LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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strcon.f
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1*> \brief \b STRCON
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/strcon.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/strcon.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/strcon.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE STRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
22* IWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER DIAG, NORM, UPLO
26* INTEGER INFO, LDA, N
27* REAL RCOND
28* ..
29* .. Array Arguments ..
30* INTEGER IWORK( * )
31* REAL A( LDA, * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> STRCON estimates the reciprocal of the condition number of a
41*> triangular matrix A, in either the 1-norm or the infinity-norm.
42*>
43*> The norm of A is computed and an estimate is obtained for
44*> norm(inv(A)), then the reciprocal of the condition number is
45*> computed as
46*> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
47*> \endverbatim
48*
49* Arguments:
50* ==========
51*
52*> \param[in] NORM
53*> \verbatim
54*> NORM is CHARACTER*1
55*> Specifies whether the 1-norm condition number or the
56*> infinity-norm condition number is required:
57*> = '1' or 'O': 1-norm;
58*> = 'I': Infinity-norm.
59*> \endverbatim
60*>
61*> \param[in] UPLO
62*> \verbatim
63*> UPLO is CHARACTER*1
64*> = 'U': A is upper triangular;
65*> = 'L': A is lower triangular.
66*> \endverbatim
67*>
68*> \param[in] DIAG
69*> \verbatim
70*> DIAG is CHARACTER*1
71*> = 'N': A is non-unit triangular;
72*> = 'U': A is unit triangular.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The order of the matrix A. N >= 0.
79*> \endverbatim
80*>
81*> \param[in] A
82*> \verbatim
83*> A is REAL array, dimension (LDA,N)
84*> The triangular matrix A. If UPLO = 'U', the leading N-by-N
85*> upper triangular part of the array A contains the upper
86*> triangular matrix, and the strictly lower triangular part of
87*> A is not referenced. If UPLO = 'L', the leading N-by-N lower
88*> triangular part of the array A contains the lower triangular
89*> matrix, and the strictly upper triangular part of A is not
90*> referenced. If DIAG = 'U', the diagonal elements of A are
91*> also not referenced and are assumed to be 1.
92*> \endverbatim
93*>
94*> \param[in] LDA
95*> \verbatim
96*> LDA is INTEGER
97*> The leading dimension of the array A. LDA >= max(1,N).
98*> \endverbatim
99*>
100*> \param[out] RCOND
101*> \verbatim
102*> RCOND is REAL
103*> The reciprocal of the condition number of the matrix A,
104*> computed as RCOND = 1/(norm(A) * norm(inv(A))).
105*> \endverbatim
106*>
107*> \param[out] WORK
108*> \verbatim
109*> WORK is REAL array, dimension (3*N)
110*> \endverbatim
111*>
112*> \param[out] IWORK
113*> \verbatim
114*> IWORK is INTEGER array, dimension (N)
115*> \endverbatim
116*>
117*> \param[out] INFO
118*> \verbatim
119*> INFO is INTEGER
120*> = 0: successful exit
121*> < 0: if INFO = -i, the i-th argument had an illegal value
122*> \endverbatim
123*
124* Authors:
125* ========
126*
127*> \author Univ. of Tennessee
128*> \author Univ. of California Berkeley
129*> \author Univ. of Colorado Denver
130*> \author NAG Ltd.
131*
132*> \ingroup realOTHERcomputational
133*
134* =====================================================================
135 SUBROUTINE strcon( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
136 \$ IWORK, INFO )
137*
138* -- LAPACK computational routine --
139* -- LAPACK is a software package provided by Univ. of Tennessee, --
140* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141*
142* .. Scalar Arguments ..
143 CHARACTER DIAG, NORM, UPLO
144 INTEGER INFO, LDA, N
145 REAL RCOND
146* ..
147* .. Array Arguments ..
148 INTEGER IWORK( * )
149 REAL A( LDA, * ), WORK( * )
150* ..
151*
152* =====================================================================
153*
154* .. Parameters ..
155 REAL ONE, ZERO
156 parameter( one = 1.0e+0, zero = 0.0e+0 )
157* ..
158* .. Local Scalars ..
159 LOGICAL NOUNIT, ONENRM, UPPER
160 CHARACTER NORMIN
161 INTEGER IX, KASE, KASE1
162 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
163* ..
164* .. Local Arrays ..
165 INTEGER ISAVE( 3 )
166* ..
167* .. External Functions ..
168 LOGICAL LSAME
169 INTEGER ISAMAX
170 REAL SLAMCH, SLANTR
171 EXTERNAL lsame, isamax, slamch, slantr
172* ..
173* .. External Subroutines ..
174 EXTERNAL slacn2, slatrs, srscl, xerbla
175* ..
176* .. Intrinsic Functions ..
177 INTRINSIC abs, max, real
178* ..
179* .. Executable Statements ..
180*
181* Test the input parameters.
182*
183 info = 0
184 upper = lsame( uplo, 'U' )
185 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
186 nounit = lsame( diag, 'N' )
187*
188 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
189 info = -1
190 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
191 info = -2
192 ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
193 info = -3
194 ELSE IF( n.LT.0 ) THEN
195 info = -4
196 ELSE IF( lda.LT.max( 1, n ) ) THEN
197 info = -6
198 END IF
199 IF( info.NE.0 ) THEN
200 CALL xerbla( 'STRCON', -info )
201 RETURN
202 END IF
203*
204* Quick return if possible
205*
206 IF( n.EQ.0 ) THEN
207 rcond = one
208 RETURN
209 END IF
210*
211 rcond = zero
212 smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
213*
214* Compute the norm of the triangular matrix A.
215*
216 anorm = slantr( norm, uplo, diag, n, n, a, lda, work )
217*
218* Continue only if ANORM > 0.
219*
220 IF( anorm.GT.zero ) THEN
221*
222* Estimate the norm of the inverse of A.
223*
224 ainvnm = zero
225 normin = 'N'
226 IF( onenrm ) THEN
227 kase1 = 1
228 ELSE
229 kase1 = 2
230 END IF
231 kase = 0
232 10 CONTINUE
233 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
234 IF( kase.NE.0 ) THEN
235 IF( kase.EQ.kase1 ) THEN
236*
237* Multiply by inv(A).
238*
239 CALL slatrs( uplo, 'No transpose', diag, normin, n, a,
240 \$ lda, work, scale, work( 2*n+1 ), info )
241 ELSE
242*
243* Multiply by inv(A**T).
244*
245 CALL slatrs( uplo, 'Transpose', diag, normin, n, a, lda,
246 \$ work, scale, work( 2*n+1 ), info )
247 END IF
248 normin = 'Y'
249*
250* Multiply by 1/SCALE if doing so will not cause overflow.
251*
252 IF( scale.NE.one ) THEN
253 ix = isamax( n, work, 1 )
254 xnorm = abs( work( ix ) )
255 IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
256 \$ GO TO 20
257 CALL srscl( n, scale, work, 1 )
258 END IF
259 GO TO 10
260 END IF
261*
262* Compute the estimate of the reciprocal condition number.
263*
264 IF( ainvnm.NE.zero )
265 \$ rcond = ( one / anorm ) / ainvnm
266 END IF
267*
268 20 CONTINUE
269 RETURN
270*
271* End of STRCON
272*
273 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
SLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: slatrs.f:238
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:84
subroutine strcon(NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, IWORK, INFO)
STRCON
Definition: strcon.f:137