LAPACK  3.10.0
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
9 *> Download CTPCON + dependencies
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 *> \ingroup complexOTHERcomputational
126 *
127 * =====================================================================
128  SUBROUTINE ctpcon( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK,
129  $ INFO )
130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER DIAG, NORM, UPLO
137  INTEGER INFO, N
138  REAL RCOND
139 * ..
140 * .. Array Arguments ..
141  REAL RWORK( * )
142  COMPLEX AP( * ), WORK( * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Parameters ..
148  REAL ONE, ZERO
149  parameter( one = 1.0e+0, zero = 0.0e+0 )
150 * ..
151 * .. Local Scalars ..
152  LOGICAL NOUNIT, ONENRM, UPPER
153  CHARACTER NORMIN
154  INTEGER IX, KASE, KASE1
155  REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
156  COMPLEX ZDUM
157 * ..
158 * .. Local Arrays ..
159  INTEGER ISAVE( 3 )
160 * ..
161 * .. External Functions ..
162  LOGICAL LSAME
163  INTEGER ICAMAX
164  REAL CLANTP, SLAMCH
165  EXTERNAL lsame, icamax, clantp, slamch
166 * ..
167 * .. External Subroutines ..
168  EXTERNAL clacn2, clatps, csrscl, xerbla
169 * ..
170 * .. Intrinsic Functions ..
171  INTRINSIC abs, aimag, max, real
172 * ..
173 * .. Statement Functions ..
174  REAL CABS1
175 * ..
176 * .. Statement Function definitions ..
177  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
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  END IF
197  IF( info.NE.0 ) THEN
198  CALL xerbla( 'CTPCON', -info )
199  RETURN
200  END IF
201 *
202 * Quick return if possible
203 *
204  IF( n.EQ.0 ) THEN
205  rcond = one
206  RETURN
207  END IF
208 *
209  rcond = zero
210  smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
211 *
212 * Compute the norm of the triangular matrix A.
213 *
214  anorm = clantp( norm, uplo, diag, n, ap, rwork )
215 *
216 * Continue only if ANORM > 0.
217 *
218  IF( anorm.GT.zero ) THEN
219 *
220 * Estimate the norm of the inverse of A.
221 *
222  ainvnm = zero
223  normin = 'N'
224  IF( onenrm ) THEN
225  kase1 = 1
226  ELSE
227  kase1 = 2
228  END IF
229  kase = 0
230  10 CONTINUE
231  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
232  IF( kase.NE.0 ) THEN
233  IF( kase.EQ.kase1 ) THEN
234 *
235 * Multiply by inv(A).
236 *
237  CALL clatps( uplo, 'No transpose', diag, normin, n, ap,
238  $ work, scale, rwork, info )
239  ELSE
240 *
241 * Multiply by inv(A**H).
242 *
243  CALL clatps( uplo, 'Conjugate transpose', diag, normin,
244  $ n, ap, work, scale, rwork, info )
245  END IF
246  normin = 'Y'
247 *
248 * Multiply by 1/SCALE if doing so will not cause overflow.
249 *
250  IF( scale.NE.one ) THEN
251  ix = icamax( n, work, 1 )
252  xnorm = cabs1( work( ix ) )
253  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
254  $ GO TO 20
255  CALL csrscl( n, scale, work, 1 )
256  END IF
257  GO TO 10
258  END IF
259 *
260 * Compute the estimate of the reciprocal condition number.
261 *
262  IF( ainvnm.NE.zero )
263  $ rcond = ( one / anorm ) / ainvnm
264  END IF
265 *
266  20 CONTINUE
267  RETURN
268 *
269 * End of CTPCON
270 *
271  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:84
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:231
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:133
subroutine ctpcon(NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO)
CTPCON
Definition: ctpcon.f:130