LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
zla_gerpvgrw.f
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1 *> \brief \b ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLA_GERPVGRW( N, NCOLS, A, LDA, AF,
22 * LDAF )
23 *
24 * .. Scalar Arguments ..
25 * INTEGER N, NCOLS, LDA, LDAF
26 * ..
27 * .. Array Arguments ..
28 * COMPLEX*16 A( LDA, * ), AF( LDAF, * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *>
38 *> ZLA_GERPVGRW computes the reciprocal pivot growth factor
39 *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
40 *> much less than 1, the stability of the LU factorization of the
41 *> (equilibrated) matrix A could be poor. This also means that the
42 *> solution X, estimated condition numbers, and error bounds could be
43 *> unreliable.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of linear equations, i.e., the order of the
53 *> matrix A. N >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] NCOLS
57 *> \verbatim
58 *> NCOLS is INTEGER
59 *> The number of columns of the matrix A. NCOLS >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] A
63 *> \verbatim
64 *> A is DOUBLE PRECISION array, dimension (LDA,N)
65 *> On entry, the N-by-N matrix A.
66 *> \endverbatim
67 *>
68 *> \param[in] LDA
69 *> \verbatim
70 *> LDA is INTEGER
71 *> The leading dimension of the array A. LDA >= max(1,N).
72 *> \endverbatim
73 *>
74 *> \param[in] AF
75 *> \verbatim
76 *> AF is DOUBLE PRECISION array, dimension (LDAF,N)
77 *> The factors L and U from the factorization
78 *> A = P*L*U as computed by ZGETRF.
79 *> \endverbatim
80 *>
81 *> \param[in] LDAF
82 *> \verbatim
83 *> LDAF is INTEGER
84 *> The leading dimension of the array AF. LDAF >= max(1,N).
85 *> \endverbatim
86 *
87 * Authors:
88 * ========
89 *
90 *> \author Univ. of Tennessee
91 *> \author Univ. of California Berkeley
92 *> \author Univ. of Colorado Denver
93 *> \author NAG Ltd.
94 *
95 *> \date September 2012
96 *
97 *> \ingroup complex16GEcomputational
98 *
99 * =====================================================================
100  DOUBLE PRECISION FUNCTION zla_gerpvgrw( N, NCOLS, A, LDA, AF,
101  \$ ldaf )
102 *
103 * -- LAPACK computational routine (version 3.4.2) --
104 * -- LAPACK is a software package provided by Univ. of Tennessee, --
105 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106 * September 2012
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
149  END