4329
|
1 SUBROUTINE ZGECON( NORM, N, A, LDA, ANORM, RCOND, WORK, RWORK, |
|
2 $ INFO ) |
|
3 * |
7034
|
4 * -- LAPACK routine (version 3.1) -- |
|
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
|
6 * November 2006 |
|
7 * |
|
8 * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. |
4329
|
9 * |
|
10 * .. Scalar Arguments .. |
|
11 CHARACTER NORM |
|
12 INTEGER INFO, LDA, N |
|
13 DOUBLE PRECISION ANORM, RCOND |
|
14 * .. |
|
15 * .. Array Arguments .. |
|
16 DOUBLE PRECISION RWORK( * ) |
|
17 COMPLEX*16 A( LDA, * ), WORK( * ) |
|
18 * .. |
|
19 * |
|
20 * Purpose |
|
21 * ======= |
|
22 * |
|
23 * ZGECON estimates the reciprocal of the condition number of a general |
|
24 * complex matrix A, in either the 1-norm or the infinity-norm, using |
|
25 * the LU factorization computed by ZGETRF. |
|
26 * |
|
27 * An estimate is obtained for norm(inv(A)), and the reciprocal of the |
|
28 * condition number is computed as |
|
29 * RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
|
30 * |
|
31 * Arguments |
|
32 * ========= |
|
33 * |
|
34 * NORM (input) CHARACTER*1 |
|
35 * Specifies whether the 1-norm condition number or the |
|
36 * infinity-norm condition number is required: |
|
37 * = '1' or 'O': 1-norm; |
|
38 * = 'I': Infinity-norm. |
|
39 * |
|
40 * N (input) INTEGER |
|
41 * The order of the matrix A. N >= 0. |
|
42 * |
|
43 * A (input) COMPLEX*16 array, dimension (LDA,N) |
|
44 * The factors L and U from the factorization A = P*L*U |
|
45 * as computed by ZGETRF. |
|
46 * |
|
47 * LDA (input) INTEGER |
|
48 * The leading dimension of the array A. LDA >= max(1,N). |
|
49 * |
|
50 * ANORM (input) DOUBLE PRECISION |
|
51 * If NORM = '1' or 'O', the 1-norm of the original matrix A. |
|
52 * If NORM = 'I', the infinity-norm of the original matrix A. |
|
53 * |
|
54 * RCOND (output) DOUBLE PRECISION |
|
55 * The reciprocal of the condition number of the matrix A, |
|
56 * computed as RCOND = 1/(norm(A) * norm(inv(A))). |
|
57 * |
|
58 * WORK (workspace) COMPLEX*16 array, dimension (2*N) |
|
59 * |
|
60 * RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) |
|
61 * |
|
62 * INFO (output) INTEGER |
|
63 * = 0: successful exit |
|
64 * < 0: if INFO = -i, the i-th argument had an illegal value |
|
65 * |
|
66 * ===================================================================== |
|
67 * |
|
68 * .. Parameters .. |
|
69 DOUBLE PRECISION ONE, ZERO |
|
70 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) |
|
71 * .. |
|
72 * .. Local Scalars .. |
|
73 LOGICAL ONENRM |
|
74 CHARACTER NORMIN |
|
75 INTEGER IX, KASE, KASE1 |
|
76 DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU |
|
77 COMPLEX*16 ZDUM |
|
78 * .. |
7034
|
79 * .. Local Arrays .. |
|
80 INTEGER ISAVE( 3 ) |
|
81 * .. |
4329
|
82 * .. External Functions .. |
|
83 LOGICAL LSAME |
|
84 INTEGER IZAMAX |
|
85 DOUBLE PRECISION DLAMCH |
|
86 EXTERNAL LSAME, IZAMAX, DLAMCH |
|
87 * .. |
|
88 * .. External Subroutines .. |
7034
|
89 EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS |
4329
|
90 * .. |
|
91 * .. Intrinsic Functions .. |
|
92 INTRINSIC ABS, DBLE, DIMAG, MAX |
|
93 * .. |
|
94 * .. Statement Functions .. |
|
95 DOUBLE PRECISION CABS1 |
|
96 * .. |
|
97 * .. Statement Function definitions .. |
|
98 CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) |
|
99 * .. |
|
100 * .. Executable Statements .. |
|
101 * |
|
102 * Test the input parameters. |
|
103 * |
|
104 INFO = 0 |
|
105 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) |
|
106 IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN |
|
107 INFO = -1 |
|
108 ELSE IF( N.LT.0 ) THEN |
|
109 INFO = -2 |
|
110 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
|
111 INFO = -4 |
|
112 ELSE IF( ANORM.LT.ZERO ) THEN |
|
113 INFO = -5 |
|
114 END IF |
|
115 IF( INFO.NE.0 ) THEN |
|
116 CALL XERBLA( 'ZGECON', -INFO ) |
|
117 RETURN |
|
118 END IF |
|
119 * |
|
120 * Quick return if possible |
|
121 * |
|
122 RCOND = ZERO |
|
123 IF( N.EQ.0 ) THEN |
|
124 RCOND = ONE |
|
125 RETURN |
|
126 ELSE IF( ANORM.EQ.ZERO ) THEN |
|
127 RETURN |
|
128 END IF |
|
129 * |
|
130 SMLNUM = DLAMCH( 'Safe minimum' ) |
|
131 * |
|
132 * Estimate the norm of inv(A). |
|
133 * |
|
134 AINVNM = ZERO |
|
135 NORMIN = 'N' |
|
136 IF( ONENRM ) THEN |
|
137 KASE1 = 1 |
|
138 ELSE |
|
139 KASE1 = 2 |
|
140 END IF |
|
141 KASE = 0 |
|
142 10 CONTINUE |
7034
|
143 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) |
4329
|
144 IF( KASE.NE.0 ) THEN |
|
145 IF( KASE.EQ.KASE1 ) THEN |
|
146 * |
|
147 * Multiply by inv(L). |
|
148 * |
|
149 CALL ZLATRS( 'Lower', 'No transpose', 'Unit', NORMIN, N, A, |
|
150 $ LDA, WORK, SL, RWORK, INFO ) |
|
151 * |
|
152 * Multiply by inv(U). |
|
153 * |
|
154 CALL ZLATRS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N, |
|
155 $ A, LDA, WORK, SU, RWORK( N+1 ), INFO ) |
|
156 ELSE |
|
157 * |
|
158 * Multiply by inv(U'). |
|
159 * |
|
160 CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit', |
|
161 $ NORMIN, N, A, LDA, WORK, SU, RWORK( N+1 ), |
|
162 $ INFO ) |
|
163 * |
|
164 * Multiply by inv(L'). |
|
165 * |
|
166 CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Unit', NORMIN, |
|
167 $ N, A, LDA, WORK, SL, RWORK, INFO ) |
|
168 END IF |
|
169 * |
|
170 * Divide X by 1/(SL*SU) if doing so will not cause overflow. |
|
171 * |
|
172 SCALE = SL*SU |
|
173 NORMIN = 'Y' |
|
174 IF( SCALE.NE.ONE ) THEN |
|
175 IX = IZAMAX( N, WORK, 1 ) |
|
176 IF( SCALE.LT.CABS1( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO ) |
|
177 $ GO TO 20 |
|
178 CALL ZDRSCL( N, SCALE, WORK, 1 ) |
|
179 END IF |
|
180 GO TO 10 |
|
181 END IF |
|
182 * |
|
183 * Compute the estimate of the reciprocal condition number. |
|
184 * |
|
185 IF( AINVNM.NE.ZERO ) |
|
186 $ RCOND = ( ONE / AINVNM ) / ANORM |
|
187 * |
|
188 20 CONTINUE |
|
189 RETURN |
|
190 * |
|
191 * End of ZGECON |
|
192 * |
|
193 END |