LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cppcon.f
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1 *> \brief \b CPPCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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7 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, N
26 * REAL ANORM, RCOND
27 * ..
28 * .. Array Arguments ..
29 * REAL RWORK( * )
30 * COMPLEX AP( * ), WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CPPCON estimates the reciprocal of the condition number (in the
40 *> 1-norm) of a complex Hermitian positive definite packed matrix using
41 *> the Cholesky factorization A = U**H*U or A = L*L**H computed by
42 *> CPPTRF.
43 *>
44 *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
45 *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
46 *> \endverbatim
47 *
48 * Arguments:
49 * ==========
50 *
51 *> \param[in] UPLO
52 *> \verbatim
53 *> UPLO is CHARACTER*1
54 *> = 'U': Upper triangle of A is stored;
55 *> = 'L': Lower triangle of A is stored.
56 *> \endverbatim
57 *>
58 *> \param[in] N
59 *> \verbatim
60 *> N is INTEGER
61 *> The order of the matrix A. N >= 0.
62 *> \endverbatim
63 *>
64 *> \param[in] AP
65 *> \verbatim
66 *> AP is COMPLEX array, dimension (N*(N+1)/2)
67 *> The triangular factor U or L from the Cholesky factorization
68 *> A = U**H*U or A = L*L**H, packed columnwise in a linear
69 *> array. The j-th column of U or L is stored in the array AP
70 *> as follows:
71 *> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
72 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
73 *> \endverbatim
74 *>
75 *> \param[in] ANORM
76 *> \verbatim
77 *> ANORM is REAL
78 *> The 1-norm (or infinity-norm) of the Hermitian matrix A.
79 *> \endverbatim
80 *>
81 *> \param[out] RCOND
82 *> \verbatim
83 *> RCOND is REAL
84 *> The reciprocal of the condition number of the matrix A,
85 *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
86 *> estimate of the 1-norm of inv(A) computed in this routine.
87 *> \endverbatim
88 *>
89 *> \param[out] WORK
90 *> \verbatim
91 *> WORK is COMPLEX array, dimension (2*N)
92 *> \endverbatim
93 *>
94 *> \param[out] RWORK
95 *> \verbatim
96 *> RWORK is REAL array, dimension (N)
97 *> \endverbatim
98 *>
99 *> \param[out] INFO
100 *> \verbatim
101 *> INFO is INTEGER
102 *> = 0: successful exit
103 *> < 0: if INFO = -i, the i-th argument had an illegal value
104 *> \endverbatim
105 *
106 * Authors:
107 * ========
108 *
109 *> \author Univ. of Tennessee
110 *> \author Univ. of California Berkeley
111 *> \author Univ. of Colorado Denver
112 *> \author NAG Ltd.
113 *
114 *> \ingroup complexOTHERcomputational
115 *
116 * =====================================================================
117  SUBROUTINE cppcon( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
118 *
119 * -- LAPACK computational routine --
120 * -- LAPACK is a software package provided by Univ. of Tennessee, --
121 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
122 *
123 * .. Scalar Arguments ..
124  CHARACTER UPLO
125  INTEGER INFO, N
126  REAL ANORM, RCOND
127 * ..
128 * .. Array Arguments ..
129  REAL RWORK( * )
130  COMPLEX AP( * ), WORK( * )
131 * ..
132 *
133 * =====================================================================
134 *
135 * .. Parameters ..
136  REAL ONE, ZERO
137  parameter( one = 1.0e+0, zero = 0.0e+0 )
138 * ..
139 * .. Local Scalars ..
140  LOGICAL UPPER
141  CHARACTER NORMIN
142  INTEGER IX, KASE
143  REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
144  COMPLEX ZDUM
145 * ..
146 * .. Local Arrays ..
147  INTEGER ISAVE( 3 )
148 * ..
149 * .. External Functions ..
150  LOGICAL LSAME
151  INTEGER ICAMAX
152  REAL SLAMCH
153  EXTERNAL lsame, icamax, slamch
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL clacn2, clatps, csrscl, xerbla
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC abs, aimag, real
160 * ..
161 * .. Statement Functions ..
162  REAL CABS1
163 * ..
164 * .. Statement Function definitions ..
165  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
166 * ..
167 * .. Executable Statements ..
168 *
169 * Test the input parameters.
170 *
171  info = 0
172  upper = lsame( uplo, 'U' )
173  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
174  info = -1
175  ELSE IF( n.LT.0 ) THEN
176  info = -2
177  ELSE IF( anorm.LT.zero ) THEN
178  info = -4
179  END IF
180  IF( info.NE.0 ) THEN
181  CALL xerbla( 'CPPCON', -info )
182  RETURN
183  END IF
184 *
185 * Quick return if possible
186 *
187  rcond = zero
188  IF( n.EQ.0 ) THEN
189  rcond = one
190  RETURN
191  ELSE IF( anorm.EQ.zero ) THEN
192  RETURN
193  END IF
194 *
195  smlnum = slamch( 'Safe minimum' )
196 *
197 * Estimate the 1-norm of the inverse.
198 *
199  kase = 0
200  normin = 'N'
201  10 CONTINUE
202  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
203  IF( kase.NE.0 ) THEN
204  IF( upper ) THEN
205 *
206 * Multiply by inv(U**H).
207 *
208  CALL clatps( 'Upper', 'Conjugate transpose', 'Non-unit',
209  $ normin, n, ap, work, scalel, rwork, info )
210  normin = 'Y'
211 *
212 * Multiply by inv(U).
213 *
214  CALL clatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
215  $ ap, work, scaleu, rwork, info )
216  ELSE
217 *
218 * Multiply by inv(L).
219 *
220  CALL clatps( 'Lower', 'No transpose', 'Non-unit', normin, n,
221  $ ap, work, scalel, rwork, info )
222  normin = 'Y'
223 *
224 * Multiply by inv(L**H).
225 *
226  CALL clatps( 'Lower', 'Conjugate transpose', 'Non-unit',
227  $ normin, n, ap, work, scaleu, rwork, info )
228  END IF
229 *
230 * Multiply by 1/SCALE if doing so will not cause overflow.
231 *
232  scale = scalel*scaleu
233  IF( scale.NE.one ) THEN
234  ix = icamax( n, work, 1 )
235  IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
236  $ GO TO 20
237  CALL csrscl( n, scale, work, 1 )
238  END IF
239  GO TO 10
240  END IF
241 *
242 * Compute the estimate of the reciprocal condition number.
243 *
244  IF( ainvnm.NE.zero )
245  $ rcond = ( one / ainvnm ) / anorm
246 *
247  20 CONTINUE
248  RETURN
249 *
250 * End of CPPCON
251 *
252  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 cppcon(UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO)
CPPCON
Definition: cppcon.f:118