Contents
ssptrd - reduce a real symmetric matrix A stored in packed
form to symmetric tridiagonal form T by an orthogonal simi-
larity transformation
SUBROUTINE SSPTRD(UPLO, N, AP, D, E, TAU, INFO)
CHARACTER * 1 UPLO
INTEGER N, INFO
REAL AP(*), D(*), E(*), TAU(*)
SUBROUTINE SSPTRD_64(UPLO, N, AP, D, E, TAU, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, INFO
REAL AP(*), D(*), E(*), TAU(*)
F95 INTERFACE
SUBROUTINE SPTRD(UPLO, [N], AP, D, E, TAU, [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, INFO
REAL, DIMENSION(:) :: AP, D, E, TAU
SUBROUTINE SPTRD_64(UPLO, [N], AP, D, E, TAU, [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, INFO
REAL, DIMENSION(:) :: AP, D, E, TAU
C INTERFACE
#include <sunperf.h>
void ssptrd(char uplo, int n, float *ap, float *d, float *e,
float *tau, int *info);
void ssptrd_64(char uplo, long n, float *ap, float *d, float
*e, float *tau, long *info);
ssptrd reduces a real symmetric matrix A stored in packed
form to symmetric tridiagonal form T by an orthogonal simi-
larity 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.
AP (input)
Real array, dimension (N*(N+1)/2) On entry, the
upper or lower triangle of the symmetric 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 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 tridiagonal 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.
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 ele-
ments 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)
Real 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 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 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 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 AP,
overwriting A(i+2:n,i), and tau is stored in TAU(i).