dsptrd (3p)

Name

dsptrd - metric tridiagonal form T by an orthogonal similarity transformation

Synopsis

SUBROUTINE DSPTRD(UPLO, N, AP, D, E, TAU, INFO)

CHARACTER*1 UPLO
INTEGER N, INFO
DOUBLE PRECISION AP(*), D(*), E(*), TAU(*)

SUBROUTINE DSPTRD_64(UPLO, N, AP, D, E, TAU, INFO)

CHARACTER*1 UPLO
INTEGER*8 N, INFO
DOUBLE PRECISION AP(*), D(*), E(*), TAU(*)




F95 INTERFACE
SUBROUTINE SPTRD(UPLO, N, AP, D, E, TAU, INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER :: N, INFO
REAL(8), DIMENSION(:) :: AP, D, E, TAU

SUBROUTINE SPTRD_64(UPLO, N, AP, D, E, TAU, INFO)

CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, INFO
REAL(8), DIMENSION(:) :: AP, D, E, TAU




C INTERFACE
#include <sunperf.h>

void dsptrd(char uplo, int n, double *ap, double *d, double *e,  double
*tau, int *info);

void  dsptrd_64(char  uplo,  long  n, double *ap, double *d, double *e,
double *tau, long *info);

Description

Oracle Solaris Studio Performance Library                           dsptrd(3P)



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


SYNOPSIS
       SUBROUTINE DSPTRD(UPLO, N, AP, D, E, TAU, INFO)

       CHARACTER*1 UPLO
       INTEGER N, INFO
       DOUBLE PRECISION AP(*), D(*), E(*), TAU(*)

       SUBROUTINE DSPTRD_64(UPLO, N, AP, D, E, TAU, INFO)

       CHARACTER*1 UPLO
       INTEGER*8 N, INFO
       DOUBLE PRECISION AP(*), D(*), E(*), TAU(*)




   F95 INTERFACE
       SUBROUTINE SPTRD(UPLO, N, AP, D, E, TAU, INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER :: N, INFO
       REAL(8), DIMENSION(:) :: AP, D, E, TAU

       SUBROUTINE SPTRD_64(UPLO, N, AP, D, E, TAU, INFO)

       CHARACTER(LEN=1) :: UPLO
       INTEGER(8) :: N, INFO
       REAL(8), DIMENSION(:) :: AP, D, E, TAU




   C INTERFACE
       #include <sunperf.h>

       void dsptrd(char uplo, int n, double *ap, double *d, double *e,  double
                 *tau, int *info);

       void  dsptrd_64(char  uplo,  long  n, double *ap, double *d, double *e,
                 double *tau, long *info);



PURPOSE
       dsptrd 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)
                 Double precision 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  corre-
                 sponding  elements  of the tridiagonal matrix T, and the ele-
                 ments above the first superdiagonal, with the array TAU, rep-
                 resent  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 subdi-
                 agonal, with the array TAU, represent the orthogonal matrix Q
                 as a product of elementary reflectors. See Further Details.


       D (output)
                 Double precision array, dimension (N) The  diagonal  elements
                 of the tridiagonal matrix T: D(i) = A(i,i).


       E (output)
                 Double precision 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)
                 Double precision 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 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                        dsptrd(3P)