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
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LAPACK                          Version 3.12.0                 SRC/dsptrd.f(3)