Annotation of rpl/lapack/lapack/zspcon.f, revision 1.18
1.9 bertrand 1: *> \brief \b ZSPCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download ZSPCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspcon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspcon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspcon.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
1.15 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, N
26: * DOUBLE PRECISION ANORM, RCOND
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IPIV( * )
30: * COMPLEX*16 AP( * ), WORK( * )
31: * ..
1.15 bertrand 32: *
1.9 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZSPCON estimates the reciprocal of the condition number (in the
40: *> 1-norm) of a complex symmetric packed matrix A using the
41: *> factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
42: *>
43: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
44: *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
45: *> \endverbatim
46: *
47: * Arguments:
48: * ==========
49: *
50: *> \param[in] UPLO
51: *> \verbatim
52: *> UPLO is CHARACTER*1
53: *> Specifies whether the details of the factorization are stored
54: *> as an upper or lower triangular matrix.
55: *> = 'U': Upper triangular, form is A = U*D*U**T;
56: *> = 'L': Lower triangular, form is A = L*D*L**T.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> The order of the matrix A. N >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] AP
66: *> \verbatim
67: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
68: *> The block diagonal matrix D and the multipliers used to
69: *> obtain the factor U or L as computed by ZSPTRF, stored as a
70: *> packed triangular matrix.
71: *> \endverbatim
72: *>
73: *> \param[in] IPIV
74: *> \verbatim
75: *> IPIV is INTEGER array, dimension (N)
76: *> Details of the interchanges and the block structure of D
77: *> as determined by ZSPTRF.
78: *> \endverbatim
79: *>
80: *> \param[in] ANORM
81: *> \verbatim
82: *> ANORM is DOUBLE PRECISION
83: *> The 1-norm of the original matrix A.
84: *> \endverbatim
85: *>
86: *> \param[out] RCOND
87: *> \verbatim
88: *> RCOND is DOUBLE PRECISION
89: *> The reciprocal of the condition number of the matrix A,
90: *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
91: *> estimate of the 1-norm of inv(A) computed in this routine.
92: *> \endverbatim
93: *>
94: *> \param[out] WORK
95: *> \verbatim
96: *> WORK is COMPLEX*16 array, dimension (2*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: *
1.15 bertrand 109: *> \author Univ. of Tennessee
110: *> \author Univ. of California Berkeley
111: *> \author Univ. of Colorado Denver
112: *> \author NAG Ltd.
1.9 bertrand 113: *
114: *> \ingroup complex16OTHERcomputational
115: *
116: * =====================================================================
1.1 bertrand 117: SUBROUTINE ZSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
118: *
1.18 ! bertrand 119: * -- LAPACK computational routine --
1.1 bertrand 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: DOUBLE PRECISION ANORM, RCOND
127: * ..
128: * .. Array Arguments ..
129: INTEGER IPIV( * )
130: COMPLEX*16 AP( * ), WORK( * )
131: * ..
132: *
133: * =====================================================================
134: *
135: * .. Parameters ..
136: DOUBLE PRECISION ONE, ZERO
137: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
138: * ..
139: * .. Local Scalars ..
140: LOGICAL UPPER
141: INTEGER I, IP, KASE
142: DOUBLE PRECISION AINVNM
143: * ..
144: * .. Local Arrays ..
145: INTEGER ISAVE( 3 )
146: * ..
147: * .. External Functions ..
148: LOGICAL LSAME
149: EXTERNAL LSAME
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL XERBLA, ZLACN2, ZSPTRS
153: * ..
154: * .. Executable Statements ..
155: *
156: * Test the input parameters.
157: *
158: INFO = 0
159: UPPER = LSAME( UPLO, 'U' )
160: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
161: INFO = -1
162: ELSE IF( N.LT.0 ) THEN
163: INFO = -2
164: ELSE IF( ANORM.LT.ZERO ) THEN
165: INFO = -5
166: END IF
167: IF( INFO.NE.0 ) THEN
168: CALL XERBLA( 'ZSPCON', -INFO )
169: RETURN
170: END IF
171: *
172: * Quick return if possible
173: *
174: RCOND = ZERO
175: IF( N.EQ.0 ) THEN
176: RCOND = ONE
177: RETURN
178: ELSE IF( ANORM.LE.ZERO ) THEN
179: RETURN
180: END IF
181: *
182: * Check that the diagonal matrix D is nonsingular.
183: *
184: IF( UPPER ) THEN
185: *
186: * Upper triangular storage: examine D from bottom to top
187: *
188: IP = N*( N+1 ) / 2
189: DO 10 I = N, 1, -1
190: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
191: $ RETURN
192: IP = IP - I
193: 10 CONTINUE
194: ELSE
195: *
196: * Lower triangular storage: examine D from top to bottom.
197: *
198: IP = 1
199: DO 20 I = 1, N
200: IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
201: $ RETURN
202: IP = IP + N - I + 1
203: 20 CONTINUE
204: END IF
205: *
206: * Estimate the 1-norm of the inverse.
207: *
208: KASE = 0
209: 30 CONTINUE
210: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
211: IF( KASE.NE.0 ) THEN
212: *
1.8 bertrand 213: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 214: *
215: CALL ZSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
216: GO TO 30
217: END IF
218: *
219: * Compute the estimate of the reciprocal condition number.
220: *
221: IF( AINVNM.NE.ZERO )
222: $ RCOND = ( ONE / AINVNM ) / ANORM
223: *
224: RETURN
225: *
226: * End of ZSPCON
227: *
228: END
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