CentOS 7.0 - man page for chetd2 (centos section 3)

Linux & Unix Commands - Search Man Pages

Man Page or Keyword Search:   man
Select Man Page Set:       apropos Keyword Search (sections above)


chetd2.f(3)				      LAPACK				      chetd2.f(3)

NAME
       chetd2.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chetd2 (UPLO, N, A, LDA, D, E, TAU, INFO)
	   CHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary
	   similarity transformation (unblocked algorithm).

Function/Subroutine Documentation
   subroutine chetd2 (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real,
       dimension( * )D, real, dimension( * )E, complex, dimension( * )TAU, integerINFO)
       CHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary
       similarity transformation (unblocked algorithm).

       Purpose:

	    CHETD2 reduces a complex Hermitian matrix A to real symmetric
	    tridiagonal form T by a unitary similarity transformation:
	    Q**H * A * Q = T.

       Parameters:
	   UPLO

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

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   A

		     A is COMPLEX array, dimension (LDA,N)
		     On entry, the Hermitian 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 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 unitary
		     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 unitary matrix Q as a product
		     of elementary reflectors. See Further Details.

	   LDA

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

	   D

		     D is REAL array, dimension (N)
		     The diagonal elements of the tridiagonal matrix T:
		     D(i) = A(i,i).

	   E

		     E is REAL 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 COMPLEX 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.

       Date:
	   September 2012

       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**H

	     where tau is a complex scalar, and v is a complex 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**H

	     where tau is a complex scalar, and v is a complex 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).

       Definition at line 176 of file chetd2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      chetd2.f(3)
Unix & Linux Commands & Man Pages : ©2000 - 2018 Unix and Linux Forums


All times are GMT -4. The time now is 12:42 PM.

Unix & Linux Forums Content Copyright©1993-2018. All Rights Reserved.
×
UNIX.COM Login
Username:
Password:  
Show Password





Not a Forum Member?
Forgot Password?