sppt02()

subroutine sppt02	(	character	UPLO,
		integer	N,
		integer	NRHS,
		real, dimension( * )	A,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( * )	RWORK,
		real	RESID
	)

SPPT02

Purpose:

 SPPT02 computes the residual in the solution of a symmetric system
 of linear equations  A*x = b  when packed storage is used for the
 coefficient matrix.  The ratio computed is

    RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),

 where EPS is the machine precision.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular
[in]	N	N is INTEGER The number of rows and columns of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of columns of B, the matrix of right hand sides. NRHS >= 0.
[in]	A	A is REAL array, dimension (N*(N+1)/2) The original symmetric matrix A, stored as a packed triangular matrix.
[in]	X	X is REAL array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[in,out]	B	B is REAL array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	RWORK	RWORK is REAL array, dimension (N)
[out]	RESID	RESID is REAL The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 124 of file sppt02.f.

*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDB, LDX, N, NRHS
      REAL               RESID
*     ..
*     .. Array Arguments ..
      REAL               A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      REAL               ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      REAL               SASUM, SLAMCH, SLANSP
      EXTERNAL           sasum, slamch, slansp
*     ..
*     .. External Subroutines ..
      EXTERNAL           sspmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0 or NRHS = 0.
*
      IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = slamch( 'Epsilon' )
      anorm = slansp( '1', uplo, n, a, rwork )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
*     Compute  B - A*X  for the matrix of right hand sides B.
*
      DO 10 j = 1, nrhs
         CALL sspmv( uplo, n, -one, a, x( 1, j ), 1, one, b( 1, j ), 1 )
   10 CONTINUE
*
*     Compute the maximum over the number of right hand sides of
*        norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
*
      resid = zero
      DO 20 j = 1, nrhs
         bnorm = sasum( n, b( 1, j ), 1 )
         xnorm = sasum( n, x( 1, j ), 1 )
         IF( xnorm.LE.zero ) THEN
            resid = one / eps
         ELSE
            resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
         END IF
   20 CONTINUE
*
      RETURN
*
*     End of SPPT02
*

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