# spbtf2.f man page

spbtf2.f —

## Synopsis

### Functions/Subroutines

subroutinespbtf2(UPLO, N, KD, AB, LDAB, INFO)SPBTF2computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

## Function/Subroutine Documentation

### subroutine spbtf2 (characterUPLO, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, integerINFO)

**SPBTF2** computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

**Purpose:**

```
SPBTF2 computes the Cholesky factorization of a real symmetric
positive definite band matrix A.
The factorization has the form
A = U**T * U , if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix, U**T is the transpose of U, and
L is lower triangular.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
```

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
```

*N*

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

*KD*

```
KD is INTEGER
The number of super-diagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
```

*AB*

```
AB is 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,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 triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T of the band
matrix A, in the same storage format as A.
```

*LDAB*

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

*INFO*

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

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**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.
```

Definition at line 143 of file spbtf2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

spbtf2(3) is an alias of spbtf2.f(3).