1: *> \brief \b ZPPCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZPPCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zppcon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zppcon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zppcon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
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: *> \ingroup complex16OTHERcomputational
115: *
116: * =====================================================================
117: SUBROUTINE ZPPCON( 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: DOUBLE PRECISION ANORM, RCOND
127: * ..
128: * .. Array Arguments ..
129: DOUBLE PRECISION RWORK( * )
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: CHARACTER NORMIN
142: INTEGER IX, KASE
143: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
144: COMPLEX*16 ZDUM
145: * ..
146: * .. Local Arrays ..
147: INTEGER ISAVE( 3 )
148: * ..
149: * .. External Functions ..
150: LOGICAL LSAME
151: INTEGER IZAMAX
152: DOUBLE PRECISION DLAMCH
153: EXTERNAL LSAME, IZAMAX, DLAMCH
154: * ..
155: * .. External Subroutines ..
156: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATPS
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC ABS, DBLE, DIMAG
160: * ..
161: * .. Statement Functions ..
162: DOUBLE PRECISION CABS1
163: * ..
164: * .. Statement Function definitions ..
165: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( 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( 'ZPPCON', -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 = DLAMCH( 'Safe minimum' )
196: *
197: * Estimate the 1-norm of the inverse.
198: *
199: KASE = 0
200: NORMIN = 'N'
201: 10 CONTINUE
202: CALL ZLACN2( 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 ZLATPS( '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 ZLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
215: $ AP, WORK, SCALEU, RWORK, INFO )
216: ELSE
217: *
218: * Multiply by inv(L).
219: *
220: CALL ZLATPS( '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 ZLATPS( '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 = IZAMAX( N, WORK, 1 )
235: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
236: $ GO TO 20
237: CALL ZDRSCL( 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 ZPPCON
251: *
252: END
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