dpbtrs(3S)

NAME
     DPBTRS - solve a system of linear equations A*X = B with a symmetric
     positive definite band matrix A using the Cholesky factorization A =
     U**T*U or A = L*L**T computed by DPBTRF

SYNOPSIS
     SUBROUTINE DPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, KD, LDAB, LDB, N, NRHS

         DOUBLE         PRECISION AB( LDAB, * ), B( LDB, * )

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
     DPBTRS solves a system of linear equations A*X = B with a symmetric
     positive definite band matrix A using the Cholesky factorization A =
     U**T*U or A = L*L**T computed by DPBTRF.

ARGUMENTS
     UPLO    (input) CHARACTER*1
             = 'U':  Upper triangular factor stored in AB;
             = 'L':  Lower triangular factor stored in AB.

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

     KD      (input) INTEGER
             The number of superdiagonals of the matrix A if UPLO = 'U', or
             the number of subdiagonals if UPLO = 'L'.  KD >= 0.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrix B.  NRHS >= 0.

     AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
             The triangular factor U or L from the Cholesky factorization A =
             U**T*U or A = L*L**T of the band matrix A, stored in the first
             KD+1 rows of the array.  The j-th column of U or L is stored in
             the j-th column of the array AB as follows:  if UPLO ='U',
             AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L',
             AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

     LDAB    (input) INTEGER
             The leading dimension of the array AB.  LDAB >= KD+1.

     B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
             On entry, the right hand side matrix B.  On exit, the solution
             matrix X.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,N).

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

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

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