spbtrs(3)

NAME

SPBTRS - solve a system of linear equations A*X = B with a

symmetric positive definite band matrix A using the Cholesky fac

torization A = U**T*U or A = L*L**T computed by SPBTRF

SYNOPSIS

SUBROUTINE SPBTRS( UPLO, N, KD, NRHS, AB,  LDAB,  B,  LDB,
INFO )
    CHARACTER      UPLO
    INTEGER        INFO, KD, LDAB, LDB, N, NRHS
    REAL           AB( LDAB, * ), B( LDB, * )

PURPOSE

SPBTRS solves a system of linear equations A*X = B with a

symmetric positive definite band matrix A using the Cholesky fac

torization A = U**T*U or A = L*L**T computed by SPBTRF.

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) REAL 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) REAL 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 ille

gal value

LAPACK version 3.0 15 June 2000

SPBTRS(3)