redhat man page for dsptrd

DSPTRD(l)								 )								 DSPTRD(l)

NAME
       DSPTRD - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity transformation

SYNOPSIS
       SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION AP( * ), D( * ), E( * ), TAU( * )

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.

ARGUMENTS
       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

       N       (input) INTEGER
	       The order of the matrix A.  N >= 0.

       AP      (input/output) 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  ele-
	       ments  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	(output) DOUBLE PRECISION array, dimension
	       (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).

       E       (output) 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     (output) DOUBLE PRECISION array, dimension (N-1)
	       The scalar factors of the elementary reflectors (see Further Details).

       INFO    (output) INTEGER
	       = 0:  successful exit
	       < 0:  if INFO = -i, the i-th argument had an illegal value

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'

       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'

       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).

LAPACK version 3.0						   15 June 2000 							 DSPTRD(l)