dpbtf2(3S)

NAME
     DPBTF2 - compute the Cholesky factorization of a real symmetric positive
     definite band matrix A

SYNOPSIS
     SUBROUTINE DPBTF2( UPLO, N, KD, AB, LDAB, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, KD, LDAB, N

         DOUBLE         PRECISION AB( LDAB, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DPBTF2 computes the Cholesky factorization of a real symmetric 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) DOUBLE PRECISION 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'*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 illegal 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.


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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