LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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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*
8*> Download SLA_GERPVGRW + dependencies
9*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_gerpvgrw.f">
10*> [TGZ]</a>
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12*> [ZIP]</a>
13*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_gerpvgrw.f">
14*> [TXT]</a>
15*
16* Definition:
17* ===========
18*
19* REAL FUNCTION SLA_GERPVGRW( N, NCOLS, A, LDA, AF, LDAF )
20*
21* .. Scalar Arguments ..
22* INTEGER N, NCOLS, LDA, LDAF
23* ..
24* .. Array Arguments ..
25* REAL A( LDA, * ), AF( LDAF, * )
26* ..
27*
28*
29*> \par Purpose:
30* =============
31*>
32*> \verbatim
33*>
34*> SLA_GERPVGRW computes the reciprocal pivot growth factor
35*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
36*> much less than 1, the stability of the LU factorization of the
37*> (equilibrated) matrix A could be poor. This also means that the
38*> solution X, estimated condition numbers, and error bounds could be
39*> unreliable.
40*> \endverbatim
41*
42* Arguments:
43* ==========
44*
45*> \param[in] N
46*> \verbatim
47*> N is INTEGER
48*> The number of linear equations, i.e., the order of the
49*> matrix A. N >= 0.
50*> \endverbatim
51*>
52*> \param[in] NCOLS
53*> \verbatim
54*> NCOLS is INTEGER
55*> The number of columns of the matrix A. NCOLS >= 0.
56*> \endverbatim
57*>
58*> \param[in] A
59*> \verbatim
60*> A is REAL array, dimension (LDA,N)
61*> On entry, the N-by-N matrix A.
62*> \endverbatim
63*>
64*> \param[in] LDA
65*> \verbatim
66*> LDA is INTEGER
67*> The leading dimension of the array A. LDA >= max(1,N).
68*> \endverbatim
69*>
70*> \param[in] AF
71*> \verbatim
72*> AF is REAL array, dimension (LDAF,N)
73*> The factors L and U from the factorization
74*> A = P*L*U as computed by SGETRF.
75*> \endverbatim
76*>
77*> \param[in] LDAF
78*> \verbatim
79*> LDAF is INTEGER
80*> The leading dimension of the array AF. LDAF >= max(1,N).
81*> \endverbatim
82*
83* Authors:
84* ========
85*
86*> \author Univ. of Tennessee
87*> \author Univ. of California Berkeley
88*> \author Univ. of Colorado Denver
89*> \author NAG Ltd.
90*
91*> \ingroup la_gerpvgrw
92*
93* =====================================================================
94 REAL function sla_gerpvgrw( n, ncols, a, lda, af, ldaf )
95*
96* -- LAPACK computational routine --
97* -- LAPACK is a software package provided by Univ. of Tennessee, --
98* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99*
100* .. Scalar Arguments ..
101 INTEGER n, ncols, lda, ldaf
102* ..
103* .. Array Arguments ..
104 REAL a( lda, * ), af( ldaf, * )
105* ..
106*
107* =====================================================================
108*
109* .. Local Scalars ..
110 INTEGER i, j
111 REAL amax, umax, rpvgrw
112* ..
113* .. Intrinsic Functions ..
114 INTRINSIC abs, max, min
115* ..
116* .. Executable Statements ..
117*
118 rpvgrw = 1.0
119
120 DO j = 1, ncols
121 amax = 0.0
122 umax = 0.0
123 DO i = 1, n
124 amax = max( abs( a( i, j ) ), amax )
125 END DO
126 DO i = 1, j
127 umax = max( abs( af( i, j ) ), umax )
128 END DO
129 IF ( umax /= 0.0 ) THEN
130 rpvgrw = min( amax / umax, rpvgrw )
131 END IF
132 END DO
133 sla_gerpvgrw = rpvgrw
134*
135* End of SLA_GERPVGRW
136*
137 END
real function sla_gerpvgrw(n, ncols, a, lda, af, ldaf)
SLA_GERPVGRW