1: *> \brief \b ZTBCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZTBCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztbcon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztbcon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztbcon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
22: * RWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER DIAG, NORM, UPLO
26: * INTEGER INFO, KD, LDAB, N
27: * DOUBLE PRECISION RCOND
28: * ..
29: * .. Array Arguments ..
30: * DOUBLE PRECISION RWORK( * )
31: * COMPLEX*16 AB( LDAB, * ), WORK( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZTBCON estimates the reciprocal of the condition number of a
41: *> triangular band matrix A, in either the 1-norm or the infinity-norm.
42: *>
43: *> The norm of A is computed and an estimate is obtained for
44: *> norm(inv(A)), then the reciprocal of the condition number is
45: *> computed as
46: *> RCOND = 1 / ( norm(A) * norm(inv(A)) ).
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] NORM
53: *> \verbatim
54: *> NORM is CHARACTER*1
55: *> Specifies whether the 1-norm condition number or the
56: *> infinity-norm condition number is required:
57: *> = '1' or 'O': 1-norm;
58: *> = 'I': Infinity-norm.
59: *> \endverbatim
60: *>
61: *> \param[in] UPLO
62: *> \verbatim
63: *> UPLO is CHARACTER*1
64: *> = 'U': A is upper triangular;
65: *> = 'L': A is lower triangular.
66: *> \endverbatim
67: *>
68: *> \param[in] DIAG
69: *> \verbatim
70: *> DIAG is CHARACTER*1
71: *> = 'N': A is non-unit triangular;
72: *> = 'U': A is unit triangular.
73: *> \endverbatim
74: *>
75: *> \param[in] N
76: *> \verbatim
77: *> N is INTEGER
78: *> The order of the matrix A. N >= 0.
79: *> \endverbatim
80: *>
81: *> \param[in] KD
82: *> \verbatim
83: *> KD is INTEGER
84: *> The number of superdiagonals or subdiagonals of the
85: *> triangular band matrix A. KD >= 0.
86: *> \endverbatim
87: *>
88: *> \param[in] AB
89: *> \verbatim
90: *> AB is COMPLEX*16 array, dimension (LDAB,N)
91: *> The upper or lower triangular band matrix A, stored in the
92: *> first kd+1 rows of the array. The j-th column of A is stored
93: *> in the j-th column of the array AB as follows:
94: *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
95: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
96: *> If DIAG = 'U', the diagonal elements of A are not referenced
97: *> and are assumed to be 1.
98: *> \endverbatim
99: *>
100: *> \param[in] LDAB
101: *> \verbatim
102: *> LDAB is INTEGER
103: *> The leading dimension of the array AB. LDAB >= KD+1.
104: *> \endverbatim
105: *>
106: *> \param[out] RCOND
107: *> \verbatim
108: *> RCOND is DOUBLE PRECISION
109: *> The reciprocal of the condition number of the matrix A,
110: *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
111: *> \endverbatim
112: *>
113: *> \param[out] WORK
114: *> \verbatim
115: *> WORK is COMPLEX*16 array, dimension (2*N)
116: *> \endverbatim
117: *>
118: *> \param[out] RWORK
119: *> \verbatim
120: *> RWORK is DOUBLE PRECISION array, dimension (N)
121: *> \endverbatim
122: *>
123: *> \param[out] INFO
124: *> \verbatim
125: *> INFO is INTEGER
126: *> = 0: successful exit
127: *> < 0: if INFO = -i, the i-th argument had an illegal value
128: *> \endverbatim
129: *
130: * Authors:
131: * ========
132: *
133: *> \author Univ. of Tennessee
134: *> \author Univ. of California Berkeley
135: *> \author Univ. of Colorado Denver
136: *> \author NAG Ltd.
137: *
138: *> \ingroup complex16OTHERcomputational
139: *
140: * =====================================================================
141: SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK,
142: $ RWORK, INFO )
143: *
144: * -- LAPACK computational routine --
145: * -- LAPACK is a software package provided by Univ. of Tennessee, --
146: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147: *
148: * .. Scalar Arguments ..
149: CHARACTER DIAG, NORM, UPLO
150: INTEGER INFO, KD, LDAB, N
151: DOUBLE PRECISION RCOND
152: * ..
153: * .. Array Arguments ..
154: DOUBLE PRECISION RWORK( * )
155: COMPLEX*16 AB( LDAB, * ), WORK( * )
156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
161: DOUBLE PRECISION ONE, ZERO
162: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
163: * ..
164: * .. Local Scalars ..
165: LOGICAL NOUNIT, ONENRM, UPPER
166: CHARACTER NORMIN
167: INTEGER IX, KASE, KASE1
168: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
169: COMPLEX*16 ZDUM
170: * ..
171: * .. Local Arrays ..
172: INTEGER ISAVE( 3 )
173: * ..
174: * .. External Functions ..
175: LOGICAL LSAME
176: INTEGER IZAMAX
177: DOUBLE PRECISION DLAMCH, ZLANTB
178: EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTB
179: * ..
180: * .. External Subroutines ..
181: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATBS
182: * ..
183: * .. Intrinsic Functions ..
184: INTRINSIC ABS, DBLE, DIMAG, MAX
185: * ..
186: * .. Statement Functions ..
187: DOUBLE PRECISION CABS1
188: * ..
189: * .. Statement Function definitions ..
190: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
191: * ..
192: * .. Executable Statements ..
193: *
194: * Test the input parameters.
195: *
196: INFO = 0
197: UPPER = LSAME( UPLO, 'U' )
198: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
199: NOUNIT = LSAME( DIAG, 'N' )
200: *
201: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
202: INFO = -1
203: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
204: INFO = -2
205: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
206: INFO = -3
207: ELSE IF( N.LT.0 ) THEN
208: INFO = -4
209: ELSE IF( KD.LT.0 ) THEN
210: INFO = -5
211: ELSE IF( LDAB.LT.KD+1 ) THEN
212: INFO = -7
213: END IF
214: IF( INFO.NE.0 ) THEN
215: CALL XERBLA( 'ZTBCON', -INFO )
216: RETURN
217: END IF
218: *
219: * Quick return if possible
220: *
221: IF( N.EQ.0 ) THEN
222: RCOND = ONE
223: RETURN
224: END IF
225: *
226: RCOND = ZERO
227: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( N, 1 ) )
228: *
229: * Compute the 1-norm of the triangular matrix A or A**H.
230: *
231: ANORM = ZLANTB( NORM, UPLO, DIAG, N, KD, AB, LDAB, RWORK )
232: *
233: * Continue only if ANORM > 0.
234: *
235: IF( ANORM.GT.ZERO ) THEN
236: *
237: * Estimate the 1-norm of the inverse of A.
238: *
239: AINVNM = ZERO
240: NORMIN = 'N'
241: IF( ONENRM ) THEN
242: KASE1 = 1
243: ELSE
244: KASE1 = 2
245: END IF
246: KASE = 0
247: 10 CONTINUE
248: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
249: IF( KASE.NE.0 ) THEN
250: IF( KASE.EQ.KASE1 ) THEN
251: *
252: * Multiply by inv(A).
253: *
254: CALL ZLATBS( UPLO, 'No transpose', DIAG, NORMIN, N, KD,
255: $ AB, LDAB, WORK, SCALE, RWORK, INFO )
256: ELSE
257: *
258: * Multiply by inv(A**H).
259: *
260: CALL ZLATBS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
261: $ N, KD, AB, LDAB, WORK, SCALE, RWORK, INFO )
262: END IF
263: NORMIN = 'Y'
264: *
265: * Multiply by 1/SCALE if doing so will not cause overflow.
266: *
267: IF( SCALE.NE.ONE ) THEN
268: IX = IZAMAX( N, WORK, 1 )
269: XNORM = CABS1( WORK( IX ) )
270: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
271: $ GO TO 20
272: CALL ZDRSCL( N, SCALE, WORK, 1 )
273: END IF
274: GO TO 10
275: END IF
276: *
277: * Compute the estimate of the reciprocal condition number.
278: *
279: IF( AINVNM.NE.ZERO )
280: $ RCOND = ( ONE / ANORM ) / AINVNM
281: END IF
282: *
283: 20 CONTINUE
284: RETURN
285: *
286: * End of ZTBCON
287: *
288: END
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