1*> \brief \b ZTPT03
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
12*                          TSCAL, X, LDX, B, LDB, WORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          DIAG, TRANS, UPLO
16*       INTEGER            LDB, LDX, N, NRHS
17*       DOUBLE PRECISION   RESID, SCALE, TSCAL
18*       ..
19*       .. Array Arguments ..
20*       DOUBLE PRECISION   CNORM( * )
21*       COMPLEX*16         AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> ZTPT03 computes the residual for the solution to a scaled triangular
31*> system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b,
32*> when the triangular matrix A is stored in packed format.  Here A**T
33*> denotes the transpose of A, A**H denotes the conjugate transpose of
34*> A, s is a scalar, and x and b are N by NRHS matrices.  The test ratio
35*> is the maximum over the number of right hand sides of
36*>    norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
37*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
38*> \endverbatim
39*
40*  Arguments:
41*  ==========
42*
43*> \param[in] UPLO
44*> \verbatim
45*>          UPLO is CHARACTER*1
46*>          Specifies whether the matrix A is upper or lower triangular.
47*>          = 'U':  Upper triangular
48*>          = 'L':  Lower triangular
49*> \endverbatim
50*>
51*> \param[in] TRANS
52*> \verbatim
53*>          TRANS is CHARACTER*1
54*>          Specifies the operation applied to A.
55*>          = 'N':  A *x = s*b     (No transpose)
56*>          = 'T':  A**T *x = s*b  (Transpose)
57*>          = 'C':  A**H *x = s*b  (Conjugate transpose)
58*> \endverbatim
59*>
60*> \param[in] DIAG
61*> \verbatim
62*>          DIAG is CHARACTER*1
63*>          Specifies whether or not the matrix A is unit triangular.
64*>          = 'N':  Non-unit triangular
65*>          = 'U':  Unit triangular
66*> \endverbatim
67*>
68*> \param[in] N
69*> \verbatim
70*>          N is INTEGER
71*>          The order of the matrix A.  N >= 0.
72*> \endverbatim
73*>
74*> \param[in] NRHS
75*> \verbatim
76*>          NRHS is INTEGER
77*>          The number of right hand sides, i.e., the number of columns
78*>          of the matrices X and B.  NRHS >= 0.
79*> \endverbatim
80*>
81*> \param[in] AP
82*> \verbatim
83*>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
84*>          The upper or lower triangular matrix A, packed columnwise in
85*>          a linear array.  The j-th column of A is stored in the array
86*>          AP as follows:
87*>          if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
88*>          if UPLO = 'L',
89*>             AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
90*> \endverbatim
91*>
92*> \param[in] SCALE
93*> \verbatim
94*>          SCALE is DOUBLE PRECISION
95*>          The scaling factor s used in solving the triangular system.
96*> \endverbatim
97*>
98*> \param[in] CNORM
99*> \verbatim
100*>          CNORM is DOUBLE PRECISION array, dimension (N)
101*>          The 1-norms of the columns of A, not counting the diagonal.
102*> \endverbatim
103*>
104*> \param[in] TSCAL
105*> \verbatim
106*>          TSCAL is DOUBLE PRECISION
107*>          The scaling factor used in computing the 1-norms in CNORM.
108*>          CNORM actually contains the column norms of TSCAL*A.
109*> \endverbatim
110*>
111*> \param[in] X
112*> \verbatim
113*>          X is COMPLEX*16 array, dimension (LDX,NRHS)
114*>          The computed solution vectors for the system of linear
115*>          equations.
116*> \endverbatim
117*>
118*> \param[in] LDX
119*> \verbatim
120*>          LDX is INTEGER
121*>          The leading dimension of the array X.  LDX >= max(1,N).
122*> \endverbatim
123*>
124*> \param[in] B
125*> \verbatim
126*>          B is COMPLEX*16 array, dimension (LDB,NRHS)
127*>          The right hand side vectors for the system of linear
128*>          equations.
129*> \endverbatim
130*>
131*> \param[in] LDB
132*> \verbatim
133*>          LDB is INTEGER
134*>          The leading dimension of the array B.  LDB >= max(1,N).
135*> \endverbatim
136*>
137*> \param[out] WORK
138*> \verbatim
139*>          WORK is COMPLEX*16 array, dimension (N)
140*> \endverbatim
141*>
142*> \param[out] RESID
143*> \verbatim
144*>          RESID is DOUBLE PRECISION
145*>          The maximum over the number of right hand sides of
146*>          norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
147*> \endverbatim
148*
149*  Authors:
150*  ========
151*
152*> \author Univ. of Tennessee
153*> \author Univ. of California Berkeley
154*> \author Univ. of Colorado Denver
155*> \author NAG Ltd.
156*
157*> \date November 2011
158*
159*> \ingroup complex16_lin
160*
161*  =====================================================================
162      SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
163     $                   TSCAL, X, LDX, B, LDB, WORK, RESID )
164*
165*  -- LAPACK test routine (version 3.4.0) --
166*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
167*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168*     November 2011
169*
170*     .. Scalar Arguments ..
171      CHARACTER          DIAG, TRANS, UPLO
172      INTEGER            LDB, LDX, N, NRHS
173      DOUBLE PRECISION   RESID, SCALE, TSCAL
174*     ..
175*     .. Array Arguments ..
176      DOUBLE PRECISION   CNORM( * )
177      COMPLEX*16         AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
178*     ..
179*
180*  =====================================================================
181*
182*     .. Parameters ..
183      DOUBLE PRECISION   ONE, ZERO
184      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
185*     ..
186*     .. Local Scalars ..
187      INTEGER            IX, J, JJ
188      DOUBLE PRECISION   EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
189*     ..
190*     .. External Functions ..
191      LOGICAL            LSAME
192      INTEGER            IZAMAX
193      DOUBLE PRECISION   DLAMCH
194      EXTERNAL           LSAME, IZAMAX, DLAMCH
195*     ..
196*     .. External Subroutines ..
197      EXTERNAL           ZAXPY, ZCOPY, ZDSCAL, ZTPMV
198*     ..
199*     .. Intrinsic Functions ..
200      INTRINSIC          ABS, DBLE, DCMPLX, MAX
201*     ..
202*     .. Executable Statements ..
203*
204*     Quick exit if N = 0.
205*
206      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
207         RESID = ZERO
208         RETURN
209      END IF
210      EPS = DLAMCH( 'Epsilon' )
211      SMLNUM = DLAMCH( 'Safe minimum' )
212*
213*     Compute the norm of the triangular matrix A using the column
214*     norms already computed by ZLATPS.
215*
216      TNORM = 0.D0
217      IF( LSAME( DIAG, 'N' ) ) THEN
218         IF( LSAME( UPLO, 'U' ) ) THEN
219            JJ = 1
220            DO 10 J = 1, N
221               TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
222               JJ = JJ + J
223   10       CONTINUE
224         ELSE
225            JJ = 1
226            DO 20 J = 1, N
227               TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
228               JJ = JJ + N - J + 1
229   20       CONTINUE
230         END IF
231      ELSE
232         DO 30 J = 1, N
233            TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
234   30    CONTINUE
235      END IF
236*
237*     Compute the maximum over the number of right hand sides of
238*        norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
239*
240      RESID = ZERO
241      DO 40 J = 1, NRHS
242         CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 )
243         IX = IZAMAX( N, WORK, 1 )
244         XNORM = MAX( ONE, ABS( X( IX, J ) ) )
245         XSCAL = ( ONE / XNORM ) / DBLE( N )
246         CALL ZDSCAL( N, XSCAL, WORK, 1 )
247         CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
248         CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
249         IX = IZAMAX( N, WORK, 1 )
250         ERR = TSCAL*ABS( WORK( IX ) )
251         IX = IZAMAX( N, X( 1, J ), 1 )
252         XNORM = ABS( X( IX, J ) )
253         IF( ERR*SMLNUM.LE.XNORM ) THEN
254            IF( XNORM.GT.ZERO )
255     $         ERR = ERR / XNORM
256         ELSE
257            IF( ERR.GT.ZERO )
258     $         ERR = ONE / EPS
259         END IF
260         IF( ERR*SMLNUM.LE.TNORM ) THEN
261            IF( TNORM.GT.ZERO )
262     $         ERR = ERR / TNORM
263         ELSE
264            IF( ERR.GT.ZERO )
265     $         ERR = ONE / EPS
266         END IF
267         RESID = MAX( RESID, ERR )
268   40 CONTINUE
269*
270      RETURN
271*
272*     End of ZTPT03
273*
274      END
275