spbtf2.f - Man Page

SRC/spbtf2.f

Synopsis

Functions/Subroutines

subroutine spbtf2 (uplo, n, kd, ab, ldab, info)
SPBTF2 computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix (unblocked algorithm).

Function/Subroutine Documentation

subroutine spbtf2 (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, integer info)

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 principal minor of order k
is not positive, and the factorization could not be
completed.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

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 141 of file spbtf2.f.

Author

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Referenced By

The man page spbtf2(3) is an alias of spbtf2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK