LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ sla_syrpvgrw()

real function sla_syrpvgrw ( character*1  UPLO,
integer  N,
integer  INFO,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( ldaf, * )  AF,
integer  LDAF,
integer, dimension( * )  IPIV,
real, dimension( * )  WORK 
)

SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

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

Purpose:
 SLA_SYRPVGRW 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]N
          N is INTEGER
     The number of linear equations, i.e., the order of the
     matrix A.  N >= 0.
[in]INFO
          INFO is INTEGER
     The value of INFO returned from SSYTRF, .i.e., the pivot in
     column INFO is exactly 0.
[in]A
          A is REAL 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 REAL array, dimension (LDAF,N)
     The block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by SSYTRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
[in]IPIV
          IPIV is INTEGER array, dimension (N)
     Details of the interchanges and the block structure of D
     as determined by SSYTRF.
[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 120 of file sla_syrpvgrw.f.

122*
123* -- LAPACK computational routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER*1 UPLO
129 INTEGER N, INFO, LDA, LDAF
130* ..
131* .. Array Arguments ..
132 INTEGER IPIV( * )
133 REAL A( LDA, * ), AF( LDAF, * ), WORK( * )
134* ..
135*
136* =====================================================================
137*
138* .. Local Scalars ..
139 INTEGER NCOLS, I, J, K, KP
140 REAL AMAX, UMAX, RPVGRW, TMP
141 LOGICAL UPPER
142* ..
143* .. Intrinsic Functions ..
144 INTRINSIC abs, max, min
145* ..
146* .. External Functions ..
147 EXTERNAL lsame
148 LOGICAL LSAME
149* ..
150* .. Executable Statements ..
151*
152 upper = lsame( 'Upper', uplo )
153 IF ( info.EQ.0 ) THEN
154 IF ( upper ) THEN
155 ncols = 1
156 ELSE
157 ncols = n
158 END IF
159 ELSE
160 ncols = info
161 END IF
162
163 rpvgrw = 1.0
164 DO i = 1, 2*n
165 work( i ) = 0.0
166 END DO
167*
168* Find the max magnitude entry of each column of A. Compute the max
169* for all N columns so we can apply the pivot permutation while
170* looping below. Assume a full factorization is the common case.
171*
172 IF ( upper ) THEN
173 DO j = 1, n
174 DO i = 1, j
175 work( n+i ) = max( abs( a( i, j ) ), work( n+i ) )
176 work( n+j ) = max( abs( a( i, j ) ), work( n+j ) )
177 END DO
178 END DO
179 ELSE
180 DO j = 1, n
181 DO i = j, n
182 work( n+i ) = max( abs( a( i, j ) ), work( n+i ) )
183 work( n+j ) = max( abs( a( i, j ) ), work( n+j ) )
184 END DO
185 END DO
186 END IF
187*
188* Now find the max magnitude entry of each column of U or L. Also
189* permute the magnitudes of A above so they're in the same order as
190* the factor.
191*
192* The iteration orders and permutations were copied from ssytrs.
193* Calls to SSWAP would be severe overkill.
194*
195 IF ( upper ) THEN
196 k = n
197 DO WHILE ( k .LT. ncols .AND. k.GT.0 )
198 IF ( ipiv( k ).GT.0 ) THEN
199! 1x1 pivot
200 kp = ipiv( k )
201 IF ( kp .NE. k ) THEN
202 tmp = work( n+k )
203 work( n+k ) = work( n+kp )
204 work( n+kp ) = tmp
205 END IF
206 DO i = 1, k
207 work( k ) = max( abs( af( i, k ) ), work( k ) )
208 END DO
209 k = k - 1
210 ELSE
211! 2x2 pivot
212 kp = -ipiv( k )
213 tmp = work( n+k-1 )
214 work( n+k-1 ) = work( n+kp )
215 work( n+kp ) = tmp
216 DO i = 1, k-1
217 work( k ) = max( abs( af( i, k ) ), work( k ) )
218 work( k-1 ) = max( abs( af( i, k-1 ) ), work( k-1 ) )
219 END DO
220 work( k ) = max( abs( af( k, k ) ), work( k ) )
221 k = k - 2
222 END IF
223 END DO
224 k = ncols
225 DO WHILE ( k .LE. n )
226 IF ( ipiv( k ).GT.0 ) THEN
227 kp = ipiv( k )
228 IF ( kp .NE. k ) THEN
229 tmp = work( n+k )
230 work( n+k ) = work( n+kp )
231 work( n+kp ) = tmp
232 END IF
233 k = k + 1
234 ELSE
235 kp = -ipiv( k )
236 tmp = work( n+k )
237 work( n+k ) = work( n+kp )
238 work( n+kp ) = tmp
239 k = k + 2
240 END IF
241 END DO
242 ELSE
243 k = 1
244 DO WHILE ( k .LE. ncols )
245 IF ( ipiv( k ).GT.0 ) THEN
246! 1x1 pivot
247 kp = ipiv( k )
248 IF ( kp .NE. k ) THEN
249 tmp = work( n+k )
250 work( n+k ) = work( n+kp )
251 work( n+kp ) = tmp
252 END IF
253 DO i = k, n
254 work( k ) = max( abs( af( i, k ) ), work( k ) )
255 END DO
256 k = k + 1
257 ELSE
258! 2x2 pivot
259 kp = -ipiv( k )
260 tmp = work( n+k+1 )
261 work( n+k+1 ) = work( n+kp )
262 work( n+kp ) = tmp
263 DO i = k+1, n
264 work( k ) = max( abs( af( i, k ) ), work( k ) )
265 work( k+1 ) = max( abs( af(i, k+1 ) ), work( k+1 ) )
266 END DO
267 work( k ) = max( abs( af( k, k ) ), work( k ) )
268 k = k + 2
269 END IF
270 END DO
271 k = ncols
272 DO WHILE ( k .GE. 1 )
273 IF ( ipiv( k ).GT.0 ) THEN
274 kp = ipiv( k )
275 IF ( kp .NE. k ) THEN
276 tmp = work( n+k )
277 work( n+k ) = work( n+kp )
278 work( n+kp ) = tmp
279 END IF
280 k = k - 1
281 ELSE
282 kp = -ipiv( k )
283 tmp = work( n+k )
284 work( n+k ) = work( n+kp )
285 work( n+kp ) = tmp
286 k = k - 2
287 ENDIF
288 END DO
289 END IF
290*
291* Compute the *inverse* of the max element growth factor. Dividing
292* by zero would imply the largest entry of the factor's column is
293* zero. Than can happen when either the column of A is zero or
294* massive pivots made the factor underflow to zero. Neither counts
295* as growth in itself, so simply ignore terms with zero
296* denominators.
297*
298 IF ( upper ) THEN
299 DO i = ncols, n
300 umax = work( i )
301 amax = work( n+i )
302 IF ( umax /= 0.0 ) THEN
303 rpvgrw = min( amax / umax, rpvgrw )
304 END IF
305 END DO
306 ELSE
307 DO i = 1, ncols
308 umax = work( i )
309 amax = work( n+i )
310 IF ( umax /= 0.0 ) THEN
311 rpvgrw = min( amax / umax, rpvgrw )
312 END IF
313 END DO
314 END IF
315
316 sla_syrpvgrw = rpvgrw
317*
318* End of SLA_SYRPVGRW
319*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function sla_syrpvgrw(UPLO, N, INFO, A, LDA, AF, LDAF, IPIV, WORK)
SLA_SYRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite m...
Definition: sla_syrpvgrw.f:122
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