dtpt02()

subroutine dtpt02	(	character	UPLO,
		character	TRANS,
		character	DIAG,
		integer	N,
		integer	NRHS,
		double precision, dimension( * )	AP,
		double precision, dimension( ldx, * )	X,
		integer	LDX,
		double precision, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	WORK,
		double precision	RESID
	)

DTPT02

Purpose:

 DTPT02 computes the residual for the computed solution to a
 triangular system of linear equations  A*x = b  or  A'*x = b  when
 the triangular matrix A is stored in packed format.  Here A' is the
 transpose of A and x and b are N by NRHS matrices.  The test ratio is
 the maximum over the number of right hand sides of
    norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
 where op(A) denotes A or A' and EPS is the machine epsilon.

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'*x = b (Transpose) = 'C': A'*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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
[out]	RESID	RESID is DOUBLE PRECISION 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 139 of file dtpt02.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
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DASUM, DLAMCH, DLANTP
      EXTERNAL           lsame, dasum, dlamch, dlantp
*     ..
*     .. External Subroutines ..
      EXTERNAL           daxpy, dcopy, dtpmv
*     ..
*     .. 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 A or A'.
*
      IF( lsame( trans, 'N' ) ) THEN
         anorm = dlantp( '1', uplo, diag, n, ap, work )
      ELSE
         anorm = dlantp( 'I', uplo, diag, n, ap, work )
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = dlamch( '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 dcopy( n, x( 1, j ), 1, work, 1 )
         CALL dtpmv( uplo, trans, diag, n, ap, work, 1 )
         CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
         bnorm = dasum( n, work, 1 )
         xnorm = dasum( 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 DTPT02
*

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