# sgbbrd.f man page

sgbbrd.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine sgbbrd (characterVECT, integerM, integerN, integerNCC, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( * )D, real, dimension( * )E, real, dimension( ldq, * )Q, integerLDQ, real, dimension( ldpt, * )PT, integerLDPT, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK, integerINFO)

**SGBBRD**

**Purpose:**

```
SGBBRD 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 REAL 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 REAL array, dimension (min(M,N))
The diagonal elements of the bidiagonal matrix B.
```

*E*

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

*Q*

```
Q is REAL 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 REAL 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 REAL 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 REAL 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 187 of file sgbbrd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

sgbbrd(3) is an alias of sgbbrd.f(3).