LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ cla_porpvgrw()

real function cla_porpvgrw ( character*1  UPLO,
integer  NCOLS,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldaf, * )  AF,
integer  LDAF,
real, dimension( * )  WORK 
)

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

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

Purpose:
 CLA_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 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 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 CPOTRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
[out]WORK
          WORK is REAL array, dimension (2*N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 104 of file cla_porpvgrw.f.

105*
106* -- LAPACK computational routine --
107* -- LAPACK is a software package provided by Univ. of Tennessee, --
108* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
109*
110* .. Scalar Arguments ..
111 CHARACTER*1 UPLO
112 INTEGER NCOLS, LDA, LDAF
113* ..
114* .. Array Arguments ..
115 COMPLEX A( LDA, * ), AF( LDAF, * )
116 REAL WORK( * )
117* ..
118*
119* =====================================================================
120*
121* .. Local Scalars ..
122 INTEGER I, J
123 REAL AMAX, UMAX, RPVGRW
124 LOGICAL UPPER
125 COMPLEX ZDUM
126* ..
127* .. External Functions ..
128 EXTERNAL lsame
129 LOGICAL LSAME
130* ..
131* .. Intrinsic Functions ..
132 INTRINSIC abs, max, min, real, aimag
133* ..
134* .. Statement Functions ..
135 REAL CABS1
136* ..
137* .. Statement Function Definitions ..
138 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
139* ..
140* .. Executable Statements ..
141 upper = lsame( 'Upper', uplo )
142*
143* SPOTRF will have factored only the NCOLSxNCOLS leading minor, so
144* we restrict the growth search to that minor and use only the first
145* 2*NCOLS workspace entries.
146*
147 rpvgrw = 1.0
148 DO i = 1, 2*ncols
149 work( i ) = 0.0
150 END DO
151*
152* Find the max magnitude entry of each column.
153*
154 IF ( upper ) THEN
155 DO j = 1, ncols
156 DO i = 1, j
157 work( ncols+j ) =
158 $ max( cabs1( a( i, j ) ), work( ncols+j ) )
159 END DO
160 END DO
161 ELSE
162 DO j = 1, ncols
163 DO i = j, ncols
164 work( ncols+j ) =
165 $ max( cabs1( a( i, j ) ), work( ncols+j ) )
166 END DO
167 END DO
168 END IF
169*
170* Now find the max magnitude entry of each column of the factor in
171* AF. No pivoting, so no permutations.
172*
173 IF ( lsame( 'Upper', uplo ) ) THEN
174 DO j = 1, ncols
175 DO i = 1, j
176 work( j ) = max( cabs1( af( i, j ) ), work( j ) )
177 END DO
178 END DO
179 ELSE
180 DO j = 1, ncols
181 DO i = j, ncols
182 work( j ) = max( cabs1( af( i, j ) ), work( j ) )
183 END DO
184 END DO
185 END IF
186*
187* Compute the *inverse* of the max element growth factor. Dividing
188* by zero would imply the largest entry of the factor's column is
189* zero. Than can happen when either the column of A is zero or
190* massive pivots made the factor underflow to zero. Neither counts
191* as growth in itself, so simply ignore terms with zero
192* denominators.
193*
194 IF ( lsame( 'Upper', uplo ) ) THEN
195 DO i = 1, ncols
196 umax = work( i )
197 amax = work( ncols+i )
198 IF ( umax /= 0.0 ) THEN
199 rpvgrw = min( amax / umax, rpvgrw )
200 END IF
201 END DO
202 ELSE
203 DO i = 1, ncols
204 umax = work( i )
205 amax = work( ncols+i )
206 IF ( umax /= 0.0 ) THEN
207 rpvgrw = min( amax / umax, rpvgrw )
208 END IF
209 END DO
210 END IF
211
212 cla_porpvgrw = rpvgrw
213*
214* End of CLA_PORPVGRW
215*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function cla_porpvgrw(UPLO, NCOLS, A, LDA, AF, LDAF, WORK)
CLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian...
Definition: cla_porpvgrw.f:105
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