.TH ZHBTRD 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZHBTRD - a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation .SH SYNOPSIS .TP 19 SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO, VECT .TP 19 .ti +4 INTEGER INFO, KD, LDAB, LDQ, N .TP 19 .ti +4 DOUBLE PRECISION D( * ), E( * ) .TP 19 .ti +4 COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * ) .SH PURPOSE ZHBTRD reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. .br .SH ARGUMENTS .TP 8 VECT (input) CHARACTER*1 = \(aqN\(aq: do not form Q; .br = \(aqV\(aq: form Q; .br = \(aqU\(aq: update a matrix X, by forming X*Q. .TP 8 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq, or the number of subdiagonals if UPLO = \(aqL\(aq. KD >= 0. .TP 8 AB (input/output) COMPLEX*16 array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = \(aqU\(aq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = \(aqU\(aq) or the first subdiagonal (if UPLO = \(aqL\(aq) are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. .TP 8 D (output) DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T. .TP 8 E (output) DOUBLE PRECISION array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = \(aqU\(aq; E(i) = T(i+1,i) if UPLO = \(aqL\(aq. .TP 8 Q (input/output) COMPLEX*16 array, dimension (LDQ,N) On entry, if VECT = \(aqU\(aq, then Q must contain an N-by-N matrix X; if VECT = \(aqN\(aq or \(aqV\(aq, then Q need not be set. On exit: if VECT = \(aqV\(aq, Q contains the N-by-N unitary matrix Q; if VECT = \(aqU\(aq, Q contains the product X*Q; if VECT = \(aqN\(aq, the array Q is not referenced. .TP 8 LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = \(aqV\(aq or \(aqU\(aq. .TP 8 WORK (workspace) COMPLEX*16 array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .SH FURTHER DETAILS Modified by Linda Kaufman, Bell Labs. .br