# dgbbrd.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dgbbrd.f

## SYNOPSIS

### Functions/Subroutines

subroutine dgbbrd (VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT, LDPT, C, LDC, WORK, INFO)
DGBBRD

## Function/Subroutine Documentation

### subroutine dgbbrd (character VECT, integer M, integer N, integer NCC, integer KL, integer KU, 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( ldpt, * ) PT, integer LDPT, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK, integer INFO)

DGBBRD

Purpose:

``` DGBBRD reduces a real general m-by-n band matrix A to upper
bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.

The routine computes B, and optionally forms Q or P**T, or computes
Q**T*C for a given matrix C.
```

Parameters:

VECT

```          VECT is CHARACTER*1
Specifies whether or not the matrices Q and P**T are to be
formed.
= 'N': do not form Q or P**T;
= 'Q': form Q only;
= 'P': form P**T only;
= 'B': form both.
```

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.
```

N

```          N is INTEGER
The number of columns of the matrix A.  N >= 0.
```

NCC

```          NCC is INTEGER
The number of columns of the matrix C.  NCC >= 0.
```

KL

```          KL is INTEGER
The number of subdiagonals of the matrix A. KL >= 0.
```

KU

```          KU is INTEGER
The number of superdiagonals of the matrix A. KU >= 0.
```

AB

```          AB is DOUBLE PRECISION array, dimension (LDAB,N)
On entry, the m-by-n band matrix A, stored in rows 1 to
KL+KU+1. The j-th column of A is stored in the j-th column of
the array AB as follows:
AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
On exit, A is overwritten by values generated during the
reduction.
```

LDAB

```          LDAB is INTEGER
The leading dimension of the array A. LDAB >= KL+KU+1.
```

D

```          D is DOUBLE PRECISION array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.
```

E

```          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
The superdiagonal elements of the bidiagonal matrix B.
```

Q

```          Q is DOUBLE PRECISION array, dimension (LDQ,M)
If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.
If VECT = 'N' or 'P', the array Q is not referenced.
```

LDQ

```          LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise.
```

PT

```          PT is DOUBLE PRECISION array, dimension (LDPT,N)
If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.
If VECT = 'N' or 'Q', the array PT is not referenced.
```

LDPT

```          LDPT is INTEGER
The leading dimension of the array PT.
LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise.
```

C

```          C is DOUBLE PRECISION array, dimension (LDC,NCC)
On entry, an m-by-ncc matrix C.
On exit, C is overwritten by Q**T*C.
C is not referenced if NCC = 0.
```

LDC

```          LDC is INTEGER
The leading dimension of the array C.
LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0.
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (2*max(M,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