# zhbtrd.f - Man Page

SRC/zhbtrd.f

## Synopsis

### Functions/Subroutines

subroutine **zhbtrd** (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)**ZHBTRD**

## Function/Subroutine Documentation

### subroutine zhbtrd (character vect, character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work, integer info)

**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 = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Modified by Linda Kaufman, Bell Labs.

Definition at line **161** of file **zhbtrd.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zhbtrd(3) is an alias of zhbtrd.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK