
NAMEzhetd2.f SYNOPSISFunctions/Subroutinessubroutine zhetd2 (UPLO, N, A, LDA, D, E, TAU, INFO) Function/Subroutine Documentationsubroutine zhetd2 (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( * )TAU, integerINFO)ZHETD2 reduces a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm). Purpose:ZHETD2 reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. UPLO
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UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangularN N is INTEGER The order of the matrix A. N >= 0.A A is COMPLEX*16 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.LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).D D is DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i).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'.TAU TAU is COMPLEX*16 array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details).INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Further Details:
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). AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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