1*> \brief \b DTRT01
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 DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
12*                          WORK, 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   A( LDA, * ), AINV( LDAINV, * ), WORK( * )
21*       ..
22*
23*
24*> \par Purpose:
25*  =============
26*>
27*> \verbatim
28*>
29*> DTRT01 computes the residual for a triangular matrix A times its
30*> inverse:
31*>    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
32*> where EPS is the machine epsilon.
33*> \endverbatim
34*
35*  Arguments:
36*  ==========
37*
38*> \param[in] UPLO
39*> \verbatim
40*>          UPLO is CHARACTER*1
41*>          Specifies whether the matrix A is upper or lower triangular.
42*>          = 'U':  Upper triangular
43*>          = 'L':  Lower triangular
44*> \endverbatim
45*>
46*> \param[in] DIAG
47*> \verbatim
48*>          DIAG is CHARACTER*1
49*>          Specifies whether or not the matrix A is unit triangular.
50*>          = 'N':  Non-unit triangular
51*>          = 'U':  Unit triangular
52*> \endverbatim
53*>
54*> \param[in] N
55*> \verbatim
56*>          N is INTEGER
57*>          The order of the matrix A.  N >= 0.
58*> \endverbatim
59*>
60*> \param[in] A
61*> \verbatim
62*>          A is DOUBLE PRECISION array, dimension (LDA,N)
63*>          The triangular matrix A.  If UPLO = 'U', the leading n by n
64*>          upper triangular part of the array A contains the upper
65*>          triangular matrix, and the strictly lower triangular part of
66*>          A is not referenced.  If UPLO = 'L', the leading n by n lower
67*>          triangular part of the array A contains the lower triangular
68*>          matrix, and the strictly upper triangular part of A is not
69*>          referenced.  If DIAG = 'U', the diagonal elements of A are
70*>          also not referenced and are assumed to be 1.
71*> \endverbatim
72*>
73*> \param[in] LDA
74*> \verbatim
75*>          LDA is INTEGER
76*>          The leading dimension of the array A.  LDA >= max(1,N).
77*> \endverbatim
78*>
79*> \param[in,out] AINV
80*> \verbatim
81*>          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
82*>          On entry, the (triangular) inverse of the matrix A, in the
83*>          same storage format as A.
84*>          On exit, the contents of AINV are destroyed.
85*> \endverbatim
86*>
87*> \param[in] LDAINV
88*> \verbatim
89*>          LDAINV is INTEGER
90*>          The leading dimension of the array AINV.  LDAINV >= max(1,N).
91*> \endverbatim
92*>
93*> \param[out] RCOND
94*> \verbatim
95*>          RCOND is DOUBLE PRECISION
96*>          The reciprocal condition number of A, computed as
97*>          1/(norm(A) * norm(AINV)).
98*> \endverbatim
99*>
100*> \param[out] WORK
101*> \verbatim
102*>          WORK is DOUBLE PRECISION array, dimension (N)
103*> \endverbatim
104*>
105*> \param[out] RESID
106*> \verbatim
107*>          RESID is DOUBLE PRECISION
108*>          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
109*> \endverbatim
110*
111*  Authors:
112*  ========
113*
114*> \author Univ. of Tennessee
115*> \author Univ. of California Berkeley
116*> \author Univ. of Colorado Denver
117*> \author NAG Ltd.
118*
119*> \date December 2016
120*
121*> \ingroup double_lin
122*
123*  =====================================================================
124      SUBROUTINE DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
125     $                   WORK, RESID )
126*
127*  -- LAPACK test routine (version 3.7.0) --
128*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
129*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130*     December 2016
131*
132*     .. Scalar Arguments ..
133      CHARACTER          DIAG, UPLO
134      INTEGER            LDA, LDAINV, N
135      DOUBLE PRECISION   RCOND, RESID
136*     ..
137*     .. Array Arguments ..
138      DOUBLE PRECISION   A( LDA, * ), AINV( LDAINV, * ), WORK( * )
139*     ..
140*
141*  =====================================================================
142*
143*     .. Parameters ..
144      DOUBLE PRECISION   ZERO, ONE
145      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
146*     ..
147*     .. Local Scalars ..
148      INTEGER            J
149      DOUBLE PRECISION   AINVNM, ANORM, EPS
150*     ..
151*     .. External Functions ..
152      LOGICAL            LSAME
153      DOUBLE PRECISION   DLAMCH, DLANTR
154      EXTERNAL           LSAME, DLAMCH, DLANTR
155*     ..
156*     .. External Subroutines ..
157      EXTERNAL           DTRMV
158*     ..
159*     .. Intrinsic Functions ..
160      INTRINSIC          DBLE
161*     ..
162*     .. Executable Statements ..
163*
164*     Quick exit if N = 0
165*
166      IF( N.LE.0 ) THEN
167         RCOND = ONE
168         RESID = ZERO
169         RETURN
170      END IF
171*
172*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
173*
174      EPS = DLAMCH( 'Epsilon' )
175      ANORM = DLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK )
176      AINVNM = DLANTR( '1', UPLO, DIAG, N, N, AINV, LDAINV, WORK )
177      IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
178         RCOND = ZERO
179         RESID = ONE / EPS
180         RETURN
181      END IF
182      RCOND = ( ONE / ANORM ) / AINVNM
183*
184*     Set the diagonal of AINV to 1 if AINV has unit diagonal.
185*
186      IF( LSAME( DIAG, 'U' ) ) THEN
187         DO 10 J = 1, N
188            AINV( J, J ) = ONE
189   10    CONTINUE
190      END IF
191*
192*     Compute A * AINV, overwriting AINV.
193*
194      IF( LSAME( UPLO, 'U' ) ) THEN
195         DO 20 J = 1, N
196            CALL DTRMV( 'Upper', 'No transpose', DIAG, J, A, LDA,
197     $                  AINV( 1, J ), 1 )
198   20    CONTINUE
199      ELSE
200         DO 30 J = 1, N
201            CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J+1, A( J, J ),
202     $                  LDA, AINV( J, J ), 1 )
203   30    CONTINUE
204      END IF
205*
206*     Subtract 1 from each diagonal element to form A*AINV - I.
207*
208      DO 40 J = 1, N
209         AINV( J, J ) = AINV( J, J ) - ONE
210   40 CONTINUE
211*
212*     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
213*
214      RESID = DLANTR( '1', UPLO, 'Non-unit', N, N, AINV, LDAINV, WORK )
215*
216      RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
217*
218      RETURN
219*
220*     End of DTRT01
221*
222      END
223