LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ sla_gerpvgrw()

real function sla_gerpvgrw ( integer  N,
integer  NCOLS,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldaf, * )  AF,
integer  LDAF 
)

SLA_GERPVGRW

Download SLA_GERPVGRW + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SLA_GERPVGRW computes the reciprocal pivot growth factor
 norm(A)/norm(U). The "max absolute element" norm is used. If this is
 much less than 1, the stability of the LU factorization of the
 (equilibrated) matrix A could be poor. This also means that the
 solution X, estimated condition numbers, and error bounds could be
 unreliable.
Parameters
[in]N
          N is INTEGER
     The number of linear equations, i.e., the order of the
     matrix A.  N >= 0.
[in]NCOLS
          NCOLS is INTEGER
     The number of columns of the matrix A. NCOLS >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
     On entry, the N-by-N matrix A.
[in]LDA
          LDA is INTEGER
     The leading dimension of the array A.  LDA >= max(1,N).
[in]AF
          AF is REAL array, dimension (LDAF,N)
     The factors L and U from the factorization
     A = P*L*U as computed by SGETRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 99 of file sla_gerpvgrw.f.

99 *
100 * -- LAPACK computational routine (version 3.7.0) --
101 * -- LAPACK is a software package provided by Univ. of Tennessee, --
102 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
103 * December 2016
104 *
105 * .. Scalar Arguments ..
106  INTEGER n, ncols, lda, ldaf
107 * ..
108 * .. Array Arguments ..
109  REAL a( lda, * ), af( ldaf, * )
110 * ..
111 *
112 * =====================================================================
113 *
114 * .. Local Scalars ..
115  INTEGER i, j
116  REAL amax, umax, rpvgrw
117 * ..
118 * .. Intrinsic Functions ..
119  INTRINSIC abs, max, min
120 * ..
121 * .. Executable Statements ..
122 *
123  rpvgrw = 1.0
124 
125  DO j = 1, ncols
126  amax = 0.0
127  umax = 0.0
128  DO i = 1, n
129  amax = max( abs( a( i, j ) ), amax )
130  END DO
131  DO i = 1, j
132  umax = max( abs( af( i, j ) ), umax )
133  END DO
134  IF ( umax /= 0.0 ) THEN
135  rpvgrw = min( amax / umax, rpvgrw )
136  END IF
137  END DO
138  sla_gerpvgrw = rpvgrw
real function sla_gerpvgrw(N, NCOLS, A, LDA, AF, LDAF)
SLA_GERPVGRW
Definition: sla_gerpvgrw.f:99
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