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, ∗ )

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

  —  LAPACK version 2.0  —  08 October 1994