1 DOUBLE PRECISION FUNCTION DLA_SYRCOND( UPLO, N, A, LDA, AF, LDAF,
2 $ IPIV, CMODE, C, INFO, WORK,
3 $ IWORK )
4 *
5 * -- LAPACK routine (version 3.2.1) --
6 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
7 * -- Jason Riedy of Univ. of California Berkeley. --
8 * -- April 2009 --
9 *
10 * -- LAPACK is a software package provided by Univ. of Tennessee, --
11 * -- Univ. of California Berkeley and NAG Ltd. --
12 *
13 IMPLICIT NONE
14 * ..
15 * .. Scalar Arguments ..
16 CHARACTER UPLO
17 INTEGER N, LDA, LDAF, INFO, CMODE
18 * ..
19 * .. Array Arguments
20 INTEGER IWORK( * ), IPIV( * )
21 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
28 * where op2 is determined by CMODE as follows
29 * CMODE = 1 op2(C) = C
30 * CMODE = 0 op2(C) = I
31 * CMODE = -1 op2(C) = inv(C)
32 * The Skeel condition number cond(A) = norminf( |inv(A)||A| )
33 * is computed by computing scaling factors R such that
34 * diag(R)*A*op2(C) is row equilibrated and computing the standard
35 * infinity-norm condition number.
36 *
37 * Arguments
38 * ==========
39 *
40 * UPLO (input) CHARACTER*1
41 * = 'U': Upper triangle of A is stored;
42 * = 'L': Lower triangle of A is stored.
43 *
44 * N (input) INTEGER
45 * The number of linear equations, i.e., the order of the
46 * matrix A. N >= 0.
47 *
48 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
49 * On entry, the N-by-N matrix A.
50 *
51 * LDA (input) INTEGER
52 * The leading dimension of the array A. LDA >= max(1,N).
53 *
54 * AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
55 * The block diagonal matrix D and the multipliers used to
56 * obtain the factor U or L as computed by DSYTRF.
57 *
58 * LDAF (input) INTEGER
59 * The leading dimension of the array AF. LDAF >= max(1,N).
60 *
61 * IPIV (input) INTEGER array, dimension (N)
62 * Details of the interchanges and the block structure of D
63 * as determined by DSYTRF.
64 *
65 * CMODE (input) INTEGER
66 * Determines op2(C) in the formula op(A) * op2(C) as follows:
67 * CMODE = 1 op2(C) = C
68 * CMODE = 0 op2(C) = I
69 * CMODE = -1 op2(C) = inv(C)
70 *
71 * C (input) DOUBLE PRECISION array, dimension (N)
72 * The vector C in the formula op(A) * op2(C).
73 *
74 * INFO (output) INTEGER
75 * = 0: Successful exit.
76 * i > 0: The ith argument is invalid.
77 *
78 * WORK (input) DOUBLE PRECISION array, dimension (3*N).
79 * Workspace.
80 *
81 * IWORK (input) INTEGER array, dimension (N).
82 * Workspace.
83 *
84 * =====================================================================
85 *
86 * .. Local Scalars ..
87 CHARACTER NORMIN
88 INTEGER KASE, I, J
89 DOUBLE PRECISION AINVNM, SMLNUM, TMP
90 LOGICAL UP
91 * ..
92 * .. Local Arrays ..
93 INTEGER ISAVE( 3 )
94 * ..
95 * .. External Functions ..
96 LOGICAL LSAME
97 INTEGER IDAMAX
98 DOUBLE PRECISION DLAMCH
99 EXTERNAL LSAME, IDAMAX, DLAMCH
100 * ..
101 * .. External Subroutines ..
102 EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA, DSYTRS
103 * ..
104 * .. Intrinsic Functions ..
105 INTRINSIC ABS, MAX
106 * ..
107 * .. Executable Statements ..
108 *
109 DLA_SYRCOND = 0.0D+0
110 *
111 INFO = 0
112 IF( N.LT.0 ) THEN
113 INFO = -2
114 END IF
115 IF( INFO.NE.0 ) THEN
116 CALL XERBLA( 'DLA_SYRCOND', -INFO )
117 RETURN
118 END IF
119 IF( N.EQ.0 ) THEN
120 DLA_SYRCOND = 1.0D+0
121 RETURN
122 END IF
123 UP = .FALSE.
124 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
125 *
126 * Compute the equilibration matrix R such that
127 * inv(R)*A*C has unit 1-norm.
128 *
129 IF ( UP ) THEN
130 DO I = 1, N
131 TMP = 0.0D+0
132 IF ( CMODE .EQ. 1 ) THEN
133 DO J = 1, I
134 TMP = TMP + ABS( A( J, I ) * C( J ) )
135 END DO
136 DO J = I+1, N
137 TMP = TMP + ABS( A( I, J ) * C( J ) )
138 END DO
139 ELSE IF ( CMODE .EQ. 0 ) THEN
140 DO J = 1, I
141 TMP = TMP + ABS( A( J, I ) )
142 END DO
143 DO J = I+1, N
144 TMP = TMP + ABS( A( I, J ) )
145 END DO
146 ELSE
147 DO J = 1, I
148 TMP = TMP + ABS( A( J, I ) / C( J ) )
149 END DO
150 DO J = I+1, N
151 TMP = TMP + ABS( A( I, J ) / C( J ) )
152 END DO
153 END IF
154 WORK( 2*N+I ) = TMP
155 END DO
156 ELSE
157 DO I = 1, N
158 TMP = 0.0D+0
159 IF ( CMODE .EQ. 1 ) THEN
160 DO J = 1, I
161 TMP = TMP + ABS( A( I, J ) * C( J ) )
162 END DO
163 DO J = I+1, N
164 TMP = TMP + ABS( A( J, I ) * C( J ) )
165 END DO
166 ELSE IF ( CMODE .EQ. 0 ) THEN
167 DO J = 1, I
168 TMP = TMP + ABS( A( I, J ) )
169 END DO
170 DO J = I+1, N
171 TMP = TMP + ABS( A( J, I ) )
172 END DO
173 ELSE
174 DO J = 1, I
175 TMP = TMP + ABS( A( I, J) / C( J ) )
176 END DO
177 DO J = I+1, N
178 TMP = TMP + ABS( A( J, I) / C( J ) )
179 END DO
180 END IF
181 WORK( 2*N+I ) = TMP
182 END DO
183 ENDIF
184 *
185 * Estimate the norm of inv(op(A)).
186 *
187 SMLNUM = DLAMCH( 'Safe minimum' )
188 AINVNM = 0.0D+0
189 NORMIN = 'N'
190
191 KASE = 0
192 10 CONTINUE
193 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
194 IF( KASE.NE.0 ) THEN
195 IF( KASE.EQ.2 ) THEN
196 *
197 * Multiply by R.
198 *
199 DO I = 1, N
200 WORK( I ) = WORK( I ) * WORK( 2*N+I )
201 END DO
202
203 IF ( UP ) THEN
204 CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
205 ELSE
206 CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
207 ENDIF
208 *
209 * Multiply by inv(C).
210 *
211 IF ( CMODE .EQ. 1 ) THEN
212 DO I = 1, N
213 WORK( I ) = WORK( I ) / C( I )
214 END DO
215 ELSE IF ( CMODE .EQ. -1 ) THEN
216 DO I = 1, N
217 WORK( I ) = WORK( I ) * C( I )
218 END DO
219 END IF
220 ELSE
221 *
222 * Multiply by inv(C**T).
223 *
224 IF ( CMODE .EQ. 1 ) THEN
225 DO I = 1, N
226 WORK( I ) = WORK( I ) / C( I )
227 END DO
228 ELSE IF ( CMODE .EQ. -1 ) THEN
229 DO I = 1, N
230 WORK( I ) = WORK( I ) * C( I )
231 END DO
232 END IF
233
234 IF ( UP ) THEN
235 CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
236 ELSE
237 CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
238 ENDIF
239 *
240 * Multiply by R.
241 *
242 DO I = 1, N
243 WORK( I ) = WORK( I ) * WORK( 2*N+I )
244 END DO
245 END IF
246 *
247 GO TO 10
248 END IF
249 *
250 * Compute the estimate of the reciprocal condition number.
251 *
252 IF( AINVNM .NE. 0.0D+0 )
253 $ DLA_SYRCOND = ( 1.0D+0 / AINVNM )
254 *
255 RETURN
256 *
257 END
2 $ IPIV, CMODE, C, INFO, WORK,
3 $ IWORK )
4 *
5 * -- LAPACK routine (version 3.2.1) --
6 * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
7 * -- Jason Riedy of Univ. of California Berkeley. --
8 * -- April 2009 --
9 *
10 * -- LAPACK is a software package provided by Univ. of Tennessee, --
11 * -- Univ. of California Berkeley and NAG Ltd. --
12 *
13 IMPLICIT NONE
14 * ..
15 * .. Scalar Arguments ..
16 CHARACTER UPLO
17 INTEGER N, LDA, LDAF, INFO, CMODE
18 * ..
19 * .. Array Arguments
20 INTEGER IWORK( * ), IPIV( * )
21 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ), C( * )
22 * ..
23 *
24 * Purpose
25 * =======
26 *
27 * DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C)
28 * where op2 is determined by CMODE as follows
29 * CMODE = 1 op2(C) = C
30 * CMODE = 0 op2(C) = I
31 * CMODE = -1 op2(C) = inv(C)
32 * The Skeel condition number cond(A) = norminf( |inv(A)||A| )
33 * is computed by computing scaling factors R such that
34 * diag(R)*A*op2(C) is row equilibrated and computing the standard
35 * infinity-norm condition number.
36 *
37 * Arguments
38 * ==========
39 *
40 * UPLO (input) CHARACTER*1
41 * = 'U': Upper triangle of A is stored;
42 * = 'L': Lower triangle of A is stored.
43 *
44 * N (input) INTEGER
45 * The number of linear equations, i.e., the order of the
46 * matrix A. N >= 0.
47 *
48 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
49 * On entry, the N-by-N matrix A.
50 *
51 * LDA (input) INTEGER
52 * The leading dimension of the array A. LDA >= max(1,N).
53 *
54 * AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
55 * The block diagonal matrix D and the multipliers used to
56 * obtain the factor U or L as computed by DSYTRF.
57 *
58 * LDAF (input) INTEGER
59 * The leading dimension of the array AF. LDAF >= max(1,N).
60 *
61 * IPIV (input) INTEGER array, dimension (N)
62 * Details of the interchanges and the block structure of D
63 * as determined by DSYTRF.
64 *
65 * CMODE (input) INTEGER
66 * Determines op2(C) in the formula op(A) * op2(C) as follows:
67 * CMODE = 1 op2(C) = C
68 * CMODE = 0 op2(C) = I
69 * CMODE = -1 op2(C) = inv(C)
70 *
71 * C (input) DOUBLE PRECISION array, dimension (N)
72 * The vector C in the formula op(A) * op2(C).
73 *
74 * INFO (output) INTEGER
75 * = 0: Successful exit.
76 * i > 0: The ith argument is invalid.
77 *
78 * WORK (input) DOUBLE PRECISION array, dimension (3*N).
79 * Workspace.
80 *
81 * IWORK (input) INTEGER array, dimension (N).
82 * Workspace.
83 *
84 * =====================================================================
85 *
86 * .. Local Scalars ..
87 CHARACTER NORMIN
88 INTEGER KASE, I, J
89 DOUBLE PRECISION AINVNM, SMLNUM, TMP
90 LOGICAL UP
91 * ..
92 * .. Local Arrays ..
93 INTEGER ISAVE( 3 )
94 * ..
95 * .. External Functions ..
96 LOGICAL LSAME
97 INTEGER IDAMAX
98 DOUBLE PRECISION DLAMCH
99 EXTERNAL LSAME, IDAMAX, DLAMCH
100 * ..
101 * .. External Subroutines ..
102 EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA, DSYTRS
103 * ..
104 * .. Intrinsic Functions ..
105 INTRINSIC ABS, MAX
106 * ..
107 * .. Executable Statements ..
108 *
109 DLA_SYRCOND = 0.0D+0
110 *
111 INFO = 0
112 IF( N.LT.0 ) THEN
113 INFO = -2
114 END IF
115 IF( INFO.NE.0 ) THEN
116 CALL XERBLA( 'DLA_SYRCOND', -INFO )
117 RETURN
118 END IF
119 IF( N.EQ.0 ) THEN
120 DLA_SYRCOND = 1.0D+0
121 RETURN
122 END IF
123 UP = .FALSE.
124 IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
125 *
126 * Compute the equilibration matrix R such that
127 * inv(R)*A*C has unit 1-norm.
128 *
129 IF ( UP ) THEN
130 DO I = 1, N
131 TMP = 0.0D+0
132 IF ( CMODE .EQ. 1 ) THEN
133 DO J = 1, I
134 TMP = TMP + ABS( A( J, I ) * C( J ) )
135 END DO
136 DO J = I+1, N
137 TMP = TMP + ABS( A( I, J ) * C( J ) )
138 END DO
139 ELSE IF ( CMODE .EQ. 0 ) THEN
140 DO J = 1, I
141 TMP = TMP + ABS( A( J, I ) )
142 END DO
143 DO J = I+1, N
144 TMP = TMP + ABS( A( I, J ) )
145 END DO
146 ELSE
147 DO J = 1, I
148 TMP = TMP + ABS( A( J, I ) / C( J ) )
149 END DO
150 DO J = I+1, N
151 TMP = TMP + ABS( A( I, J ) / C( J ) )
152 END DO
153 END IF
154 WORK( 2*N+I ) = TMP
155 END DO
156 ELSE
157 DO I = 1, N
158 TMP = 0.0D+0
159 IF ( CMODE .EQ. 1 ) THEN
160 DO J = 1, I
161 TMP = TMP + ABS( A( I, J ) * C( J ) )
162 END DO
163 DO J = I+1, N
164 TMP = TMP + ABS( A( J, I ) * C( J ) )
165 END DO
166 ELSE IF ( CMODE .EQ. 0 ) THEN
167 DO J = 1, I
168 TMP = TMP + ABS( A( I, J ) )
169 END DO
170 DO J = I+1, N
171 TMP = TMP + ABS( A( J, I ) )
172 END DO
173 ELSE
174 DO J = 1, I
175 TMP = TMP + ABS( A( I, J) / C( J ) )
176 END DO
177 DO J = I+1, N
178 TMP = TMP + ABS( A( J, I) / C( J ) )
179 END DO
180 END IF
181 WORK( 2*N+I ) = TMP
182 END DO
183 ENDIF
184 *
185 * Estimate the norm of inv(op(A)).
186 *
187 SMLNUM = DLAMCH( 'Safe minimum' )
188 AINVNM = 0.0D+0
189 NORMIN = 'N'
190
191 KASE = 0
192 10 CONTINUE
193 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
194 IF( KASE.NE.0 ) THEN
195 IF( KASE.EQ.2 ) THEN
196 *
197 * Multiply by R.
198 *
199 DO I = 1, N
200 WORK( I ) = WORK( I ) * WORK( 2*N+I )
201 END DO
202
203 IF ( UP ) THEN
204 CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
205 ELSE
206 CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
207 ENDIF
208 *
209 * Multiply by inv(C).
210 *
211 IF ( CMODE .EQ. 1 ) THEN
212 DO I = 1, N
213 WORK( I ) = WORK( I ) / C( I )
214 END DO
215 ELSE IF ( CMODE .EQ. -1 ) THEN
216 DO I = 1, N
217 WORK( I ) = WORK( I ) * C( I )
218 END DO
219 END IF
220 ELSE
221 *
222 * Multiply by inv(C**T).
223 *
224 IF ( CMODE .EQ. 1 ) THEN
225 DO I = 1, N
226 WORK( I ) = WORK( I ) / C( I )
227 END DO
228 ELSE IF ( CMODE .EQ. -1 ) THEN
229 DO I = 1, N
230 WORK( I ) = WORK( I ) * C( I )
231 END DO
232 END IF
233
234 IF ( UP ) THEN
235 CALL DSYTRS( 'U', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
236 ELSE
237 CALL DSYTRS( 'L', N, 1, AF, LDAF, IPIV, WORK, N, INFO )
238 ENDIF
239 *
240 * Multiply by R.
241 *
242 DO I = 1, N
243 WORK( I ) = WORK( I ) * WORK( 2*N+I )
244 END DO
245 END IF
246 *
247 GO TO 10
248 END IF
249 *
250 * Compute the estimate of the reciprocal condition number.
251 *
252 IF( AINVNM .NE. 0.0D+0 )
253 $ DLA_SYRCOND = ( 1.0D+0 / AINVNM )
254 *
255 RETURN
256 *
257 END