LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
ctpcon.f
Go to the documentation of this file.
1 *> \brief \b CTPCON
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/ctpcon.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctpcon.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctpcon.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER DIAG, NORM, UPLO
26 * INTEGER INFO, N
27 * REAL RCOND
28 * ..
29 * .. Array Arguments ..
30 * REAL RWORK( * )
31 * COMPLEX AP( * ), WORK( * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CTPCON estimates the reciprocal of the condition number of a packed
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] AP
82 *> \verbatim
83 *> AP is COMPLEX array, dimension (N*(N+1)/2)
84 *> The upper or lower triangular matrix A, packed columnwise in
85 *> a linear array. The j-th column of A is stored in the array
86 *> AP as follows:
87 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
88 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
89 *> If DIAG = 'U', the diagonal elements of A are not referenced
90 *> and are assumed to be 1.
91 *> \endverbatim
92 *>
93 *> \param[out] RCOND
94 *> \verbatim
95 *> RCOND is REAL
96 *> The reciprocal of the condition number of the matrix A,
97 *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
98 *> \endverbatim
99 *>
100 *> \param[out] WORK
101 *> \verbatim
102 *> WORK is COMPLEX array, dimension (2*N)
103 *> \endverbatim
104 *>
105 *> \param[out] RWORK
106 *> \verbatim
107 *> RWORK is REAL array, dimension (N)
108 *> \endverbatim
109 *>
110 *> \param[out] INFO
111 *> \verbatim
112 *> INFO is INTEGER
113 *> = 0: successful exit
114 *> < 0: if INFO = -i, the i-th argument had an illegal value
115 *> \endverbatim
116 *
117 * Authors:
118 * ========
119 *
120 *> \author Univ. of Tennessee
121 *> \author Univ. of California Berkeley
122 *> \author Univ. of Colorado Denver
123 *> \author NAG Ltd.
124 *
125 *> \date November 2011
126 *
127 *> \ingroup complexOTHERcomputational
128 *
129 * =====================================================================
130  SUBROUTINE ctpcon( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK,
131  \$ info )
132 *
133 * -- LAPACK computational routine (version 3.4.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * November 2011
137 *
138 * .. Scalar Arguments ..
139  CHARACTER DIAG, NORM, UPLO
140  INTEGER INFO, N
141  REAL RCOND
142 * ..
143 * .. Array Arguments ..
144  REAL RWORK( * )
145  COMPLEX AP( * ), WORK( * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  REAL ONE, ZERO
152  parameter ( one = 1.0e+0, zero = 0.0e+0 )
153 * ..
154 * .. Local Scalars ..
155  LOGICAL NOUNIT, ONENRM, UPPER
156  CHARACTER NORMIN
157  INTEGER IX, KASE, KASE1
158  REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
159  COMPLEX ZDUM
160 * ..
161 * .. Local Arrays ..
162  INTEGER ISAVE( 3 )
163 * ..
164 * .. External Functions ..
165  LOGICAL LSAME
166  INTEGER ICAMAX
167  REAL CLANTP, SLAMCH
168  EXTERNAL lsame, icamax, clantp, slamch
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL clacn2, clatps, csrscl, xerbla
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC abs, aimag, max, real
175 * ..
176 * .. Statement Functions ..
177  REAL CABS1
178 * ..
179 * .. Statement Function definitions ..
180  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( AIMAG( zdum ) )
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input parameters.
185 *
186  info = 0
187  upper = lsame( uplo, 'U' )
188  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
189  nounit = lsame( diag, 'N' )
190 *
191  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
192  info = -1
193  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
194  info = -2
195  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
196  info = -3
197  ELSE IF( n.LT.0 ) THEN
198  info = -4
199  END IF
200  IF( info.NE.0 ) THEN
201  CALL xerbla( 'CTPCON', -info )
202  RETURN
203  END IF
204 *
205 * Quick return if possible
206 *
207  IF( n.EQ.0 ) THEN
208  rcond = one
209  RETURN
210  END IF
211 *
212  rcond = zero
213  smlnum = slamch( 'Safe minimum' )*REAL( MAX( 1, N ) )
214 *
215 * Compute the norm of the triangular matrix A.
216 *
217  anorm = clantp( norm, uplo, diag, n, ap, rwork )
218 *
219 * Continue only if ANORM > 0.
220 *
221  IF( anorm.GT.zero ) THEN
222 *
223 * Estimate the norm of the inverse of A.
224 *
225  ainvnm = zero
226  normin = 'N'
227  IF( onenrm ) THEN
228  kase1 = 1
229  ELSE
230  kase1 = 2
231  END IF
232  kase = 0
233  10 CONTINUE
234  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
235  IF( kase.NE.0 ) THEN
236  IF( kase.EQ.kase1 ) THEN
237 *
238 * Multiply by inv(A).
239 *
240  CALL clatps( uplo, 'No transpose', diag, normin, n, ap,
241  \$ work, scale, rwork, info )
242  ELSE
243 *
244 * Multiply by inv(A**H).
245 *
246  CALL clatps( uplo, 'Conjugate transpose', diag, normin,
247  \$ n, ap, work, scale, rwork, info )
248  END IF
249  normin = 'Y'
250 *
251 * Multiply by 1/SCALE if doing so will not cause overflow.
252 *
253  IF( scale.NE.one ) THEN
254  ix = icamax( n, work, 1 )
255  xnorm = cabs1( work( ix ) )
256  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
257  \$ GO TO 20
258  CALL csrscl( n, scale, work, 1 )
259  END IF
260  GO TO 10
261  END IF
262 *
263 * Compute the estimate of the reciprocal condition number.
264 *
265  IF( ainvnm.NE.zero )
266  \$ rcond = ( one / anorm ) / ainvnm
267  END IF
268 *
269  20 CONTINUE
270  RETURN
271 *
272 * End of CTPCON
273 *
274  END
subroutine clatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
CLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: clatps.f:233
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:86
subroutine ctpcon(NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO)
CTPCON
Definition: ctpcon.f:132
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:135