LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
sla_gerpvgrw.f
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1 *> \brief \b SLA_GERPVGRW
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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13 *> [ZIP]</a>
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION SLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER N, NCOLS, LDA, LDAF
25 * ..
26 * .. Array Arguments ..
27 * REAL A( LDA, * ), AF( LDAF, * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> SLA_GERPVGRW computes the reciprocal pivot growth factor
37 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
38 *> much less than 1, the stability of the LU factorization of the
39 *> (equilibrated) matrix A could be poor. This also means that the
40 *> solution X, estimated condition numbers, and error bounds could be
41 *> unreliable.
42 *> \endverbatim
43 *
44 * Arguments:
45 * ==========
46 *
47 *> \param[in] N
48 *> \verbatim
49 *> N is INTEGER
50 *> The number of linear equations, i.e., the order of the
51 *> matrix A. N >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] NCOLS
55 *> \verbatim
56 *> NCOLS is INTEGER
57 *> The number of columns of the matrix A. NCOLS >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] A
61 *> \verbatim
62 *> A is REAL array, dimension (LDA,N)
63 *> On entry, the N-by-N matrix A.
64 *> \endverbatim
65 *>
66 *> \param[in] LDA
67 *> \verbatim
68 *> LDA is INTEGER
69 *> The leading dimension of the array A. LDA >= max(1,N).
70 *> \endverbatim
71 *>
72 *> \param[in] AF
73 *> \verbatim
74 *> AF is REAL array, dimension (LDAF,N)
75 *> The factors L and U from the factorization
76 *> A = P*L*U as computed by SGETRF.
77 *> \endverbatim
78 *>
79 *> \param[in] LDAF
80 *> \verbatim
81 *> LDAF is INTEGER
82 *> The leading dimension of the array AF. LDAF >= max(1,N).
83 *> \endverbatim
84 *
85 * Authors:
86 * ========
87 *
88 *> \author Univ. of Tennessee
89 *> \author Univ. of California Berkeley
90 *> \author Univ. of Colorado Denver
91 *> \author NAG Ltd.
92 *
93 *> \ingroup realGEcomputational
94 *
95 * =====================================================================
96  REAL function sla_gerpvgrw( n, ncols, a, lda, af, ldaf )
97 *
98 * -- LAPACK computational routine --
99 * -- LAPACK is a software package provided by Univ. of Tennessee, --
100 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
101 *
102 * .. Scalar Arguments ..
103  INTEGER n, ncols, lda, ldaf
104 * ..
105 * .. Array Arguments ..
106  REAL a( lda, * ), af( ldaf, * )
107 * ..
108 *
109 * =====================================================================
110 *
111 * .. Local Scalars ..
112  INTEGER i, j
113  REAL amax, umax, rpvgrw
114 * ..
115 * .. Intrinsic Functions ..
116  INTRINSIC abs, max, min
117 * ..
118 * .. Executable Statements ..
119 *
120  rpvgrw = 1.0
121
122  DO j = 1, ncols
123  amax = 0.0
124  umax = 0.0
125  DO i = 1, n
126  amax = max( abs( a( i, j ) ), amax )
127  END DO
128  DO i = 1, j
129  umax = max( abs( af( i, j ) ), umax )
130  END DO
131  IF ( umax /= 0.0 ) THEN
132  rpvgrw = min( amax / umax, rpvgrw )
133  END IF
134  END DO
135  sla_gerpvgrw = rpvgrw
136 *
137 * End of SLA_GERPVGRW
138 *
139  END
real function sla_gerpvgrw(N, NCOLS, A, LDA, AF, LDAF)
SLA_GERPVGRW
Definition: sla_gerpvgrw.f:97