LAPACK  3.4.0
LAPACK: Linear Algebra PACKage
Functions/Subroutines
zgtrfs.f File Reference

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Functions/Subroutines

subroutine ZGTRFS (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
 ZGTRFS

Function/Subroutine Documentation

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 
)

ZGTRFS

Download ZGTRFS + dependencies [TGZ] [ZIP] [TXT]
Purpose: 

 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.
Parameters:
[in]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)
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.
[in]DL
          DL is COMPLEX*16 array, dimension (N-1)
          The (n-1) subdiagonal elements of A.
[in]D
          D is COMPLEX*16 array, dimension (N)
          The diagonal elements of A.
[in]DU
          DU is COMPLEX*16 array, dimension (N-1)
          The (n-1) superdiagonal elements of A.
[in]DLF
          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.
[in]DF
          DF is COMPLEX*16 array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from
          the LU factorization of A.
[in]DUF
          DUF is COMPLEX*16 array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U.
[in]DU2
          DU2 is COMPLEX*16 array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U.
[in]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.
[in]B
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).
[in,out]X
          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.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(1,N).
[out]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.
[out]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).
[out]WORK
          WORK is COMPLEX*16 array, dimension (2*N)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (N)
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
Internal Parameters: 
  ITMAX is the maximum number of steps of iterative refinement.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011

Definition at line 209 of file zgtrfs.f.

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