DPBTRS(3)      LAPACK routine of NEC Numeric Library Collection      DPBTRS(3)



NAME
       DPBTRS

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



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

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

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

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

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

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

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

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



LAPACK routine                  31 October 2017                      DPBTRS(3)