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dsytd2(3P)		    Sun Performance Library		    dsytd2(3P)

NAME
       dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form
       T by an orthogonal similarity transformation

SYNOPSIS
       SUBROUTINE DSYTD2(UPLO, N, A, LDA, D, E, TAU, INFO)

       CHARACTER * 1 UPLO
       INTEGER N, LDA, INFO
       DOUBLE PRECISION A(LDA,*), D(*), E(*), TAU(*)

       SUBROUTINE DSYTD2_64(UPLO, N, A, LDA, D, E, TAU, INFO)

       CHARACTER * 1 UPLO
       INTEGER*8 N, LDA, INFO
       DOUBLE PRECISION A(LDA,*), D(*), E(*), TAU(*)

   F95 INTERFACE
       SUBROUTINE SYTD2(UPLO, N, A, [LDA], D, E, TAU, [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, LDA, INFO
       REAL(8), DIMENSION(:) :: D, E, TAU
       REAL(8), DIMENSION(:,:) :: A

       SUBROUTINE SYTD2_64(UPLO, N, A, [LDA], D, E, TAU, [INFO])

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, LDA, INFO
       REAL(8), DIMENSION(:) :: D, E, TAU
       REAL(8), DIMENSION(:,:) :: A

   C INTERFACE
       #include <sunperf.h>

       void dsytd2(char uplo, int n, double *a, int lda, double *d, double *e,
		 double *tau, int *info);

       void  dsytd2_64(char uplo, long n, double *a, long lda, double *d, dou‐
		 ble *e, double *tau, long *info);

PURPOSE
       dsytd2 reduces a real symmetric matrix A to symmetric tridiagonal  form
       T by an orthogonal similarity transformation: Q' * A * Q = T.

ARGUMENTS
       UPLO (input)
		 Specifies  whether  the upper or lower triangular part of the
		 symmetric matrix A is stored:
		 = 'U':	 Upper triangular
		 = 'L':	 Lower triangular

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

       A (input) On entry, the symmetric matrix A.  If UPLO = 'U', the leading
		 n-by-n upper triangular part of A contains the upper triangu‐
		 lar part of the matrix A, and the strictly  lower  triangular
		 part  of  A is not referenced.	 If UPLO = 'L', the leading n-
		 by-n lower triangular part of A contains the lower triangular
		 part  of the matrix A, and the strictly upper triangular part
		 of A is not referenced.  On exit, if UPLO = 'U', the diagonal
		 and  first  superdiagonal  of A are overwritten by the corre‐
		 sponding elements of the tridiagonal matrix T, and  the  ele‐
		 ments above the first superdiagonal, with the array TAU, rep‐
		 resent 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 subdi‐
		 agonal, with the array TAU, represent the orthogonal matrix Q
		 as a product of elementary reflectors. See Further Details.

       LDA (input)
		 The leading dimension of the array A.	LDA >= max(1,N).

       D (output)
		 The  diagonal	elements  of  the tridiagonal matrix T: D(i) =
		 A(i,i).

       E (output)
		 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)
		 The  scalar factors of the elementary reflectors (see Further
		 Details).

       INFO (output)
		 = 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
       A(1:i-1,i+1), and tau 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  A(i+2:n,i),
       and tau in TAU(i).

       The  contents  of  A  on exit are illustrated by the following examples
       with n = 5:

       if UPLO = 'U':			    if UPLO = 'L':

	 (  d	e   v2	v3  v4 )	      (	 d		    )
	 (	d   e	v3  v4 )	      (	 e   d		    )
	 (	    d	e   v4 )	      (	 v1  e	 d	    )
	 (		d   e  )	      (	 v1  v2	 e   d	    )
	 (		    d  )	      (	 v1  v2	 v3  e	 d  )

       where d and e denote diagonal and off-diagonal elements of  T,  and  vi
       denotes an element of the vector defining H(i).

				  6 Mar 2009			    dsytd2(3P)
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