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# cptsv

```
NAME
CPTSV - 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 CPTSV( N, NRHS, D, E, B, LDB, INFO )

INTEGER       INFO, LDB, N, NRHS

REAL          D( * )

COMPLEX       B( LDB, * ), E( * )

PURPOSE
CPTSV 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 or A = U**H*D*U, and the fac-
tored form of A is then used to solve the system of equa-
tions.

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) REAL 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 =
U**H*D*U or A = L*D*L**H.

E       (input/output) COMPLEX array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tri-
diagonal 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 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.
```