---
name: "chbtrd.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/chbtrd.f"
---

# chbtrd.f(3)

## NAME

SRC/chbtrd.f

## SYNOPSIS

### Functions/Subroutines

subroutine **chbtrd** (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)\
 **CHBTRD**

## Function/Subroutine Documentation

### subroutine chbtrd (character vect, character uplo, integer n, integer kd, complex, dimension( ldab, \* ) ab, integer ldab, real, dimension( \* ) d, real, dimension( \* ) e, complex, dimension( ldq, \* ) q, integer ldq, complex, dimension( \* ) work, integer info)

**CHBTRD**

**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.
!>
```

**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 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 REAL array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T.
!>
```

*E*

```
!>          E is 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*

```
!>          Q is 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*

```
!>          LDQ is INTEGER
!>          The leading dimension of the array Q.
!>          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
!>
```

*WORK*

```
!>          WORK is COMPLEX 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 **chbtrd.f**.

## Author

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