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Интерактивная система просмотра системных руководств (man-ов)

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ssytrd (3)
  • >> ssytrd (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         ssytrd - reduce a real symmetric matrix A to real  symmetric
         tridiagonal  form  T by an orthogonal similarity transforma-
         tion
    
    SYNOPSIS
         SUBROUTINE SSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK,  LWORK,
                   INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, LDA, LWORK, N
    
         REAL A( LDA, * ), D( * ), E( * ), TAU( * ), WORK( * )
    
    
    
         #include <sunperf.h>
    
         void ssytrd(char uplo, int n, float *sa, int lda, float  *d,
                   float *e, float *tau, int *info) ;
    
    PURPOSE
         SSYTRD reduces a real symmetric matrix A to  real  symmetric
         tridiagonal  form  T by an orthogonal similarity transforma-
         tion:  Q**T * A * Q = T.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The order of the matrix A.  N >= 0.
    
         A         (input/output) REAL array, dimension (LDA,N)
                   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)
                   INTEGER The leading dimension of the array A.  LDA
                   >= max(1,N).
    
         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  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  elementary  reflectors
                   (see Further Details).
    
         WORK      (workspace/output) REAL array, dimension (LWORK)
                   On exit, if INFO = 0, WORK(1) returns the  optimal
                   LWORK.
    
         LWORK     (input) INTEGER
                   The dimension of the array WORK.  LWORK >= 1.  For
                   optimum performance LWORK >= N*NB, where NB is the
                   optimal blocksize.
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal 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
         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).
    
    
    
    


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