# zpbstf.f man page

zpbstf.f —

## Synopsis

### Functions/Subroutines

subroutinezpbstf(UPLO, N, KD, AB, LDAB, INFO)ZPBSTF

## Function/Subroutine Documentation

### subroutine zpbstf (characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, integerINFO)

**ZPBSTF**

**Purpose:**

```
ZPBSTF computes a split Cholesky factorization of a complex
Hermitian positive definite band matrix A.
This routine is designed to be used in conjunction with ZHBGST.
The factorization has the form A = S**H*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.
```

**Parameters:**

*UPLO*

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

*N*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*KD*

```
KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
```

*AB*

```
AB is COMPLEX*16 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,j-kd)<=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**H*S. See Further Details.
```

*LDAB*

```
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
```

*INFO*

```
INFO is 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.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**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**H s64**H s75**H
* a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54**H s65**H s76**H
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**H s23**H s34**H s54 s65 s76 *
a31 a42 a53 a64 a64 * * s13**H s24**H s53 s64 s75 * *
Array elements marked * are not used by the routine; s12**H denotes
conjg(s12); the diagonal elements of S are real.
```

Definition at line 154 of file zpbstf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zpbstf(3) is an alias of zpbstf.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK