1: *> \brief \b DTRCON
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DTRCON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrcon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrcon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrcon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
22: * IWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER DIAG, NORM, UPLO
26: * INTEGER INFO, LDA, N
27: * DOUBLE PRECISION RCOND
28: * ..
29: * .. Array Arguments ..
30: * INTEGER IWORK( * )
31: * DOUBLE PRECISION A( LDA, * ), WORK( * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DTRCON estimates the reciprocal of the condition number of a
41: *> triangular 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] A
82: *> \verbatim
83: *> A is DOUBLE PRECISION array, dimension (LDA,N)
84: *> The triangular matrix A. If UPLO = 'U', the leading N-by-N
85: *> upper triangular part of the array A contains the upper
86: *> triangular matrix, and the strictly lower triangular part of
87: *> A is not referenced. If UPLO = 'L', the leading N-by-N lower
88: *> triangular part of the array A contains the lower triangular
89: *> matrix, and the strictly upper triangular part of A is not
90: *> referenced. If DIAG = 'U', the diagonal elements of A are
91: *> also not referenced and are assumed to be 1.
92: *> \endverbatim
93: *>
94: *> \param[in] LDA
95: *> \verbatim
96: *> LDA is INTEGER
97: *> The leading dimension of the array A. LDA >= max(1,N).
98: *> \endverbatim
99: *>
100: *> \param[out] RCOND
101: *> \verbatim
102: *> RCOND is DOUBLE PRECISION
103: *> The reciprocal of the condition number of the matrix A,
104: *> computed as RCOND = 1/(norm(A) * norm(inv(A))).
105: *> \endverbatim
106: *>
107: *> \param[out] WORK
108: *> \verbatim
109: *> WORK is DOUBLE PRECISION array, dimension (3*N)
110: *> \endverbatim
111: *>
112: *> \param[out] IWORK
113: *> \verbatim
114: *> IWORK is INTEGER array, dimension (N)
115: *> \endverbatim
116: *>
117: *> \param[out] INFO
118: *> \verbatim
119: *> INFO is INTEGER
120: *> = 0: successful exit
121: *> < 0: if INFO = -i, the i-th argument had an illegal value
122: *> \endverbatim
123: *
124: * Authors:
125: * ========
126: *
127: *> \author Univ. of Tennessee
128: *> \author Univ. of California Berkeley
129: *> \author Univ. of Colorado Denver
130: *> \author NAG Ltd.
131: *
132: *> \ingroup doubleOTHERcomputational
133: *
134: * =====================================================================
135: SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
136: $ IWORK, INFO )
137: *
138: * -- LAPACK computational routine --
139: * -- LAPACK is a software package provided by Univ. of Tennessee, --
140: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141: *
142: * .. Scalar Arguments ..
143: CHARACTER DIAG, NORM, UPLO
144: INTEGER INFO, LDA, N
145: DOUBLE PRECISION RCOND
146: * ..
147: * .. Array Arguments ..
148: INTEGER IWORK( * )
149: DOUBLE PRECISION A( LDA, * ), WORK( * )
150: * ..
151: *
152: * =====================================================================
153: *
154: * .. Parameters ..
155: DOUBLE PRECISION ONE, ZERO
156: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
157: * ..
158: * .. Local Scalars ..
159: LOGICAL NOUNIT, ONENRM, UPPER
160: CHARACTER NORMIN
161: INTEGER IX, KASE, KASE1
162: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
163: * ..
164: * .. Local Arrays ..
165: INTEGER ISAVE( 3 )
166: * ..
167: * .. External Functions ..
168: LOGICAL LSAME
169: INTEGER IDAMAX
170: DOUBLE PRECISION DLAMCH, DLANTR
171: EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTR
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC ABS, DBLE, MAX
178: * ..
179: * .. Executable Statements ..
180: *
181: * Test the input parameters.
182: *
183: INFO = 0
184: UPPER = LSAME( UPLO, 'U' )
185: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
186: NOUNIT = LSAME( DIAG, 'N' )
187: *
188: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
189: INFO = -1
190: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
191: INFO = -2
192: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
193: INFO = -3
194: ELSE IF( N.LT.0 ) THEN
195: INFO = -4
196: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
197: INFO = -6
198: END IF
199: IF( INFO.NE.0 ) THEN
200: CALL XERBLA( 'DTRCON', -INFO )
201: RETURN
202: END IF
203: *
204: * Quick return if possible
205: *
206: IF( N.EQ.0 ) THEN
207: RCOND = ONE
208: RETURN
209: END IF
210: *
211: RCOND = ZERO
212: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
213: *
214: * Compute the norm of the triangular matrix A.
215: *
216: ANORM = DLANTR( NORM, UPLO, DIAG, N, N, A, LDA, WORK )
217: *
218: * Continue only if ANORM > 0.
219: *
220: IF( ANORM.GT.ZERO ) THEN
221: *
222: * Estimate the norm of the inverse of A.
223: *
224: AINVNM = ZERO
225: NORMIN = 'N'
226: IF( ONENRM ) THEN
227: KASE1 = 1
228: ELSE
229: KASE1 = 2
230: END IF
231: KASE = 0
232: 10 CONTINUE
233: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
234: IF( KASE.NE.0 ) THEN
235: IF( KASE.EQ.KASE1 ) THEN
236: *
237: * Multiply by inv(A).
238: *
239: CALL DLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
240: $ LDA, WORK, SCALE, WORK( 2*N+1 ), INFO )
241: ELSE
242: *
243: * Multiply by inv(A**T).
244: *
245: CALL DLATRS( UPLO, 'Transpose', DIAG, NORMIN, N, A, LDA,
246: $ WORK, SCALE, WORK( 2*N+1 ), INFO )
247: END IF
248: NORMIN = 'Y'
249: *
250: * Multiply by 1/SCALE if doing so will not cause overflow.
251: *
252: IF( SCALE.NE.ONE ) THEN
253: IX = IDAMAX( N, WORK, 1 )
254: XNORM = ABS( WORK( IX ) )
255: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
256: $ GO TO 20
257: CALL DRSCL( N, SCALE, WORK, 1 )
258: END IF
259: GO TO 10
260: END IF
261: *
262: * Compute the estimate of the reciprocal condition number.
263: *
264: IF( AINVNM.NE.ZERO )
265: $ RCOND = ( ONE / ANORM ) / AINVNM
266: END IF
267: *
268: 20 CONTINUE
269: RETURN
270: *
271: * End of DTRCON
272: *
273: END
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