# dsbtrd.f - Man Page

SRC/dsbtrd.f

## Synopsis

### Functions/Subroutines

subroutine dsbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD

## Function/Subroutine Documentation

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

DSBTRD

Purpose:

``` DSBTRD reduces a real symmetric band matrix A to symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**T * 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 DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the upper or lower triangle of the symmetric 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 DOUBLE PRECISION 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 orthogonal 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 DOUBLE PRECISION 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

NAG Ltd.

Further Details:

`  Modified by Linda Kaufman, Bell Labs.`

Definition at line 161 of file dsbtrd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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