1 SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
2 $ 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 ZLACN2 in place of ZLACON, 10 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( * )
18 COMPLEX*16 A( LDA, * ), WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * ZHECON estimates the reciprocal of the condition number of a complex
25 * Hermitian matrix A using the factorization A = U*D*U**H or
26 * A = L*D*L**H computed by ZHETRF.
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**H;
38 * = 'L': Lower triangular, form is A = L*D*L**H.
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 block diagonal matrix D and the multipliers used to
45 * obtain the factor U or L as computed by ZHETRF.
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 ZHETRF.
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) COMPLEX*16 array, dimension (2*N)
63 *
64 * INFO (output) INTEGER
65 * = 0: successful exit
66 * < 0: if INFO = -i, the i-th argument had an illegal value
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 DOUBLE PRECISION ONE, ZERO
72 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
73 * ..
74 * .. Local Scalars ..
75 LOGICAL UPPER
76 INTEGER I, KASE
77 DOUBLE PRECISION AINVNM
78 * ..
79 * .. Local Arrays ..
80 INTEGER ISAVE( 3 )
81 * ..
82 * .. External Functions ..
83 LOGICAL LSAME
84 EXTERNAL LSAME
85 * ..
86 * .. External Subroutines ..
87 EXTERNAL XERBLA, ZHETRS, ZLACN2
88 * ..
89 * .. Intrinsic Functions ..
90 INTRINSIC MAX
91 * ..
92 * .. Executable Statements ..
93 *
94 * Test the input parameters.
95 *
96 INFO = 0
97 UPPER = LSAME( UPLO, 'U' )
98 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
99 INFO = -1
100 ELSE IF( N.LT.0 ) THEN
101 INFO = -2
102 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
103 INFO = -4
104 ELSE IF( ANORM.LT.ZERO ) THEN
105 INFO = -6
106 END IF
107 IF( INFO.NE.0 ) THEN
108 CALL XERBLA( 'ZHECON', -INFO )
109 RETURN
110 END IF
111 *
112 * Quick return if possible
113 *
114 RCOND = ZERO
115 IF( N.EQ.0 ) THEN
116 RCOND = ONE
117 RETURN
118 ELSE IF( ANORM.LE.ZERO ) THEN
119 RETURN
120 END IF
121 *
122 * Check that the diagonal matrix D is nonsingular.
123 *
124 IF( UPPER ) THEN
125 *
126 * Upper triangular storage: examine D from bottom to top
127 *
128 DO 10 I = N, 1, -1
129 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
130 $ RETURN
131 10 CONTINUE
132 ELSE
133 *
134 * Lower triangular storage: examine D from top to bottom.
135 *
136 DO 20 I = 1, N
137 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
138 $ RETURN
139 20 CONTINUE
140 END IF
141 *
142 * Estimate the 1-norm of the inverse.
143 *
144 KASE = 0
145 30 CONTINUE
146 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
147 IF( KASE.NE.0 ) THEN
148 *
149 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
150 *
151 CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
152 GO TO 30
153 END IF
154 *
155 * Compute the estimate of the reciprocal condition number.
156 *
157 IF( AINVNM.NE.ZERO )
158 $ RCOND = ( ONE / AINVNM ) / ANORM
159 *
160 RETURN
161 *
162 * End of ZHECON
163 *
164 END
2 $ 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 ZLACN2 in place of ZLACON, 10 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( * )
18 COMPLEX*16 A( LDA, * ), WORK( * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * ZHECON estimates the reciprocal of the condition number of a complex
25 * Hermitian matrix A using the factorization A = U*D*U**H or
26 * A = L*D*L**H computed by ZHETRF.
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**H;
38 * = 'L': Lower triangular, form is A = L*D*L**H.
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 block diagonal matrix D and the multipliers used to
45 * obtain the factor U or L as computed by ZHETRF.
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 ZHETRF.
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) COMPLEX*16 array, dimension (2*N)
63 *
64 * INFO (output) INTEGER
65 * = 0: successful exit
66 * < 0: if INFO = -i, the i-th argument had an illegal value
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 DOUBLE PRECISION ONE, ZERO
72 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
73 * ..
74 * .. Local Scalars ..
75 LOGICAL UPPER
76 INTEGER I, KASE
77 DOUBLE PRECISION AINVNM
78 * ..
79 * .. Local Arrays ..
80 INTEGER ISAVE( 3 )
81 * ..
82 * .. External Functions ..
83 LOGICAL LSAME
84 EXTERNAL LSAME
85 * ..
86 * .. External Subroutines ..
87 EXTERNAL XERBLA, ZHETRS, ZLACN2
88 * ..
89 * .. Intrinsic Functions ..
90 INTRINSIC MAX
91 * ..
92 * .. Executable Statements ..
93 *
94 * Test the input parameters.
95 *
96 INFO = 0
97 UPPER = LSAME( UPLO, 'U' )
98 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
99 INFO = -1
100 ELSE IF( N.LT.0 ) THEN
101 INFO = -2
102 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
103 INFO = -4
104 ELSE IF( ANORM.LT.ZERO ) THEN
105 INFO = -6
106 END IF
107 IF( INFO.NE.0 ) THEN
108 CALL XERBLA( 'ZHECON', -INFO )
109 RETURN
110 END IF
111 *
112 * Quick return if possible
113 *
114 RCOND = ZERO
115 IF( N.EQ.0 ) THEN
116 RCOND = ONE
117 RETURN
118 ELSE IF( ANORM.LE.ZERO ) THEN
119 RETURN
120 END IF
121 *
122 * Check that the diagonal matrix D is nonsingular.
123 *
124 IF( UPPER ) THEN
125 *
126 * Upper triangular storage: examine D from bottom to top
127 *
128 DO 10 I = N, 1, -1
129 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
130 $ RETURN
131 10 CONTINUE
132 ELSE
133 *
134 * Lower triangular storage: examine D from top to bottom.
135 *
136 DO 20 I = 1, N
137 IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
138 $ RETURN
139 20 CONTINUE
140 END IF
141 *
142 * Estimate the 1-norm of the inverse.
143 *
144 KASE = 0
145 30 CONTINUE
146 CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
147 IF( KASE.NE.0 ) THEN
148 *
149 * Multiply by inv(L*D*L**H) or inv(U*D*U**H).
150 *
151 CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
152 GO TO 30
153 END IF
154 *
155 * Compute the estimate of the reciprocal condition number.
156 *
157 IF( AINVNM.NE.ZERO )
158 $ RCOND = ( ONE / AINVNM ) / ANORM
159 *
160 RETURN
161 *
162 * End of ZHECON
163 *
164 END