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RedHat 9 (Linux i386) - man page for dsptrd (redhat section l)

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 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 reflec-
	       tors; 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)


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