slatrd.f(3)							      LAPACK							       slatrd.f(3)

NAME

       slatrd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slatrd (UPLO, N, NB, A, LDA, E, TAU, W, LDW)
	   SLATRD

Function/Subroutine Documentation
   subroutine slatrd (characterUPLO, integerN, integerNB, real, dimension( lda, * )A, integerLDA, real, dimension( * )E, real, dimension( * )TAU,
       real, dimension( ldw, * )W, integerLDW)
       SLATRD

       Purpose:

	    SLATRD reduces NB rows and columns of a real symmetric matrix A to
	    symmetric tridiagonal form by an orthogonal similarity
	    transformation Q**T * A * Q, and returns the matrices V and W which are
	    needed to apply the transformation to the unreduced part of A.

	    If UPLO = 'U', SLATRD reduces the last NB rows and columns of a
	    matrix, of which the upper triangle is supplied;
	    if UPLO = 'L', SLATRD reduces the first NB rows and columns of a
	    matrix, of which the lower triangle is supplied.

	    This is an auxiliary routine called by SSYTRD.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     Specifies whether the upper or lower triangular part of the
		     symmetric matrix A is stored:
		     = 'U': Upper triangular
		     = 'L': Lower triangular

	   N

		     N is INTEGER
		     The order of the matrix A.

	   NB

		     NB is INTEGER
		     The number of rows and columns to be reduced.

	   A

		     A is REAL array, dimension (LDA,N)
		     On entry, the symmetric matrix A.	If UPLO = 'U', the leading
		     n-by-n upper triangular part of A contains the upper
		     triangular 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 last NB columns have been reduced to
		       tridiagonal form, with the diagonal elements overwriting
		       the diagonal elements of A; the elements above the diagonal
		       with the array TAU, represent the orthogonal matrix Q as a
		       product of elementary reflectors;
		     if UPLO = 'L', the first NB columns have been reduced to
		       tridiagonal form, with the diagonal elements overwriting
		       the diagonal elements of A; the elements below the diagonal
		       with the array TAU, represent the  orthogonal matrix Q as a
		       product of elementary reflectors.
		     See Further Details.

	   LDA

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

	   E

		     E is REAL array, dimension (N-1)
		     If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
		     elements of the last NB columns of the reduced matrix;
		     if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
		     the first NB columns of the reduced matrix.

	   TAU

		     TAU is REAL array, dimension (N-1)
		     The scalar factors of the elementary reflectors, stored in
		     TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
		     See Further Details.

	   W

		     W is REAL array, dimension (LDW,NB)
		     The n-by-nb matrix W required to update the unreduced part
		     of A.

	   LDW

		     LDW is INTEGER
		     The leading dimension of the array W. LDW >= max(1,N).

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     If UPLO = 'U', the matrix Q is represented as a product of elementary
	     reflectors

		Q = H(n) H(n-1) . . . H(n-nb+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:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
	     and tau in TAU(i-1).

	     If UPLO = 'L', the matrix Q is represented as a product of elementary
	     reflectors

		Q = H(1) H(2) . . . H(nb).

	     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+1:n) is stored on exit in A(i+1:n,i),
	     and tau in TAU(i).

	     The elements of the vectors v together form the n-by-nb matrix V
	     which is needed, with W, to apply the transformation to the unreduced
	     part of the matrix, using a symmetric rank-2k update of the form:
	     A := A - V*W**T - W*V**T.

	     The contents of A on exit are illustrated by the following examples
	     with n = 5 and nb = 2:

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

	       (  a   a   a   v4  v5 )		    (  d		  )
	       (      a   a   v4  v5 )		    (  1   d		  )
	       (	  a   1   v5 )		    (  v1  1   a	  )
	       (	      d   1  )		    (  v1  v2  a   a	  )
	       (		  d  )		    (  v1  v2  a   a   a  )

	     where d denotes a diagonal element of the reduced matrix, a denotes
	     an element of the original matrix that is unchanged, and vi denotes
	     an element of the vector defining H(i).

       Definition at line 199 of file slatrd.f.

Author
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Version 3.4.1							  Sun May 26 2013						       slatrd.f(3)