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dgerfs.f File Reference

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Functions/Subroutines

subroutine dgerfs (TRANS, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
 DGERFS More...
 

Function/Subroutine Documentation

subroutine dgerfs ( character  TRANS,
integer  N,
integer  NRHS,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldaf, * )  AF,
integer  LDAF,
integer, dimension( * )  IPIV,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( ldx, * )  X,
integer  LDX,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
double precision, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

DGERFS

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Purpose:
 DGERFS improves the computed solution to a system of linear
 equations 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 = 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 matrices B and X.  NRHS >= 0.
[in]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The original N-by-N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]AF
          AF is DOUBLE PRECISION array, dimension (LDAF,N)
          The factors L and U from the factorization A = P*L*U
          as computed by DGETRF.
[in]LDAF
          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DGETRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i).
[in]B
          B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by DGETRS.
          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 DOUBLE PRECISION array, dimension (3*N)
[out]IWORK
          IWORK is INTEGER 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 185 of file dgerfs.f.

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