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*> \brief \b ZTPT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
* TSCAL, X, LDX, B, LDB, WORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, TRANS, UPLO
* INTEGER LDB, LDX, N, NRHS
* DOUBLE PRECISION RESID, SCALE, TSCAL
* ..
* .. Array Arguments ..
* DOUBLE PRECISION CNORM( * )
* COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTPT03 computes the residual for the solution to a scaled triangular
*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b,
*> when the triangular matrix A is stored in packed format. Here A**T
*> denotes the transpose of A, A**H denotes the conjugate transpose of
*> A, s is a scalar, and x and b are N by NRHS matrices. The test ratio
*> is the maximum over the number of right hand sides of
*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the matrix A is upper or lower triangular.
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the operation applied to A.
*> = 'N': A *x = s*b (No transpose)
*> = 'T': A**T *x = s*b (Transpose)
*> = 'C': A**H *x = s*b (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> Specifies whether or not the matrix A is unit triangular.
*> = 'N': Non-unit triangular
*> = 'U': Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrices X and B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] AP
*> \verbatim
*> AP is COMPLEX*16 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.
*> \endverbatim
*>
*> \param[in] SCALE
*> \verbatim
*> SCALE is DOUBLE PRECISION
*> The scaling factor s used in solving the triangular system.
*> \endverbatim
*>
*> \param[in] CNORM
*> \verbatim
*> CNORM is DOUBLE PRECISION array, dimension (N)
*> The 1-norms of the columns of A, not counting the diagonal.
*> \endverbatim
*>
*> \param[in] TSCAL
*> \verbatim
*> TSCAL is DOUBLE PRECISION
*> The scaling factor used in computing the 1-norms in CNORM.
*> CNORM actually contains the column norms of TSCAL*A.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (LDX,NRHS)
*> The computed solution vectors for the system of linear
*> equations.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the array X. LDX >= max(1,N).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB,NRHS)
*> The right hand side vectors for the system of linear
*> equations.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The maximum over the number of right hand sides of
*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
$ TSCAL, X, LDX, B, LDB, WORK, RESID )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION RESID, SCALE, TSCAL
* ..
* .. Array Arguments ..
DOUBLE PRECISION CNORM( * )
COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER IX, J, JJ
DOUBLE PRECISION EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IZAMAX
DOUBLE PRECISION DLAMCH
EXTERNAL LSAME, IZAMAX, DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL ZAXPY, ZCOPY, ZDSCAL, ZTPMV
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX, MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
EPS = DLAMCH( 'Epsilon' )
SMLNUM = DLAMCH( 'Safe minimum' )
*
* Compute the norm of the triangular matrix A using the column
* norms already computed by ZLATPS.
*
TNORM = 0.D0
IF( LSAME( DIAG, 'N' ) ) THEN
IF( LSAME( UPLO, 'U' ) ) THEN
JJ = 1
DO 10 J = 1, N
TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
JJ = JJ + J
10 CONTINUE
ELSE
JJ = 1
DO 20 J = 1, N
TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
JJ = JJ + N - J + 1
20 CONTINUE
END IF
ELSE
DO 30 J = 1, N
TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
30 CONTINUE
END IF
*
* Compute the maximum over the number of right hand sides of
* norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
*
RESID = ZERO
DO 40 J = 1, NRHS
CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 )
IX = IZAMAX( N, WORK, 1 )
XNORM = MAX( ONE, ABS( X( IX, J ) ) )
XSCAL = ( ONE / XNORM ) / DBLE( N )
CALL ZDSCAL( N, XSCAL, WORK, 1 )
CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
IX = IZAMAX( N, WORK, 1 )
ERR = TSCAL*ABS( WORK( IX ) )
IX = IZAMAX( N, X( 1, J ), 1 )
XNORM = ABS( X( IX, J ) )
IF( ERR*SMLNUM.LE.XNORM ) THEN
IF( XNORM.GT.ZERO )
$ ERR = ERR / XNORM
ELSE
IF( ERR.GT.ZERO )
$ ERR = ONE / EPS
END IF
IF( ERR*SMLNUM.LE.TNORM ) THEN
IF( TNORM.GT.ZERO )
$ ERR = ERR / TNORM
ELSE
IF( ERR.GT.ZERO )
$ ERR = ONE / EPS
END IF
RESID = MAX( RESID, ERR )
40 CONTINUE
*
RETURN
*
* End of ZTPT03
*
END
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