zptrfs(3S)

NAME
     ZPTRFS - improve 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

SYNOPSIS
     SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
                        BERR, WORK, RWORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, LDB, LDX, N, NRHS

         DOUBLE         PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
                        RWORK( * )

         COMPLEX*16     B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     ZPTRFS 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.

ARGUMENTS
     UPLO    (input) 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.)

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrix B.  NRHS >= 0.
     D       (input) DOUBLE PRECISION array, dimension (N)
             The n real diagonal elements of the tridiagonal matrix A.

     E       (input) COMPLEX*16 array, dimension (N-1)
             The (n-1) off-diagonal elements of the tridiagonal matrix A (see
             UPLO).

     DF      (input) DOUBLE PRECISION array, dimension (N)
             The n diagonal elements of the diagonal matrix D from the
             factorization computed by ZPTTRF.

     EF      (input) COMPLEX*16 array, dimension (N-1)
             The (n-1) off-diagonal elements of the unit bidiagonal factor U
             or L from the factorization computed by ZPTTRF (see UPLO).

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

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

     X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
             On entry, the solution matrix X, as computed by ZPTTRS.  On exit,
             the improved solution matrix X.

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

     FERR    (output) DOUBLE PRECISION 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).

     BERR    (output) 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    (workspace) COMPLEX*16 array, dimension (N)

     RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value

PARAMETERS
     ITMAX is the maximum number of steps of iterative refinement.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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