1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
|
SUBROUTINE CHPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* Modified to call CLACN2 in place of CLACON, 10 Feb 03, SJH.
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, N
REAL ANORM, RCOND
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX AP( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CHPCON estimates the reciprocal of the condition number of a complex
* Hermitian packed matrix A using the factorization A = U*D*U**H or
* A = L*D*L**H computed by CHPTRF.
*
* An estimate is obtained for norm(inv(A)), and the reciprocal of the
* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the details of the factorization are stored
* as an upper or lower triangular matrix.
* = 'U': Upper triangular, form is A = U*D*U**H;
* = 'L': Lower triangular, form is A = L*D*L**H.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* AP (input) COMPLEX array, dimension (N*(N+1)/2)
* The block diagonal matrix D and the multipliers used to
* obtain the factor U or L as computed by CHPTRF, stored as a
* packed triangular matrix.
*
* IPIV (input) INTEGER array, dimension (N)
* Details of the interchanges and the block structure of D
* as determined by CHPTRF.
*
* ANORM (input) REAL
* The 1-norm of the original matrix A.
*
* RCOND (output) REAL
* The reciprocal of the condition number of the matrix A,
* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
* estimate of the 1-norm of inv(A) computed in this routine.
*
* WORK (workspace) COMPLEX array, dimension (2*N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IP, KASE
REAL AINVNM
* ..
* .. Local Arrays ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CHPTRS, CLACN2, XERBLA
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( ANORM.LT.ZERO ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHPCON', -INFO )
RETURN
END IF
*
* Quick return if possible
*
RCOND = ZERO
IF( N.EQ.0 ) THEN
RCOND = ONE
RETURN
ELSE IF( ANORM.LE.ZERO ) THEN
RETURN
END IF
*
* Check that the diagonal matrix D is nonsingular.
*
IF( UPPER ) THEN
*
* Upper triangular storage: examine D from bottom to top
*
IP = N*( N+1 ) / 2
DO 10 I = N, 1, -1
IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
$ RETURN
IP = IP - I
10 CONTINUE
ELSE
*
* Lower triangular storage: examine D from top to bottom.
*
IP = 1
DO 20 I = 1, N
IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
$ RETURN
IP = IP + N - I + 1
20 CONTINUE
END IF
*
* Estimate the 1-norm of the inverse.
*
KASE = 0
30 CONTINUE
CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
*
* Multiply by inv(L*D*L') or inv(U*D*U').
*
CALL CHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
GO TO 30
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM.NE.ZERO )
$ RCOND = ( ONE / AINVNM ) / ANORM
*
RETURN
*
* End of CHPCON
*
END
|
