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

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Functions/Subroutines

subroutine CPTRFS (UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
 CPTRFS

Function/Subroutine Documentation

subroutine CPTRFS ( CHARACTER  UPLO,
INTEGER  N,
INTEGER  NRHS,
REAL, dimension( * )  D,
COMPLEX, dimension( * )  E,
REAL, dimension( * )  DF,
COMPLEX, dimension( * )  EF,
COMPLEX, dimension( ldb, * )  B,
INTEGER  LDB,
COMPLEX, dimension( ldx, * )  X,
INTEGER  LDX,
REAL, dimension( * )  FERR,
REAL, dimension( * )  BERR,
COMPLEX, dimension( * )  WORK,
REAL, dimension( * )  RWORK,
INTEGER  INFO 
)

CPTRFS

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Purpose: 

 CPTRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is Hermitian positive definite
 and tridiagonal, and provides error bounds and backward error
 estimates for the solution.
Parameters:
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the superdiagonal or the subdiagonal of the
          tridiagonal matrix A is stored and the form of the
          factorization:
          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
          (The two forms are equivalent if A is real.)
[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]D
          D is REAL array, dimension (N)
          The n real diagonal elements of the tridiagonal matrix A.
[in]E
          E is COMPLEX array, dimension (N-1)
          The (n-1) off-diagonal elements of the tridiagonal matrix A
          (see UPLO).
[in]DF
          DF is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from
          the factorization computed by CPTTRF.
[in]EF
          EF is COMPLEX array, dimension (N-1)
          The (n-1) off-diagonal elements of the unit bidiagonal
          factor U or L from the factorization computed by CPTTRF
          (see UPLO).
[in]B
          B is COMPLEX 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 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by CPTTRS.
          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 REAL array, dimension (NRHS)
          The 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).
[out]BERR
          BERR is REAL 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 array, dimension (N)
[out]RWORK
          RWORK is REAL 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 183 of file cptrfs.f.

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