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chptrd(3P)		    Sun Performance Library		    chptrd(3P)

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 * 1 UPLO
       COMPLEX AP(*), TAU(*)
       INTEGER N, INFO
       REAL D(*), E(*)

       SUBROUTINE CHPTRD_64(UPLO, N, AP, D, E, TAU, INFO)

       CHARACTER * 1 UPLO
       COMPLEX AP(*), TAU(*)
       INTEGER*8 N, INFO
       REAL D(*), E(*)

   F95 INTERFACE
       SUBROUTINE HPTRD(UPLO, [N], AP, D, E, TAU, [INFO])

       CHARACTER(LEN=1) :: UPLO
       COMPLEX, DIMENSION(:) :: AP, TAU
       INTEGER :: N, INFO
       REAL, DIMENSION(:) :: D, E

       SUBROUTINE HPTRD_64(UPLO, [N], AP, D, E, TAU, [INFO])

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

   C INTERFACE
       #include <sunperf.h>

       void  chptrd(char uplo, int n, complex *ap, float *d, float *e, complex
		 *tau, int *info);

       void chptrd_64(char uplo, long n, complex *ap, float *d, float *e, com‐
		 plex *tau, long *info);

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)
		 = 'U':	 Upper triangle of A is stored;
		 = 'L':	 Lower triangle of A is stored.

       N (input) 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  overwrit‐
		 ten  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 ele‐
		 ments 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.

       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)
		 = 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).

				  6 Mar 2009			    chptrd(3P)
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