LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
sppcon.f
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1 *> \brief \b SPPCON
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, N
26 * REAL ANORM, RCOND
27 * ..
28 * .. Array Arguments ..
29 * INTEGER IWORK( * )
30 * REAL AP( * ), WORK( * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> SPPCON estimates the reciprocal of the condition number (in the
40 *> 1-norm) of a real symmetric positive definite packed matrix using
41 *> the Cholesky factorization A = U**T*U or A = L*L**T computed by
42 *> SPPTRF.
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 REAL array, dimension (N*(N+1)/2)
67 *> The triangular factor U or L from the Cholesky factorization
68 *> A = U**T*U or A = L*L**T, 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 symmetric 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 REAL array, dimension (3*N)
92 *> \endverbatim
93 *>
94 *> \param[out] IWORK
95 *> \verbatim
96 *> IWORK is INTEGER 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 realOTHERcomputational
115 *
116 * =====================================================================
117  SUBROUTINE sppcon( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, 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  INTEGER IWORK( * )
130  REAL 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 * ..
145 * .. Local Arrays ..
146  INTEGER ISAVE( 3 )
147 * ..
148 * .. External Functions ..
149  LOGICAL LSAME
150  INTEGER ISAMAX
151  REAL SLAMCH
152  EXTERNAL lsame, isamax, slamch
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL slacn2, slatps, srscl, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs
159 * ..
160 * .. Executable Statements ..
161 *
162 * Test the input parameters.
163 *
164  info = 0
165  upper = lsame( uplo, 'U' )
166  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
167  info = -1
168  ELSE IF( n.LT.0 ) THEN
169  info = -2
170  ELSE IF( anorm.LT.zero ) THEN
171  info = -4
172  END IF
173  IF( info.NE.0 ) THEN
174  CALL xerbla( 'SPPCON', -info )
175  RETURN
176  END IF
177 *
178 * Quick return if possible
179 *
180  rcond = zero
181  IF( n.EQ.0 ) THEN
182  rcond = one
183  RETURN
184  ELSE IF( anorm.EQ.zero ) THEN
185  RETURN
186  END IF
187 *
188  smlnum = slamch( 'Safe minimum' )
189 *
190 * Estimate the 1-norm of the inverse.
191 *
192  kase = 0
193  normin = 'N'
194  10 CONTINUE
195  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
196  IF( kase.NE.0 ) THEN
197  IF( upper ) THEN
198 *
199 * Multiply by inv(U**T).
200 *
201  CALL slatps( 'Upper', 'Transpose', 'Non-unit', normin, n,
202  $ ap, work, scalel, work( 2*n+1 ), info )
203  normin = 'Y'
204 *
205 * Multiply by inv(U).
206 *
207  CALL slatps( 'Upper', 'No transpose', 'Non-unit', normin, n,
208  $ ap, work, scaleu, work( 2*n+1 ), info )
209  ELSE
210 *
211 * Multiply by inv(L).
212 *
213  CALL slatps( 'Lower', 'No transpose', 'Non-unit', normin, n,
214  $ ap, work, scalel, work( 2*n+1 ), info )
215  normin = 'Y'
216 *
217 * Multiply by inv(L**T).
218 *
219  CALL slatps( 'Lower', 'Transpose', 'Non-unit', normin, n,
220  $ ap, work, scaleu, work( 2*n+1 ), info )
221  END IF
222 *
223 * Multiply by 1/SCALE if doing so will not cause overflow.
224 *
225  scale = scalel*scaleu
226  IF( scale.NE.one ) THEN
227  ix = isamax( n, work, 1 )
228  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
229  $ GO TO 20
230  CALL srscl( n, scale, work, 1 )
231  END IF
232  GO TO 10
233  END IF
234 *
235 * Compute the estimate of the reciprocal condition number.
236 *
237  IF( ainvnm.NE.zero )
238  $ rcond = ( one / ainvnm ) / anorm
239 *
240  20 CONTINUE
241  RETURN
242 *
243 * End of SPPCON
244 *
245  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slacn2(N, V, X, ISGN, EST, KASE, ISAVE)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: slacn2.f:136
subroutine slatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
SLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: slatps.f:229
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:84
subroutine sppcon(UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO)
SPPCON
Definition: sppcon.f:118