dgtrfs.f3

!>
!> DGTRFS 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.
!> 

TRANS

!>          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 = Transpose)
!> 

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!> 

DL

!>          DL is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) subdiagonal elements of A.
!> 

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of A.
!> 

DU

!>          DU is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) superdiagonal elements of A.
!> 

DLF

!>          DLF is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A as computed by DGTTRF.
!> 

DF

!>          DF is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!> 

DUF

!>          DUF is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) elements of the first superdiagonal of U.
!> 

DU2

!>          DU2 is DOUBLE PRECISION array, dimension (N-2)
!>          The (n-2) elements of the second superdiagonal of U.
!> 

IPIV

!>          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.
!> 

B

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          The right hand side matrix B.
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!> 

X

!>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          On entry, the solution matrix X, as computed by DGTTRS.
!>          On exit, the improved solution matrix X.
!> 

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(1,N).
!> 

FERR

!>          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.
!> 

BERR

!>          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).
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (3*N)
!> 

IWORK

!>          IWORK is INTEGER array, dimension (N)
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 

!>  ITMAX is the maximum number of steps of iterative refinement.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

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