chptrd man page on YellowDog

Man page or keyword search:  
man Server   18644 pages
apropos Keyword Search (all sections)
Output format
YellowDog logo
[printable version]

CHPTRD(l)			       )			     CHPTRD(l)

NAME
       CHPTRD  -  reduce a complex Hermitian matrix A stored in packed form to
       real symmetric tridiagonal form T by a unitary  similarity  transforma‐
       tion

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   REAL		  D( * ), E( * )

	   COMPLEX	  AP( * ), TAU( * )

PURPOSE
       CHPTRD  reduces	a  complex Hermitian matrix A stored in packed form to
       real symmetric tridiagonal form T by a unitary  similarity  transforma‐
       tion: Q**H * 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) COMPLEX array, dimension (N*(N+1)/2)
	       On  entry,  the upper or lower triangle of the Hermitian 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  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 subdiag‐
	       onal,  with  the array TAU, represent the unitary matrix Q as a
	       product of  elementary  reflectors.  See	 Further  Details.   D
	       (output) REAL array, dimension (N) The diagonal elements of the
	       tridiagonal matrix T: D(i) = A(i,i).

       E       (output) 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     (output) COMPLEX 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 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  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 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 AP, overwriting
       A(i+2:n,i), and tau is stored in TAU(i).

LAPACK version 3.0		 15 June 2000			     CHPTRD(l)
[top]

List of man pages available for YellowDog

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net