Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H *U or A = L*L**H computed by ZPBTRF

**SYNOPSIS**

SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, LDB, N, NRHS COMPLEX*16 AB( LDAB, * ), B( LDB, * )

**PURPOSE**

ZPBTRS solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H *U or A = L*L**H computed by ZPBTRF.

**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) COMPLEX*16 array, dimension (LDAB,N) The triangular factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H 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) COMPLEX*16 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 routine (version 3.3.1) April 2011 ZPBTRS(3lapack)