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Skip the current step: the subdiagonal info is just noise.
Lookahead over
Inner loop
If eigenvectors are desired, then save rotations.
If eigenvectors are desired, then apply saved rotations.
Eigenvalue found.
QR Iteration
Look for small superdiagonal element.
If remaining matrix is 2-by-2, use DLAE2 or DLAEV2
to compute its eigensystem.
Form shift.
Do not do a lookahead!
This is the lookahead loop, going until we have
convergence or too many steps have been taken.
Inner loop
Find GP & RP for the next iteration
Goto put in by G. Henry to fix ALPHA problem
GP = ( ( OLDGP+P )-( D( L )-P ) ) /
$ ( TWO*( C*OLDRP-B )+SAFMIN )
Make sure that we are making progress
Skip the current step: the subdiagonal info is just noise.
Lookahead over
If eigenvectors are desired, then save rotations.
If eigenvectors are desired, then apply saved rotations.
Eigenvalue found.
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001 SUBROUTINE ZSTEQR2( COMPZ , N , D , E , Z , LDZ , NR , WORK , INFO )
002
003 * -- ScaLAPACK routine(version 1.7) --
004 * Univ. of Tennessee , Univ. of California Berkeley , NAG Ltd. ,
005 * Courant Institute , Argonne National Lab , and Rice University
006 * November 15 , 1997
007
008 * .. Scalar Arguments ..
009 CHARACTER COMPZ
010 INTEGER INFO , LDZ , N , NR
011 * ..
012 * .. Array Arguments ..
013 DOUBLE PRECISION D( * ) , E( * ) , WORK( * )
014 COMPLEX*16 Z( LDZ , * )
015 * ..
016
017 * Purpose
018 * === ====
019
020 * ZSTEQR2 is a modified version of LAPACK routine ZSTEQR.
021 * ZSTEQR2 computes all eigenvalues and , optionally , eigenvectors of a
022 * symmetric tridiagonal matrix using the implicit QL or QR method.
023 * ZSTEQR2 is modified from ZSTEQR to allow each ScaLAPACK process
024 * running ZSTEQR2 to perform updates on a distributed matrix Q.
025 * Proper usage of ZSTEQR2 can be gleaned from
026 * examination of ScaLAPACK's * PZHEEV.
027 * ZSTEQR2 incorporates changes attributed to Greg Henry.
028
029 * Arguments
030 * === ======
031
032 * COMPZ(input) CHARACTER*1
033 * = 'N' : Compute eigenvalues only.
034 * = 'I' : Compute eigenvalues and eigenvectors of the
035 * tridiagonal matrix. Z must be initialized to the
036 * identity matrix by PZLASET or ZLASET prior
037 * to entering this subroutine.
038
039 * N(input) INTEGER
040 * The order of the matrix. N >= 0.
041
042 * D(input / output) DOUBLE PRECISION array , dimension(N)
043 * On entry , the diagonal elements of the tridiagonal matrix.
044 * On exit , if INFO = 0 , the eigenvalues in ascending order.
045
046 * E(input / output) DOUBLE PRECISION array , dimension(N - 1)
047 * On entry , the(n - 1) subdiagonal elements of the tridiagonal
048 * matrix.
049 * On exit , E has been destroyed.
050
051 * Z(local input / local output) COMPLEX*16 array , global
052 * dimension(N , N) , local dimension(LDZ , NR).
053 * On entry , if COMPZ = 'V' , then Z contains the orthogonal
054 * matrix used in the reduction to tridiagonal form.
055 * On exit , if INFO = 0 , then if COMPZ = 'V' , Z contains the
056 * orthonormal eigenvectors of the original symmetric matrix ,
057 * and if COMPZ = 'I' , Z contains the orthonormal eigenvectors
058 * of the symmetric tridiagonal matrix.
059 * If COMPZ = 'N' , then Z is not referenced.
060
061 * LDZ(input) INTEGER
062 * The leading dimension of the array Z. LDZ >= 1 , and if
063 * eigenvectors are desired , then LDZ >= max(1 , N).
064
065 * NR(input) INTEGER
066 * NR = MAX(1 , NUMROC( N , NB , MYPROW , 0 , NPROCS ) ).
067 * If COMPZ = 'N' , then NR is not referenced.
068
069 * WORK(workspace) DOUBLE PRECISION array , dimension(max(1 , 2*N - 2))
070 * If COMPZ = 'N' , then WORK is not referenced.
071
072 * INFO(output) INTEGER
073 * = 0 : successful exit
074 * < 0 : if INFO = - i , the i - th argument had an illegal value
075 * > 0 : the algorithm has failed to find all the eigenvalues in
076 * a total of 30*N iterations ; if INFO = i , then i
077 * elements of E have not converged to zero ; on exit , D
078 * and E contain the elements of a symmetric tridiagonal
079 * matrix which is orthogonally similar to the original
080 * matrix.
081
082 * === ==================================================================
083
084 * .. Parameters ..
085 DOUBLE PRECISION ZERO , ONE , TWO , THREE , HALF
086 PARAMETER( ZERO = 0.0D0 , ONE = 1.0D0 , TWO = 2.0D0 ,
087 $THREE = 3.0D0 , HALF = 0.5D0 )
088 COMPLEX*16 CONE
089 PARAMETER( CONE =( 1.0D0 , 1.0D0 ) )
090 INTEGER MAXIT , NMAXLOOK
091 PARAMETER( MAXIT = 30 , NMAXLOOK = 15 )
092 * ..
093 * .. Local Scalars ..
094 INTEGER I , ICOMPZ , II , ILAST , ISCALE , J , JTOT , K , L ,
095 $L1 , LEND , LENDM1 , LENDP1 , LENDSV , LM1 , LSV , M ,
096 $MM , MM1 , NLOOK , NM1 , NMAXIT
097 DOUBLE PRECISION ANORM , B , C , EPS , EPS2 , F , G , GP , OLDEL , OLDGP ,
098 $OLDRP , P , R , RP , RT1 , RT2 , S , SAFMAX , SAFMIN ,
099 $SSFMAX , SSFMIN , TST , TST1
100 * ..
101 * .. External Functions ..
102 LOGICAL LSAME
103 DOUBLE PRECISION DLAMCH , DLANST , DLAPY2
104 EXTERNAL LSAME , DLAMCH , DLANST , DLAPY2
105 * ..
106 * .. External Subroutines ..
107 EXTERNAL DLAEV2 , DLARTG , DLASCL , DSTERF , XERBLA , ZLASR ,
108 $ZSWAP
109 * ..
110 * .. Intrinsic Functions ..
111 INTRINSIC ABS , MAX , SIGN , SQRT
112 * ..
113 * .. Executable Statements ..
114
115 * Test the input parameters.
116
117 ILAST = 0
118 INFO = 0
119
120 IF( LSAME( COMPZ , 'N' ) ) THEN
120  
121 ICOMPZ = 0
122 ELSEIF( LSAME( COMPZ , 'I' ) ) THEN
123 ICOMPZ = 1
124 ELSE
124
125 ICOMPZ = - 1
126 ENDIF
127 IF( ICOMPZ.LT.0 ) THEN
127
128 INFO = - 1
129 ELSEIF( N.LT.0 ) THEN
130 INFO = - 2
131 ELSEIF( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1 , NR ) ) THEN
132 INFO = - 6
133 ENDIF
134 IF( INFO.NE.0 ) THEN
134
135 CALL XERBLA( 'ZSTEQR2' , - INFO )
136 RETURN
137 ENDIF
138
139 * Quick return if possible
140
141 IF( N.EQ.0 )
141
142 $ RETURN
143
144 * If eigenvectors aren't not desired , this is faster
145
146 IF( ICOMPZ.EQ.0 ) THEN
146
147 CALL DSTERF( N , D , E , INFO )
148 RETURN
149 ENDIF
150
151 IF( N.EQ.1 ) THEN
151
152 Z( 1 , 1 ) = CONE
153 RETURN
154 ENDIF
155
156 * Determine the unit roundoff and over / underflow thresholds.
157
158 EPS = DLAMCH( 'E' )
159 EPS2 = EPS**2
160 SAFMIN = DLAMCH( 'S' )
161 SAFMAX = ONE / SAFMIN
162 SSFMAX = SQRT( SAFMAX ) / THREE
163 SSFMIN = SQRT( SAFMIN ) / EPS2
164
165 * Compute the eigenvalues and eigenvectors of the tridiagonal
166 * matrix.
167
168 NMAXIT = N*MAXIT
169 JTOT = 0
170
171 * Determine where the matrix splits and choose QL or QR iteration
172 * for each block , according to whether top or bottom diagonal
173 * element is smaller.
174
175 L1 = 1
176 NM1 = N - 1
177
178 10 CONTINUE
179 IF( L1.GT.N )
179
180 $ GOTO 220
181 IF( L1.GT.1 )
181
182 $ E( L1 - 1 ) = ZERO
183 IF( L1.LE.NM1 ) THEN
183
184 DO 20 M = L1 , NM1
184
185 TST = ABS( E( M ) )
186 IF( TST.EQ.ZERO )
186
187 $ GOTO 30
188 IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M +
189 $ 1 ) ) ) )*EPS ) THEN
190 E( M ) = ZERO
191 GOTO 30
192 ENDIF
193 20 CONTINUE
193
194 ENDIF
195 M = N
196
197 30 CONTINUE
198 L = L1
199 LSV = L
200 LEND = M
201 LENDSV = LEND
202 L1 = M + 1
203 IF( LEND.EQ.L )
203
204 $ GOTO 10
205
206 * Scale submatrix in rows and columns L to LEND
207
208 ANORM = DLANST( 'I' , LEND - L + 1 , D( L ) , E( L ) )
209 ISCALE = 0
210 IF( ANORM.EQ.ZERO )
210
211 $ GOTO 10
212 IF( ANORM.GT.SSFMAX ) THEN
212
213 ISCALE = 1
214 CALL DLASCL( 'G' , 0 , 0 , ANORM , SSFMAX , LEND - L + 1 , 1 , D( L ) , N ,
215 $ INFO )
216 CALL DLASCL( 'G' , 0 , 0 , ANORM , SSFMAX , LEND - L , 1 , E( L ) , N ,
217 $ INFO )
218 ELSEIF( ANORM.LT.SSFMIN ) THEN
219 ISCALE = 2
220 CALL DLASCL( 'G' , 0 , 0 , ANORM , SSFMIN , LEND - L + 1 , 1 , D( L ) , N ,
221 $ INFO )
222 CALL DLASCL( 'G' , 0 , 0 , ANORM , SSFMIN , LEND - L , 1 , E( L ) , N ,
223 $ INFO )
224 ENDIF
225
226 * Choose between QL and QR iteration
227
228 IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN
228
229 LEND = LSV
230 L = LENDSV
231 ENDIF
232
233 IF( LEND.GT.L ) THEN
234
235 * QL Iteration
236
237 * Look for small subdiagonal element.
238
239 40 CONTINUE
240 IF( L.NE.LEND ) THEN
240
241 LENDM1 = LEND - 1
242 DO 50 M = L , LENDM1
242
243 TST = ABS( E( M ) )**2
244 IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M + 1 ) ) +
245 $ SAFMIN )GOTO 60
246 50 CONTINUE
247 ENDIF
248
249 M = LEND
250
251 60 CONTINUE
252 IF( M.LT.LEND )
252
253 $ E( M ) = ZERO
254 P = D( L )
255 IF( M.EQ.L )
255
256 $ GOTO 110
257
258 * If remaining matrix is 2 - by - 2 , use DLAE2 or DLAEV2
259 * to compute its eigensystem.
260
261 IF( M.EQ.L + 1 ) THEN
261
262 CALL DLAEV2( D( L ) , E( L ) , D( L + 1 ) , RT1 , RT2 , C , S )
263 WORK( L ) = C
264 WORK( N - 1 + L ) = S
265 CALL ZLASR( 'R' , 'V' , 'B' , NR , 2 , WORK( L ) , WORK( N - 1 + L ) ,
266 $ Z( 1 , L ) , LDZ )
267 D( L ) = RT1
268 D( L + 1 ) = RT2
269 E( L ) = ZERO
270 L = L + 2
271 IF( L.LE.LEND )
271
272 $ GOTO 40
273 GOTO 200
274 ENDIF
275
276 IF( JTOT.EQ.NMAXIT )
276
277 $ GOTO 200
278 JTOT = JTOT + 1
279
280 * Form shift.
281
282 G =( D( L + 1 ) - P ) / ( TWO*E( L ) )
283 R = DLAPY2( G , ONE )
284 G = D( M ) - P + ( E( L ) / ( G + SIGN( R , G ) ) )
285
286 IF( ICOMPZ.EQ.0 ) THEN
287 * Do not do a lookahead !
287
288 GOTO 90
289 ENDIF
290
291 OLDEL = ABS( E( L ) )
292 GP = G
293 RP = R
294 TST = ABS( E( L ) )**2
295 TST = TST / (( EPS2*ABS( D( L ) ) )*ABS( D( L + 1 ) ) + SAFMIN )
296
297 NLOOK = 1
298 IF(( TST.GT.ONE ) .AND.( NLOOK.LE.NMAXLOOK ) ) THEN
299 70 CONTINUE
300
301 * This is the lookahead loop , going until we have
302 * convergence or too many steps have been taken.
303
304 S = ONE
305 C = ONE
306 P = ZERO
307 MM1 = M - 1
308 DO 80 I = MM1 , L , - 1
308
309 F = S*E( I )
310 B = C*E( I )
311 CALL DLARTG( GP , F , C , S , RP )
312 GP = D( I + 1 ) - P
313 RP =( D( I ) - GP )*S + TWO*C*B
314 P = S*RP
315 IF( I.NE.L )
315
316 $ GP = C*RP - B
317 80 CONTINUE
318 OLDGP = GP
319 OLDRP = RP
320 * Find GP & RP for the next iteration
321 IF( ABS( C*OLDRP - B ).GT.SAFMIN ) THEN
321
322 GP =(( OLDGP + P ) - ( D( L ) - P ) ) / ( TWO*( C*OLDRP - B ) )
323 ELSE
324
325 * Goto put in by G. Henry to fix ALPHA problem
326
326
327 GOTO 90
328 * GP =(( OLDGP + P ) - ( D( L ) - P ) ) /
329 * $( TWO*( C*OLDRP - B ) + SAFMIN )
330 ENDIF
331 RP = DLAPY2( GP , ONE )
332 GP = D( M ) - ( D( L ) - P ) +
333 $(( C*OLDRP - B ) / ( GP + SIGN( RP , GP ) ) )
334 TST1 = TST
335 TST = ABS( C*OLDRP - B )**2
336 TST = TST / (( EPS2*ABS( D( L ) - P ) )*ABS( OLDGP + P ) +
337 $SAFMIN )
338 * Make sure that we are making progress
339 IF( ABS( C*OLDRP - B ).GT.0.9D0*OLDEL ) THEN
339
340 IF( ABS( C*OLDRP - B ).GT.OLDEL ) THEN
340
341 GP = G
342 RP = R
343 ENDIF
344 TST = HALF
345 ELSE
345
346 OLDEL = ABS( C*OLDRP - B )
347 ENDIF
348 NLOOK = NLOOK + 1
349 IF(( TST.GT.ONE ) .AND.( NLOOK.LE.NMAXLOOK ) )
349
350 $ GOTO 70
351 ENDIF
352
353 IF(( TST.LE.ONE ) .AND.( TST.NE.HALF ) .AND.
354 $( ABS( P ).LT.EPS*ABS( D( L ) ) ) .AND.
355 $( ILAST.EQ.L ) .AND.( ABS( E( L ) )**2.LE.10000.0D0*
356 $(( EPS2*ABS( D( L ) ) )*ABS( D( L + 1 ) ) + SAFMIN ) ) ) THEN
357 190 CONTINUE
358 D( L ) = P
359
360 L = L - 1
361 IF( L.GE.LEND )
361
362 $ GOTO 120
363 GOTO 200
364
365 ENDIF
366
367 * Undo scaling if necessary
368
369 200 CONTINUE
370 IF( ISCALE.EQ.1 ) THEN
370
371 CALL DLASCL( 'G' , 0 , 0 , SSFMAX , ANORM , LENDSV - LSV + 1 , 1 ,
372 $ D( LSV ) , N , INFO )
373 CALL DLASCL( 'G' , 0 , 0 , SSFMAX , ANORM , LENDSV - LSV , 1 , E( LSV ) ,
374 $ N , INFO )
375 ELSEIF( ISCALE.EQ.2 ) THEN
376 CALL DLASCL( 'G' , 0 , 0 , SSFMIN , ANORM , LENDSV - LSV + 1 , 1 ,
377 $D( LSV ) , N , INFO )
378 CALL DLASCL( 'G' , 0 , 0 , SSFMIN , ANORM , LENDSV - LSV , 1 , E( LSV ) ,
379 $N , INFO )
380 ENDIF
381
382 * Check for no convergence to an eigenvalue after a total
383 * of N*MAXIT iterations.
384
385 IF( JTOT.LT.NMAXIT )
385
386 $ GOTO 10
387 DO 210 I = 1 , N - 1
387
388 IF( E( I ).NE.ZERO )
388
389 $ INFO = INFO + 1
390 210 CONTINUE
390
391 GOTO 250
392
393 * Order eigenvalues and eigenvectors.
394
395 220 CONTINUE
396
397 * Use Selection Sort to minimize swaps of eigenvectors
398
399 DO 240 II = 2 , N
399
400 I = II - 1
401 K = I
402 P = D( I )
403 DO 230 J = II , N
403
404 IF( D( J ).LT.P ) THEN
404
405 K = J
406 P = D( J )
407 ENDIF
408 230 CONTINUE
408
409 IF( K.NE.I ) THEN
409
410 D( K ) = D( I )
411 D( I ) = P
412 CALL ZSWAP( NR , Z( 1 , I ) , 1 , Z( 1 , K ) , 1 )
413 ENDIF
414 240 CONTINUE
415
416 250 CONTINUE
417 * WRITE( * , FMT = * )'JTOT' , JTOT
418 RETURN
419
420 * End of DSTEQR2
421
422 END68
44
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Variables in Routine ZSTEQR2()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| CHARACTER | 1 | 1 |
| COMPLEX*16 | 2 | ? |
| DOUBLE PRECISION | 34 | 136 |
| INTEGER | 28 | 112 |
| LOGICAL | 1 | 1 |
| TOTAL | 66 | 250 |
List of Variables
CHARACTER
COMPLEX*16
DOUBLE PRECISION
| ANORM | B | C | D( * ) | DLAMCH |
| DLANST | DLAPY2 | E( * ) | EPS | EPS2 |
| F | G | GP | HALF | OLDEL |
| OLDGP | OLDRP | ONE | P | R |
| RP | RT1 | RT2 | S | SAFMAX |
| SAFMIN | SSFMAX | SSFMIN | THREE | TST |
| TST1 | TWO | WORK( * ) | ZERO | |
INTEGER
| I | ICOMPZ | II | ILAST | INFO |
| ISCALE | J | JTOT | K | L |
| L1 | LDZ | LEND | LENDM1 | LENDP1 |
| LENDSV | LM1 | LSV | M | MAXIT |
| MM | MM1 | N | NLOOK | NM1 |
| NMAXIT | NMAXLOOK | NR | | |
LOGICAL
Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | ANORM | <--- | EANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ), IANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ), LANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ), LENDANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ), DANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ), DLANSTANORM = DLANST( 'I', LEND-L+1, D( L ), E( L ) ) |
| B | <--- | EB = C*E( I ), IB = C*E( I ), CB = C*E( I ) |
| C | <--- | ONEC = ONE |
| D | <--- | ID( K ) = D( I ), PD( L ) = P{2D( I ) = P}, RT1D( L ) = RT1, RT2D( L+1 ) = RT2, DD( K ) = D( I ) |
| E | <--- | ZEROE( M ) = ZERO{2E( L ) = ZERO} |
| EPS | <--- | EEPS = DLAMCH( 'E' ), DLAMCHEPS = DLAMCH( 'E' ) |
| EPS2 | <--- | EPSEPS2 = EPS**2 |
| F | <--- | EF = S*E( I ), IF = S*E( I ), SF = S*E( I ) |
| G | <--- | EG = ( D( L+1 )-P ) / ( TWO*E( L ) ){2G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) )}, GG = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ), LG = ( D( L+1 )-P ) / ( TWO*E( L ) ){2G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) )}, MG = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ), PG = ( D( L+1 )-P ) / ( TWO*E( L ) ){2G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) )}, RG = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ), DG = ( D( L+1 )-P ) / ( TWO*E( L ) ){2G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) )}, TWOG = ( D( L+1 )-P ) / ( TWO*E( L ) ) |
| GP | <--- | GGP = G{2GP = G}, GPGP = D( M ) - ( D( L )-P ) +, IGP = D( I+1 ) - P, BGP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ){2GP = D( M ) - ( D( L )-P ) +}, LGP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ){2GP = D( M ) - ( D( L )-P ) +}, CGP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ){2GP = D( M ) - ( D( L )-P ) +}, MGP = D( M ) - ( D( L )-P ) +, OLDGPGP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ), OLDRPGP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ){2GP = D( M ) - ( D( L )-P ) +}, PGP = D( I+1 ) - P{2GP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ), 3GP = D( M ) - ( D( L )-P ) +}, RPGP = D( M ) - ( D( L )-P ) +, DGP = D( I+1 ) - P{2GP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ), 3GP = D( M ) - ( D( L )-P ) +}, TWOGP = ( ( OLDGP+P )-( D( L )-P ) ) / ( TWO*( C*OLDRP-B ) ) |
| I | <--- | III = II - 1, LDO 80 I = MM1, L, -1, MM1DO 80 I = MM1, L, -1, NDO 210 I = 1, N - 1 |
| II | <--- | NDO 240 II = 2, N |
| J | <--- | IIDO 230 J = II, N, NDO 230 J = II, N |
| JTOT | <--- | JTOTJTOT = JTOT + 1 |
| K | <--- | IK = I, JK = J |
| L | <--- | LL = L + 2{2L = L - 1}, L1L = L1, LENDSVL = LENDSV |
| L1 | <--- | ML1 = M + 1 |
| LEND | <--- | LSVLEND = LSV, MLEND = M |
| LENDM1 | <--- | LENDLENDM1 = LEND - 1 |
| LENDSV | <--- | LENDLENDSV = LEND |
| LSV | <--- | LLSV = L |
| M | <--- | LDO 50 M = L, LENDM1, L1DO 20 M = L1, NM1, LENDM = LEND, LENDM1DO 50 M = L, LENDM1, NM = N, NM1DO 20 M = L1, NM1 |
| MM1 | <--- | MMM1 = M - 1 |
| NLOOK | <--- | NLOOKNLOOK = NLOOK + 1 |
| NM1 | <--- | NNM1 = N - 1 |
| NMAXIT | <--- | MAXITNMAXIT = N*MAXIT, NNMAXIT = N*MAXIT |
| OLDEL | <--- | EOLDEL = ABS( E( L ) ), BOLDEL = ABS( C*OLDRP-B ), LOLDEL = ABS( E( L ) ), COLDEL = ABS( C*OLDRP-B ), OLDRPOLDEL = ABS( C*OLDRP-B ) |
| OLDGP | <--- | GPOLDGP = GP |
| OLDRP | <--- | RPOLDRP = RP |
| P | <--- | IP = D( I ), JP = D( J ), LP = D( L ), RPP = S*RP, SP = S*RP, DP = D( L ){2P = D( I ), 3P = D( J )}, ZEROP = ZERO |
| R | <--- | GR = DLAPY2( G, ONE ), ONER = DLAPY2( G, ONE ), DLAPY2R = DLAPY2( G, ONE ) |
| RP | <--- | GPRP = ( D( I )-GP )*S + TWO*C*B{2RP = DLAPY2( GP, ONE )}, IRP = ( D( I )-GP )*S + TWO*C*B, BRP = ( D( I )-GP )*S + TWO*C*B, CRP = ( D( I )-GP )*S + TWO*C*B, ONERP = DLAPY2( GP, ONE ), RRP = R{2RP = R}, SRP = ( D( I )-GP )*S + TWO*C*B, DRP = ( D( I )-GP )*S + TWO*C*B, TWORP = ( D( I )-GP )*S + TWO*C*B, DLAPY2RP = DLAPY2( GP, ONE ) |
| S | <--- | ONES = ONE |
| SAFMAX | <--- | ONESAFMAX = ONE / SAFMIN, SAFMINSAFMAX = ONE / SAFMIN |
| SAFMIN | <--- | SSAFMIN = DLAMCH( 'S' ), DLAMCHSAFMIN = DLAMCH( 'S' ) |
| SSFMAX | <--- | SAFMAXSSFMAX = SQRT( SAFMAX ) / THREE, THREESSFMAX = SQRT( SAFMAX ) / THREE |
| SSFMIN | <--- | EPS2SSFMIN = SQRT( SAFMIN ) / EPS2, SAFMINSSFMIN = SQRT( SAFMIN ) / EPS2 |
| TST | <--- | ETST = ABS( E( M ) ){2TST = ABS( E( M ) )**2, 3TST = ABS( E( L ) )**2}, EPS2TST = TST / ( ( EPS2*ABS( D( L ) ) )*ABS( D( L+1 ) )+SAFMIN ){2TST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+}, HALFTST = HALF, BTST = ABS( C*OLDRP-B )**2, LTST = ABS( E( L ) )**2{2TST = TST / ( ( EPS2*ABS( D( L ) ) )*ABS( D( L+1 ) )+SAFMIN ), 3TST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+}, CTST = ABS( C*OLDRP-B )**2, MTST = ABS( E( M ) ){2TST = ABS( E( M ) )**2}, OLDGPTST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+, OLDRPTST = ABS( C*OLDRP-B )**2, PTST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+, SAFMINTST = TST / ( ( EPS2*ABS( D( L ) ) )*ABS( D( L+1 ) )+SAFMIN ){2TST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+}, DTST = TST / ( ( EPS2*ABS( D( L ) ) )*ABS( D( L+1 ) )+SAFMIN ){2TST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+}, TSTTST = TST / ( ( EPS2*ABS( D( L ) ) )*ABS( D( L+1 ) )+SAFMIN ){2TST = TST / ( ( EPS2*ABS( D( L )-P ) )*ABS( OLDGP+P )+} |
| TST1 | <--- | TSTTST1 = TST |
| WORK | <--- | CWORK( L ) = C, SWORK( N-1+L ) = S |
| Z | <--- | CONEZ( 1, 1 ) = CONE |
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|
Analysis elements of the routine ZSTEQR2()
Put the mouse over each element to display detailed matching information
 Assigned variables |
| | | ANORM , B , C , COMPZ , CONE , EPS , EPS2 , F , G , GP , HALF , I , ICOMPZ , II , ILAST , INFO , ISCALE , J , JTOT , K , L , L1 , LDZ , LEND , LENDM1 , LENDSV , LSV , M , MAXIT , MM1 , N , NLOOK , NM1 , NMAXIT , NMAXLOOK , NR , OLDEL , OLDGP , OLDRP , ONE , P , R , RP , S , SAFMAX , SAFMIN , SSFMAX , SSFMIN , THREE , TST , TST1 , TWO , Z , ZERO |
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| Active variables |
| | | ANORM , B , C , COMPZ , CONE , D , DLAMCH , DLANST , DLAPY2 , E , EPS , EPS2 , F , G , GP , HALF , I , ICOMPZ , II , ILAST , INFO , ISCALE , J , JTOT , K , L , L1 , LDZ , LEND , LENDM1 , LENDP1 , LENDSV , LM1 , LSAME , LSV , M , MAXIT , MM , MM1 , N , NLOOK , NM1 , NMAXIT , NMAXLOOK , NR , OLDEL , OLDGP , OLDRP , ONE , P , R , RP , RT1 , RT2 , s , SAFMAX , SAFMIN , SSFMAX , SSFMIN , THREE , TST , TST1 , TWO , WORK , Z , zero |
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| Accessed arrays [ array name : associated index ] |
| |  D | : * , I , I , I , I , I+1 , J , J , K , L , L , L , L , L , L , L , L , L , L , L , L , L , L , L , L+1 , L+1 , L+1 , L+1 , L+1 , LEND , LSV , LSV , M , M , M , M , M+1 |
| | DLAMCH | : 'E' , 'S' |
| | DLANST | : 'I', LEND-L+1, D( L ), E( L ) |
| | DLAPY2 | : G, ONE , GP, ONE |
| | E | : * , I , I , I , L , L , L , L , L , L , L , L , L , L , L1-1 , LSV , LSV , M , M , M , M |
| | LSAME | : COMPZ, 'I' , COMPZ, 'N' |
| | WORK | : * , L , L , N-1+L , N-1+L |
| | Z | : 1, 1 , 1, I , 1, K , 1, L , LDZ, * |
|
| Conditional statements [ statement : associated predicate ] |
| | do | : ( 20 M = L1 , NM1 ) , ( 50 M = L , LENDM1 ) , ( not do a lookahead ! ) , ( a lookahead ! ) , ( 80 I = MM1 , L , - 1 ) , ( 210 I = 1 , N - 1 ) , ( 240 II = 2 , N ) , ( 230 J = II , N ) |
| | elseif | : ( (LSAME( COMPZ , 'I' ) ) ) , ( N.LT.0 ) , ( (ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1 , NR ) ) ) , ( ANORM.LT.SSFMIN ) , ( ISCALE.EQ.2 ) |
| | for | : ( each block , according to whether top or bottom diagonal ) , ( small subdiagonal element. ) , ( the next iteration ) , ( no convergence to an eigenvalue after a total ) |
| | if | : ( INFO = 0 , the eigenvalues in ascending order. ) , ( COMPZ = 'V' , ) , ( INFO = 0 , ) , ( COMPZ = 'V' , Z contains the ) , ( COMPZ = 'I' , Z contains the orthonormal eigenvectors ) , ( COMPZ = 'N' , ) , ( COMPZ = 'N' , ) , ( COMPZ = 'N' , ) , ( INFO = - i , the i - th argument had an illegal value ) , ( INFO = i , ) , ( (LSAME( COMPZ , 'N' ) ) ) , ( ICOMPZ.LT.0 ) , ( INFO.NE.0 ) , ( possible ) , ( N.EQ.0 ) , ( eigenvectors aren't not desired , this is faster ) , ( ICOMPZ.EQ.0 ) , ( N.EQ.1 ) , ( L1.GT.N ) , ( L1.GT.1 ) , ( L1.LE.NM1 ) , ( TST.EQ.ZERO ) , ( (TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M + ) , ( LEND.EQ.L ) , ( ANORM.EQ.ZERO ) , ( ANORM.GT.SSFMAX ) , ( (ABS( D( LEND ) ).LT.ABS( D( L ) ) ) ) , ( LEND.GT.L ) , ( L.NE.LEND ) , ( (TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M + 1 ) ) + ) , ( M.LT.LEND ) , ( M.EQ.L ) , ( remaining matrix is 2 - by - 2 , use DLAE2 or DLAEV2 ) , ( M.EQ.L + 1 ) , ( L.LE.LEND ) , ( JTOT.EQ.NMAXIT ) , ( ICOMPZ.EQ.0 ) , ( (( TST.GT.ONE ) .AND. ( NLOOK.LE.NMAXLOOK ) ) ) , ( I.NE.L ) , ( (ABS( C*OLDRP - B ).GT.SAFMIN ) ) , ( (ABS( C*OLDRP - B ).GT.0.9D0*OLDEL ) ) , ( (ABS( C*OLDRP - B ).GT.OLDEL ) ) , ( (( TST.GT.ONE ) .AND. ( NLOOK.LE.NMAXLOOK ) ) ) , ( (( TST.LE.ONE ) .AND. ( TST.NE.HALF ) .AND. ) , ( L.GE.LEND ) , ( necessary ) , ( ISCALE.EQ.1 ) , ( JTOT.LT.NMAXIT ) , ( (E( I ).NE.ZERO ) ) , ( (D( J ).LT.P ) ) , ( K.NE.I ) |
| | until | : ( we have ) |
|
| List of variables |
ANORM
B
C
COMPZ
CONE
D( * )
DLAMCH
| DLANST
DLAPY2
E( * )
EPS
EPS2
F
G
GP
| HALF
I
ICOMPZ
II
ILAST
INFO
ISCALE
J
| JTOT
K
L
L1
LDZ
LEND
LENDM1
LENDP1
| LENDSV
LM1
LSAME
LSV
M
MAXIT
MM
MM1
| N
NLOOK
NM1
NMAXIT
NMAXLOOK
NR
OLDEL
OLDGP
| OLDRP
ONE
P
R
RP
RT1
RT2
S
| SAFMAX
SAFMIN
SSFMAX
SSFMIN
THREE
TST
TST1
TWO
| WORK( * )
Z( LDZ, * )
ZERO | | close
| |
ANORM
B
C
COMPZ
CONE
D( * )
DLAMCH
DLANST
DLAPY2
E( * )
EPS
EPS2
F
G
GP
HALF
I
ICOMPZ
II
ILAST
INFO
ISCALE
J
JTOT
K
L
L1
LDZ
LEND
LENDM1
LENDP1
LENDSV
LM1
LSAME
LSV
M
MAXIT
MM
MM1
N
NLOOK
NM1
NMAXIT
NMAXLOOK
NR
OLDEL
OLDGP
OLDRP
ONE
P
R
RP
RT1
RT2
S
SAFMAX
SAFMIN
SSFMAX
SSFMIN
THREE
TST
TST1
TWO
WORK( * )
Z( LDZ, * )
ZERO
| |
