zhptrd(3P) Sun Performance Library zhptrd(3P)NAMEzhptrd - reduce a complex Hermitian matrix A stored in packed form to
real symmetric tridiagonal form T by a unitary similarity transforma‐
tion
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);
PURPOSEzhptrd 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*16 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) DOUBLE PRECISION array, dimension (N)
The diagonal elements of the tridiagonal matrix T: D(i) =
A(i,i).
E (output) DOUBLE PRECISION 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*16 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 zhptrd(3P)