LAPACK  3.6.1
LAPACK: Linear Algebra PACKage
double precision function zla_herpvgrw ( character*1  UPLO,
integer  N,
integer  INFO,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( ldaf, * )  AF,
integer  LDAF,
integer, dimension( * )  IPIV,
double precision, dimension( * )  WORK 
)

ZLA_HERPVGRW

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

Purpose: 
 ZLA_HERPVGRW 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 ZHETRF, .i.e., the pivot in
     column INFO is exactly 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 block diagonal matrix D and the multipliers used to
     obtain the factor U or L as computed by ZHETRF.
[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 ZHETRF.
[in]WORK
          WORK is DOUBLE PRECISION array, dimension (2*N)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2016

Definition at line 125 of file zla_herpvgrw.f.

125 *
126 * -- LAPACK computational routine (version 3.6.1) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * June 2016
130 *
131 * .. Scalar Arguments ..
132  CHARACTER*1 uplo
133  INTEGER n, info, lda, ldaf
134 * ..
135 * .. Array Arguments ..
136  INTEGER ipiv( * )
137  COMPLEX*16 a( lda, * ), af( ldaf, * )
138  DOUBLE PRECISION work( * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Local Scalars ..
144  INTEGER ncols, i, j, k, kp
145  DOUBLE PRECISION amax, umax, rpvgrw, tmp
146  LOGICAL upper, lsame
147  COMPLEX*16 zdum
148 * ..
149 * .. External Functions ..
150  EXTERNAL lsame, zlaset
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC abs, REAL, dimag, max, min
154 * ..
155 * .. Statement Functions ..
156  DOUBLE PRECISION cabs1
157 * ..
158 * .. Statement Function Definitions ..
159  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
160 * ..
161 * .. Executable Statements ..
162 *
163  upper = lsame( 'Upper', uplo )
164  IF ( info.EQ.0 ) THEN
165  IF (upper) THEN
166  ncols = 1
167  ELSE
168  ncols = n
169  END IF
170  ELSE
171  ncols = info
172  END IF
173 
174  rpvgrw = 1.0d+0
175  DO i = 1, 2*n
176  work( i ) = 0.0d+0
177  END DO
178 *
179 * Find the max magnitude entry of each column of A. Compute the max
180 * for all N columns so we can apply the pivot permutation while
181 * looping below. Assume a full factorization is the common case.
182 *
183  IF ( upper ) THEN
184  DO j = 1, n
185  DO i = 1, j
186  work( n+i ) = max( cabs1( a( i,j ) ), work( n+i ) )
187  work( n+j ) = max( cabs1( a( i,j ) ), work( n+j ) )
188  END DO
189  END DO
190  ELSE
191  DO j = 1, n
192  DO i = j, n
193  work( n+i ) = max( cabs1( a( i, j ) ), work( n+i ) )
194  work( n+j ) = max( cabs1( a( i, j ) ), work( n+j ) )
195  END DO
196  END DO
197  END IF
198 *
199 * Now find the max magnitude entry of each column of U or L. Also
200 * permute the magnitudes of A above so they're in the same order as
201 * the factor.
202 *
203 * The iteration orders and permutations were copied from zsytrs.
204 * Calls to SSWAP would be severe overkill.
205 *
206  IF ( upper ) THEN
207  k = n
208  DO WHILE ( k .LT. ncols .AND. k.GT.0 )
209  IF ( ipiv( k ).GT.0 ) THEN
210 ! 1x1 pivot
211  kp = ipiv( k )
212  IF ( kp .NE. k ) THEN
213  tmp = work( n+k )
214  work( n+k ) = work( n+kp )
215  work( n+kp ) = tmp
216  END IF
217  DO i = 1, k
218  work( k ) = max( cabs1( af( i, k ) ), work( k ) )
219  END DO
220  k = k - 1
221  ELSE
222 ! 2x2 pivot
223  kp = -ipiv( k )
224  tmp = work( n+k-1 )
225  work( n+k-1 ) = work( n+kp )
226  work( n+kp ) = tmp
227  DO i = 1, k-1
228  work( k ) = max( cabs1( af( i, k ) ), work( k ) )
229  work( k-1 ) =
230  $ max( cabs1( af( i, k-1 ) ), work( k-1 ) )
231  END DO
232  work( k ) = max( cabs1( af( k, k ) ), work( k ) )
233  k = k - 2
234  END IF
235  END DO
236  k = ncols
237  DO WHILE ( k .LE. n )
238  IF ( ipiv( k ).GT.0 ) THEN
239  kp = ipiv( k )
240  IF ( kp .NE. k ) THEN
241  tmp = work( n+k )
242  work( n+k ) = work( n+kp )
243  work( n+kp ) = tmp
244  END IF
245  k = k + 1
246  ELSE
247  kp = -ipiv( k )
248  tmp = work( n+k )
249  work( n+k ) = work( n+kp )
250  work( n+kp ) = tmp
251  k = k + 2
252  END IF
253  END DO
254  ELSE
255  k = 1
256  DO WHILE ( k .LE. ncols )
257  IF ( ipiv( k ).GT.0 ) THEN
258 ! 1x1 pivot
259  kp = ipiv( k )
260  IF ( kp .NE. k ) THEN
261  tmp = work( n+k )
262  work( n+k ) = work( n+kp )
263  work( n+kp ) = tmp
264  END IF
265  DO i = k, n
266  work( k ) = max( cabs1( af( i, k ) ), work( k ) )
267  END DO
268  k = k + 1
269  ELSE
270 ! 2x2 pivot
271  kp = -ipiv( k )
272  tmp = work( n+k+1 )
273  work( n+k+1 ) = work( n+kp )
274  work( n+kp ) = tmp
275  DO i = k+1, n
276  work( k ) = max( cabs1( af( i, k ) ), work( k ) )
277  work( k+1 ) =
278  $ max( cabs1( af( i, k+1 ) ) , work( k+1 ) )
279  END DO
280  work(k) = max( cabs1( af( k, k ) ), work( k ) )
281  k = k + 2
282  END IF
283  END DO
284  k = ncols
285  DO WHILE ( k .GE. 1 )
286  IF ( ipiv( k ).GT.0 ) THEN
287  kp = ipiv( k )
288  IF ( kp .NE. k ) THEN
289  tmp = work( n+k )
290  work( n+k ) = work( n+kp )
291  work( n+kp ) = tmp
292  END IF
293  k = k - 1
294  ELSE
295  kp = -ipiv( k )
296  tmp = work( n+k )
297  work( n+k ) = work( n+kp )
298  work( n+kp ) = tmp
299  k = k - 2
300  ENDIF
301  END DO
302  END IF
303 *
304 * Compute the *inverse* of the max element growth factor. Dividing
305 * by zero would imply the largest entry of the factor's column is
306 * zero. Than can happen when either the column of A is zero or
307 * massive pivots made the factor underflow to zero. Neither counts
308 * as growth in itself, so simply ignore terms with zero
309 * denominators.
310 *
311  IF ( upper ) THEN
312  DO i = ncols, n
313  umax = work( i )
314  amax = work( n+i )
315  IF ( umax /= 0.0d+0 ) THEN
316  rpvgrw = min( amax / umax, rpvgrw )
317  END IF
318  END DO
319  ELSE
320  DO i = 1, ncols
321  umax = work( i )
322  amax = work( n+i )
323  IF ( umax /= 0.0d+0 ) THEN
324  rpvgrw = min( amax / umax, rpvgrw )
325  END IF
326  END DO
327  END IF
328 
329  zla_herpvgrw = rpvgrw
zlaset
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
Definition: zlaset.f:108
zla_herpvgrw
double precision function zla_herpvgrw(UPLO, N, INFO, A, LDA, AF, LDAF, IPIV, WORK)
ZLA_HERPVGRW
Definition: zla_herpvgrw.f:125
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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