zhetd2 (l)  Linux Man Pages
zhetd2: reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation
NAME
ZHETD2  reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformationSYNOPSIS
 SUBROUTINE ZHETD2(
 UPLO, N, A, LDA, D, E, TAU, INFO )
 CHARACTER UPLO
 INTEGER INFO, LDA, N
 DOUBLE PRECISION D( * ), E( * )
 COMPLEX*16 A( LDA, * ), TAU( * )
PURPOSE
ZHETD2 reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Qaq * A * Q = T.ARGUMENTS
 UPLO (input) CHARACTER*1

Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored:
= aqUaq: Upper triangular
= aqLaq: Lower triangular  N (input) INTEGER
 The order of the matrix A. N >= 0.
 A (input/output) COMPLEX*16 array, dimension (LDA,N)
 On entry, the Hermitian matrix A. If UPLO = aqUaq, 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 = aqLaq, 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 = aqUaq, 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 = aqLaq, 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 (input) INTEGER The leading dimension of the array A. LDA >= max(1,N).
 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 (N1)
 The offdiagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = aqUaq, E(i) = A(i+1,i) if UPLO = aqLaq.
 TAU (output) COMPLEX*16 array, dimension (N1)
 The scalar factors of the elementary reflectors (see Further Details).
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
FURTHER DETAILS
If UPLO = aqUaq, the matrix Q is represented as a product of elementary reflectorsQ
Each H(i) has the form
H(i)
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 = aqLaq, the matrix Q is represented as a product of elementary reflectors
Q
Each H(i) has the form
H(i)
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 = aqUaq: if UPLO = aqLaq: