---
name: "sgbbrd.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/sgbbrd.f"
---

# sgbbrd.f(3)

## NAME

SRC/sgbbrd.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sgbbrd** (vect, m, n, ncc, kl, ku, ab, ldab, d, e, q, ldq, pt, ldpt, c, ldc, work, info)\
 **SGBBRD**

## Function/Subroutine Documentation

### subroutine sgbbrd (character vect, integer m, integer n, integer ncc, integer kl, integer ku, real, dimension( ldab, \* ) ab, integer ldab, real, dimension( \* ) d, real, dimension( \* ) e, real, dimension( ldq, \* ) q, integer ldq, real, dimension( ldpt, \* ) pt, integer ldpt, real, dimension( ldc, \* ) c, integer ldc, real, dimension( \* ) work, integer info)

**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.

Definition at line **185** of file **sgbbrd.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.