Contents
chptrd - reduce a complex Hermitian matrix A stored in
packed form to real symmetric tridiagonal form T by a uni-
tary similarity transformation
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, complex *tau, long *info);
chptrd reduces a complex Hermitian matrix A stored in packed
form to real symmetric tridiagonal form T by a unitary simi-
larity transformation: Q**H * A * Q = T.
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) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Her-
mitian 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 superdiago-
nal of A are overwritten by the corresponding ele-
ments of the tridiagonal matrix T, and the ele-
ments 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 tri-
diagonal 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 ille-
gal value
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).