LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
dtrcon.f
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1 *> \brief \b DTRCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DTRCON( 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 * DOUBLE PRECISION RCOND
28 * ..
29 * .. Array Arguments ..
30 * INTEGER IWORK( * )
31 * DOUBLE PRECISION A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> DTRCON 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 DOUBLE PRECISION 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 DOUBLE PRECISION
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 DOUBLE PRECISION 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 doubleOTHERcomputational
133 *
134 * =====================================================================
135  SUBROUTINE dtrcon( 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  DOUBLE PRECISION RCOND
146 * ..
147 * .. Array Arguments ..
148  INTEGER IWORK( * )
149  DOUBLE PRECISION A( LDA, * ), WORK( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  DOUBLE PRECISION ONE, ZERO
156  parameter( one = 1.0d+0, zero = 0.0d+0 )
157 * ..
158 * .. Local Scalars ..
159  LOGICAL NOUNIT, ONENRM, UPPER
160  CHARACTER NORMIN
161  INTEGER IX, KASE, KASE1
162  DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
163 * ..
164 * .. Local Arrays ..
165  INTEGER ISAVE( 3 )
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME
169  INTEGER IDAMAX
170  DOUBLE PRECISION DLAMCH, DLANTR
171  EXTERNAL lsame, idamax, dlamch, dlantr
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL dlacn2, dlatrs, drscl, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, dble, max
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( 'DTRCON', -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 = dlamch( 'Safe minimum' )*dble( max( 1, n ) )
213 *
214 * Compute the norm of the triangular matrix A.
215 *
216  anorm = dlantr( 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 dlacn2( 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 dlatrs( 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 dlatrs( 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 = idamax( n, work, 1 )
254  xnorm = abs( work( ix ) )
255  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
256  \$ GO TO 20
257  CALL drscl( 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 DTRCON
272 *
273  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:84
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
subroutine dlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: dlatrs.f:238
subroutine dtrcon(NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, IWORK, INFO)
DTRCON
Definition: dtrcon.f:137