1 SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
2 $ IWORK, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
10 *
11 * .. Scalar Arguments ..
12 CHARACTER UPLO
13 INTEGER INFO, LDA, N
14 DOUBLE PRECISION ANORM, RCOND
15 * ..
16 * .. Array Arguments ..
17 INTEGER IPIV( * ), IWORK( * )
18 DOUBLE PRECISION A( LDA, * ), WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * DSYCON estimates the reciprocal of the condition number (in the
25 * 1-norm) of a real symmetric matrix A using the factorization
26 * A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
27 *
28 * An estimate is obtained for norm(inv(A)), and the reciprocal of the
29 * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
30 *
31 * Arguments
32 * =========
33 *
34 * UPLO (input) CHARACTER*1
35 * Specifies whether the details of the factorization are stored
36 * as an upper or lower triangular matrix.
37 * = 'U': Upper triangular, form is A = U*D*U**T;
38 * = 'L': Lower triangular, form is A = L*D*L**T.
39 *
40 * N (input) INTEGER
41 * The order of the matrix A. N >= 0.
42 *
43 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
44 * The block diagonal matrix D and the multipliers used to
45 * obtain the factor U or L as computed by DSYTRF.
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= max(1,N).
49 *
50 * IPIV (input) INTEGER array, dimension (N)
51 * Details of the interchanges and the block structure of D
52 * as determined by DSYTRF.
53 *
54 * ANORM (input) DOUBLE PRECISION
55 * The 1-norm of the original matrix A.
56 *
57 * RCOND (output) DOUBLE PRECISION
58 * The reciprocal of the condition number of the matrix A,
59 * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
60 * estimate of the 1-norm of inv(A) computed in this routine.
61 *
62 * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
63 *
64 * IWORK (workspace) INTEGER array, dimension (N)
65 *
66 * INFO (output) INTEGER
67 * = 0: successful exit
68 * < 0: if INFO = -i, the i-th argument had an illegal value
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 DOUBLE PRECISION ONE, ZERO
74 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
75 * ..
76 * .. Local Scalars ..
77 LOGICAL UPPER
78 INTEGER I, KASE
79 DOUBLE PRECISION AINVNM
80 * ..
81 * .. Local Arrays ..
82 INTEGER ISAVE( 3 )
83 * ..
84 * .. External Functions ..
85 LOGICAL LSAME
86 EXTERNAL LSAME
87 * ..
88 * .. External Subroutines ..
89 EXTERNAL DLACN2, DSYTRS, XERBLA
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC MAX
93 * ..
94 * .. Executable Statements ..
95 *
96 * Test the input parameters.
97 *
98 INFO = 0
99 UPPER = LSAME( UPLO, 'U' )
100 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
101 INFO = -1
102 ELSE IF( N.LT.0 ) THEN
103 INFO = -2
104 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
105 INFO = -4
106 ELSE IF( ANORM.LT.ZERO ) THEN
107 INFO = -6
108 END IF
109 IF( INFO.NE.0 ) THEN
110 CALL XERBLA( 'DSYCON', -INFO )
111 RETURN
112 END IF
113 *
114 * Quick return if possible
115 *
116 RCOND = ZERO
117 IF( N.EQ.0 ) THEN
118 RCOND = ONE
119 RETURN
120 ELSE IF( ANORM.LE.ZERO ) THEN
121 RETURN
122 END IF
123 *
124 * Check that the diagonal matrix D is nonsingular.
125 *
126 IF( UPPER ) THEN
127 *
128 * Upper triangular storage: examine D from bottom to top
129 *
130 DO 10 I = N, 1, -1
131 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
132 $ RETURN
133 10 CONTINUE
134 ELSE
135 *
136 * Lower triangular storage: examine D from top to bottom.
137 *
138 DO 20 I = 1, N
139 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
140 $ RETURN
141 20 CONTINUE
142 END IF
143 *
144 * Estimate the 1-norm of the inverse.
145 *
146 KASE = 0
147 30 CONTINUE
148 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
149 IF( KASE.NE.0 ) THEN
150 *
151 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
152 *
153 CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
154 GO TO 30
155 END IF
156 *
157 * Compute the estimate of the reciprocal condition number.
158 *
159 IF( AINVNM.NE.ZERO )
160 $ RCOND = ( ONE / AINVNM ) / ANORM
161 *
162 RETURN
163 *
164 * End of DSYCON
165 *
166 END
2 $ IWORK, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
10 *
11 * .. Scalar Arguments ..
12 CHARACTER UPLO
13 INTEGER INFO, LDA, N
14 DOUBLE PRECISION ANORM, RCOND
15 * ..
16 * .. Array Arguments ..
17 INTEGER IPIV( * ), IWORK( * )
18 DOUBLE PRECISION A( LDA, * ), WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * DSYCON estimates the reciprocal of the condition number (in the
25 * 1-norm) of a real symmetric matrix A using the factorization
26 * A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
27 *
28 * An estimate is obtained for norm(inv(A)), and the reciprocal of the
29 * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
30 *
31 * Arguments
32 * =========
33 *
34 * UPLO (input) CHARACTER*1
35 * Specifies whether the details of the factorization are stored
36 * as an upper or lower triangular matrix.
37 * = 'U': Upper triangular, form is A = U*D*U**T;
38 * = 'L': Lower triangular, form is A = L*D*L**T.
39 *
40 * N (input) INTEGER
41 * The order of the matrix A. N >= 0.
42 *
43 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
44 * The block diagonal matrix D and the multipliers used to
45 * obtain the factor U or L as computed by DSYTRF.
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= max(1,N).
49 *
50 * IPIV (input) INTEGER array, dimension (N)
51 * Details of the interchanges and the block structure of D
52 * as determined by DSYTRF.
53 *
54 * ANORM (input) DOUBLE PRECISION
55 * The 1-norm of the original matrix A.
56 *
57 * RCOND (output) DOUBLE PRECISION
58 * The reciprocal of the condition number of the matrix A,
59 * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
60 * estimate of the 1-norm of inv(A) computed in this routine.
61 *
62 * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
63 *
64 * IWORK (workspace) INTEGER array, dimension (N)
65 *
66 * INFO (output) INTEGER
67 * = 0: successful exit
68 * < 0: if INFO = -i, the i-th argument had an illegal value
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 DOUBLE PRECISION ONE, ZERO
74 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
75 * ..
76 * .. Local Scalars ..
77 LOGICAL UPPER
78 INTEGER I, KASE
79 DOUBLE PRECISION AINVNM
80 * ..
81 * .. Local Arrays ..
82 INTEGER ISAVE( 3 )
83 * ..
84 * .. External Functions ..
85 LOGICAL LSAME
86 EXTERNAL LSAME
87 * ..
88 * .. External Subroutines ..
89 EXTERNAL DLACN2, DSYTRS, XERBLA
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC MAX
93 * ..
94 * .. Executable Statements ..
95 *
96 * Test the input parameters.
97 *
98 INFO = 0
99 UPPER = LSAME( UPLO, 'U' )
100 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
101 INFO = -1
102 ELSE IF( N.LT.0 ) THEN
103 INFO = -2
104 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
105 INFO = -4
106 ELSE IF( ANORM.LT.ZERO ) THEN
107 INFO = -6
108 END IF
109 IF( INFO.NE.0 ) THEN
110 CALL XERBLA( 'DSYCON', -INFO )
111 RETURN
112 END IF
113 *
114 * Quick return if possible
115 *
116 RCOND = ZERO
117 IF( N.EQ.0 ) THEN
118 RCOND = ONE
119 RETURN
120 ELSE IF( ANORM.LE.ZERO ) THEN
121 RETURN
122 END IF
123 *
124 * Check that the diagonal matrix D is nonsingular.
125 *
126 IF( UPPER ) THEN
127 *
128 * Upper triangular storage: examine D from bottom to top
129 *
130 DO 10 I = N, 1, -1
131 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
132 $ RETURN
133 10 CONTINUE
134 ELSE
135 *
136 * Lower triangular storage: examine D from top to bottom.
137 *
138 DO 20 I = 1, N
139 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
140 $ RETURN
141 20 CONTINUE
142 END IF
143 *
144 * Estimate the 1-norm of the inverse.
145 *
146 KASE = 0
147 30 CONTINUE
148 CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
149 IF( KASE.NE.0 ) THEN
150 *
151 * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
152 *
153 CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
154 GO TO 30
155 END IF
156 *
157 * Compute the estimate of the reciprocal condition number.
158 *
159 IF( AINVNM.NE.ZERO )
160 $ RCOND = ( ONE / AINVNM ) / ANORM
161 *
162 RETURN
163 *
164 * End of DSYCON
165 *
166 END