ssptrd (3p)

Name

ssptrd - metric tridiagonal form T by an orthogonal similarity transformation

Synopsis

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);

Description

Oracle Solaris Studio Performance Library                           ssptrd(3P)



NAME
       ssptrd - reduce a real symmetric matrix A stored in packed form to sym-
       metric tridiagonal form T by an orthogonal similarity transformation


SYNOPSIS
       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);



PURPOSE
       ssptrd reduces a real symmetric matrix A stored in packed form to  sym-
       metric  tridiagonal  form T by an orthogonal similarity transformation:
       Q**T * 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)
                 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 tridi-
                 agonal 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)
                 Real array, dimension (N-1) The scalar factors of the elemen-
                 tary 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 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, overwrit-
       ing 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, overwrit-
       ing A(i+2:n,i), and tau is stored in TAU(i).




                                  7 Nov 2015                        ssptrd(3P)