LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dla_porpvgrw.f
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1*> \brief \b DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_porpvgrw.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_porpvgrw.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_porpvgrw.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* DOUBLE PRECISION FUNCTION DLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
22* LDAF, WORK )
23*
24* .. Scalar Arguments ..
25* CHARACTER*1 UPLO
26* INTEGER NCOLS, LDA, LDAF
27* ..
28* .. Array Arguments ..
29* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*>
39*> DLA_PORPVGRW computes the reciprocal pivot growth factor
40*> norm(A)/norm(U). The "max absolute element" norm is used. If this is
41*> much less than 1, the stability of the LU factorization of the
42*> (equilibrated) matrix A could be poor. This also means that the
43*> solution X, estimated condition numbers, and error bounds could be
44*> unreliable.
45*> \endverbatim
46*
47* Arguments:
48* ==========
49*
50*> \param[in] UPLO
51*> \verbatim
52*> UPLO is CHARACTER*1
53*> = 'U': Upper triangle of A is stored;
54*> = 'L': Lower triangle of A is stored.
55*> \endverbatim
56*>
57*> \param[in] NCOLS
58*> \verbatim
59*> NCOLS is INTEGER
60*> The number of columns of the matrix A. NCOLS >= 0.
61*> \endverbatim
62*>
63*> \param[in] A
64*> \verbatim
65*> A is DOUBLE PRECISION array, dimension (LDA,N)
66*> On entry, the N-by-N matrix A.
67*> \endverbatim
68*>
69*> \param[in] LDA
70*> \verbatim
71*> LDA is INTEGER
72*> The leading dimension of the array A. LDA >= max(1,N).
73*> \endverbatim
74*>
75*> \param[in] AF
76*> \verbatim
77*> AF is DOUBLE PRECISION array, dimension (LDAF,N)
78*> The triangular factor U or L from the Cholesky factorization
79*> A = U**T*U or A = L*L**T, as computed by DPOTRF.
80*> \endverbatim
81*>
82*> \param[in] LDAF
83*> \verbatim
84*> LDAF is INTEGER
85*> The leading dimension of the array AF. LDAF >= max(1,N).
86*> \endverbatim
87*>
88*> \param[out] WORK
89*> \verbatim
90*> WORK is DOUBLE PRECISION array, dimension (2*N)
91*> \endverbatim
92*
93* Authors:
94* ========
95*
96*> \author Univ. of Tennessee
97*> \author Univ. of California Berkeley
98*> \author Univ. of Colorado Denver
99*> \author NAG Ltd.
100*
101*> \ingroup doublePOcomputational
102*
103* =====================================================================
104 DOUBLE PRECISION FUNCTION dla_porpvgrw( UPLO, NCOLS, A, LDA, AF,
105 \$ LDAF, WORK )
106*
107* -- LAPACK computational routine --
108* -- LAPACK is a software package provided by Univ. of Tennessee, --
109* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
110*
111* .. Scalar Arguments ..
112 CHARACTER*1 uplo
113 INTEGER ncols, lda, ldaf
114* ..
115* .. Array Arguments ..
116 DOUBLE PRECISION a( lda, * ), af( ldaf, * ), work( * )
117* ..
118*
119* =====================================================================
120*
121* .. Local Scalars ..
122 INTEGER i, j
123 DOUBLE PRECISION amax, umax, rpvgrw
124 LOGICAL upper
125* ..
126* .. Intrinsic Functions ..
127 INTRINSIC abs, max, min
128* ..
129* .. External Functions ..
130 EXTERNAL lsame
131 LOGICAL lsame
132* ..
133* .. Executable Statements ..
134*
135 upper = lsame( 'Upper', uplo )
136*
137* DPOTRF will have factored only the NCOLSxNCOLS leading minor, so
138* we restrict the growth search to that minor and use only the first
139* 2*NCOLS workspace entries.
140*
141 rpvgrw = 1.0d+0
142 DO i = 1, 2*ncols
143 work( i ) = 0.0d+0
144 END DO
145*
146* Find the max magnitude entry of each column.
147*
148 IF ( upper ) THEN
149 DO j = 1, ncols
150 DO i = 1, j
151 work( ncols+j ) =
152 \$ max( abs( a( i, j ) ), work( ncols+j ) )
153 END DO
154 END DO
155 ELSE
156 DO j = 1, ncols
157 DO i = j, ncols
158 work( ncols+j ) =
159 \$ max( abs( a( i, j ) ), work( ncols+j ) )
160 END DO
161 END DO
162 END IF
163*
164* Now find the max magnitude entry of each column of the factor in
165* AF. No pivoting, so no permutations.
166*
167 IF ( lsame( 'Upper', uplo ) ) THEN
168 DO j = 1, ncols
169 DO i = 1, j
170 work( j ) = max( abs( af( i, j ) ), work( j ) )
171 END DO
172 END DO
173 ELSE
174 DO j = 1, ncols
175 DO i = j, ncols
176 work( j ) = max( abs( af( i, j ) ), work( j ) )
177 END DO
178 END DO
179 END IF
180*
181* Compute the *inverse* of the max element growth factor. Dividing
182* by zero would imply the largest entry of the factor's column is
183* zero. Than can happen when either the column of A is zero or
184* massive pivots made the factor underflow to zero. Neither counts
185* as growth in itself, so simply ignore terms with zero
186* denominators.
187*
188 IF ( lsame( 'Upper', uplo ) ) THEN
189 DO i = 1, ncols
190 umax = work( i )
191 amax = work( ncols+i )
192 IF ( umax /= 0.0d+0 ) THEN
193 rpvgrw = min( amax / umax, rpvgrw )
194 END IF
195 END DO
196 ELSE
197 DO i = 1, ncols
198 umax = work( i )
199 amax = work( ncols+i )
200 IF ( umax /= 0.0d+0 ) THEN
201 rpvgrw = min( amax / umax, rpvgrw )
202 END IF
203 END DO
204 END IF
205
206 dla_porpvgrw = rpvgrw
207*
208* End of DLA_PORPVGRW
209*
210 END
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dla_porpvgrw(UPLO, NCOLS, A, LDA, AF, LDAF, WORK)
DLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian...
Definition: dla_porpvgrw.f:106