1: *> \brief \b ZLA_GBRCOND_X
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLA_GBRCOND_X + 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/zla_gbrcond_x.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
22: * LDAB, AFB, LDAFB, IPIV,
23: * X, INFO, WORK, RWORK )
24: *
25: * .. Scalar Arguments ..
26: * CHARACTER TRANS
27: * INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IPIV( * )
31: * COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
32: * $ X( * )
33: * DOUBLE PRECISION RWORK( * )
34: *
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> ZLA_GBRCOND_X Computes the infinity norm condition number of
43: *> op(A) * diag(X) where X is a COMPLEX*16 vector.
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] TRANS
50: *> \verbatim
51: *> TRANS is CHARACTER*1
52: *> Specifies the form of the system of equations:
53: *> = 'N': A * X = B (No transpose)
54: *> = 'T': A**T * X = B (Transpose)
55: *> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The number of linear equations, i.e., the order of the
62: *> matrix A. N >= 0.
63: *> \endverbatim
64: *>
65: *> \param[in] KL
66: *> \verbatim
67: *> KL is INTEGER
68: *> The number of subdiagonals within the band of A. KL >= 0.
69: *> \endverbatim
70: *>
71: *> \param[in] KU
72: *> \verbatim
73: *> KU is INTEGER
74: *> The number of superdiagonals within the band of A. KU >= 0.
75: *> \endverbatim
76: *>
77: *> \param[in] AB
78: *> \verbatim
79: *> AB is COMPLEX*16 array, dimension (LDAB,N)
80: *> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
81: *> The j-th column of A is stored in the j-th column of the
82: *> array AB as follows:
83: *> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
84: *> \endverbatim
85: *>
86: *> \param[in] LDAB
87: *> \verbatim
88: *> LDAB is INTEGER
89: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
90: *> \endverbatim
91: *>
92: *> \param[in] AFB
93: *> \verbatim
94: *> AFB is COMPLEX*16 array, dimension (LDAFB,N)
95: *> Details of the LU factorization of the band matrix A, as
96: *> computed by ZGBTRF. U is stored as an upper triangular
97: *> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
98: *> and the multipliers used during the factorization are stored
99: *> in rows KL+KU+2 to 2*KL+KU+1.
100: *> \endverbatim
101: *>
102: *> \param[in] LDAFB
103: *> \verbatim
104: *> LDAFB is INTEGER
105: *> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
106: *> \endverbatim
107: *>
108: *> \param[in] IPIV
109: *> \verbatim
110: *> IPIV is INTEGER array, dimension (N)
111: *> The pivot indices from the factorization A = P*L*U
112: *> as computed by ZGBTRF; row i of the matrix was interchanged
113: *> with row IPIV(i).
114: *> \endverbatim
115: *>
116: *> \param[in] X
117: *> \verbatim
118: *> X is COMPLEX*16 array, dimension (N)
119: *> The vector X in the formula op(A) * diag(X).
120: *> \endverbatim
121: *>
122: *> \param[out] INFO
123: *> \verbatim
124: *> INFO is INTEGER
125: *> = 0: Successful exit.
126: *> i > 0: The ith argument is invalid.
127: *> \endverbatim
128: *>
129: *> \param[in] WORK
130: *> \verbatim
131: *> WORK is COMPLEX*16 array, dimension (2*N).
132: *> Workspace.
133: *> \endverbatim
134: *>
135: *> \param[in] RWORK
136: *> \verbatim
137: *> RWORK is DOUBLE PRECISION array, dimension (N).
138: *> Workspace.
139: *> \endverbatim
140: *
141: * Authors:
142: * ========
143: *
144: *> \author Univ. of Tennessee
145: *> \author Univ. of California Berkeley
146: *> \author Univ. of Colorado Denver
147: *> \author NAG Ltd.
148: *
149: *> \date November 2011
150: *
151: *> \ingroup complex16GBcomputational
152: *
153: * =====================================================================
154: DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
155: $ LDAB, AFB, LDAFB, IPIV,
156: $ X, INFO, WORK, RWORK )
157: *
158: * -- LAPACK computational routine (version 3.4.0) --
159: * -- LAPACK is a software package provided by Univ. of Tennessee, --
160: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161: * November 2011
162: *
163: * .. Scalar Arguments ..
164: CHARACTER TRANS
165: INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
166: * ..
167: * .. Array Arguments ..
168: INTEGER IPIV( * )
169: COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ),
170: $ X( * )
171: DOUBLE PRECISION RWORK( * )
172: *
173: *
174: * =====================================================================
175: *
176: * .. Local Scalars ..
177: LOGICAL NOTRANS
178: INTEGER KASE, I, J
179: DOUBLE PRECISION AINVNM, ANORM, TMP
180: COMPLEX*16 ZDUM
181: * ..
182: * .. Local Arrays ..
183: INTEGER ISAVE( 3 )
184: * ..
185: * .. External Functions ..
186: LOGICAL LSAME
187: EXTERNAL LSAME
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL ZLACN2, ZGBTRS, XERBLA
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC ABS, MAX
194: * ..
195: * .. Statement Functions ..
196: DOUBLE PRECISION CABS1
197: * ..
198: * .. Statement Function Definitions ..
199: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
200: * ..
201: * .. Executable Statements ..
202: *
203: ZLA_GBRCOND_X = 0.0D+0
204: *
205: INFO = 0
206: NOTRANS = LSAME( TRANS, 'N' )
207: IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') .AND. .NOT.
208: $ LSAME( TRANS, 'C' ) ) THEN
209: INFO = -1
210: ELSE IF( N.LT.0 ) THEN
211: INFO = -2
212: ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN
213: INFO = -3
214: ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
215: INFO = -4
216: ELSE IF( LDAB.LT.KL+KU+1 ) THEN
217: INFO = -6
218: ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN
219: INFO = -8
220: END IF
221: IF( INFO.NE.0 ) THEN
222: CALL XERBLA( 'ZLA_GBRCOND_X', -INFO )
223: RETURN
224: END IF
225: *
226: * Compute norm of op(A)*op2(C).
227: *
228: KD = KU + 1
229: KE = KL + 1
230: ANORM = 0.0D+0
231: IF ( NOTRANS ) THEN
232: DO I = 1, N
233: TMP = 0.0D+0
234: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
235: TMP = TMP + CABS1( AB( KD+I-J, J) * X( J ) )
236: END DO
237: RWORK( I ) = TMP
238: ANORM = MAX( ANORM, TMP )
239: END DO
240: ELSE
241: DO I = 1, N
242: TMP = 0.0D+0
243: DO J = MAX( I-KL, 1 ), MIN( I+KU, N )
244: TMP = TMP + CABS1( AB( KE-I+J, I ) * X( J ) )
245: END DO
246: RWORK( I ) = TMP
247: ANORM = MAX( ANORM, TMP )
248: END DO
249: END IF
250: *
251: * Quick return if possible.
252: *
253: IF( N.EQ.0 ) THEN
254: ZLA_GBRCOND_X = 1.0D+0
255: RETURN
256: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
257: RETURN
258: END IF
259: *
260: * Estimate the norm of inv(op(A)).
261: *
262: AINVNM = 0.0D+0
263: *
264: KASE = 0
265: 10 CONTINUE
266: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
267: IF( KASE.NE.0 ) THEN
268: IF( KASE.EQ.2 ) THEN
269: *
270: * Multiply by R.
271: *
272: DO I = 1, N
273: WORK( I ) = WORK( I ) * RWORK( I )
274: END DO
275: *
276: IF ( NOTRANS ) THEN
277: CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
278: $ IPIV, WORK, N, INFO )
279: ELSE
280: CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
281: $ LDAFB, IPIV, WORK, N, INFO )
282: ENDIF
283: *
284: * Multiply by inv(X).
285: *
286: DO I = 1, N
287: WORK( I ) = WORK( I ) / X( I )
288: END DO
289: ELSE
290: *
291: * Multiply by inv(X**H).
292: *
293: DO I = 1, N
294: WORK( I ) = WORK( I ) / X( I )
295: END DO
296: *
297: IF ( NOTRANS ) THEN
298: CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB,
299: $ LDAFB, IPIV, WORK, N, INFO )
300: ELSE
301: CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB,
302: $ IPIV, WORK, N, INFO )
303: END IF
304: *
305: * Multiply by R.
306: *
307: DO I = 1, N
308: WORK( I ) = WORK( I ) * RWORK( I )
309: END DO
310: END IF
311: GO TO 10
312: END IF
313: *
314: * Compute the estimate of the reciprocal condition number.
315: *
316: IF( AINVNM .NE. 0.0D+0 )
317: $ ZLA_GBRCOND_X = 1.0D+0 / AINVNM
318: *
319: RETURN
320: *
321: END
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