LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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ctrt03.f
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1*> \brief \b CTRT03
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 CTRT03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
12* CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER DIAG, TRANS, UPLO
16* INTEGER LDA, LDB, LDX, N, NRHS
17* REAL RESID, SCALE, TSCAL
18* ..
19* .. Array Arguments ..
20* REAL CNORM( * )
21* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
22* $ X( LDX, * )
23* ..
24*
25*
26*> \par Purpose:
27* =============
28*>
29*> \verbatim
30*>
31*> CTRT03 computes the residual for the solution to a scaled triangular
32*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b.
33*> Here A is a triangular matrix, A**T denotes the transpose of A, A**H
34*> denotes the conjugate transpose of A, s is a scalar, and x and b are
35*> N by NRHS matrices. The test ratio is the maximum over the number of
36*> right hand sides of
37*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
38*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
39*> \endverbatim
40*
41* Arguments:
42* ==========
43*
44*> \param[in] UPLO
45*> \verbatim
46*> UPLO is CHARACTER*1
47*> Specifies whether the matrix A is upper or lower triangular.
48*> = 'U': Upper triangular
49*> = 'L': Lower triangular
50*> \endverbatim
51*>
52*> \param[in] TRANS
53*> \verbatim
54*> TRANS is CHARACTER*1
55*> Specifies the operation applied to A.
56*> = 'N': A *x = s*b (No transpose)
57*> = 'T': A**T *x = s*b (Transpose)
58*> = 'C': A**H *x = s*b (Conjugate transpose)
59*> \endverbatim
60*>
61*> \param[in] DIAG
62*> \verbatim
63*> DIAG is CHARACTER*1
64*> Specifies whether or not the matrix A is unit triangular.
65*> = 'N': Non-unit triangular
66*> = 'U': Unit triangular
67*> \endverbatim
68*>
69*> \param[in] N
70*> \verbatim
71*> N is INTEGER
72*> The order of the matrix A. N >= 0.
73*> \endverbatim
74*>
75*> \param[in] NRHS
76*> \verbatim
77*> NRHS is INTEGER
78*> The number of right hand sides, i.e., the number of columns
79*> of the matrices X and B. NRHS >= 0.
80*> \endverbatim
81*>
82*> \param[in] A
83*> \verbatim
84*> A is COMPLEX array, dimension (LDA,N)
85*> The triangular matrix A. If UPLO = 'U', the leading n by n
86*> upper triangular part of the array A contains the upper
87*> triangular matrix, and the strictly lower triangular part of
88*> A is not referenced. If UPLO = 'L', the leading n by n lower
89*> triangular part of the array A contains the lower triangular
90*> matrix, and the strictly upper triangular part of A is not
91*> referenced. If DIAG = 'U', the diagonal elements of A are
92*> also not referenced and are assumed to be 1.
93*> \endverbatim
94*>
95*> \param[in] LDA
96*> \verbatim
97*> LDA is INTEGER
98*> The leading dimension of the array A. LDA >= max(1,N).
99*> \endverbatim
100*>
101*> \param[in] SCALE
102*> \verbatim
103*> SCALE is REAL
104*> The scaling factor s used in solving the triangular system.
105*> \endverbatim
106*>
107*> \param[in] CNORM
108*> \verbatim
109*> CNORM is REAL array, dimension (N)
110*> The 1-norms of the columns of A, not counting the diagonal.
111*> \endverbatim
112*>
113*> \param[in] TSCAL
114*> \verbatim
115*> TSCAL is REAL
116*> The scaling factor used in computing the 1-norms in CNORM.
117*> CNORM actually contains the column norms of TSCAL*A.
118*> \endverbatim
119*>
120*> \param[in] X
121*> \verbatim
122*> X is COMPLEX array, dimension (LDX,NRHS)
123*> The computed solution vectors for the system of linear
124*> equations.
125*> \endverbatim
126*>
127*> \param[in] LDX
128*> \verbatim
129*> LDX is INTEGER
130*> The leading dimension of the array X. LDX >= max(1,N).
131*> \endverbatim
132*>
133*> \param[in] B
134*> \verbatim
135*> B is COMPLEX array, dimension (LDB,NRHS)
136*> The right hand side vectors for the system of linear
137*> equations.
138*> \endverbatim
139*>
140*> \param[in] LDB
141*> \verbatim
142*> LDB is INTEGER
143*> The leading dimension of the array B. LDB >= max(1,N).
144*> \endverbatim
145*>
146*> \param[out] WORK
147*> \verbatim
148*> WORK is COMPLEX array, dimension (N)
149*> \endverbatim
150*>
151*> \param[out] RESID
152*> \verbatim
153*> RESID is REAL
154*> The maximum over the number of right hand sides of
155*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
156*> \endverbatim
157*
158* Authors:
159* ========
160*
161*> \author Univ. of Tennessee
162*> \author Univ. of California Berkeley
163*> \author Univ. of Colorado Denver
164*> \author NAG Ltd.
165*
166*> \ingroup complex_lin
167*
168* =====================================================================
169 SUBROUTINE ctrt03( UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE,
170 $ CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID )
171*
172* -- LAPACK test routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 CHARACTER DIAG, TRANS, UPLO
178 INTEGER LDA, LDB, LDX, N, NRHS
179 REAL RESID, SCALE, TSCAL
180* ..
181* .. Array Arguments ..
182 REAL CNORM( * )
183 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
184 $ x( ldx, * )
185* ..
186*
187* =====================================================================
188*
189* .. Parameters ..
190 REAL ONE, ZERO
191 parameter( one = 1.0e+0, zero = 0.0e+0 )
192* ..
193* .. Local Scalars ..
194 INTEGER IX, J
195 REAL EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
196* ..
197* .. External Functions ..
198 LOGICAL LSAME
199 INTEGER ICAMAX
200 REAL SLAMCH
201 EXTERNAL lsame, icamax, slamch
202* ..
203* .. External Subroutines ..
204 EXTERNAL caxpy, ccopy, csscal, ctrmv
205* ..
206* .. Intrinsic Functions ..
207 INTRINSIC abs, cmplx, max, real
208* ..
209* .. Executable Statements ..
210*
211* Quick exit if N = 0
212*
213 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
214 resid = zero
215 RETURN
216 END IF
217 eps = slamch( 'Epsilon' )
218 smlnum = slamch( 'Safe minimum' )
219*
220* Compute the norm of the triangular matrix A using the column
221* norms already computed by CLATRS.
222*
223 tnorm = zero
224 IF( lsame( diag, 'N' ) ) THEN
225 DO 10 j = 1, n
226 tnorm = max( tnorm, tscal*abs( a( j, j ) )+cnorm( j ) )
227 10 CONTINUE
228 ELSE
229 DO 20 j = 1, n
230 tnorm = max( tnorm, tscal+cnorm( j ) )
231 20 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(op(A)) * norm(x) * EPS ).
236*
237 resid = zero
238 DO 30 j = 1, nrhs
239 CALL ccopy( n, x( 1, j ), 1, work, 1 )
240 ix = icamax( n, work, 1 )
241 xnorm = max( one, abs( x( ix, j ) ) )
242 xscal = ( one / xnorm ) / real( n )
243 CALL csscal( n, xscal, work, 1 )
244 CALL ctrmv( uplo, trans, diag, n, a, lda, work, 1 )
245 CALL caxpy( n, cmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
246 ix = icamax( n, work, 1 )
247 err = tscal*abs( work( ix ) )
248 ix = icamax( 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 30 CONTINUE
266*
267 RETURN
268*
269* End of CTRT03
270*
271 END
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine ctrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV
Definition: ctrmv.f:147
subroutine ctrt03(UPLO, TRANS, DIAG, N, NRHS, A, LDA, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
CTRT03
Definition: ctrt03.f:171