NAME

ZPTSV - compute the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices

SYNOPSIS

SUBROUTINE ZPTSV(
N, NRHS, D, E, B, LDB, INFO )

INTEGER INFO, LDB, N, NRHS

DOUBLE PRECISION D( ∗ )

COMPLEX∗16 B( LDB, ∗ ), E( ∗ )

PURPOSE

ZPTSV computes the solution to a complex system of linear equations A∗X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. 
 
A is factored as A = L∗D∗L∗∗H, and the factored form of A is then used to solve the system of equations.
 

ARGUMENTS

N       (input) INTEGER
The order of the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns of the matrix B.  NRHS >= 0.

D       (input/output) DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix A.  On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L∗D∗L∗∗H.

E       (input/output) COMPLEX∗16 array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A.  On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L∗D∗L∗∗H factorization of A.  E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U∗∗H∗D∗U factorization of A.

B       (input/output) COMPLEX∗16 array, dimension (LDB,N)
On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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
> 0:  if INFO = i, the leading minor of order i is not positive definite, and the solution has not been computed.  The factorization has not been completed unless i = N.

  —  LAPACK version 2.0  —  08 October 1994