Contents
ssytrd - reduce a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transforma-
tion
SUBROUTINE SSYTRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
CHARACTER * 1 UPLO
INTEGER N, LDA, LWORK, INFO
REAL A(LDA,*), D(*), E(*), TAU(*), WORK(*)
SUBROUTINE SSYTRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, LDA, LWORK, INFO
REAL A(LDA,*), D(*), E(*), TAU(*), WORK(*)
F95 INTERFACE
SUBROUTINE SYTRD(UPLO, N, A, [LDA], D, E, TAU, [WORK], [LWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: D, E, TAU, WORK
REAL, DIMENSION(:,:) :: A
SUBROUTINE SYTRD_64(UPLO, N, A, [LDA], D, E, TAU, [WORK], [LWORK],
[INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: D, E, TAU, WORK
REAL, DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void ssytrd(char uplo, int n, float *a, int lda, float *d,
float *e, float *tau, int *info);
void ssytrd_64(char uplo, long n, float *a, long lda, float
*d, float *e, float *tau, long *info);
ssytrd reduces a real symmetric matrix A to real symmetric
tridiagonal form T by an orthogonal similarity
transformation: Q**T * 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.
A (input) On entry, the symmetric matrix A. If UPLO = 'U',
the leading N-by-N upper triangular part of A con-
tains the upper triangular part of the matrix A,
and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading N-by-N
lower triangular part of A contains the lower tri-
angular part of the matrix A, and the strictly
upper triangular part of A is not referenced. On
exit, if UPLO = 'U', the diagonal and first super-
diagonal of A are overwritten by the corresponding
elements of the tridiagonal matrix T, and the ele-
ments above the first superdiagonal, with the
array TAU, represent the orthogonal 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 orthogonal matrix Q as a product of elementary
reflectors. See Further Details.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
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).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= 1. For
optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
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 real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau 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 real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in
A(i+2:n,i), and tau in TAU(i).
The contents of A on exit are illustrated by the following
examples with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d
)
( d e v3 v4 ) ( e d
)
( d e v4 ) ( v1 e d
)
( d e ) ( v1 v2 e d
)
( d ) ( v1 v2 v3 e d
)
where d and e denote diagonal and off-diagonal elements of
T, and vi denotes an element of the vector defining H(i).