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

```
CPBTRF(3F)							    CPBTRF(3F)

```

### NAME[Toc][Back]

```     CPBTRF - compute the Cholesky factorization of a complex Hermitian
positive definite band matrix A
```

### SYNOPSIS[Toc][Back]

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

CHARACTER	UPLO

INTEGER	INFO, KD, LDAB,	N

COMPLEX	AB( LDAB, * )
```

### PURPOSE[Toc][Back]

```     CPBTRF computes the Cholesky factorization	of a complex Hermitian
positive definite band matrix A.

The factorization has the form
A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,	if UPLO	= 'L',
where U is	an upper triangular matrix and L is lower triangular.

```

### 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) COMPLEX array, dimension (LDAB,N)
On	entry, the upper or lower triangle of the Hermitian 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 triangular factor U or L	from the
Cholesky factorization A =	U**H*U or A = L*L**H of	the band
matrix A, in the same storage format as A.

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

Page 1

CPBTRF(3F)							    CPBTRF(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i,	the leading minor of order i is	not positive
definite, and the factorization could not be completed.

FURTHER	DETAILS
The band storage scheme is	illustrated by the following example, when N =
6,	KD = 2,	and UPLO = 'U':

On	entry:			     On	exit:

*    *	  a13  a24  a35	 a46	  *    *   u13	u24  u35  u46
*   a12  a23  a34  a45	 a56	  *   u12  u23	u34  u45  u56
a11  a22  a33  a44  a55	 a66	 u11  u22  u33	u44  u55  u66

Similarly,	if UPLO	= 'L' the format of A is as follows:

On	entry:			     On	exit:

a11  a22  a33  a44  a55	 a66	 l11  l22  l33	l44  l55  l66
a21  a32  a43  a54  a65	  *	 l21  l32  l43	l54  l65   *
a31  a42  a53  a64   *	  *	 l31  l42  l53	l64   *	   *

Array elements marked * are not used by the routine.

Contributed by
Peter Mayes and Giuseppe Radicati,	IBM ECSEC, Rome, March 23, 1989
CPBTRF(3F)							    CPBTRF(3F)

```

### NAME[Toc][Back]

```     CPBTRF - compute the Cholesky factorization of a complex Hermitian
positive definite band matrix A
```

### SYNOPSIS[Toc][Back]

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

CHARACTER	UPLO

INTEGER	INFO, KD, LDAB,	N

COMPLEX	AB( LDAB, * )
```

### PURPOSE[Toc][Back]

```     CPBTRF computes the Cholesky factorization	of a complex Hermitian
positive definite band matrix A.

The factorization has the form
A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,	if UPLO	= 'L',
where U is	an upper triangular matrix and L is lower triangular.

```

### 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) COMPLEX array, dimension (LDAB,N)
On	entry, the upper or lower triangle of the Hermitian 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 triangular factor U or L	from the
Cholesky factorization A =	U**H*U or A = L*L**H of	the band
matrix A, in the same storage format as A.

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

Page 1

CPBTRF(3F)							    CPBTRF(3F)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i,	the leading minor of order i is	not positive
definite, and the factorization could not be completed.

FURTHER	DETAILS
The band storage scheme is	illustrated by the following example, when N =
6,	KD = 2,	and UPLO = 'U':

On	entry:			     On	exit:

*    *	  a13  a24  a35	 a46	  *    *   u13	u24  u35  u46
*   a12  a23  a34  a45	 a56	  *   u12  u23	u34  u45  u56
a11  a22  a33  a44  a55	 a66	 u11  u22  u33	u44  u55  u66

Similarly,	if UPLO	= 'L' the format of A is as follows:

On	entry:			     On	exit:

a11  a22  a33  a44  a55	 a66	 l11  l22  l33	l44  l55  l66
a21  a32  a43  a54  a65	  *	 l21  l32  l43	l54  l65   *
a31  a42  a53  a64   *	  *	 l31  l42  l53	l64   *	   *

Array elements marked * are not used by the routine.

Contributed by
Peter Mayes and Giuseppe Radicati,	IBM ECSEC, Rome, March 23, 1989

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