zhptrd

NAME

zhptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation

SYNOPSIS

  SUBROUTINE ZHPTRD( UPLO, N, AP, D, E, TAU, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX AP(*), TAU(*)
  INTEGER N, INFO
  DOUBLE PRECISION D(*), E(*)
 
  SUBROUTINE ZHPTRD_64( UPLO, N, AP, D, E, TAU, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX AP(*), TAU(*)
  INTEGER*8 N, INFO
  DOUBLE PRECISION D(*), E(*)

F95 INTERFACE

  SUBROUTINE HPTRD( UPLO, [N], AP, D, E, TAU, [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:) :: AP, TAU
  INTEGER :: N, INFO
  REAL(8), DIMENSION(:) :: D, E
 
  SUBROUTINE HPTRD_64( UPLO, [N], AP, D, E, TAU, [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:) :: AP, TAU
  INTEGER(8) :: N, INFO
  REAL(8), DIMENSION(:) :: D, E

C INTERFACE

#include <sunperf.h>

void zhptrd(char uplo, int n, doublecomplex *ap, double *d, double *e, doublecomplex *tau, int *info);

void zhptrd_64(char uplo, long n, doublecomplex *ap, double *d, double *e, doublecomplex *tau, long *info);

PURPOSE

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

ARGUMENTS

* UPLO (input)
* N (input): The order of the matrix A. N >= 0.
* AP (input): 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
* 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)