zhprfs.f (3) - Linux Manuals


zhprfs.f -



subroutine zhprfs (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)

Function/Subroutine Documentation

subroutine zhprfs (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP, complex*16, dimension( * )AFP, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)



 ZHPRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is Hermitian indefinite
 and packed, and provides error bounds and backward error estimates
 for the solution.




          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.


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


          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.


          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
          The upper or lower triangle of the Hermitian matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.


          AFP is COMPLEX*16 array, dimension (N*(N+1)/2)
          The factored form of the matrix A.  AFP contains the block
          diagonal matrix D and the multipliers used to obtain the
          factor U or L from the factorization A = U*D*U**H or
          A = L*D*L**H as computed by ZHPTRF, stored as a packed
          triangular matrix.


          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D
          as determined by ZHPTRF.


          B is COMPLEX*16 array, dimension (LDB,NRHS)
          The right hand side matrix B.


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


          X is COMPLEX*16 array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by ZHPTRS.
          On exit, the improved solution matrix X.


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


          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 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 is COMPLEX*16 array, dimension (2*N)


          RWORK is DOUBLE PRECISION array, dimension (N)


          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.



Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


November 2011

Definition at line 180 of file zhprfs.f.


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