LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ 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.

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

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).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2016

Definition at line 102 of file zla_gerpvgrw.f.

102 *
103 * -- LAPACK computational routine (version 3.7.0) --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 * June 2016
107 *
108 * .. Scalar Arguments ..
109  INTEGER n, ncols, lda, ldaf
110 * ..
111 * .. Array Arguments ..
112  COMPLEX*16 a( lda, * ), af( ldaf, * )
113 * ..
114 *
115 * =====================================================================
116 *
117 * .. Local Scalars ..
118  INTEGER i, j
119  DOUBLE PRECISION amax, umax, rpvgrw
120  COMPLEX*16 zdum
121 * ..
122 * .. Intrinsic Functions ..
123  INTRINSIC max, min, abs, REAL, dimag
124 * ..
125 * .. Statement Functions ..
126  DOUBLE PRECISION cabs1
127 * ..
128 * .. Statement Function Definitions ..
129  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
130 * ..
131 * .. Executable Statements ..
132 *
133  rpvgrw = 1.0d+0
134 
135  DO j = 1, ncols
136  amax = 0.0d+0
137  umax = 0.0d+0
138  DO i = 1, n
139  amax = max( cabs1( a( i, j ) ), amax )
140  END DO
141  DO i = 1, j
142  umax = max( cabs1( af( i, j ) ), umax )
143  END DO
144  IF ( umax /= 0.0d+0 ) THEN
145  rpvgrw = min( amax / umax, rpvgrw )
146  END IF
147  END DO
148  zla_gerpvgrw = rpvgrw
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:102
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