NAME

SYNOPSIS

  SUBROUTINE SPBTF2( UPLO, N, KD, AB, LDAB, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, KD, LDAB, INFO
  REAL AB(LDAB,*)
 
  SUBROUTINE SPBTF2_64( UPLO, N, KD, AB, LDAB, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, KD, LDAB, INFO
  REAL AB(LDAB,*)
 

F95 INTERFACE

  SUBROUTINE PBTF2( UPLO, [N], KD, AB, [LDAB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, KD, LDAB, INFO
  REAL, DIMENSION(:,:) :: AB
 
  SUBROUTINE PBTF2_64( UPLO, [N], KD, AB, [LDAB], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, KD, LDAB, INFO
  REAL, DIMENSION(:,:) :: AB
 

C INTERFACE

void spbtf2(char uplo, int n, int kd, float *ab, int ldab, int *info);

void spbtf2_64(char uplo, long n, long kd, float *ab, long ldab, long *info);

PURPOSE

The factorization has the form

   A = U' * U ,  if UPLO = 'U', or
   A = L  * L',  if UPLO = 'L',

where U is an upper triangular matrix, U' is the transpose of U, and L is lower triangular.

This is the unblocked version of the algorithm, calling Level 2 BLAS.

ARGUMENTS

* UPLO (input)

Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:

* N (input)

The order of the matrix A. N >= 0.

* KD (input)

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

* AB (input/output)

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'*U or A = L*L' of the band matrix A, in the same storage format as A.

* LDAB (input)

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

* INFO (output)