 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zla_gerpvgrw()

 double precision function zla_gerpvgrw ( integer N, integer NCOLS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF )

ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

Purpose:
``` ZLA_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*16 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*16 array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).```

Definition at line 98 of file zla_gerpvgrw.f.

100*
101* -- LAPACK computational routine --
102* -- LAPACK is a software package provided by Univ. of Tennessee, --
103* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104*
105* .. Scalar Arguments ..
106 INTEGER N, NCOLS, LDA, LDAF
107* ..
108* .. Array Arguments ..
109 COMPLEX*16 A( LDA, * ), AF( LDAF, * )
110* ..
111*
112* =====================================================================
113*
114* .. Local Scalars ..
115 INTEGER I, J
116 DOUBLE PRECISION AMAX, UMAX, RPVGRW
117 COMPLEX*16 ZDUM
118* ..
119* .. Intrinsic Functions ..
120 INTRINSIC max, min, abs, real, dimag
121* ..
122* .. Statement Functions ..
123 DOUBLE PRECISION CABS1
124* ..
125* .. Statement Function Definitions ..
126 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
127* ..
128* .. Executable Statements ..
129*
130 rpvgrw = 1.0d+0
131
132 DO j = 1, ncols
133 amax = 0.0d+0
134 umax = 0.0d+0
135 DO i = 1, n
136 amax = max( cabs1( a( i, j ) ), amax )
137 END DO
138 DO i = 1, j
139 umax = max( cabs1( af( i, j ) ), umax )
140 END DO
141 IF ( umax /= 0.0d+0 ) THEN
142 rpvgrw = min( amax / umax, rpvgrw )
143 END IF
144 END DO
145 zla_gerpvgrw = rpvgrw
146*
147* End of ZLA_GERPVGRW
148*
double precision function zla_gerpvgrw(N, NCOLS, A, LDA, AF, LDAF)
ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.
Definition: zla_gerpvgrw.f:100
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