ssptrd - reduce a real symmetric matrix A stored in packed form to symmetric tridiagonal form T by an orthogonal similarity 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(*)
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
#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 similarity transformation: Q**T * A * Q = T.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
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(i)
= A(i,i).
E(i)
= A(i,i+1)
if UPLO = 'U', E(i)
= A(i+1,i)
if UPLO = 'L'.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal 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).