.TH ZPBTRS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
ZPBTRS - 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
.SH SYNOPSIS
.TP 19
SUBROUTINE ZPBTRS(
UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, KD, LDAB, LDB, N, NRHS
.TP 19
.ti +4
COMPLEX*16
AB( LDAB, * ), B( LDB, * )
.SH 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.
.SH ARGUMENTS
.TP 8
UPLO (input) CHARACTER*1
= \(aqU\(aq: Upper triangular factor stored in AB;
.br
= \(aqL\(aq: Lower triangular factor stored in AB.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq,
or the number of subdiagonals if UPLO = \(aqL\(aq. KD >= 0.
.TP 8
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
.TP 8
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 =\(aqU\(aq, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =\(aqL\(aq, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
.TP 8
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
.TP 8
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value