LAPACK 3.12.0
LAPACK: Linear Algebra PACKage

subroutine dsytrd  (  character  uplo, 
integer  n,  
double precision, dimension( lda, * )  a,  
integer  lda,  
double precision, dimension( * )  d,  
double precision, dimension( * )  e,  
double precision, dimension( * )  tau,  
double precision, dimension( * )  work,  
integer  lwork,  
integer  info  
) 
DSYTRD
Download DSYTRD + dependencies [TGZ] [ZIP] [TXT]
DSYTRD reduces a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation: Q**T * A * Q = T.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in,out]  A  A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading NbyN upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading NbyN lower triangular part of A contains the lower triangular 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 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. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[out]  D  D is DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). 
[out]  E  E is DOUBLE PRECISION array, dimension (N1) The offdiagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. 
[out]  TAU  TAU is DOUBLE PRECISION array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[out]  WORK  WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. 
[in]  LWORK  LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n1) . . . H(2) H(1). Each H(i) has the form H(i) = I  tau * v * v**T where tau is a real scalar, and v is a real vector with v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in A(1:i1,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(n1). Each H(i) has the form H(i) = I  tau * v * v**T 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 offdiagonal elements of T, and vi denotes an element of the vector defining H(i).
Definition at line 191 of file dsytrd.f.