zpbsv (l)  Linux Man Pages
zpbsv: computes the solution to a complex system of linear equations A * X = B,
NAME
ZPBSV  computes the solution to a complex system of linear equations A * X = B,SYNOPSIS
 SUBROUTINE ZPBSV(
 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
ZPBSV computes the solution to a complex system of linear equationsA
The Cholesky decomposition is used to factor A as
A
A
where U is an upper triangular band matrix, and L is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as A. The factored form of A is then used to solve the system of equations A * X = B.
ARGUMENTS
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.  N (input) INTEGER
 The number of linear equations, i.e., 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/output) COMPLEX*16 array, dimension (LDAB,N)
 On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The jth column of A is stored in the jth column of the array AB as follows: if UPLO = aqUaq, AB(KD+1+ij,j) = A(i,j) for max(1,jKD)<=i<=j; if UPLO = aqLaq, AB(1+ij,j) = A(i,j) for j<=i<=min(N,j+KD). See below for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, in the same storage format as A.
 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 NbyNRHS right hand side matrix B. On exit, if INFO = 0, the NbyNRHS 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 ith argument had an illegal value
> 0: if INFO = i, the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed.
FURTHER DETAILS
The band storage scheme is illustrated by the following example, when N = 6, KD = 2, and UPLO = aqUaq:On entry: On exit:
a11
On entry: On exit:
a11
a21
a31