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## zhptrd()

subroutine zhptrd | ( | character | uplo,
|  | integer | n,
|  | complex*16, dimension( * ) | ap,
|  | double precision, dimension( * ) | d,
|  | double precision, dimension( * ) | e,
|  | complex*16, dimension( * ) | tau,
|  | integer | info )

ZHPTRD

Download ZHPTRD + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZHPTRD reduces a complex Hermitian matrix A stored in packed form to
      !> real symmetric tridiagonal form T by a unitary similarity
      !> transformation: Q**H * A * Q = T.
      !>

Parameters

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          = 'U':  Upper triangle of A is stored;
      !>          = 'L':  Lower triangle of A is stored.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix A.  N >= 0.
      !>

  [in,out]

  AP

      !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
      !>          On entry, the upper or lower triangle of the Hermitian matrix
      !>          A, packed columnwise in a linear array.  The j-th column of A
      !>          is stored in the array AP as follows:
      !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
      !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
      !>          On exit, if UPLO = 'U', the diagonal and first superdiagonal
      !>          of A are overwritten by the corresponding elements of the
      !>          tridiagonal matrix T, and the elements above the first
      !>          superdiagonal, with the array TAU, represent the unitary
      !>          matrix Q as a product of elementary reflectors; if UPLO
      !>          = 'L', the diagonal and first subdiagonal of A are over-
      !>          written by the corresponding elements of the tridiagonal
      !>          matrix T, and the elements below the first subdiagonal, with
      !>          the array TAU, represent the unitary matrix Q as a product
      !>          of elementary reflectors. See Further Details.
      !>

  [out]

  D

      !>          D is DOUBLE PRECISION array, dimension (N)
      !>          The diagonal elements of the tridiagonal matrix T:
      !>          D(i) = A(i,i).
      !>

  [out]

  E

      !>          E is DOUBLE PRECISION array, dimension (N-1)
      !>          The off-diagonal elements of the tridiagonal matrix T:
      !>          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
      !>

  [out]

  TAU

      !>          TAU is COMPLEX*16 array, dimension (N-1)
      !>          The scalar factors of the elementary reflectors (see Further
      !>          Details).
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Further Details:

      !>
      !>  If UPLO = 'U', the matrix Q is represented as a product of elementary
      !>  reflectors
      !>
      !>     Q = H(n-1) . . . H(2) H(1).
      !>
      !>  Each H(i) has the form
      !>
      !>     H(i) = I - tau * v * v**H
      !>
      !>  where tau is a complex scalar, and v is a complex vector with
      !>  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
      !>  overwriting A(1:i-1,i+1), and tau is stored in TAU(i).
      !>
      !>  If UPLO = 'L', the matrix Q is represented as a product of elementary
      !>  reflectors
      !>
      !>     Q = H(1) H(2) . . . H(n-1).
      !>
      !>  Each H(i) has the form
      !>
      !>     H(i) = I - tau * v * v**H
      !>
      !>  where tau is a complex scalar, and v is a complex vector with
      !>  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
      !>  overwriting A(i+2:n,i), and tau is stored in TAU(i).
      !>