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NAME
     spbtf2 - compute the Cholesky factorization of a  real  sym-
     metric positive definite band matrix A

SYNOPSIS
     SUBROUTINE SPBTF2( UPLO, N, KD, AB, LDAB, INFO )

     CHARACTER UPLO

     INTEGER INFO, KD, LDAB, N

     REAL AB( LDAB, * )



     #include <sunperf.h>

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

PURPOSE
     SPBTF2 computes the Cholesky factorization of  a  real  sym-
     metric positive definite band matrix A.

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

     N         (input) INTEGER
               The order of the matrix A.  N >= 0.

     KD        (input) 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        (input/output) REAL array, dimension (LDAB,N)
               On entry, the upper or lower triangle of the  sym-
               metric  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) INTEGER
               The leading dimension of the array  AB.   LDAB  >=
               KD+1.

     INFO      (output) INTEGER
               = 0: successful exit
               < 0: if INFO = -k, the k-th argument had an  ille-
               gal value
               > 0: if INFO = k, the leading minor of order k  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.

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