.TH "dgbsv.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
dgbsv.f \- 
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdgbsv\fP (N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO)"
.br
.RI "\fI\fB DGBSV computes the solution to system of linear equations A * X = B for GB matrices\fP (simple driver) \fP"
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dgbsv (integerN, integerKL, integerKU, integerNRHS, double precision, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, integerINFO)"

.PP
\fB DGBSV computes the solution to system of linear equations A * X = B for GB matrices\fP (simple driver)  
.PP
\fBPurpose: \fP
.RS 4

.PP
.nf
 DGBSV computes the solution to a real system of linear equations
 A * X = B, where A is a band matrix of order N with KL subdiagonals
 and KU superdiagonals, and X and B are N-by-NRHS matrices.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as A = L * U, where L is a product of permutation
 and unit lower triangular matrices with KL subdiagonals, and U is
 upper triangular with KL+KU superdiagonals.  The factored form of A
 is then used to solve the system of equations A * X = B.
.fi
.PP
 
.RE
.PP
\fBParameters:\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of linear equations, i.e., the order 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
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is DOUBLE PRECISION 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(N,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 (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i).
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS right hand side matrix B.
          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
.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 the solution has not been computed.
.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
\fBDate:\fP
.RS 4
November 2011 
.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 163 of file dgbsv\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.