root / src / lapack / double / dlasq3.f @ 10
Historique | Voir | Annoter | Télécharger (8,21 ko)
| 1 |
SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, |
|---|---|
| 2 |
$ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, |
| 3 |
$ DN2, G, TAU ) |
| 4 |
* |
| 5 |
* -- LAPACK routine (version 3.2.2) -- |
| 6 |
* |
| 7 |
* -- Contributed by Osni Marques of the Lawrence Berkeley National -- |
| 8 |
* -- Laboratory and Beresford Parlett of the Univ. of California at -- |
| 9 |
* -- Berkeley -- |
| 10 |
* -- June 2010 -- |
| 11 |
* |
| 12 |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 13 |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 14 |
* |
| 15 |
* .. Scalar Arguments .. |
| 16 |
LOGICAL IEEE |
| 17 |
INTEGER I0, ITER, N0, NDIV, NFAIL, PP |
| 18 |
DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, |
| 19 |
$ QMAX, SIGMA, TAU |
| 20 |
* .. |
| 21 |
* .. Array Arguments .. |
| 22 |
DOUBLE PRECISION Z( * ) |
| 23 |
* .. |
| 24 |
* |
| 25 |
* Purpose |
| 26 |
* ======= |
| 27 |
* |
| 28 |
* DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. |
| 29 |
* In case of failure it changes shifts, and tries again until output |
| 30 |
* is positive. |
| 31 |
* |
| 32 |
* Arguments |
| 33 |
* ========= |
| 34 |
* |
| 35 |
* I0 (input) INTEGER |
| 36 |
* First index. |
| 37 |
* |
| 38 |
* N0 (input/output) INTEGER |
| 39 |
* Last index. |
| 40 |
* |
| 41 |
* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) |
| 42 |
* Z holds the qd array. |
| 43 |
* |
| 44 |
* PP (input/output) INTEGER |
| 45 |
* PP=0 for ping, PP=1 for pong. |
| 46 |
* PP=2 indicates that flipping was applied to the Z array |
| 47 |
* and that the initial tests for deflation should not be |
| 48 |
* performed. |
| 49 |
* |
| 50 |
* DMIN (output) DOUBLE PRECISION |
| 51 |
* Minimum value of d. |
| 52 |
* |
| 53 |
* SIGMA (output) DOUBLE PRECISION |
| 54 |
* Sum of shifts used in current segment. |
| 55 |
* |
| 56 |
* DESIG (input/output) DOUBLE PRECISION |
| 57 |
* Lower order part of SIGMA |
| 58 |
* |
| 59 |
* QMAX (input) DOUBLE PRECISION |
| 60 |
* Maximum value of q. |
| 61 |
* |
| 62 |
* NFAIL (output) INTEGER |
| 63 |
* Number of times shift was too big. |
| 64 |
* |
| 65 |
* ITER (output) INTEGER |
| 66 |
* Number of iterations. |
| 67 |
* |
| 68 |
* NDIV (output) INTEGER |
| 69 |
* Number of divisions. |
| 70 |
* |
| 71 |
* IEEE (input) LOGICAL |
| 72 |
* Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). |
| 73 |
* |
| 74 |
* TTYPE (input/output) INTEGER |
| 75 |
* Shift type. |
| 76 |
* |
| 77 |
* DMIN1 (input/output) DOUBLE PRECISION |
| 78 |
* |
| 79 |
* DMIN2 (input/output) DOUBLE PRECISION |
| 80 |
* |
| 81 |
* DN (input/output) DOUBLE PRECISION |
| 82 |
* |
| 83 |
* DN1 (input/output) DOUBLE PRECISION |
| 84 |
* |
| 85 |
* DN2 (input/output) DOUBLE PRECISION |
| 86 |
* |
| 87 |
* G (input/output) DOUBLE PRECISION |
| 88 |
* |
| 89 |
* TAU (input/output) DOUBLE PRECISION |
| 90 |
* |
| 91 |
* These are passed as arguments in order to save their values |
| 92 |
* between calls to DLASQ3. |
| 93 |
* |
| 94 |
* ===================================================================== |
| 95 |
* |
| 96 |
* .. Parameters .. |
| 97 |
DOUBLE PRECISION CBIAS |
| 98 |
PARAMETER ( CBIAS = 1.50D0 ) |
| 99 |
DOUBLE PRECISION ZERO, QURTR, HALF, ONE, TWO, HUNDRD |
| 100 |
PARAMETER ( ZERO = 0.0D0, QURTR = 0.250D0, HALF = 0.5D0, |
| 101 |
$ ONE = 1.0D0, TWO = 2.0D0, HUNDRD = 100.0D0 ) |
| 102 |
* .. |
| 103 |
* .. Local Scalars .. |
| 104 |
INTEGER IPN4, J4, N0IN, NN, TTYPE |
| 105 |
DOUBLE PRECISION EPS, S, T, TEMP, TOL, TOL2 |
| 106 |
* .. |
| 107 |
* .. External Subroutines .. |
| 108 |
EXTERNAL DLASQ4, DLASQ5, DLASQ6 |
| 109 |
* .. |
| 110 |
* .. External Function .. |
| 111 |
DOUBLE PRECISION DLAMCH |
| 112 |
LOGICAL DISNAN |
| 113 |
EXTERNAL DISNAN, DLAMCH |
| 114 |
* .. |
| 115 |
* .. Intrinsic Functions .. |
| 116 |
INTRINSIC ABS, MAX, MIN, SQRT |
| 117 |
* .. |
| 118 |
* .. Executable Statements .. |
| 119 |
* |
| 120 |
N0IN = N0 |
| 121 |
EPS = DLAMCH( 'Precision' ) |
| 122 |
TOL = EPS*HUNDRD |
| 123 |
TOL2 = TOL**2 |
| 124 |
* |
| 125 |
* Check for deflation. |
| 126 |
* |
| 127 |
10 CONTINUE |
| 128 |
* |
| 129 |
IF( N0.LT.I0 ) |
| 130 |
$ RETURN |
| 131 |
IF( N0.EQ.I0 ) |
| 132 |
$ GO TO 20 |
| 133 |
NN = 4*N0 + PP |
| 134 |
IF( N0.EQ.( I0+1 ) ) |
| 135 |
$ GO TO 40 |
| 136 |
* |
| 137 |
* Check whether E(N0-1) is negligible, 1 eigenvalue. |
| 138 |
* |
| 139 |
IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND. |
| 140 |
$ Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) ) |
| 141 |
$ GO TO 30 |
| 142 |
* |
| 143 |
20 CONTINUE |
| 144 |
* |
| 145 |
Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA |
| 146 |
N0 = N0 - 1 |
| 147 |
GO TO 10 |
| 148 |
* |
| 149 |
* Check whether E(N0-2) is negligible, 2 eigenvalues. |
| 150 |
* |
| 151 |
30 CONTINUE |
| 152 |
* |
| 153 |
IF( Z( NN-9 ).GT.TOL2*SIGMA .AND. |
| 154 |
$ Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) ) |
| 155 |
$ GO TO 50 |
| 156 |
* |
| 157 |
40 CONTINUE |
| 158 |
* |
| 159 |
IF( Z( NN-3 ).GT.Z( NN-7 ) ) THEN |
| 160 |
S = Z( NN-3 ) |
| 161 |
Z( NN-3 ) = Z( NN-7 ) |
| 162 |
Z( NN-7 ) = S |
| 163 |
END IF |
| 164 |
IF( Z( NN-5 ).GT.Z( NN-3 )*TOL2 ) THEN |
| 165 |
T = HALF*( ( Z( NN-7 )-Z( NN-3 ) )+Z( NN-5 ) ) |
| 166 |
S = Z( NN-3 )*( Z( NN-5 ) / T ) |
| 167 |
IF( S.LE.T ) THEN |
| 168 |
S = Z( NN-3 )*( Z( NN-5 ) / |
| 169 |
$ ( T*( ONE+SQRT( ONE+S / T ) ) ) ) |
| 170 |
ELSE |
| 171 |
S = Z( NN-3 )*( Z( NN-5 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) |
| 172 |
END IF |
| 173 |
T = Z( NN-7 ) + ( S+Z( NN-5 ) ) |
| 174 |
Z( NN-3 ) = Z( NN-3 )*( Z( NN-7 ) / T ) |
| 175 |
Z( NN-7 ) = T |
| 176 |
END IF |
| 177 |
Z( 4*N0-7 ) = Z( NN-7 ) + SIGMA |
| 178 |
Z( 4*N0-3 ) = Z( NN-3 ) + SIGMA |
| 179 |
N0 = N0 - 2 |
| 180 |
GO TO 10 |
| 181 |
* |
| 182 |
50 CONTINUE |
| 183 |
IF( PP.EQ.2 ) |
| 184 |
$ PP = 0 |
| 185 |
* |
| 186 |
* Reverse the qd-array, if warranted. |
| 187 |
* |
| 188 |
IF( DMIN.LE.ZERO .OR. N0.LT.N0IN ) THEN |
| 189 |
IF( CBIAS*Z( 4*I0+PP-3 ).LT.Z( 4*N0+PP-3 ) ) THEN |
| 190 |
IPN4 = 4*( I0+N0 ) |
| 191 |
DO 60 J4 = 4*I0, 2*( I0+N0-1 ), 4 |
| 192 |
TEMP = Z( J4-3 ) |
| 193 |
Z( J4-3 ) = Z( IPN4-J4-3 ) |
| 194 |
Z( IPN4-J4-3 ) = TEMP |
| 195 |
TEMP = Z( J4-2 ) |
| 196 |
Z( J4-2 ) = Z( IPN4-J4-2 ) |
| 197 |
Z( IPN4-J4-2 ) = TEMP |
| 198 |
TEMP = Z( J4-1 ) |
| 199 |
Z( J4-1 ) = Z( IPN4-J4-5 ) |
| 200 |
Z( IPN4-J4-5 ) = TEMP |
| 201 |
TEMP = Z( J4 ) |
| 202 |
Z( J4 ) = Z( IPN4-J4-4 ) |
| 203 |
Z( IPN4-J4-4 ) = TEMP |
| 204 |
60 CONTINUE |
| 205 |
IF( N0-I0.LE.4 ) THEN |
| 206 |
Z( 4*N0+PP-1 ) = Z( 4*I0+PP-1 ) |
| 207 |
Z( 4*N0-PP ) = Z( 4*I0-PP ) |
| 208 |
END IF |
| 209 |
DMIN2 = MIN( DMIN2, Z( 4*N0+PP-1 ) ) |
| 210 |
Z( 4*N0+PP-1 ) = MIN( Z( 4*N0+PP-1 ), Z( 4*I0+PP-1 ), |
| 211 |
$ Z( 4*I0+PP+3 ) ) |
| 212 |
Z( 4*N0-PP ) = MIN( Z( 4*N0-PP ), Z( 4*I0-PP ), |
| 213 |
$ Z( 4*I0-PP+4 ) ) |
| 214 |
QMAX = MAX( QMAX, Z( 4*I0+PP-3 ), Z( 4*I0+PP+1 ) ) |
| 215 |
DMIN = -ZERO |
| 216 |
END IF |
| 217 |
END IF |
| 218 |
* |
| 219 |
* Choose a shift. |
| 220 |
* |
| 221 |
CALL DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1, |
| 222 |
$ DN2, TAU, TTYPE, G ) |
| 223 |
* |
| 224 |
* Call dqds until DMIN > 0. |
| 225 |
* |
| 226 |
70 CONTINUE |
| 227 |
* |
| 228 |
CALL DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN, |
| 229 |
$ DN1, DN2, IEEE ) |
| 230 |
* |
| 231 |
NDIV = NDIV + ( N0-I0+2 ) |
| 232 |
ITER = ITER + 1 |
| 233 |
* |
| 234 |
* Check status. |
| 235 |
* |
| 236 |
IF( DMIN.GE.ZERO .AND. DMIN1.GT.ZERO ) THEN |
| 237 |
* |
| 238 |
* Success. |
| 239 |
* |
| 240 |
GO TO 90 |
| 241 |
* |
| 242 |
ELSE IF( DMIN.LT.ZERO .AND. DMIN1.GT.ZERO .AND. |
| 243 |
$ Z( 4*( N0-1 )-PP ).LT.TOL*( SIGMA+DN1 ) .AND. |
| 244 |
$ ABS( DN ).LT.TOL*SIGMA ) THEN |
| 245 |
* |
| 246 |
* Convergence hidden by negative DN. |
| 247 |
* |
| 248 |
Z( 4*( N0-1 )-PP+2 ) = ZERO |
| 249 |
DMIN = ZERO |
| 250 |
GO TO 90 |
| 251 |
ELSE IF( DMIN.LT.ZERO ) THEN |
| 252 |
* |
| 253 |
* TAU too big. Select new TAU and try again. |
| 254 |
* |
| 255 |
NFAIL = NFAIL + 1 |
| 256 |
IF( TTYPE.LT.-22 ) THEN |
| 257 |
* |
| 258 |
* Failed twice. Play it safe. |
| 259 |
* |
| 260 |
TAU = ZERO |
| 261 |
ELSE IF( DMIN1.GT.ZERO ) THEN |
| 262 |
* |
| 263 |
* Late failure. Gives excellent shift. |
| 264 |
* |
| 265 |
TAU = ( TAU+DMIN )*( ONE-TWO*EPS ) |
| 266 |
TTYPE = TTYPE - 11 |
| 267 |
ELSE |
| 268 |
* |
| 269 |
* Early failure. Divide by 4. |
| 270 |
* |
| 271 |
TAU = QURTR*TAU |
| 272 |
TTYPE = TTYPE - 12 |
| 273 |
END IF |
| 274 |
GO TO 70 |
| 275 |
ELSE IF( DISNAN( DMIN ) ) THEN |
| 276 |
* |
| 277 |
* NaN. |
| 278 |
* |
| 279 |
IF( TAU.EQ.ZERO ) THEN |
| 280 |
GO TO 80 |
| 281 |
ELSE |
| 282 |
TAU = ZERO |
| 283 |
GO TO 70 |
| 284 |
END IF |
| 285 |
ELSE |
| 286 |
* |
| 287 |
* Possible underflow. Play it safe. |
| 288 |
* |
| 289 |
GO TO 80 |
| 290 |
END IF |
| 291 |
* |
| 292 |
* Risk of underflow. |
| 293 |
* |
| 294 |
80 CONTINUE |
| 295 |
CALL DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DN1, DN2 ) |
| 296 |
NDIV = NDIV + ( N0-I0+2 ) |
| 297 |
ITER = ITER + 1 |
| 298 |
TAU = ZERO |
| 299 |
* |
| 300 |
90 CONTINUE |
| 301 |
IF( TAU.LT.SIGMA ) THEN |
| 302 |
DESIG = DESIG + TAU |
| 303 |
T = SIGMA + DESIG |
| 304 |
DESIG = DESIG - ( T-SIGMA ) |
| 305 |
ELSE |
| 306 |
T = SIGMA + TAU |
| 307 |
DESIG = SIGMA - ( T-TAU ) + DESIG |
| 308 |
END IF |
| 309 |
SIGMA = T |
| 310 |
* |
| 311 |
RETURN |
| 312 |
* |
| 313 |
* End of DLASQ3 |
| 314 |
* |
| 315 |
END |