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
|
SUBROUTINE DTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, WORK, RAT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER N
DOUBLE PRECISION RAT, RCOND, RCONDC
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DTPT06 computes a test ratio comparing RCOND (the reciprocal
* condition number of a triangular matrix A) and RCONDC, the estimate
* computed by DTPCON. Information about the triangular matrix A is
* used if one estimate is zero and the other is non-zero to decide if
* underflow in the estimate is justified.
*
* Arguments
* =========
*
* RCOND (input) DOUBLE PRECISION
* The estimate of the reciprocal condition number obtained by
* forming the explicit inverse of the matrix A and computing
* RCOND = 1/( norm(A) * norm(inv(A)) ).
*
* RCONDC (input) DOUBLE PRECISION
* The estimate of the reciprocal condition number computed by
* DTPCON.
*
* UPLO (input) CHARACTER
* Specifies whether the matrix A is upper or lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* DIAG (input) CHARACTER
* Specifies whether or not the matrix A is unit triangular.
* = 'N': Non-unit triangular
* = 'U': Unit triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* The upper or lower triangular matrix A, packed columnwise in
* a linear array. The j-th column of A is stored in the array
* AP as follows:
* if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
* if UPLO = 'L',
* AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
*
* WORK (workspace) DOUBLE PRECISION array, dimension (N)
*
* RAT (output) DOUBLE PRECISION
* The test ratio. If both RCOND and RCONDC are nonzero,
* RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
* If RAT = 0, the two estimates are exactly the same.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLANTP
EXTERNAL DLAMCH, DLANTP
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. External Subroutines ..
EXTERNAL DLABAD
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'Epsilon' )
RMAX = MAX( RCOND, RCONDC )
RMIN = MIN( RCOND, RCONDC )
*
* Do the easy cases first.
*
IF( RMIN.LT.ZERO ) THEN
*
* Invalid value for RCOND or RCONDC, return 1/EPS.
*
RAT = ONE / EPS
*
ELSE IF( RMIN.GT.ZERO ) THEN
*
* Both estimates are positive, return RMAX/RMIN - 1.
*
RAT = RMAX / RMIN - ONE
*
ELSE IF( RMAX.EQ.ZERO ) THEN
*
* Both estimates zero.
*
RAT = ZERO
*
ELSE
*
* One estimate is zero, the other is non-zero. If the matrix is
* ill-conditioned, return the nonzero estimate multiplied by
* 1/EPS; if the matrix is badly scaled, return the nonzero
* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
* element in absolute value in A.
*
SMLNUM = DLAMCH( 'Safe minimum' )
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
ANORM = DLANTP( 'M', UPLO, DIAG, N, AP, WORK )
*
RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
END IF
*
RETURN
*
* End of DTPT06
*
END
|
