LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
zppcon.f
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1 *> \brief \b ZPPCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, N
26 * DOUBLE PRECISION ANORM, RCOND
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION RWORK( * )
30 * COMPLEX*16 AP( * ), WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> ZPPCON 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 *> ZPPTRF.
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*16 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 DOUBLE PRECISION
78 *> The 1-norm (or infinity-norm) of the Hermitian matrix A.
79 *> \endverbatim
80 *>
81 *> \param[out] RCOND
82 *> \verbatim
83 *> RCOND is DOUBLE PRECISION
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*16 array, dimension (2*N)
92 *> \endverbatim
93 *>
94 *> \param[out] RWORK
95 *> \verbatim
96 *> RWORK is DOUBLE PRECISION 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 *> \date December 2016
115 *
116 *> \ingroup complex16OTHERcomputational
117 *
118 * =====================================================================
119  SUBROUTINE zppcon( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
120 *
121 * -- LAPACK computational routine (version 3.7.0) --
122 * -- LAPACK is a software package provided by Univ. of Tennessee, --
123 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
124 * December 2016
125 *
126 * .. Scalar Arguments ..
127  CHARACTER UPLO
128  INTEGER INFO, N
129  DOUBLE PRECISION ANORM, RCOND
130 * ..
131 * .. Array Arguments ..
132  DOUBLE PRECISION RWORK( * )
133  COMPLEX*16 AP( * ), WORK( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  DOUBLE PRECISION ONE, ZERO
140  parameter( one = 1.0d+0, zero = 0.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL UPPER
144  CHARACTER NORMIN
145  INTEGER IX, KASE
146  DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147  COMPLEX*16 ZDUM
148 * ..
149 * .. Local Arrays ..
150  INTEGER ISAVE( 3 )
151 * ..
152 * .. External Functions ..
153  LOGICAL LSAME
154  INTEGER IZAMAX
155  DOUBLE PRECISION DLAMCH
156  EXTERNAL lsame, izamax, dlamch
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL xerbla, zdrscl, zlacn2, zlatps
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC abs, dble, dimag
163 * ..
164 * .. Statement Functions ..
165  DOUBLE PRECISION CABS1
166 * ..
167 * .. Statement Function definitions ..
168  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
169 * ..
170 * .. Executable Statements ..
171 *
172 * Test the input parameters.
173 *
174  info = 0
175  upper = lsame( uplo, 'U' )
176  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
177  info = -1
178  ELSE IF( n.LT.0 ) THEN
179  info = -2
180  ELSE IF( anorm.LT.zero ) THEN
181  info = -4
182  END IF
183  IF( info.NE.0 ) THEN
184  CALL xerbla( 'ZPPCON', -info )
185  RETURN
186  END IF
187 *
188 * Quick return if possible
189 *
190  rcond = zero
191  IF( n.EQ.0 ) THEN
192  rcond = one
193  RETURN
194  ELSE IF( anorm.EQ.zero ) THEN
195  RETURN
196  END IF
197 *
198  smlnum = dlamch( 'Safe minimum' )
199 *
200 * Estimate the 1-norm of the inverse.
201 *
202  kase = 0
203  normin = 'N'
204  10 CONTINUE
205  CALL zlacn2( n, work( n+1 ), work, ainvnm, kase, isave )
206  IF( kase.NE.0 ) THEN
207  IF( upper ) THEN
208 *
209 * Multiply by inv(U**H).
210 *
211  CALL zlatps( 'Upper', 'Conjugate transpose', 'Non-unit',
212  \$ normin, n, ap, work, scalel, rwork, info )
213  normin = 'Y'
214 *
215 * Multiply by inv(U).
216 *
217  CALL zlatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
218  \$ ap, work, scaleu, rwork, info )
219  ELSE
220 *
221 * Multiply by inv(L).
222 *
223  CALL zlatps( 'Lower', 'No transpose', 'Non-unit', normin, n,
224  \$ ap, work, scalel, rwork, info )
225  normin = 'Y'
226 *
227 * Multiply by inv(L**H).
228 *
229  CALL zlatps( 'Lower', 'Conjugate transpose', 'Non-unit',
230  \$ normin, n, ap, work, scaleu, rwork, info )
231  END IF
232 *
233 * Multiply by 1/SCALE if doing so will not cause overflow.
234 *
235  scale = scalel*scaleu
236  IF( scale.NE.one ) THEN
237  ix = izamax( n, work, 1 )
238  IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
239  \$ GO TO 20
240  CALL zdrscl( n, scale, work, 1 )
241  END IF
242  GO TO 10
243  END IF
244 *
245 * Compute the estimate of the reciprocal condition number.
246 *
247  IF( ainvnm.NE.zero )
248  \$ rcond = ( one / ainvnm ) / anorm
249 *
250  20 CONTINUE
251  RETURN
252 *
253 * End of ZPPCON
254 *
255  END
subroutine zlatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
ZLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: zlatps.f:233
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 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 zppcon(UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO)
ZPPCON
Definition: zppcon.f:120