LAPACK 3.11.0 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*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_gerpvgrw.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_gerpvgrw.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_gerpvgrw.f">
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