NAME¶

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

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.