB, LDAB, LDBB, LDZ, N

REAL	       AB( LDAB, * ), BB( LDBB,	* ), W(	* ), WORK( * ),	Z(
LDZ, * )
```

### PURPOSE[Toc][Back]

```     SSBGV computes all	the eigenvalues, and optionally, the eigenvectors of a
real generalized symmetric-definite banded	eigenproblem, of the form
A*x=(lambda)*B*x. Here A and B are	assumed	to be symmetric	and banded,
and B is also positive definite.

```

### ARGUMENTS[Toc][Back]

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

UPLO    (input) CHARACTER*1
= 'U':  Upper triangles of	A and B	are stored;
= 'L':  Lower triangles of	A and B	are stored.

N	     (input) INTEGER
The order of the matrices A and B.	 N >= 0.

KA	     (input) INTEGER
The number	of superdiagonals of the matrix	A if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'. KA >= 0.

KB	     (input) INTEGER
The number	of superdiagonals of the matrix	B if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'. KB >= 0.

AB	     (input/output) REAL array,	dimension (LDAB, N)
On	entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+1	rows of	the array.  The	j-th
column of A is stored in the j-th column of the array AB as
follows:  if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,jka)<=i<=j;
if UPLO	= 'L', AB(1+i-j,j)    =	A(i,j) for
j<=i<=min(n,j+ka).

On	exit, the contents of AB are destroyed.

Page 1

SSBGV(3F)							     SSBGV(3F)

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KA+1.

BB	     (input/output) REAL array,	dimension (LDBB, N)
On	entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1	rows of	the array.  The	j-th
column of B is stored in the j-th column of the array BB as
follows:  if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,jkb)<=i<=j;
if UPLO	= 'L', BB(1+i-j,j)    =	B(i,j) for
j<=i<=min(n,j+kb).

On	exit, the factor S from	the split Cholesky factorization B =
S**T*S, as	returned by SPBSTF.

LDBB    (input) INTEGER
The leading dimension of the array	BB.  LDBB >= KB+1.

W	     (output) REAL array, dimension (N)
If	INFO = 0, the eigenvalues in ascending order.

Z	     (output) REAL array, dimension (LDZ, N)
If	JOBZ = 'V', then if INFO = 0, Z	contains the matrix Z of
eigenvectors, with	the i-th column	of Z holding the eigenvector
associated	with W(i). The eigenvectors are	normalized so that
Z**T*B*Z =	I.  If JOBZ = 'N', then	Z is not referenced.

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

WORK    (workspace) REAL array, dimension (3*N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i,	and i is:
<=	N:  the	algorithm failed to converge:  i off-diagonal elements
of	an intermediate	tridiagonal form did not converge to zero; >
N:	  if INFO = N +	i, for 1 <= i <= N, then SPBSTF
returned INFO = i:	B is not positive definite.  The factorization
of	B could	not be completed and no	eigenvalues or eigenvectors
were computed.

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