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

```
SPBSTF(3F)							    SPBSTF(3F)

```

### NAME[Toc][Back]

```     SPBSTF - compute a	split Cholesky factorization of	a real symmetric
positive definite band matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SPBSTF(	UPLO, N, KD, AB, LDAB, INFO )

CHARACTER	UPLO

INTEGER	INFO, KD, LDAB,	N

REAL		AB( LDAB, * )
```

### PURPOSE[Toc][Back]

```     SPBSTF computes a split Cholesky factorization of a real symmetric
positive definite band matrix A.

This routine is designed to be used in conjunction	with SSBGST.

The factorization has the form  A = S**T*S	 where S is a band matrix of
the same bandwidth	as A and the following structure:

S = ( U	  )
( M	L )

where U is	upper triangular of order m = (n+kd)/2,	and L is lower
triangular	of order n-m.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

KD	     (input) INTEGER
The number	of superdiagonals of the matrix	A if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'.	KD >= 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 kd+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(kd+1+i-j,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO	= 'L', AB(1+i-j,j)    =	A(i,j) for
j<=i<=min(n,j+kd).

On	exit, if INFO =	0, the factor S	from the split Cholesky
factorization A = S**T*S. See Further Details.  LDAB    (input)
INTEGER The leading dimension of the array	AB.  LDAB >= KD+1.

Page 1

SPBSTF(3F)							    SPBSTF(3F)

INFO    (output) INTEGER
= 0: successful exit
< 0: if INFO = -i,	the i-th argument had an illegal value
> 0: if INFO = i, the factorization could not be completed,
because the updated element a(i,i)	was negative; the matrix A is
not positive definite.

FURTHER	DETAILS
The band storage scheme is	illustrated by the following example, when N =
7,	KD = 2:

S = ( s11	s12  s13		     )
(	s22  s23  s24		     )
(	     s33  s34		     )
(		  s44		     )
(	     s53  s54  s55	     )
(		  s64  s65  s66	     )
(		       s75  s76	 s77 )

If	UPLO = 'U', the	array AB holds:

on	entry:				on exit:

*	   *   a13  a24	 a35  a46  a57	 *    *	  s13  s24  s53	 s64  s75
*	  a12  a23  a34	 a45  a56  a67	 *   s12  s23  s34  s54	 s65  s76 a11
a22  a33  a44  a55	 a66  a77  s11	s22  s33  s44  s55  s66	 s77

If	UPLO = 'L', the	array AB holds:

on	entry:				on exit:

a11  a22  a33  a44	 a55  a66  a77	s11  s22  s33  s44  s55	 s66  s77 a21
a32  a43  a54  a65	 a76   *   s12	s23  s34  s54  s65  s76	  * a31	 a42
a53  a64  a64   *	  *   s13  s24	s53  s64  s75	*    *

Array elements marked * are not used by the routine.
SPBSTF(3F)							    SPBSTF(3F)

```

### NAME[Toc][Back]

```     SPBSTF - compute a	split Cholesky factorization of	a real symmetric
positive definite band matrix A
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	SPBSTF(	UPLO, N, KD, AB, LDAB, INFO )

CHARACTER	UPLO

INTEGER	INFO, KD, LDAB,	N

REAL		AB( LDAB, * )
```

### PURPOSE[Toc][Back]

```     SPBSTF computes a split Cholesky factorization of a real symmetric
positive definite band matrix A.

This routine is designed to be used in conjunction	with SSBGST.

The factorization has the form  A = S**T*S	 where S is a band matrix of
the same bandwidth	as A and the following structure:

S = ( U	  )
( M	L )

where U is	upper triangular of order m = (n+kd)/2,	and L is lower
triangular	of order n-m.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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

KD	     (input) INTEGER
The number	of superdiagonals of the matrix	A if UPLO = 'U', or
the number	of subdiagonals	if UPLO	= 'L'.	KD >= 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 kd+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(kd+1+i-j,j) = A(i,j) for max(1,jkd)<=i<=j;
if UPLO	= 'L', AB(1+i-j,j)    =	A(i,j) for
j<=i<=min(n,j+kd).

On	exit, if INFO =	0, the factor S	from the split Cholesky
factorization A = S**T*S. See Further Details.  LDAB    (input)
INTEGER The leading dimension of the array	AB.  LDAB >= KD+1.

Page 1

SPBSTF(3F)							    SPBSTF(3F)

INFO    (output) INTEGER
= 0: successful exit
< 0: if INFO = -i,	the i-th argument had an illegal value
> 0: if INFO = i, the factorization could not be completed,
because the updated element a(i,i)	was negative; the matrix A is
not positive definite.

FURTHER	DETAILS
The band storage scheme is	illustrated by the following example, when N =
7,	KD = 2:

S = ( s11	s12  s13		     )
(	s22  s23  s24		     )
(	     s33  s34		     )
(		  s44		     )
(	     s53  s54  s55	     )
(		  s64  s65  s66	     )
(		       s75  s76	 s77 )

If	UPLO = 'U', the	array AB holds:

on	entry:				on exit:

*	   *   a13  a24	 a35  a46  a57	 *    *	  s13  s24  s53	 s64  s75
*	  a12  a23  a34	 a45  a56  a67	 *   s12  s23  s34  s54	 s65  s76 a11
a22  a33  a44  a55	 a66  a77  s11	s22  s33  s44  s55  s66	 s77

If	UPLO = 'L', the	array AB holds:

on	entry:				on exit:

a11  a22  a33  a44	 a55  a66  a77	s11  s22  s33  s44  s55	 s66  s77 a21
a32  a43  a54  a65	 a76   *   s12	s23  s34  s54  s65  s76	  * a31	 a42
a53  a64  a64   *	  *   s13  s24	s53  s64  s75	*    *

Array elements marked * are not used by the routine.

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