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

.in +1c
.ti -1c
.RI "subroutine \fBzgtrfs\fP (trans, n, nrhs, dl, d, du, dlf, df, duf, du2, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)"
.br
.RI "\fBZGTRFS\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgtrfs (character trans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) dlf, complex*16, dimension( * ) df, complex*16, dimension( * ) duf, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)"

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

.PP
.nf
 ZGTRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is tridiagonal, and provides
 error bounds and backward error estimates for the solution\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations:
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  A**H * X = B  (Conjugate transpose)
.fi
.PP
.br
\fIN\fP 
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.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fINRHS\fP 
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.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
\fIDL\fP 
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.nf
          DL is COMPLEX*16 array, dimension (N-1)
          The (n-1) subdiagonal elements of A\&.
.fi
.PP
.br
\fID\fP 
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.nf
          D is COMPLEX*16 array, dimension (N)
          The diagonal elements of A\&.
.fi
.PP
.br
\fIDU\fP 
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.nf
          DU is COMPLEX*16 array, dimension (N-1)
          The (n-1) superdiagonal elements of A\&.
.fi
.PP
.br
\fIDLF\fP 
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.nf
          DLF is COMPLEX*16 array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the
          LU factorization of A as computed by ZGTTRF\&.
.fi
.PP
.br
\fIDF\fP 
.PP
.nf
          DF is COMPLEX*16 array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A\&.
.fi
.PP
.br
\fIDUF\fP 
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.nf
          DUF is COMPLEX*16 array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U\&.
.fi
.PP
.br
\fIDU2\fP 
.PP
.nf
          DU2 is COMPLEX*16 array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i)\&.  IPIV(i) will always be either
          i or i+1; IPIV(i) = i indicates a row interchange was not
          required\&.
.fi
.PP
.br
\fIB\fP 
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.nf
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B\&.
.fi
.PP
.br
\fILDB\fP 
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.nf
          LDB is INTEGER
          The leading dimension of the array B\&.  LDB >= max(1,N)\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZGTTRS\&.
          On exit, the improved solution matrix X\&.
.fi
.PP
.br
\fILDX\fP 
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.nf
          LDX is INTEGER
          The leading dimension of the array X\&.  LDX >= max(1,N)\&.
.fi
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.br
\fIFERR\fP 
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.nf
          FERR is DOUBLE PRECISION array, dimension (NRHS)
          The estimated forward error bound for each solution vector
          X(j) (the j-th column of the solution matrix X)\&.
          If XTRUE is the true solution corresponding to X(j), FERR(j)
          is an estimated upper bound for the magnitude of the largest
          element in (X(j) - XTRUE) divided by the magnitude of the
          largest element in X(j)\&.  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error\&.
.fi
.PP
.br
\fIBERR\fP 
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.nf
          BERR is DOUBLE PRECISION array, dimension (NRHS)
          The componentwise relative backward error of each solution
          vector X(j) (i\&.e\&., the smallest relative change in
          any element of A or B that makes X(j) an exact solution)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (2*N)
.fi
.PP
.br
\fIRWORK\fP 
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.nf
          RWORK is DOUBLE PRECISION array, dimension (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
.fi
.PP
 
.RE
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\fBInternal Parameters:\fP
.RS 4

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.nf
  ITMAX is the maximum number of steps of iterative refinement\&.
.fi
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.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
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Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
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NAG Ltd\&. 
.RE
.PP

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Definition at line \fB207\fP of file \fBzgtrfs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.