LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
ztrcon.f
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1 *> \brief \b ZTRCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
22 * RWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER DIAG, NORM, UPLO
26 * INTEGER INFO, LDA, N
27 * DOUBLE PRECISION RCOND
28 * ..
29 * .. Array Arguments ..
30 * DOUBLE PRECISION RWORK( * )
31 * COMPLEX*16 A( LDA, * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> ZTRCON 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 COMPLEX*16 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 COMPLEX*16 array, dimension (2*N)
110 *> \endverbatim
111 *>
112 *> \param[out] RWORK
113 *> \verbatim
114 *> RWORK is DOUBLE PRECISION 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 *> \date November 2011
133 *
134 *> \ingroup complex16OTHERcomputational
135 *
136 * =====================================================================
137  SUBROUTINE ztrcon( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
138  \$ rwork, info )
139 *
140 * -- LAPACK computational routine (version 3.4.0) --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 * November 2011
144 *
145 * .. Scalar Arguments ..
146  CHARACTER DIAG, NORM, UPLO
147  INTEGER INFO, LDA, N
148  DOUBLE PRECISION RCOND
149 * ..
150 * .. Array Arguments ..
151  DOUBLE PRECISION RWORK( * )
152  COMPLEX*16 A( lda, * ), WORK( * )
153 * ..
154 *
155 * =====================================================================
156 *
157 * .. Parameters ..
158  DOUBLE PRECISION ONE, ZERO
159  parameter ( one = 1.0d+0, zero = 0.0d+0 )
160 * ..
161 * .. Local Scalars ..
162  LOGICAL NOUNIT, ONENRM, UPPER
163  CHARACTER NORMIN
164  INTEGER IX, KASE, KASE1
165  DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
166  COMPLEX*16 ZDUM
167 * ..
168 * .. Local Arrays ..
169  INTEGER ISAVE( 3 )
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME
173  INTEGER IZAMAX
174  DOUBLE PRECISION DLAMCH, ZLANTR
175  EXTERNAL lsame, izamax, dlamch, zlantr
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL xerbla, zdrscl, zlacn2, zlatrs
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC abs, dble, dimag, max
182 * ..
183 * .. Statement Functions ..
184  DOUBLE PRECISION CABS1
185 * ..
186 * .. Statement Function definitions ..
187  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
188 * ..
189 * .. Executable Statements ..
190 *
191 * Test the input parameters.
192 *
193  info = 0
194  upper = lsame( uplo, 'U' )
195  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
196  nounit = lsame( diag, 'N' )
197 *
198  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
199  info = -1
200  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
201  info = -2
202  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
203  info = -3
204  ELSE IF( n.LT.0 ) THEN
205  info = -4
206  ELSE IF( lda.LT.max( 1, n ) ) THEN
207  info = -6
208  END IF
209  IF( info.NE.0 ) THEN
210  CALL xerbla( 'ZTRCON', -info )
211  RETURN
212  END IF
213 *
214 * Quick return if possible
215 *
216  IF( n.EQ.0 ) THEN
217  rcond = one
218  RETURN
219  END IF
220 *
221  rcond = zero
222  smlnum = dlamch( 'Safe minimum' )*dble( max( 1, n ) )
223 *
224 * Compute the norm of the triangular matrix A.
225 *
226  anorm = zlantr( norm, uplo, diag, n, n, a, lda, rwork )
227 *
228 * Continue only if ANORM > 0.
229 *
230  IF( anorm.GT.zero ) THEN
231 *
232 * Estimate the norm of the inverse of A.
233 *
234  ainvnm = zero
235  normin = 'N'
236  IF( onenrm ) THEN
237  kase1 = 1
238  ELSE
239  kase1 = 2
240  END IF
241  kase = 0
242  10 CONTINUE
243  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
244  IF( kase.NE.0 ) THEN
245  IF( kase.EQ.kase1 ) THEN
246 *
247 * Multiply by inv(A).
248 *
249  CALL zlatrs( uplo, 'No transpose', diag, normin, n, a,
250  \$ lda, work, scale, rwork, info )
251  ELSE
252 *
253 * Multiply by inv(A**H).
254 *
255  CALL zlatrs( uplo, 'Conjugate transpose', diag, normin,
256  \$ n, a, lda, work, scale, rwork, info )
257  END IF
258  normin = 'Y'
259 *
260 * Multiply by 1/SCALE if doing so will not cause overflow.
261 *
262  IF( scale.NE.one ) THEN
263  ix = izamax( n, work, 1 )
264  xnorm = cabs1( work( ix ) )
265  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
266  \$ GO TO 20
267  CALL zdrscl( n, scale, work, 1 )
268  END IF
269  GO TO 10
270  END IF
271 *
272 * Compute the estimate of the reciprocal condition number.
273 *
274  IF( ainvnm.NE.zero )
275  \$ rcond = ( one / anorm ) / ainvnm
276  END IF
277 *
278  20 CONTINUE
279  RETURN
280 *
281 * End of ZTRCON
282 *
283  END
subroutine zdrscl(N, SA, SX, INCX)
ZDRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: zdrscl.f:86
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:135
subroutine ztrcon(NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO)
ZTRCON
Definition: ztrcon.f:139
subroutine zlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
ZLATRS solves a triangular system of equations with the scale factor set to prevent overflow...
Definition: zlatrs.f:241