dsptrd.f(3)

NAME
dsptrd.f -

SYNOPSIS

  Functions/Subroutines

subroutine dsptrd (UPLO, N, AP, D, E, TAU, INFO)
DSPTRD

Function/Subroutine Documentation

  subroutine dsptrd (characterUPLO, integerN, double precision, dimension( * )AP, double precision, dimension( * )D, double precision, dimension( * )E, double precision, dimension( * )TAU, integerINFO)

DSPTRD

Purpose:

     DSPTRD reduces a real symmetric matrix A stored in packed form to
     symmetric tridiagonal form T by an orthogonal similarity
     transformation: Q**T * 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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
              On entry, the upper or lower triangle of the symmetric 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 orthogonal
              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 orthogonal matrix Q as a product
              of elementary reflectors. See Further Details.

    D

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

    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'.

    TAU

              TAU is DOUBLE PRECISION 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.

Date:
    November 2011

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**T

      where tau is a real scalar, and v is a real 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**T

      where tau is a real scalar, and v is a real 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 151 of file dsptrd.f.

Author

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