.TH "cgbtrf.f" 3 "Tue Nov 14 2017" "Version 3.8.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
cgbtrf.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBcgbtrf\fP (M, \fBN\fP, KL, KU, AB, LDAB, IPIV, INFO)"
.br
.RI "\fBCGBTRF\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine cgbtrf (integer M, integer N, integer KL, integer KU, complex, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, integer INFO)"

.PP
\fBCGBTRF\fP  
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\fBPurpose: \fP
.RS 4

.PP
.nf
 CGBTRF computes an LU factorization of a complex m-by-n band matrix A
 using partial pivoting with row interchanges.

 This is the blocked version of the algorithm, calling Level 3 BLAS.
.fi
.PP
 
.RE
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\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 COMPLEX 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
\fBDate:\fP
.RS 4
December 2016 
.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 146 of file cgbtrf\&.f\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.
