SRC/dsptrd.f(3)            Library Functions Manual            SRC/dsptrd.f(3)

NAME
       SRC/dsptrd.f

SYNOPSIS
   Functions/Subroutines
       subroutine dsptrd (uplo, n, ap, d, e, tau, info)
           DSPTRD

Function/Subroutine Documentation
   subroutine dsptrd (character uplo, integer n, double precision, dimension(
       * ) ap, double precision, dimension( * ) d, double precision,
       dimension( * ) e, double precision, dimension( * ) tau, integer info)
       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.

       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 149 of file dsptrd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/dsptrd.f(3)