LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cla_gerpvgrw()

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

CLA_GERPVGRW multiplies a square real matrix by a complex matrix.

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

Purpose:
 CLA_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 COMPLEX 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 COMPLEX array, dimension (LDAF,N)
     The factors L and U from the factorization
     A = P*L*U as computed by CGETRF.
[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 100 of file cla_gerpvgrw.f.

100 *
101 * -- LAPACK computational routine (version 3.7.0) --
102 * -- LAPACK is a software package provided by Univ. of Tennessee, --
103 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104 * December 2016
105 *
106 * .. Scalar Arguments ..
107  INTEGER n, ncols, lda, ldaf
108 * ..
109 * .. Array Arguments ..
110  COMPLEX a( lda, * ), af( ldaf, * )
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Local Scalars ..
116  INTEGER i, j
117  REAL amax, umax, rpvgrw
118  COMPLEX zdum
119 * ..
120 * .. Intrinsic Functions ..
121  INTRINSIC max, min, abs, REAL, aimag
122 * ..
123 * .. Statement Functions ..
124  REAL cabs1
125 * ..
126 * .. Statement Function Definitions ..
127  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
128 * ..
129 * .. Executable Statements ..
130 *
131  rpvgrw = 1.0
132 
133  DO j = 1, ncols
134  amax = 0.0
135  umax = 0.0
136  DO i = 1, n
137  amax = max( cabs1( a( i, j ) ), amax )
138  END DO
139  DO i = 1, j
140  umax = max( cabs1( af( i, j ) ), umax )
141  END DO
142  IF ( umax /= 0.0 ) THEN
143  rpvgrw = min( amax / umax, rpvgrw )
144  END IF
145  END DO
146  cla_gerpvgrw = rpvgrw
real function cla_gerpvgrw(N, NCOLS, A, LDA, AF, LDAF)
CLA_GERPVGRW multiplies a square real matrix by a complex matrix.
Definition: cla_gerpvgrw.f:100
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