NAME

cpbtrs - solve 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 CPBTRF

SYNOPSIS

SUBROUTINE CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

CHARACTER UPLO

INTEGER INFO, KD, LDAB, LDB, N, NRHS

COMPLEX AB( LDAB, ∗ ), B( LDB, ∗ )

#include <sunperf.h>

void cpbtrs(char uplo, int n, int kd, int nrhs, complex ∗cab, int ldab, complex ∗cb, int ldb, int ∗ info) ;

PURPOSE

CPBTRS 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 CPBTRF. 
 

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 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 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

SunOS 5.0  —  Last change: 10 Dec 1998