stpt02()

subroutine stpt02	(	character	uplo,
		character	trans,
		character	diag,
		integer	n,
		integer	nrhs,
		real, dimension( * )	ap,
		real, dimension( ldx, * )	x,
		integer	ldx,
		real, dimension( ldb, * )	b,
		integer	ldb,
		real, dimension( * )	work,
		real	resid )

STPT02

Purpose:

!>
!> STPT02 computes the residual for the computed solution to a
!> triangular system of linear equations op(A)*X = B, when the
!> triangular matrix A is stored in packed format. The test ratio is
!> the maximum over
!>    norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
!> where op(A) = A or A**T, b is the column of B, x is the solution
!> vector, and EPS is the machine epsilon.
!> The norm used is the 1-norm.
!> 

Parameters

[in]	UPLO	!> UPLO is CHARACTER*1 !> Specifies whether the matrix A is upper or lower triangular. !> = 'U': Upper triangular !> = 'L': Lower triangular !>
[in]	TRANS	!> TRANS is CHARACTER*1 !> Specifies the operation applied to A. !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate transpose = Transpose) !>
[in]	DIAG	!> DIAG is CHARACTER*1 !> Specifies whether or not the matrix A is unit triangular. !> = 'N': Non-unit triangular !> = 'U': Unit triangular !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrices X and B. NRHS >= 0. !>
[in]	AP	!> AP is REAL array, dimension (N*(N+1)/2) !> The upper or lower triangular 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((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; !> if UPLO = 'L', !> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. !>
[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]	B	!> B is REAL array, dimension (LDB,NRHS) !> The right hand side vectors for the system of linear !> equations. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	WORK	!> WORK is REAL array, dimension (N) !>
[out]	RESID	!> RESID is REAL !> The maximum over the number of right hand sides of !> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 140 of file stpt02.f.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          DIAG, TRANS, UPLO
      INTEGER            LDB, LDX, N, NRHS
      REAL               RESID
*     ..
*     .. Array Arguments ..
      REAL               AP( * ), B( LDB, * ), WORK( * ), 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 ..
      LOGICAL            LSAME
      REAL               SASUM, SLAMCH, SLANTP
      EXTERNAL           lsame, sasum, slamch, slantp
*     ..
*     .. External Subroutines ..
      EXTERNAL           saxpy, scopy, stpmv
*     ..
*     .. 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
*
*     Compute the 1-norm of op(A).
*
      IF( lsame( trans, 'N' ) ) THEN
         anorm = slantp( '1', uplo, diag, n, ap, work )
      ELSE
         anorm = slantp( 'I', uplo, diag, n, ap, work )
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = slamch( 'Epsilon' )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
*     Compute the maximum over the number of right hand sides of
*        norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
*
      resid = zero
      DO 10 j = 1, nrhs
         CALL scopy( n, x( 1, j ), 1, work, 1 )
         CALL stpmv( uplo, trans, diag, n, ap, work, 1 )
         CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
         bnorm = sasum( n, work, 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
   10 CONTINUE
*
      RETURN
*
*     End of STPT02
*

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