CPTSV (3lapack)

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, 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) 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 = L*D*L**H.

  E       (input/output) COMPLEX 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 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.