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dla_gerpvgrw.f
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1 *> \brief \b DLA_GERPVGRW
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download DLA_GERPVGRW + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gerpvgrw.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLA_GERPVGRW( N, NCOLS, A, LDA, AF,
22 * LDAF )
23 *
24 * .. Scalar Arguments ..
25 * INTEGER N, NCOLS, LDA, LDAF
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION A( LDA, * ), AF( LDAF, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *>
38 *> DLA_GERPVGRW computes the reciprocal pivot growth factor
39 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
40 *> much less than 1, the stability of the LU factorization of the
41 *> (equilibrated) matrix A could be poor. This also means that the
42 *> solution X, estimated condition numbers, and error bounds could be
43 *> unreliable.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of linear equations, i.e., the order of the
53 *> matrix A. N >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] NCOLS
57 *> \verbatim
58 *> NCOLS is INTEGER
59 *> The number of columns of the matrix A. NCOLS >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is DOUBLE PRECISION array, dimension (LDA,N)
65 *> On entry, the N-by-N matrix A.
66 *> \endverbatim
67 *>
68 *> \param[in] LDA
69 *> \verbatim
70 *> LDA is INTEGER
71 *> The leading dimension of the array A. LDA >= max(1,N).
72 *> \endverbatim
73 *>
74 *> \param[in] AF
75 *> \verbatim
76 *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
77 *> The factors L and U from the factorization
78 *> A = P*L*U as computed by DGETRF.
79 *> \endverbatim
80 *>
81 *> \param[in] LDAF
82 *> \verbatim
83 *> LDAF is INTEGER
84 *> The leading dimension of the array AF. LDAF >= max(1,N).
85 *> \endverbatim
86 *
87 * Authors:
88 * ========
89 *
90 *> \author Univ. of Tennessee
91 *> \author Univ. of California Berkeley
92 *> \author Univ. of Colorado Denver
93 *> \author NAG Ltd.
94 *
95 *> \date November 2011
96 *
97 *> \ingroup doubleGEcomputational
98 *
99 * =====================================================================
100  DOUBLE PRECISION FUNCTION dla_gerpvgrw( N, NCOLS, A, LDA, AF,
101  $ ldaf )
102 *
103 * -- LAPACK computational routine (version 3.4.0) --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 * November 2011
107 *
108 * .. Scalar Arguments ..
109  INTEGER n, ncols, lda, ldaf
110 * ..
111 * .. Array Arguments ..
112  DOUBLE PRECISION a( lda, * ), af( ldaf, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Local Scalars ..
118  INTEGER i, j
119  DOUBLE PRECISION amax, umax, rpvgrw
120 * ..
121 * .. Intrinsic Functions ..
122  INTRINSIC abs, max, min
123 * ..
124 * .. Executable Statements ..
125 *
126  rpvgrw = 1.0d+0
127 
128  DO j = 1, ncols
129  amax = 0.0d+0
130  umax = 0.0d+0
131  DO i = 1, n
132  amax = max( abs( a( i, j ) ), amax )
133  END DO
134  DO i = 1, j
135  umax = max( abs( af( i, j ) ), umax )
136  END DO
137  IF ( umax /= 0.0d+0 ) THEN
138  rpvgrw = min( amax / umax, rpvgrw )
139  END IF
140  END DO
141  dla_gerpvgrw = rpvgrw
142  END