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

 double precision function zla_porpvgrw ( character*1 UPLO, integer NCOLS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, double precision, dimension( * ) WORK )

ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Purpose:
``` ZLA_PORPVGRW 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] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by ZPOTRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (2*N)`

Definition at line 105 of file zla_porpvgrw.f.

107*
108* -- LAPACK computational routine --
109* -- LAPACK is a software package provided by Univ. of Tennessee, --
110* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
111*
112* .. Scalar Arguments ..
113 CHARACTER*1 UPLO
114 INTEGER NCOLS, LDA, LDAF
115* ..
116* .. Array Arguments ..
117 COMPLEX*16 A( LDA, * ), AF( LDAF, * )
118 DOUBLE PRECISION WORK( * )
119* ..
120*
121* =====================================================================
122*
123* .. Local Scalars ..
124 INTEGER I, J
125 DOUBLE PRECISION AMAX, UMAX, RPVGRW
126 LOGICAL UPPER
127 COMPLEX*16 ZDUM
128* ..
129* .. External Functions ..
130 EXTERNAL lsame
131 LOGICAL LSAME
132* ..
133* .. Intrinsic Functions ..
134 INTRINSIC abs, max, min, real, dimag
135* ..
136* .. Statement Functions ..
137 DOUBLE PRECISION CABS1
138* ..
139* .. Statement Function Definitions ..
140 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
141* ..
142* .. Executable Statements ..
143 upper = lsame( 'Upper', uplo )
144*
145* DPOTRF will have factored only the NCOLSxNCOLS leading minor, so
146* we restrict the growth search to that minor and use only the first
147* 2*NCOLS workspace entries.
148*
149 rpvgrw = 1.0d+0
150 DO i = 1, 2*ncols
151 work( i ) = 0.0d+0
152 END DO
153*
154* Find the max magnitude entry of each column.
155*
156 IF ( upper ) THEN
157 DO j = 1, ncols
158 DO i = 1, j
159 work( ncols+j ) =
160 \$ max( cabs1( a( i, j ) ), work( ncols+j ) )
161 END DO
162 END DO
163 ELSE
164 DO j = 1, ncols
165 DO i = j, ncols
166 work( ncols+j ) =
167 \$ max( cabs1( a( i, j ) ), work( ncols+j ) )
168 END DO
169 END DO
170 END IF
171*
172* Now find the max magnitude entry of each column of the factor in
173* AF. No pivoting, so no permutations.
174*
175 IF ( lsame( 'Upper', uplo ) ) THEN
176 DO j = 1, ncols
177 DO i = 1, j
178 work( j ) = max( cabs1( af( i, j ) ), work( j ) )
179 END DO
180 END DO
181 ELSE
182 DO j = 1, ncols
183 DO i = j, ncols
184 work( j ) = max( cabs1( af( i, j ) ), work( j ) )
185 END DO
186 END DO
187 END IF
188*
189* Compute the *inverse* of the max element growth factor. Dividing
190* by zero would imply the largest entry of the factor's column is
191* zero. Than can happen when either the column of A is zero or
192* massive pivots made the factor underflow to zero. Neither counts
193* as growth in itself, so simply ignore terms with zero
194* denominators.
195*
196 IF ( lsame( 'Upper', uplo ) ) THEN
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 ELSE
205 DO i = 1, ncols
206 umax = work( i )
207 amax = work( ncols+i )
208 IF ( umax /= 0.0d+0 ) THEN
209 rpvgrw = min( amax / umax, rpvgrw )
210 END IF
211 END DO
212 END IF
213
214 zla_porpvgrw = rpvgrw
215*
216* End of ZLA_PORPVGRW
217*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zla_porpvgrw(UPLO, NCOLS, A, LDA, AF, LDAF, WORK)
ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian...
Definition: zla_porpvgrw.f:107
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