# spbtrs (l) - Linux Manuals

## NAME

SPBTRS - 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 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 factorization A = U**T*U or A = L*L**T computed by SPBTRF.

## ARGUMENTS

UPLO (input) CHARACTER*1
= aqUaq: Upper triangular factor stored in AB;
= aqLaq: 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 = aqUaq, or the number of subdiagonals if UPLO = aqLaq. 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 =aqUaq, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO =aqLaq, 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 illegal value