# sgbbrd.f - Man Page

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.

## Referenced By

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

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