---
name: "chbtrd"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/chbtrd/3lapack"
---

# chbtrd(3lapack)

reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

## NAME

CHBTRD - reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation

## SYNOPSIS

- SUBROUTINE CHBTRD(

  VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO )

- CHARACTER

  UPLO, VECT

- INTEGER

  INFO, KD, LDAB, LDQ, N

- REAL

  D( \* ), E( \* )

- COMPLEX

  AB( LDAB, \* ), Q( LDQ, \* ), WORK( \* )

## PURPOSE

CHBTRD 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 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 (input) INTEGER

  The leading dimension of the array AB.  LDAB \>= KD+1.

- D (output) REAL array, dimension (N)

  The diagonal elements of the tridiagonal matrix T.

- E (output) REAL 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 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 array, dimension (N)

  - INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value

## FURTHER DETAILS

Modified by Linda Kaufman, Bell Labs.\