# zhbtrd.f(3) [centos man page]

zhbtrd.f(3) LAPACK zhbtrd.f(3)NAME

zhbtrd.f-SYNOPSIS

Functions/Subroutines subroutine zhbtrd (VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO) ZHBTRDFunction/Subroutine Documentation subroutine zhbtrd (characterVECT, characterUPLO, integerN, integerKD, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )D, double precision, dimension( * )E, complex*16, dimension( ldq, * )Q, integerLDQ, complex*16, dimension( * )WORK, integerINFO) ZHBTRD 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. Parameters: VECT VECT is CHARACTER*1 = 'N': do not form Q; = 'V': form Q; = 'U': update a matrix X, by forming X*Q. UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. KD KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB AB is 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', 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 = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1. D D is DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T. E E is DOUBLE PRECISION array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. Q Q is COMPLEX*16 array, dimension (LDQ,N) On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set. On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q is not referenced. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. WORK WORK is COMPLEX*16 array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Further Details: Modified by Linda Kaufman, Bell Labs. Definition at line 163 of file zhbtrd.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 zhbtrd.f(3)

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ZHBTRD(l)) ZHBTRD(l)NAME

ZHBTRD - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformationSYNOPSIS

SUBROUTINE ZHBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO ) CHARACTER UPLO, VECT INTEGER INFO, KD, LDAB, LDQ, N DOUBLE PRECISION D( * ), E( * ) COMPLEX*16 AB( LDAB, * ), Q( LDQ, * ), WORK( * )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.ARGUMENTS

VECT (input) CHARACTER*1 = 'N': do not form Q; = 'V': form Q; = 'U': update a matrix X, by forming X*Q. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. 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 = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', 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 ele- ments of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduc- tion. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. D (output) DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T. 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 = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. Q (input/output) COMPLEX*16 array, dimension (LDQ,N) On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set. On exit: if VECT = 'V', Q contains the N-by-N unitary matrix Q; if VECT = 'U', Q contains the product X*Q; if VECT = 'N', the array Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. WORK (workspace) COMPLEX*16 array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iFURTHER DETAILS

Modified by Linda Kaufman, Bell Labs.LAPACK version 3.015 June 2000 ZHBTRD(l)