.TH "SRC/sgbtf2.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/sgbtf2.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsgbtf2\fP (m, n, kl, ku, ab, ldab, ipiv, info)"
.br
.RI "\fBSGBTF2\fP computes the LU factorization of a general band matrix using the unblocked version of the algorithm\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgbtf2 (integer m, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, integer info)"

.PP
\fBSGBTF2\fP computes the LU factorization of a general band matrix using the unblocked version of the algorithm\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SGBTF2 computes an LU factorization of a real m-by-n band matrix A
!> using partial pivoting with row interchanges\&.
!>
!> This is the unblocked version of the algorithm, calling Level 2 BLAS\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIKL\fP 
.PP
.nf
!>          KL is INTEGER
!>          The number of subdiagonals within the band of A\&.  KL >= 0\&.
!> 
.fi
.PP
.br
\fIKU\fP 
.PP
.nf
!>          KU is INTEGER
!>          The number of superdiagonals within the band of A\&.  KU >= 0\&.
!> 
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
!>          AB is REAL array, dimension (LDAB,N)
!>          On entry, the matrix A in band storage, in rows KL+1 to
!>          2*KL+KU+1; rows 1 to KL of the array need not be set\&.
!>          The j-th column of A is stored in the j-th column of the
!>          array AB as follows:
!>          AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
!>
!>          On exit, details of the factorization: U is stored as an
!>          upper triangular band matrix with KL+KU superdiagonals in
!>          rows 1 to KL+KU+1, and the multipliers used during the
!>          factorization are stored in rows KL+KU+2 to 2*KL+KU+1\&.
!>          See below for further details\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= 2*KL+KU+1\&.
!> 
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
!>          IPIV is INTEGER array, dimension (min(M,N))
!>          The pivot indices; for 1 <= i <= min(M,N), row i of the
!>          matrix was interchanged with row IPIV(i)\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!>          > 0: if INFO = +i, U(i,i) is exactly zero\&. The factorization
!>               has been completed, but the factor U is exactly
!>               singular, and division by zero will occur if it is used
!>               to solve a system of equations\&.
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
!>
!>  The band storage scheme is illustrated by the following example, when
!>  M = N = 6, KL = 2, KU = 1:
!>
!>  On entry:                       On exit:
!>
!>      *    *    *    +    +    +       *    *    *   u14  u25  u36
!>      *    *    +    +    +    +       *    *   u13  u24  u35  u46
!>      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
!>     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
!>     a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
!>     a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
!>
!>  Array elements marked * are not used by the routine; elements marked
!>  + need not be set on entry, but are required by the routine to store
!>  elements of U, because of fill-in resulting from the row
!>  interchanges\&.
!> 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB144\fP of file \fBsgbtf2\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.