LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  chetrd (UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) 
CHETRD 
subroutine chetrd  (  character  UPLO, 
integer  N,  
complex, dimension( lda, * )  A,  
integer  LDA,  
real, dimension( * )  D,  
real, dimension( * )  E,  
complex, dimension( * )  TAU,  
complex, dimension( * )  WORK,  
integer  LWORK,  
integer  INFO  
) 
CHETRD
Download CHETRD + dependencies [TGZ] [ZIP] [TXT]CHETRD reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * 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 COMPLEX array, dimension (LDA,N) On entry, the Hermitian 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 unitary 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 unitary 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 REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). 
[out]  E  E is REAL 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 COMPLEX array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[out]  WORK  WORK is COMPLEX 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**H where tau is a complex scalar, and v is a complex 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**H where tau is a complex scalar, and v is a complex 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 193 of file chetrd.f.