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*> \ingroup complex16_lin
158*
159*  =====================================================================
160      SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
161     $                   TSCAL, X, LDX, B, LDB, WORK, RESID )
162*
163*  -- LAPACK test routine --
164*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
165*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166*
167*     .. Scalar Arguments ..
168      CHARACTER          DIAG, TRANS, UPLO
169      INTEGER            LDB, LDX, N, NRHS
170      DOUBLE PRECISION   RESID, SCALE, TSCAL
171*     ..
172*     .. Array Arguments ..
173      DOUBLE PRECISION   CNORM( * )
174      COMPLEX*16         AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
175*     ..
176*
177*  =====================================================================
178*
179*     .. Parameters ..
180      DOUBLE PRECISION   ONE, ZERO
181      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
182*     ..
183*     .. Local Scalars ..
184      INTEGER            IX, J, JJ
185      DOUBLE PRECISION   EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
186*     ..
187*     .. External Functions ..
188      LOGICAL            LSAME
189      INTEGER            IZAMAX
190      DOUBLE PRECISION   DLAMCH
191      EXTERNAL           LSAME, IZAMAX, DLAMCH
192*     ..
193*     .. External Subroutines ..
194      EXTERNAL           ZAXPY, ZCOPY, ZDSCAL, ZTPMV
195*     ..
196*     .. Intrinsic Functions ..
197      INTRINSIC          ABS, DBLE, DCMPLX, MAX
198*     ..
199*     .. Executable Statements ..
200*
201*     Quick exit if N = 0.
202*
203      IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
204         RESID = ZERO
205         RETURN
206      END IF
207      EPS = DLAMCH( 'Epsilon' )
208      SMLNUM = DLAMCH( 'Safe minimum' )
209*
210*     Compute the norm of the triangular matrix A using the column
211*     norms already computed by ZLATPS.
212*
213      TNORM = 0.D0
214      IF( LSAME( DIAG, 'N' ) ) THEN
215         IF( LSAME( UPLO, 'U' ) ) THEN
216            JJ = 1
217            DO 10 J = 1, N
218               TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
219               JJ = JJ + J
220   10       CONTINUE
221         ELSE
222            JJ = 1
223            DO 20 J = 1, N
224               TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
225               JJ = JJ + N - J + 1
226   20       CONTINUE
227         END IF
228      ELSE
229         DO 30 J = 1, N
230            TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
231   30    CONTINUE
232      END IF
233*
234*     Compute the maximum over the number of right hand sides of
235*        norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
236*
237      RESID = ZERO
238      DO 40 J = 1, NRHS
239         CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 )
240         IX = IZAMAX( N, WORK, 1 )
241         XNORM = MAX( ONE, ABS( X( IX, J ) ) )
242         XSCAL = ( ONE / XNORM ) / DBLE( N )
243         CALL ZDSCAL( N, XSCAL, WORK, 1 )
244         CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
245         CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 )
246         IX = IZAMAX( N, WORK, 1 )
247         ERR = TSCAL*ABS( WORK( IX ) )
248         IX = IZAMAX( N, X( 1, J ), 1 )
249         XNORM = ABS( X( IX, J ) )
250         IF( ERR*SMLNUM.LE.XNORM ) THEN
251            IF( XNORM.GT.ZERO )
252     $         ERR = ERR / XNORM
253         ELSE
254            IF( ERR.GT.ZERO )
255     $         ERR = ONE / EPS
256         END IF
257         IF( ERR*SMLNUM.LE.TNORM ) THEN
258            IF( TNORM.GT.ZERO )
259     $         ERR = ERR / TNORM
260         ELSE
261            IF( ERR.GT.ZERO )
262     $         ERR = ONE / EPS
263         END IF
264         RESID = MAX( RESID, ERR )
265   40 CONTINUE
266*
267      RETURN
268*
269*     End of ZTPT03
270*
271      END
272