1*> \brief \b ZTRT01
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 ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
12*                          RWORK, RESID )
13*
14*       .. Scalar Arguments ..
15*       CHARACTER          DIAG, UPLO
16*       INTEGER            LDA, LDAINV, N
17*       DOUBLE PRECISION   RCOND, RESID
18*       ..
19*       .. Array Arguments ..
20*       DOUBLE PRECISION   RWORK( * )
21*       COMPLEX*16         A( LDA, * ), AINV( LDAINV, * )
22*       ..
23*
24*
25*> \par Purpose:
26*  =============
27*>
28*> \verbatim
29*>
30*> ZTRT01 computes the residual for a triangular matrix A times its
31*> inverse:
32*>    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
33*> where EPS is the machine epsilon.
34*> \endverbatim
35*
36*  Arguments:
37*  ==========
38*
39*> \param[in] UPLO
40*> \verbatim
41*>          UPLO is CHARACTER*1
42*>          Specifies whether the matrix A is upper or lower triangular.
43*>          = 'U':  Upper triangular
44*>          = 'L':  Lower triangular
45*> \endverbatim
46*>
47*> \param[in] DIAG
48*> \verbatim
49*>          DIAG is CHARACTER*1
50*>          Specifies whether or not the matrix A is unit triangular.
51*>          = 'N':  Non-unit triangular
52*>          = 'U':  Unit triangular
53*> \endverbatim
54*>
55*> \param[in] N
56*> \verbatim
57*>          N is INTEGER
58*>          The order of the matrix A.  N >= 0.
59*> \endverbatim
60*>
61*> \param[in] A
62*> \verbatim
63*>          A is COMPLEX*16 array, dimension (LDA,N)
64*>          The triangular matrix A.  If UPLO = 'U', the leading n by n
65*>          upper triangular part of the array A contains the upper
66*>          triangular matrix, and the strictly lower triangular part of
67*>          A is not referenced.  If UPLO = 'L', the leading n by n lower
68*>          triangular part of the array A contains the lower triangular
69*>          matrix, and the strictly upper triangular part of A is not
70*>          referenced.  If DIAG = 'U', the diagonal elements of A are
71*>          also not referenced and are assumed to be 1.
72*> \endverbatim
73*>
74*> \param[in] LDA
75*> \verbatim
76*>          LDA is INTEGER
77*>          The leading dimension of the array A.  LDA >= max(1,N).
78*> \endverbatim
79*>
80*> \param[in] AINV
81*> \verbatim
82*>          AINV is COMPLEX*16 array, dimension (LDAINV,N)
83*>          On entry, the (triangular) inverse of the matrix A, in the
84*>          same storage format as A.
85*>          On exit, the contents of AINV are destroyed.
86*> \endverbatim
87*>
88*> \param[in] LDAINV
89*> \verbatim
90*>          LDAINV is INTEGER
91*>          The leading dimension of the array AINV.  LDAINV >= max(1,N).
92*> \endverbatim
93*>
94*> \param[out] RCOND
95*> \verbatim
96*>          RCOND is DOUBLE PRECISION
97*>          The reciprocal condition number of A, computed as
98*>          1/(norm(A) * norm(AINV)).
99*> \endverbatim
100*>
101*> \param[out] RWORK
102*> \verbatim
103*>          RWORK is DOUBLE PRECISION array, dimension (N)
104*> \endverbatim
105*>
106*> \param[out] RESID
107*> \verbatim
108*>          RESID is DOUBLE PRECISION
109*>          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
110*> \endverbatim
111*
112*  Authors:
113*  ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \date November 2011
121*
122*> \ingroup complex16_lin
123*
124*  =====================================================================
125      SUBROUTINE ZTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
126     $                   RWORK, RESID )
127*
128*  -- LAPACK test routine (version 3.4.0) --
129*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
130*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131*     November 2011
132*
133*     .. Scalar Arguments ..
134      CHARACTER          DIAG, UPLO
135      INTEGER            LDA, LDAINV, N
136      DOUBLE PRECISION   RCOND, RESID
137*     ..
138*     .. Array Arguments ..
139      DOUBLE PRECISION   RWORK( * )
140      COMPLEX*16         A( LDA, * ), AINV( LDAINV, * )
141*     ..
142*
143*  =====================================================================
144*
145*     .. Parameters ..
146      DOUBLE PRECISION   ZERO, ONE
147      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
148*     ..
149*     .. Local Scalars ..
150      INTEGER            J
151      DOUBLE PRECISION   AINVNM, ANORM, EPS
152*     ..
153*     .. External Functions ..
154      LOGICAL            LSAME
155      DOUBLE PRECISION   DLAMCH, ZLANTR
156      EXTERNAL           LSAME, DLAMCH, ZLANTR
157*     ..
158*     .. External Subroutines ..
159      EXTERNAL           ZTRMV
160*     ..
161*     .. Intrinsic Functions ..
162      INTRINSIC          DBLE
163*     ..
164*     .. Executable Statements ..
165*
166*     Quick exit if N = 0
167*
168      IF( N.LE.0 ) THEN
169         RCOND = ONE
170         RESID = ZERO
171         RETURN
172      END IF
173*
174*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
175*
176      EPS = DLAMCH( 'Epsilon' )
177      ANORM = ZLANTR( '1', UPLO, DIAG, N, N, A, LDA, RWORK )
178      AINVNM = ZLANTR( '1', UPLO, DIAG, N, N, AINV, LDAINV, RWORK )
179      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
180         RCOND = ZERO
181         RESID = ONE / EPS
182         RETURN
183      END IF
184      RCOND = ( ONE / ANORM ) / AINVNM
185*
186*     Set the diagonal of AINV to 1 if AINV has unit diagonal.
187*
188      IF( LSAME( DIAG, 'U' ) ) THEN
189         DO 10 J = 1, N
190            AINV( J, J ) = ONE
191   10    CONTINUE
192      END IF
193*
194*     Compute A * AINV, overwriting AINV.
195*
196      IF( LSAME( UPLO, 'U' ) ) THEN
197         DO 20 J = 1, N
198            CALL ZTRMV( 'Upper', 'No transpose', DIAG, J, A, LDA,
199     $                  AINV( 1, J ), 1 )
200   20    CONTINUE
201      ELSE
202         DO 30 J = 1, N
203            CALL ZTRMV( 'Lower', 'No transpose', DIAG, N-J+1, A( J, J ),
204     $                  LDA, AINV( J, J ), 1 )
205   30    CONTINUE
206      END IF
207*
208*     Subtract 1 from each diagonal element to form A*AINV - I.
209*
210      DO 40 J = 1, N
211         AINV( J, J ) = AINV( J, J ) - ONE
212   40 CONTINUE
213*
214*     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
215*
216      RESID = ZLANTR( '1', UPLO, 'Non-unit', N, N, AINV, LDAINV, RWORK )
217*
218      RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
219*
220      RETURN
221*
222*     End of ZTRT01
223*
224      END
225