SRC/chptrd.f(3)

NAME
SRC/chptrd.f

SYNOPSIS

  Functions/Subroutines
subroutine chptrd (uplo, n, ap, d, e, tau, info)
CHPTRD

Function/Subroutine Documentation

  subroutine chptrd (character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( * ) tau, integer info)

CHPTRD

Purpose:

    !>
    !> CHPTRD 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
    UPLO

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

    N

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

    AP

    !>          AP is COMPLEX 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.
    !>

    D

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

    E

    !>          E is REAL 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'.
    !>

    TAU

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

    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).
    !>

Definition at line 150 of file chptrd.f.

Author

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