LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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ztrt01.f
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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*> \ingroup complex16_lin
121*
122* =====================================================================
123 SUBROUTINE ztrt01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
124 $ RWORK, RESID )
125*
126* -- LAPACK test routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER DIAG, UPLO
132 INTEGER LDA, LDAINV, N
133 DOUBLE PRECISION RCOND, RESID
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION RWORK( * )
137 COMPLEX*16 A( LDA, * ), AINV( LDAINV, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ZERO, ONE
144 parameter( zero = 0.0d+0, one = 1.0d+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER J
148 DOUBLE PRECISION AINVNM, ANORM, EPS
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 DOUBLE PRECISION DLAMCH, ZLANTR
153 EXTERNAL lsame, dlamch, zlantr
154* ..
155* .. External Subroutines ..
156 EXTERNAL ztrmv
157* ..
158* .. Intrinsic Functions ..
159 INTRINSIC dble
160* ..
161* .. Executable Statements ..
162*
163* Quick exit if N = 0
164*
165 IF( n.LE.0 ) THEN
166 rcond = one
167 resid = zero
168 RETURN
169 END IF
170*
171* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
172*
173 eps = dlamch( 'Epsilon' )
174 anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
175 ainvnm = zlantr( '1', uplo, diag, n, n, ainv, ldainv, rwork )
176 IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
177 rcond = zero
178 resid = one / eps
179 RETURN
180 END IF
181 rcond = ( one / anorm ) / ainvnm
182*
183* Set the diagonal of AINV to 1 if AINV has unit diagonal.
184*
185 IF( lsame( diag, 'U' ) ) THEN
186 DO 10 j = 1, n
187 ainv( j, j ) = one
188 10 CONTINUE
189 END IF
190*
191* Compute A * AINV, overwriting AINV.
192*
193 IF( lsame( uplo, 'U' ) ) THEN
194 DO 20 j = 1, n
195 CALL ztrmv( 'Upper', 'No transpose', diag, j, a, lda,
196 $ ainv( 1, j ), 1 )
197 20 CONTINUE
198 ELSE
199 DO 30 j = 1, n
200 CALL ztrmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
201 $ lda, ainv( j, j ), 1 )
202 30 CONTINUE
203 END IF
204*
205* Subtract 1 from each diagonal element to form A*AINV - I.
206*
207 DO 40 j = 1, n
208 ainv( j, j ) = ainv( j, j ) - one
209 40 CONTINUE
210*
211* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
212*
213 resid = zlantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, rwork )
214*
215 resid = ( ( resid*rcond ) / dble( n ) ) / eps
216*
217 RETURN
218*
219* End of ZTRT01
220*
221 END
subroutine ztrmv(uplo, trans, diag, n, a, lda, x, incx)
ZTRMV
Definition ztrmv.f:147
subroutine ztrt01(uplo, diag, n, a, lda, ainv, ldainv, rcond, rwork, resid)
ZTRT01
Definition ztrt01.f:125