1: *> \brief \b ZGBCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGBCON + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbcon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
22: * WORK, RWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER NORM
26: * INTEGER INFO, KL, KU, LDAB, N
27: * DOUBLE PRECISION ANORM, RCOND
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * )
31: * DOUBLE PRECISION RWORK( * )
32: * COMPLEX*16 AB( LDAB, * ), WORK( * )
33: * ..
34: *
35: *
36: *> \par Purpose:
37: * =============
38: *>
39: *> \verbatim
40: *>
41: *> ZGBCON estimates the reciprocal of the condition number of a complex
42: *> general band matrix A, in either the 1-norm or the infinity-norm,
43: *> using the LU factorization computed by ZGBTRF.
44: *>
45: *> An estimate is obtained for norm(inv(A)), and the reciprocal of the
46: *> condition number is computed as
47: *> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
48: *> \endverbatim
49: *
50: * Arguments:
51: * ==========
52: *
53: *> \param[in] NORM
54: *> \verbatim
55: *> NORM is CHARACTER*1
56: *> Specifies whether the 1-norm condition number or the
57: *> infinity-norm condition number is required:
58: *> = '1' or 'O': 1-norm;
59: *> = 'I': Infinity-norm.
60: *> \endverbatim
61: *>
62: *> \param[in] N
63: *> \verbatim
64: *> N is INTEGER
65: *> The order of the matrix A. N >= 0.
66: *> \endverbatim
67: *>
68: *> \param[in] KL
69: *> \verbatim
70: *> KL is INTEGER
71: *> The number of subdiagonals within the band of A. KL >= 0.
72: *> \endverbatim
73: *>
74: *> \param[in] KU
75: *> \verbatim
76: *> KU is INTEGER
77: *> The number of superdiagonals within the band of A. KU >= 0.
78: *> \endverbatim
79: *>
80: *> \param[in] AB
81: *> \verbatim
82: *> AB is COMPLEX*16 array, dimension (LDAB,N)
83: *> Details of the LU factorization of the band matrix A, as
84: *> computed by ZGBTRF. U is stored as an upper triangular band
85: *> matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
86: *> the multipliers used during the factorization are stored in
87: *> rows KL+KU+2 to 2*KL+KU+1.
88: *> \endverbatim
89: *>
90: *> \param[in] LDAB
91: *> \verbatim
92: *> LDAB is INTEGER
93: *> The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
94: *> \endverbatim
95: *>
96: *> \param[in] IPIV
97: *> \verbatim
98: *> IPIV is INTEGER array, dimension (N)
99: *> The pivot indices; for 1 <= i <= N, row i of the matrix was
100: *> interchanged with row IPIV(i).
101: *> \endverbatim
102: *>
103: *> \param[in] ANORM
104: *> \verbatim
105: *> ANORM is DOUBLE PRECISION
106: *> If NORM = '1' or 'O', the 1-norm of the original matrix A.
107: *> If NORM = 'I', the infinity-norm of the original matrix A.
108: *> \endverbatim
109: *>
110: *> \param[out] RCOND
111: *> \verbatim
112: *> RCOND is DOUBLE PRECISION
113: *> The reciprocal of the condition number of the matrix A,
114: *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
115: *> \endverbatim
116: *>
117: *> \param[out] WORK
118: *> \verbatim
119: *> WORK is COMPLEX*16 array, dimension (2*N)
120: *> \endverbatim
121: *>
122: *> \param[out] RWORK
123: *> \verbatim
124: *> RWORK is DOUBLE PRECISION array, dimension (N)
125: *> \endverbatim
126: *>
127: *> \param[out] INFO
128: *> \verbatim
129: *> INFO is INTEGER
130: *> = 0: successful exit
131: *> < 0: if INFO = -i, the i-th argument had an illegal value
132: *> \endverbatim
133: *
134: * Authors:
135: * ========
136: *
137: *> \author Univ. of Tennessee
138: *> \author Univ. of California Berkeley
139: *> \author Univ. of Colorado Denver
140: *> \author NAG Ltd.
141: *
142: *> \ingroup complex16GBcomputational
143: *
144: * =====================================================================
145: SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND,
146: $ WORK, RWORK, INFO )
147: *
148: * -- LAPACK computational routine --
149: * -- LAPACK is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: *
152: * .. Scalar Arguments ..
153: CHARACTER NORM
154: INTEGER INFO, KL, KU, LDAB, N
155: DOUBLE PRECISION ANORM, RCOND
156: * ..
157: * .. Array Arguments ..
158: INTEGER IPIV( * )
159: DOUBLE PRECISION RWORK( * )
160: COMPLEX*16 AB( LDAB, * ), WORK( * )
161: * ..
162: *
163: * =====================================================================
164: *
165: * .. Parameters ..
166: DOUBLE PRECISION ONE, ZERO
167: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
168: * ..
169: * .. Local Scalars ..
170: LOGICAL LNOTI, ONENRM
171: CHARACTER NORMIN
172: INTEGER IX, J, JP, KASE, KASE1, KD, LM
173: DOUBLE PRECISION AINVNM, SCALE, SMLNUM
174: COMPLEX*16 T, ZDUM
175: * ..
176: * .. Local Arrays ..
177: INTEGER ISAVE( 3 )
178: * ..
179: * .. External Functions ..
180: LOGICAL LSAME
181: INTEGER IZAMAX
182: DOUBLE PRECISION DLAMCH
183: COMPLEX*16 ZDOTC
184: EXTERNAL LSAME, IZAMAX, DLAMCH, ZDOTC
185: * ..
186: * .. External Subroutines ..
187: EXTERNAL XERBLA, ZAXPY, ZDRSCL, ZLACN2, ZLATBS
188: * ..
189: * .. Intrinsic Functions ..
190: INTRINSIC ABS, DBLE, DIMAG, MIN
191: * ..
192: * .. Statement Functions ..
193: DOUBLE PRECISION CABS1
194: * ..
195: * .. Statement Function definitions ..
196: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
197: * ..
198: * .. Executable Statements ..
199: *
200: * Test the input parameters.
201: *
202: INFO = 0
203: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
204: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
205: INFO = -1
206: ELSE IF( N.LT.0 ) THEN
207: INFO = -2
208: ELSE IF( KL.LT.0 ) THEN
209: INFO = -3
210: ELSE IF( KU.LT.0 ) THEN
211: INFO = -4
212: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
213: INFO = -6
214: ELSE IF( ANORM.LT.ZERO ) THEN
215: INFO = -8
216: END IF
217: IF( INFO.NE.0 ) THEN
218: CALL XERBLA( 'ZGBCON', -INFO )
219: RETURN
220: END IF
221: *
222: * Quick return if possible
223: *
224: RCOND = ZERO
225: IF( N.EQ.0 ) THEN
226: RCOND = ONE
227: RETURN
228: ELSE IF( ANORM.EQ.ZERO ) THEN
229: RETURN
230: END IF
231: *
232: SMLNUM = DLAMCH( 'Safe minimum' )
233: *
234: * Estimate the norm of inv(A).
235: *
236: AINVNM = ZERO
237: NORMIN = 'N'
238: IF( ONENRM ) THEN
239: KASE1 = 1
240: ELSE
241: KASE1 = 2
242: END IF
243: KD = KL + KU + 1
244: LNOTI = KL.GT.0
245: KASE = 0
246: 10 CONTINUE
247: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
248: IF( KASE.NE.0 ) THEN
249: IF( KASE.EQ.KASE1 ) THEN
250: *
251: * Multiply by inv(L).
252: *
253: IF( LNOTI ) THEN
254: DO 20 J = 1, N - 1
255: LM = MIN( KL, N-J )
256: JP = IPIV( J )
257: T = WORK( JP )
258: IF( JP.NE.J ) THEN
259: WORK( JP ) = WORK( J )
260: WORK( J ) = T
261: END IF
262: CALL ZAXPY( LM, -T, AB( KD+1, J ), 1, WORK( J+1 ), 1 )
263: 20 CONTINUE
264: END IF
265: *
266: * Multiply by inv(U).
267: *
268: CALL ZLATBS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
269: $ KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
270: ELSE
271: *
272: * Multiply by inv(U**H).
273: *
274: CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
275: $ NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
276: $ INFO )
277: *
278: * Multiply by inv(L**H).
279: *
280: IF( LNOTI ) THEN
281: DO 30 J = N - 1, 1, -1
282: LM = MIN( KL, N-J )
283: WORK( J ) = WORK( J ) - ZDOTC( LM, AB( KD+1, J ), 1,
284: $ WORK( J+1 ), 1 )
285: JP = IPIV( J )
286: IF( JP.NE.J ) THEN
287: T = WORK( JP )
288: WORK( JP ) = WORK( J )
289: WORK( J ) = T
290: END IF
291: 30 CONTINUE
292: END IF
293: END IF
294: *
295: * Divide X by 1/SCALE if doing so will not cause overflow.
296: *
297: NORMIN = 'Y'
298: IF( SCALE.NE.ONE ) THEN
299: IX = IZAMAX( N, WORK, 1 )
300: IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
301: $ GO TO 40
302: CALL ZDRSCL( N, SCALE, WORK, 1 )
303: END IF
304: GO TO 10
305: END IF
306: *
307: * Compute the estimate of the reciprocal condition number.
308: *
309: IF( AINVNM.NE.ZERO )
310: $ RCOND = ( ONE / AINVNM ) / ANORM
311: *
312: 40 CONTINUE
313: RETURN
314: *
315: * End of ZGBCON
316: *
317: END
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