csprfs.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index
 

NAME

csprfs.f  

SYNOPSIS


 

Functions/Subroutines


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

Function/Subroutine Documentation

 

subroutine csprfs (character UPLO, integer N, integer NRHS, complex, dimension( * ) AP, complex, dimension( * ) AFP, integer, dimension( * ) IPIV, 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)

CSPRFS

Purpose:

 CSPRFS 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.


 

Parameters:

UPLO

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


N

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


NRHS

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


AP

          AP is COMPLEX 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

          AFP is COMPLEX 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 CSPTRF, stored as a packed
          triangular matrix.


IPIV

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


B

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


LDB

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


X

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


LDX

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


FERR

          FERR is REAL 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

          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).


WORK

          WORK is COMPLEX array, dimension (2*N)


RWORK

          RWORK is REAL array, dimension (N)


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:

December 2016

Definition at line 182 of file csprfs.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine csprfs (character UPLO, integer N, integer NRHS, complex, dimension( * ) AP, complex, dimension( * ) AFP, integer, dimension( * ) IPIV, 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)
Author