zsprfs.f man page




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

Function/Subroutine Documentation

subroutine zsprfs (character UPLO, integer N, integer NRHS, complex*16, dimension( * ) AP, complex*16, dimension( * ) AFP, 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)



 ZSPRFS improves the computed solution to a system of linear
 equations when the coefficient matrix is symmetric 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 symmetric 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**T or
          A = L*D*L**T as computed by ZSPTRF, 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 ZSPTRF.


          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 ZSPTRS.
          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.


December 2016

Definition at line 182 of file zsprfs.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zsprfs(3) is an alias of zsprfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK