LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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ctpt06.f
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1*> \brief \b CTPT06
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE CTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
12*
13* .. Scalar Arguments ..
14* CHARACTER DIAG, UPLO
15* INTEGER N
16* REAL RAT, RCOND, RCONDC
17* ..
18* .. Array Arguments ..
19* REAL RWORK( * )
20* COMPLEX AP( * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> CTPT06 computes a test ratio comparing RCOND (the reciprocal
30*> condition number of the triangular matrix A) and RCONDC, the estimate
31*> computed by CTPCON. Information about the triangular matrix is used
32*> if one estimate is zero and the other is non-zero to decide if
33*> underflow in the estimate is justified.
34*> \endverbatim
35*
36* Arguments:
37* ==========
38*
39*> \param[in] RCOND
40*> \verbatim
41*> RCOND is REAL
42*> The estimate of the reciprocal condition number obtained by
43*> forming the explicit inverse of the matrix A and computing
44*> RCOND = 1/( norm(A) * norm(inv(A)) ).
45*> \endverbatim
46*>
47*> \param[in] RCONDC
48*> \verbatim
49*> RCONDC is REAL
50*> The estimate of the reciprocal condition number computed by
51*> CTPCON.
52*> \endverbatim
53*>
54*> \param[in] UPLO
55*> \verbatim
56*> UPLO is CHARACTER
57*> Specifies whether the matrix A is upper or lower triangular.
58*> = 'U': Upper triangular
59*> = 'L': Lower triangular
60*> \endverbatim
61*>
62*> \param[in] DIAG
63*> \verbatim
64*> DIAG is CHARACTER
65*> Specifies whether or not the matrix A is unit triangular.
66*> = 'N': Non-unit triangular
67*> = 'U': Unit triangular
68*> \endverbatim
69*>
70*> \param[in] N
71*> \verbatim
72*> N is INTEGER
73*> The order of the matrix A. N >= 0.
74*> \endverbatim
75*>
76*> \param[in] AP
77*> \verbatim
78*> AP is COMPLEX array, dimension (N*(N+1)/2)
79*> The upper or lower triangular matrix A, packed columnwise in
80*> a linear array. The j-th column of A is stored in the array
81*> AP as follows:
82*> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
83*> if UPLO = 'L',
84*> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
85*> \endverbatim
86*>
87*> \param[out] RWORK
88*> \verbatim
89*> RWORK is REAL array, dimension (N)
90*> \endverbatim
91*>
92*> \param[out] RAT
93*> \verbatim
94*> RAT is REAL
95*> The test ratio. If both RCOND and RCONDC are nonzero,
96*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
97*> If RAT = 0, the two estimates are exactly the same.
98*> \endverbatim
99*
100* Authors:
101* ========
102*
103*> \author Univ. of Tennessee
104*> \author Univ. of California Berkeley
105*> \author Univ. of Colorado Denver
106*> \author NAG Ltd.
107*
108*> \ingroup complex_lin
109*
110* =====================================================================
111 SUBROUTINE ctpt06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
112*
113* -- LAPACK test routine --
114* -- LAPACK is a software package provided by Univ. of Tennessee, --
115* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
116*
117* .. Scalar Arguments ..
118 CHARACTER DIAG, UPLO
119 INTEGER N
120 REAL RAT, RCOND, RCONDC
121* ..
122* .. Array Arguments ..
123 REAL RWORK( * )
124 COMPLEX AP( * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 REAL ZERO, ONE
131 parameter( zero = 0.0e+0, one = 1.0e+0 )
132* ..
133* .. Local Scalars ..
134 REAL ANORM, BIGNUM, EPS, RMAX, RMIN
135* ..
136* .. External Functions ..
137 REAL CLANTP, SLAMCH
138 EXTERNAL clantp, slamch
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC max, min
142* ..
143* .. Executable Statements ..
144*
145 eps = slamch( 'Epsilon' )
146 rmax = max( rcond, rcondc )
147 rmin = min( rcond, rcondc )
148*
149* Do the easy cases first.
150*
151 IF( rmin.LT.zero ) THEN
152*
153* Invalid value for RCOND or RCONDC, return 1/EPS.
154*
155 rat = one / eps
156*
157 ELSE IF( rmin.GT.zero ) THEN
158*
159* Both estimates are positive, return RMAX/RMIN - 1.
160*
161 rat = rmax / rmin - one
162*
163 ELSE IF( rmax.EQ.zero ) THEN
164*
165* Both estimates zero.
166*
167 rat = zero
168*
169 ELSE
170*
171* One estimate is zero, the other is non-zero. If the matrix is
172* ill-conditioned, return the nonzero estimate multiplied by
173* 1/EPS; if the matrix is badly scaled, return the nonzero
174* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
175* element in absolute value in A.
176*
177 bignum = one / slamch( 'Safe minimum' )
178 anorm = clantp( 'M', uplo, diag, n, ap, rwork )
179*
180 rat = rmax*( min( bignum / max( one, anorm ), one / eps ) )
181 END IF
182*
183 RETURN
184*
185* End of CTPT06
186*
187 END
subroutine ctpt06(RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT)
CTPT06
Definition: ctpt06.f:112