root / src / lapack / double / dlasd4.f @ 2
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| 1 | 1 | equemene | SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO ) |
|---|---|---|---|
| 2 | 1 | equemene | * |
| 3 | 1 | equemene | * -- LAPACK auxiliary routine (version 3.2) -- |
| 4 | 1 | equemene | * -- LAPACK is a software package provided by Univ. of Tennessee, -- |
| 5 | 1 | equemene | * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
| 6 | 1 | equemene | * November 2006 |
| 7 | 1 | equemene | * |
| 8 | 1 | equemene | * .. Scalar Arguments .. |
| 9 | 1 | equemene | INTEGER I, INFO, N |
| 10 | 1 | equemene | DOUBLE PRECISION RHO, SIGMA |
| 11 | 1 | equemene | * .. |
| 12 | 1 | equemene | * .. Array Arguments .. |
| 13 | 1 | equemene | DOUBLE PRECISION D( * ), DELTA( * ), WORK( * ), Z( * ) |
| 14 | 1 | equemene | * .. |
| 15 | 1 | equemene | * |
| 16 | 1 | equemene | * Purpose |
| 17 | 1 | equemene | * ======= |
| 18 | 1 | equemene | * |
| 19 | 1 | equemene | * This subroutine computes the square root of the I-th updated |
| 20 | 1 | equemene | * eigenvalue of a positive symmetric rank-one modification to |
| 21 | 1 | equemene | * a positive diagonal matrix whose entries are given as the squares |
| 22 | 1 | equemene | * of the corresponding entries in the array d, and that |
| 23 | 1 | equemene | * |
| 24 | 1 | equemene | * 0 <= D(i) < D(j) for i < j |
| 25 | 1 | equemene | * |
| 26 | 1 | equemene | * and that RHO > 0. This is arranged by the calling routine, and is |
| 27 | 1 | equemene | * no loss in generality. The rank-one modified system is thus |
| 28 | 1 | equemene | * |
| 29 | 1 | equemene | * diag( D ) * diag( D ) + RHO * Z * Z_transpose. |
| 30 | 1 | equemene | * |
| 31 | 1 | equemene | * where we assume the Euclidean norm of Z is 1. |
| 32 | 1 | equemene | * |
| 33 | 1 | equemene | * The method consists of approximating the rational functions in the |
| 34 | 1 | equemene | * secular equation by simpler interpolating rational functions. |
| 35 | 1 | equemene | * |
| 36 | 1 | equemene | * Arguments |
| 37 | 1 | equemene | * ========= |
| 38 | 1 | equemene | * |
| 39 | 1 | equemene | * N (input) INTEGER |
| 40 | 1 | equemene | * The length of all arrays. |
| 41 | 1 | equemene | * |
| 42 | 1 | equemene | * I (input) INTEGER |
| 43 | 1 | equemene | * The index of the eigenvalue to be computed. 1 <= I <= N. |
| 44 | 1 | equemene | * |
| 45 | 1 | equemene | * D (input) DOUBLE PRECISION array, dimension ( N ) |
| 46 | 1 | equemene | * The original eigenvalues. It is assumed that they are in |
| 47 | 1 | equemene | * order, 0 <= D(I) < D(J) for I < J. |
| 48 | 1 | equemene | * |
| 49 | 1 | equemene | * Z (input) DOUBLE PRECISION array, dimension ( N ) |
| 50 | 1 | equemene | * The components of the updating vector. |
| 51 | 1 | equemene | * |
| 52 | 1 | equemene | * DELTA (output) DOUBLE PRECISION array, dimension ( N ) |
| 53 | 1 | equemene | * If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th |
| 54 | 1 | equemene | * component. If N = 1, then DELTA(1) = 1. The vector DELTA |
| 55 | 1 | equemene | * contains the information necessary to construct the |
| 56 | 1 | equemene | * (singular) eigenvectors. |
| 57 | 1 | equemene | * |
| 58 | 1 | equemene | * RHO (input) DOUBLE PRECISION |
| 59 | 1 | equemene | * The scalar in the symmetric updating formula. |
| 60 | 1 | equemene | * |
| 61 | 1 | equemene | * SIGMA (output) DOUBLE PRECISION |
| 62 | 1 | equemene | * The computed sigma_I, the I-th updated eigenvalue. |
| 63 | 1 | equemene | * |
| 64 | 1 | equemene | * WORK (workspace) DOUBLE PRECISION array, dimension ( N ) |
| 65 | 1 | equemene | * If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th |
| 66 | 1 | equemene | * component. If N = 1, then WORK( 1 ) = 1. |
| 67 | 1 | equemene | * |
| 68 | 1 | equemene | * INFO (output) INTEGER |
| 69 | 1 | equemene | * = 0: successful exit |
| 70 | 1 | equemene | * > 0: if INFO = 1, the updating process failed. |
| 71 | 1 | equemene | * |
| 72 | 1 | equemene | * Internal Parameters |
| 73 | 1 | equemene | * =================== |
| 74 | 1 | equemene | * |
| 75 | 1 | equemene | * Logical variable ORGATI (origin-at-i?) is used for distinguishing |
| 76 | 1 | equemene | * whether D(i) or D(i+1) is treated as the origin. |
| 77 | 1 | equemene | * |
| 78 | 1 | equemene | * ORGATI = .true. origin at i |
| 79 | 1 | equemene | * ORGATI = .false. origin at i+1 |
| 80 | 1 | equemene | * |
| 81 | 1 | equemene | * Logical variable SWTCH3 (switch-for-3-poles?) is for noting |
| 82 | 1 | equemene | * if we are working with THREE poles! |
| 83 | 1 | equemene | * |
| 84 | 1 | equemene | * MAXIT is the maximum number of iterations allowed for each |
| 85 | 1 | equemene | * eigenvalue. |
| 86 | 1 | equemene | * |
| 87 | 1 | equemene | * Further Details |
| 88 | 1 | equemene | * =============== |
| 89 | 1 | equemene | * |
| 90 | 1 | equemene | * Based on contributions by |
| 91 | 1 | equemene | * Ren-Cang Li, Computer Science Division, University of California |
| 92 | 1 | equemene | * at Berkeley, USA |
| 93 | 1 | equemene | * |
| 94 | 1 | equemene | * ===================================================================== |
| 95 | 1 | equemene | * |
| 96 | 1 | equemene | * .. Parameters .. |
| 97 | 1 | equemene | INTEGER MAXIT |
| 98 | 1 | equemene | PARAMETER ( MAXIT = 20 ) |
| 99 | 1 | equemene | DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, EIGHT, TEN |
| 100 | 1 | equemene | PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0, |
| 101 | 1 | equemene | $ THREE = 3.0D+0, FOUR = 4.0D+0, EIGHT = 8.0D+0, |
| 102 | 1 | equemene | $ TEN = 10.0D+0 ) |
| 103 | 1 | equemene | * .. |
| 104 | 1 | equemene | * .. Local Scalars .. |
| 105 | 1 | equemene | LOGICAL ORGATI, SWTCH, SWTCH3 |
| 106 | 1 | equemene | INTEGER II, IIM1, IIP1, IP1, ITER, J, NITER |
| 107 | 1 | equemene | DOUBLE PRECISION A, B, C, DELSQ, DELSQ2, DPHI, DPSI, DTIIM, |
| 108 | 1 | equemene | $ DTIIP, DTIPSQ, DTISQ, DTNSQ, DTNSQ1, DW, EPS, |
| 109 | 1 | equemene | $ ERRETM, ETA, PHI, PREW, PSI, RHOINV, SG2LB, |
| 110 | 1 | equemene | $ SG2UB, TAU, TEMP, TEMP1, TEMP2, W |
| 111 | 1 | equemene | * .. |
| 112 | 1 | equemene | * .. Local Arrays .. |
| 113 | 1 | equemene | DOUBLE PRECISION DD( 3 ), ZZ( 3 ) |
| 114 | 1 | equemene | * .. |
| 115 | 1 | equemene | * .. External Subroutines .. |
| 116 | 1 | equemene | EXTERNAL DLAED6, DLASD5 |
| 117 | 1 | equemene | * .. |
| 118 | 1 | equemene | * .. External Functions .. |
| 119 | 1 | equemene | DOUBLE PRECISION DLAMCH |
| 120 | 1 | equemene | EXTERNAL DLAMCH |
| 121 | 1 | equemene | * .. |
| 122 | 1 | equemene | * .. Intrinsic Functions .. |
| 123 | 1 | equemene | INTRINSIC ABS, MAX, MIN, SQRT |
| 124 | 1 | equemene | * .. |
| 125 | 1 | equemene | * .. Executable Statements .. |
| 126 | 1 | equemene | * |
| 127 | 1 | equemene | * Since this routine is called in an inner loop, we do no argument |
| 128 | 1 | equemene | * checking. |
| 129 | 1 | equemene | * |
| 130 | 1 | equemene | * Quick return for N=1 and 2. |
| 131 | 1 | equemene | * |
| 132 | 1 | equemene | INFO = 0 |
| 133 | 1 | equemene | IF( N.EQ.1 ) THEN |
| 134 | 1 | equemene | * |
| 135 | 1 | equemene | * Presumably, I=1 upon entry |
| 136 | 1 | equemene | * |
| 137 | 1 | equemene | SIGMA = SQRT( D( 1 )*D( 1 )+RHO*Z( 1 )*Z( 1 ) ) |
| 138 | 1 | equemene | DELTA( 1 ) = ONE |
| 139 | 1 | equemene | WORK( 1 ) = ONE |
| 140 | 1 | equemene | RETURN |
| 141 | 1 | equemene | END IF |
| 142 | 1 | equemene | IF( N.EQ.2 ) THEN |
| 143 | 1 | equemene | CALL DLASD5( I, D, Z, DELTA, RHO, SIGMA, WORK ) |
| 144 | 1 | equemene | RETURN |
| 145 | 1 | equemene | END IF |
| 146 | 1 | equemene | * |
| 147 | 1 | equemene | * Compute machine epsilon |
| 148 | 1 | equemene | * |
| 149 | 1 | equemene | EPS = DLAMCH( 'Epsilon' ) |
| 150 | 1 | equemene | RHOINV = ONE / RHO |
| 151 | 1 | equemene | * |
| 152 | 1 | equemene | * The case I = N |
| 153 | 1 | equemene | * |
| 154 | 1 | equemene | IF( I.EQ.N ) THEN |
| 155 | 1 | equemene | * |
| 156 | 1 | equemene | * Initialize some basic variables |
| 157 | 1 | equemene | * |
| 158 | 1 | equemene | II = N - 1 |
| 159 | 1 | equemene | NITER = 1 |
| 160 | 1 | equemene | * |
| 161 | 1 | equemene | * Calculate initial guess |
| 162 | 1 | equemene | * |
| 163 | 1 | equemene | TEMP = RHO / TWO |
| 164 | 1 | equemene | * |
| 165 | 1 | equemene | * If ||Z||_2 is not one, then TEMP should be set to |
| 166 | 1 | equemene | * RHO * ||Z||_2^2 / TWO |
| 167 | 1 | equemene | * |
| 168 | 1 | equemene | TEMP1 = TEMP / ( D( N )+SQRT( D( N )*D( N )+TEMP ) ) |
| 169 | 1 | equemene | DO 10 J = 1, N |
| 170 | 1 | equemene | WORK( J ) = D( J ) + D( N ) + TEMP1 |
| 171 | 1 | equemene | DELTA( J ) = ( D( J )-D( N ) ) - TEMP1 |
| 172 | 1 | equemene | 10 CONTINUE |
| 173 | 1 | equemene | * |
| 174 | 1 | equemene | PSI = ZERO |
| 175 | 1 | equemene | DO 20 J = 1, N - 2 |
| 176 | 1 | equemene | PSI = PSI + Z( J )*Z( J ) / ( DELTA( J )*WORK( J ) ) |
| 177 | 1 | equemene | 20 CONTINUE |
| 178 | 1 | equemene | * |
| 179 | 1 | equemene | C = RHOINV + PSI |
| 180 | 1 | equemene | W = C + Z( II )*Z( II ) / ( DELTA( II )*WORK( II ) ) + |
| 181 | 1 | equemene | $ Z( N )*Z( N ) / ( DELTA( N )*WORK( N ) ) |
| 182 | 1 | equemene | * |
| 183 | 1 | equemene | IF( W.LE.ZERO ) THEN |
| 184 | 1 | equemene | TEMP1 = SQRT( D( N )*D( N )+RHO ) |
| 185 | 1 | equemene | TEMP = Z( N-1 )*Z( N-1 ) / ( ( D( N-1 )+TEMP1 )* |
| 186 | 1 | equemene | $ ( D( N )-D( N-1 )+RHO / ( D( N )+TEMP1 ) ) ) + |
| 187 | 1 | equemene | $ Z( N )*Z( N ) / RHO |
| 188 | 1 | equemene | * |
| 189 | 1 | equemene | * The following TAU is to approximate |
| 190 | 1 | equemene | * SIGMA_n^2 - D( N )*D( N ) |
| 191 | 1 | equemene | * |
| 192 | 1 | equemene | IF( C.LE.TEMP ) THEN |
| 193 | 1 | equemene | TAU = RHO |
| 194 | 1 | equemene | ELSE |
| 195 | 1 | equemene | DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) ) |
| 196 | 1 | equemene | A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) |
| 197 | 1 | equemene | B = Z( N )*Z( N )*DELSQ |
| 198 | 1 | equemene | IF( A.LT.ZERO ) THEN |
| 199 | 1 | equemene | TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) |
| 200 | 1 | equemene | ELSE |
| 201 | 1 | equemene | TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) |
| 202 | 1 | equemene | END IF |
| 203 | 1 | equemene | END IF |
| 204 | 1 | equemene | * |
| 205 | 1 | equemene | * It can be proved that |
| 206 | 1 | equemene | * D(N)^2+RHO/2 <= SIGMA_n^2 < D(N)^2+TAU <= D(N)^2+RHO |
| 207 | 1 | equemene | * |
| 208 | 1 | equemene | ELSE |
| 209 | 1 | equemene | DELSQ = ( D( N )-D( N-1 ) )*( D( N )+D( N-1 ) ) |
| 210 | 1 | equemene | A = -C*DELSQ + Z( N-1 )*Z( N-1 ) + Z( N )*Z( N ) |
| 211 | 1 | equemene | B = Z( N )*Z( N )*DELSQ |
| 212 | 1 | equemene | * |
| 213 | 1 | equemene | * The following TAU is to approximate |
| 214 | 1 | equemene | * SIGMA_n^2 - D( N )*D( N ) |
| 215 | 1 | equemene | * |
| 216 | 1 | equemene | IF( A.LT.ZERO ) THEN |
| 217 | 1 | equemene | TAU = TWO*B / ( SQRT( A*A+FOUR*B*C )-A ) |
| 218 | 1 | equemene | ELSE |
| 219 | 1 | equemene | TAU = ( A+SQRT( A*A+FOUR*B*C ) ) / ( TWO*C ) |
| 220 | 1 | equemene | END IF |
| 221 | 1 | equemene | * |
| 222 | 1 | equemene | * It can be proved that |
| 223 | 1 | equemene | * D(N)^2 < D(N)^2+TAU < SIGMA(N)^2 < D(N)^2+RHO/2 |
| 224 | 1 | equemene | * |
| 225 | 1 | equemene | END IF |
| 226 | 1 | equemene | * |
| 227 | 1 | equemene | * The following ETA is to approximate SIGMA_n - D( N ) |
| 228 | 1 | equemene | * |
| 229 | 1 | equemene | ETA = TAU / ( D( N )+SQRT( D( N )*D( N )+TAU ) ) |
| 230 | 1 | equemene | * |
| 231 | 1 | equemene | SIGMA = D( N ) + ETA |
| 232 | 1 | equemene | DO 30 J = 1, N |
| 233 | 1 | equemene | DELTA( J ) = ( D( J )-D( I ) ) - ETA |
| 234 | 1 | equemene | WORK( J ) = D( J ) + D( I ) + ETA |
| 235 | 1 | equemene | 30 CONTINUE |
| 236 | 1 | equemene | * |
| 237 | 1 | equemene | * Evaluate PSI and the derivative DPSI |
| 238 | 1 | equemene | * |
| 239 | 1 | equemene | DPSI = ZERO |
| 240 | 1 | equemene | PSI = ZERO |
| 241 | 1 | equemene | ERRETM = ZERO |
| 242 | 1 | equemene | DO 40 J = 1, II |
| 243 | 1 | equemene | TEMP = Z( J ) / ( DELTA( J )*WORK( J ) ) |
| 244 | 1 | equemene | PSI = PSI + Z( J )*TEMP |
| 245 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 246 | 1 | equemene | ERRETM = ERRETM + PSI |
| 247 | 1 | equemene | 40 CONTINUE |
| 248 | 1 | equemene | ERRETM = ABS( ERRETM ) |
| 249 | 1 | equemene | * |
| 250 | 1 | equemene | * Evaluate PHI and the derivative DPHI |
| 251 | 1 | equemene | * |
| 252 | 1 | equemene | TEMP = Z( N ) / ( DELTA( N )*WORK( N ) ) |
| 253 | 1 | equemene | PHI = Z( N )*TEMP |
| 254 | 1 | equemene | DPHI = TEMP*TEMP |
| 255 | 1 | equemene | ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + |
| 256 | 1 | equemene | $ ABS( TAU )*( DPSI+DPHI ) |
| 257 | 1 | equemene | * |
| 258 | 1 | equemene | W = RHOINV + PHI + PSI |
| 259 | 1 | equemene | * |
| 260 | 1 | equemene | * Test for convergence |
| 261 | 1 | equemene | * |
| 262 | 1 | equemene | IF( ABS( W ).LE.EPS*ERRETM ) THEN |
| 263 | 1 | equemene | GO TO 240 |
| 264 | 1 | equemene | END IF |
| 265 | 1 | equemene | * |
| 266 | 1 | equemene | * Calculate the new step |
| 267 | 1 | equemene | * |
| 268 | 1 | equemene | NITER = NITER + 1 |
| 269 | 1 | equemene | DTNSQ1 = WORK( N-1 )*DELTA( N-1 ) |
| 270 | 1 | equemene | DTNSQ = WORK( N )*DELTA( N ) |
| 271 | 1 | equemene | C = W - DTNSQ1*DPSI - DTNSQ*DPHI |
| 272 | 1 | equemene | A = ( DTNSQ+DTNSQ1 )*W - DTNSQ*DTNSQ1*( DPSI+DPHI ) |
| 273 | 1 | equemene | B = DTNSQ*DTNSQ1*W |
| 274 | 1 | equemene | IF( C.LT.ZERO ) |
| 275 | 1 | equemene | $ C = ABS( C ) |
| 276 | 1 | equemene | IF( C.EQ.ZERO ) THEN |
| 277 | 1 | equemene | ETA = RHO - SIGMA*SIGMA |
| 278 | 1 | equemene | ELSE IF( A.GE.ZERO ) THEN |
| 279 | 1 | equemene | ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) |
| 280 | 1 | equemene | ELSE |
| 281 | 1 | equemene | ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) |
| 282 | 1 | equemene | END IF |
| 283 | 1 | equemene | * |
| 284 | 1 | equemene | * Note, eta should be positive if w is negative, and |
| 285 | 1 | equemene | * eta should be negative otherwise. However, |
| 286 | 1 | equemene | * if for some reason caused by roundoff, eta*w > 0, |
| 287 | 1 | equemene | * we simply use one Newton step instead. This way |
| 288 | 1 | equemene | * will guarantee eta*w < 0. |
| 289 | 1 | equemene | * |
| 290 | 1 | equemene | IF( W*ETA.GT.ZERO ) |
| 291 | 1 | equemene | $ ETA = -W / ( DPSI+DPHI ) |
| 292 | 1 | equemene | TEMP = ETA - DTNSQ |
| 293 | 1 | equemene | IF( TEMP.GT.RHO ) |
| 294 | 1 | equemene | $ ETA = RHO + DTNSQ |
| 295 | 1 | equemene | * |
| 296 | 1 | equemene | TAU = TAU + ETA |
| 297 | 1 | equemene | ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) ) |
| 298 | 1 | equemene | DO 50 J = 1, N |
| 299 | 1 | equemene | DELTA( J ) = DELTA( J ) - ETA |
| 300 | 1 | equemene | WORK( J ) = WORK( J ) + ETA |
| 301 | 1 | equemene | 50 CONTINUE |
| 302 | 1 | equemene | * |
| 303 | 1 | equemene | SIGMA = SIGMA + ETA |
| 304 | 1 | equemene | * |
| 305 | 1 | equemene | * Evaluate PSI and the derivative DPSI |
| 306 | 1 | equemene | * |
| 307 | 1 | equemene | DPSI = ZERO |
| 308 | 1 | equemene | PSI = ZERO |
| 309 | 1 | equemene | ERRETM = ZERO |
| 310 | 1 | equemene | DO 60 J = 1, II |
| 311 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 312 | 1 | equemene | PSI = PSI + Z( J )*TEMP |
| 313 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 314 | 1 | equemene | ERRETM = ERRETM + PSI |
| 315 | 1 | equemene | 60 CONTINUE |
| 316 | 1 | equemene | ERRETM = ABS( ERRETM ) |
| 317 | 1 | equemene | * |
| 318 | 1 | equemene | * Evaluate PHI and the derivative DPHI |
| 319 | 1 | equemene | * |
| 320 | 1 | equemene | TEMP = Z( N ) / ( WORK( N )*DELTA( N ) ) |
| 321 | 1 | equemene | PHI = Z( N )*TEMP |
| 322 | 1 | equemene | DPHI = TEMP*TEMP |
| 323 | 1 | equemene | ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + |
| 324 | 1 | equemene | $ ABS( TAU )*( DPSI+DPHI ) |
| 325 | 1 | equemene | * |
| 326 | 1 | equemene | W = RHOINV + PHI + PSI |
| 327 | 1 | equemene | * |
| 328 | 1 | equemene | * Main loop to update the values of the array DELTA |
| 329 | 1 | equemene | * |
| 330 | 1 | equemene | ITER = NITER + 1 |
| 331 | 1 | equemene | * |
| 332 | 1 | equemene | DO 90 NITER = ITER, MAXIT |
| 333 | 1 | equemene | * |
| 334 | 1 | equemene | * Test for convergence |
| 335 | 1 | equemene | * |
| 336 | 1 | equemene | IF( ABS( W ).LE.EPS*ERRETM ) THEN |
| 337 | 1 | equemene | GO TO 240 |
| 338 | 1 | equemene | END IF |
| 339 | 1 | equemene | * |
| 340 | 1 | equemene | * Calculate the new step |
| 341 | 1 | equemene | * |
| 342 | 1 | equemene | DTNSQ1 = WORK( N-1 )*DELTA( N-1 ) |
| 343 | 1 | equemene | DTNSQ = WORK( N )*DELTA( N ) |
| 344 | 1 | equemene | C = W - DTNSQ1*DPSI - DTNSQ*DPHI |
| 345 | 1 | equemene | A = ( DTNSQ+DTNSQ1 )*W - DTNSQ1*DTNSQ*( DPSI+DPHI ) |
| 346 | 1 | equemene | B = DTNSQ1*DTNSQ*W |
| 347 | 1 | equemene | IF( A.GE.ZERO ) THEN |
| 348 | 1 | equemene | ETA = ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) |
| 349 | 1 | equemene | ELSE |
| 350 | 1 | equemene | ETA = TWO*B / ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) |
| 351 | 1 | equemene | END IF |
| 352 | 1 | equemene | * |
| 353 | 1 | equemene | * Note, eta should be positive if w is negative, and |
| 354 | 1 | equemene | * eta should be negative otherwise. However, |
| 355 | 1 | equemene | * if for some reason caused by roundoff, eta*w > 0, |
| 356 | 1 | equemene | * we simply use one Newton step instead. This way |
| 357 | 1 | equemene | * will guarantee eta*w < 0. |
| 358 | 1 | equemene | * |
| 359 | 1 | equemene | IF( W*ETA.GT.ZERO ) |
| 360 | 1 | equemene | $ ETA = -W / ( DPSI+DPHI ) |
| 361 | 1 | equemene | TEMP = ETA - DTNSQ |
| 362 | 1 | equemene | IF( TEMP.LE.ZERO ) |
| 363 | 1 | equemene | $ ETA = ETA / TWO |
| 364 | 1 | equemene | * |
| 365 | 1 | equemene | TAU = TAU + ETA |
| 366 | 1 | equemene | ETA = ETA / ( SIGMA+SQRT( ETA+SIGMA*SIGMA ) ) |
| 367 | 1 | equemene | DO 70 J = 1, N |
| 368 | 1 | equemene | DELTA( J ) = DELTA( J ) - ETA |
| 369 | 1 | equemene | WORK( J ) = WORK( J ) + ETA |
| 370 | 1 | equemene | 70 CONTINUE |
| 371 | 1 | equemene | * |
| 372 | 1 | equemene | SIGMA = SIGMA + ETA |
| 373 | 1 | equemene | * |
| 374 | 1 | equemene | * Evaluate PSI and the derivative DPSI |
| 375 | 1 | equemene | * |
| 376 | 1 | equemene | DPSI = ZERO |
| 377 | 1 | equemene | PSI = ZERO |
| 378 | 1 | equemene | ERRETM = ZERO |
| 379 | 1 | equemene | DO 80 J = 1, II |
| 380 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 381 | 1 | equemene | PSI = PSI + Z( J )*TEMP |
| 382 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 383 | 1 | equemene | ERRETM = ERRETM + PSI |
| 384 | 1 | equemene | 80 CONTINUE |
| 385 | 1 | equemene | ERRETM = ABS( ERRETM ) |
| 386 | 1 | equemene | * |
| 387 | 1 | equemene | * Evaluate PHI and the derivative DPHI |
| 388 | 1 | equemene | * |
| 389 | 1 | equemene | TEMP = Z( N ) / ( WORK( N )*DELTA( N ) ) |
| 390 | 1 | equemene | PHI = Z( N )*TEMP |
| 391 | 1 | equemene | DPHI = TEMP*TEMP |
| 392 | 1 | equemene | ERRETM = EIGHT*( -PHI-PSI ) + ERRETM - PHI + RHOINV + |
| 393 | 1 | equemene | $ ABS( TAU )*( DPSI+DPHI ) |
| 394 | 1 | equemene | * |
| 395 | 1 | equemene | W = RHOINV + PHI + PSI |
| 396 | 1 | equemene | 90 CONTINUE |
| 397 | 1 | equemene | * |
| 398 | 1 | equemene | * Return with INFO = 1, NITER = MAXIT and not converged |
| 399 | 1 | equemene | * |
| 400 | 1 | equemene | INFO = 1 |
| 401 | 1 | equemene | GO TO 240 |
| 402 | 1 | equemene | * |
| 403 | 1 | equemene | * End for the case I = N |
| 404 | 1 | equemene | * |
| 405 | 1 | equemene | ELSE |
| 406 | 1 | equemene | * |
| 407 | 1 | equemene | * The case for I < N |
| 408 | 1 | equemene | * |
| 409 | 1 | equemene | NITER = 1 |
| 410 | 1 | equemene | IP1 = I + 1 |
| 411 | 1 | equemene | * |
| 412 | 1 | equemene | * Calculate initial guess |
| 413 | 1 | equemene | * |
| 414 | 1 | equemene | DELSQ = ( D( IP1 )-D( I ) )*( D( IP1 )+D( I ) ) |
| 415 | 1 | equemene | DELSQ2 = DELSQ / TWO |
| 416 | 1 | equemene | TEMP = DELSQ2 / ( D( I )+SQRT( D( I )*D( I )+DELSQ2 ) ) |
| 417 | 1 | equemene | DO 100 J = 1, N |
| 418 | 1 | equemene | WORK( J ) = D( J ) + D( I ) + TEMP |
| 419 | 1 | equemene | DELTA( J ) = ( D( J )-D( I ) ) - TEMP |
| 420 | 1 | equemene | 100 CONTINUE |
| 421 | 1 | equemene | * |
| 422 | 1 | equemene | PSI = ZERO |
| 423 | 1 | equemene | DO 110 J = 1, I - 1 |
| 424 | 1 | equemene | PSI = PSI + Z( J )*Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 425 | 1 | equemene | 110 CONTINUE |
| 426 | 1 | equemene | * |
| 427 | 1 | equemene | PHI = ZERO |
| 428 | 1 | equemene | DO 120 J = N, I + 2, -1 |
| 429 | 1 | equemene | PHI = PHI + Z( J )*Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 430 | 1 | equemene | 120 CONTINUE |
| 431 | 1 | equemene | C = RHOINV + PSI + PHI |
| 432 | 1 | equemene | W = C + Z( I )*Z( I ) / ( WORK( I )*DELTA( I ) ) + |
| 433 | 1 | equemene | $ Z( IP1 )*Z( IP1 ) / ( WORK( IP1 )*DELTA( IP1 ) ) |
| 434 | 1 | equemene | * |
| 435 | 1 | equemene | IF( W.GT.ZERO ) THEN |
| 436 | 1 | equemene | * |
| 437 | 1 | equemene | * d(i)^2 < the ith sigma^2 < (d(i)^2+d(i+1)^2)/2 |
| 438 | 1 | equemene | * |
| 439 | 1 | equemene | * We choose d(i) as origin. |
| 440 | 1 | equemene | * |
| 441 | 1 | equemene | ORGATI = .TRUE. |
| 442 | 1 | equemene | SG2LB = ZERO |
| 443 | 1 | equemene | SG2UB = DELSQ2 |
| 444 | 1 | equemene | A = C*DELSQ + Z( I )*Z( I ) + Z( IP1 )*Z( IP1 ) |
| 445 | 1 | equemene | B = Z( I )*Z( I )*DELSQ |
| 446 | 1 | equemene | IF( A.GT.ZERO ) THEN |
| 447 | 1 | equemene | TAU = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) |
| 448 | 1 | equemene | ELSE |
| 449 | 1 | equemene | TAU = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) |
| 450 | 1 | equemene | END IF |
| 451 | 1 | equemene | * |
| 452 | 1 | equemene | * TAU now is an estimation of SIGMA^2 - D( I )^2. The |
| 453 | 1 | equemene | * following, however, is the corresponding estimation of |
| 454 | 1 | equemene | * SIGMA - D( I ). |
| 455 | 1 | equemene | * |
| 456 | 1 | equemene | ETA = TAU / ( D( I )+SQRT( D( I )*D( I )+TAU ) ) |
| 457 | 1 | equemene | ELSE |
| 458 | 1 | equemene | * |
| 459 | 1 | equemene | * (d(i)^2+d(i+1)^2)/2 <= the ith sigma^2 < d(i+1)^2/2 |
| 460 | 1 | equemene | * |
| 461 | 1 | equemene | * We choose d(i+1) as origin. |
| 462 | 1 | equemene | * |
| 463 | 1 | equemene | ORGATI = .FALSE. |
| 464 | 1 | equemene | SG2LB = -DELSQ2 |
| 465 | 1 | equemene | SG2UB = ZERO |
| 466 | 1 | equemene | A = C*DELSQ - Z( I )*Z( I ) - Z( IP1 )*Z( IP1 ) |
| 467 | 1 | equemene | B = Z( IP1 )*Z( IP1 )*DELSQ |
| 468 | 1 | equemene | IF( A.LT.ZERO ) THEN |
| 469 | 1 | equemene | TAU = TWO*B / ( A-SQRT( ABS( A*A+FOUR*B*C ) ) ) |
| 470 | 1 | equemene | ELSE |
| 471 | 1 | equemene | TAU = -( A+SQRT( ABS( A*A+FOUR*B*C ) ) ) / ( TWO*C ) |
| 472 | 1 | equemene | END IF |
| 473 | 1 | equemene | * |
| 474 | 1 | equemene | * TAU now is an estimation of SIGMA^2 - D( IP1 )^2. The |
| 475 | 1 | equemene | * following, however, is the corresponding estimation of |
| 476 | 1 | equemene | * SIGMA - D( IP1 ). |
| 477 | 1 | equemene | * |
| 478 | 1 | equemene | ETA = TAU / ( D( IP1 )+SQRT( ABS( D( IP1 )*D( IP1 )+ |
| 479 | 1 | equemene | $ TAU ) ) ) |
| 480 | 1 | equemene | END IF |
| 481 | 1 | equemene | * |
| 482 | 1 | equemene | IF( ORGATI ) THEN |
| 483 | 1 | equemene | II = I |
| 484 | 1 | equemene | SIGMA = D( I ) + ETA |
| 485 | 1 | equemene | DO 130 J = 1, N |
| 486 | 1 | equemene | WORK( J ) = D( J ) + D( I ) + ETA |
| 487 | 1 | equemene | DELTA( J ) = ( D( J )-D( I ) ) - ETA |
| 488 | 1 | equemene | 130 CONTINUE |
| 489 | 1 | equemene | ELSE |
| 490 | 1 | equemene | II = I + 1 |
| 491 | 1 | equemene | SIGMA = D( IP1 ) + ETA |
| 492 | 1 | equemene | DO 140 J = 1, N |
| 493 | 1 | equemene | WORK( J ) = D( J ) + D( IP1 ) + ETA |
| 494 | 1 | equemene | DELTA( J ) = ( D( J )-D( IP1 ) ) - ETA |
| 495 | 1 | equemene | 140 CONTINUE |
| 496 | 1 | equemene | END IF |
| 497 | 1 | equemene | IIM1 = II - 1 |
| 498 | 1 | equemene | IIP1 = II + 1 |
| 499 | 1 | equemene | * |
| 500 | 1 | equemene | * Evaluate PSI and the derivative DPSI |
| 501 | 1 | equemene | * |
| 502 | 1 | equemene | DPSI = ZERO |
| 503 | 1 | equemene | PSI = ZERO |
| 504 | 1 | equemene | ERRETM = ZERO |
| 505 | 1 | equemene | DO 150 J = 1, IIM1 |
| 506 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 507 | 1 | equemene | PSI = PSI + Z( J )*TEMP |
| 508 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 509 | 1 | equemene | ERRETM = ERRETM + PSI |
| 510 | 1 | equemene | 150 CONTINUE |
| 511 | 1 | equemene | ERRETM = ABS( ERRETM ) |
| 512 | 1 | equemene | * |
| 513 | 1 | equemene | * Evaluate PHI and the derivative DPHI |
| 514 | 1 | equemene | * |
| 515 | 1 | equemene | DPHI = ZERO |
| 516 | 1 | equemene | PHI = ZERO |
| 517 | 1 | equemene | DO 160 J = N, IIP1, -1 |
| 518 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 519 | 1 | equemene | PHI = PHI + Z( J )*TEMP |
| 520 | 1 | equemene | DPHI = DPHI + TEMP*TEMP |
| 521 | 1 | equemene | ERRETM = ERRETM + PHI |
| 522 | 1 | equemene | 160 CONTINUE |
| 523 | 1 | equemene | * |
| 524 | 1 | equemene | W = RHOINV + PHI + PSI |
| 525 | 1 | equemene | * |
| 526 | 1 | equemene | * W is the value of the secular function with |
| 527 | 1 | equemene | * its ii-th element removed. |
| 528 | 1 | equemene | * |
| 529 | 1 | equemene | SWTCH3 = .FALSE. |
| 530 | 1 | equemene | IF( ORGATI ) THEN |
| 531 | 1 | equemene | IF( W.LT.ZERO ) |
| 532 | 1 | equemene | $ SWTCH3 = .TRUE. |
| 533 | 1 | equemene | ELSE |
| 534 | 1 | equemene | IF( W.GT.ZERO ) |
| 535 | 1 | equemene | $ SWTCH3 = .TRUE. |
| 536 | 1 | equemene | END IF |
| 537 | 1 | equemene | IF( II.EQ.1 .OR. II.EQ.N ) |
| 538 | 1 | equemene | $ SWTCH3 = .FALSE. |
| 539 | 1 | equemene | * |
| 540 | 1 | equemene | TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) |
| 541 | 1 | equemene | DW = DPSI + DPHI + TEMP*TEMP |
| 542 | 1 | equemene | TEMP = Z( II )*TEMP |
| 543 | 1 | equemene | W = W + TEMP |
| 544 | 1 | equemene | ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + |
| 545 | 1 | equemene | $ THREE*ABS( TEMP ) + ABS( TAU )*DW |
| 546 | 1 | equemene | * |
| 547 | 1 | equemene | * Test for convergence |
| 548 | 1 | equemene | * |
| 549 | 1 | equemene | IF( ABS( W ).LE.EPS*ERRETM ) THEN |
| 550 | 1 | equemene | GO TO 240 |
| 551 | 1 | equemene | END IF |
| 552 | 1 | equemene | * |
| 553 | 1 | equemene | IF( W.LE.ZERO ) THEN |
| 554 | 1 | equemene | SG2LB = MAX( SG2LB, TAU ) |
| 555 | 1 | equemene | ELSE |
| 556 | 1 | equemene | SG2UB = MIN( SG2UB, TAU ) |
| 557 | 1 | equemene | END IF |
| 558 | 1 | equemene | * |
| 559 | 1 | equemene | * Calculate the new step |
| 560 | 1 | equemene | * |
| 561 | 1 | equemene | NITER = NITER + 1 |
| 562 | 1 | equemene | IF( .NOT.SWTCH3 ) THEN |
| 563 | 1 | equemene | DTIPSQ = WORK( IP1 )*DELTA( IP1 ) |
| 564 | 1 | equemene | DTISQ = WORK( I )*DELTA( I ) |
| 565 | 1 | equemene | IF( ORGATI ) THEN |
| 566 | 1 | equemene | C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2 |
| 567 | 1 | equemene | ELSE |
| 568 | 1 | equemene | C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2 |
| 569 | 1 | equemene | END IF |
| 570 | 1 | equemene | A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW |
| 571 | 1 | equemene | B = DTIPSQ*DTISQ*W |
| 572 | 1 | equemene | IF( C.EQ.ZERO ) THEN |
| 573 | 1 | equemene | IF( A.EQ.ZERO ) THEN |
| 574 | 1 | equemene | IF( ORGATI ) THEN |
| 575 | 1 | equemene | A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ*( DPSI+DPHI ) |
| 576 | 1 | equemene | ELSE |
| 577 | 1 | equemene | A = Z( IP1 )*Z( IP1 ) + DTISQ*DTISQ*( DPSI+DPHI ) |
| 578 | 1 | equemene | END IF |
| 579 | 1 | equemene | END IF |
| 580 | 1 | equemene | ETA = B / A |
| 581 | 1 | equemene | ELSE IF( A.LE.ZERO ) THEN |
| 582 | 1 | equemene | ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) |
| 583 | 1 | equemene | ELSE |
| 584 | 1 | equemene | ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) |
| 585 | 1 | equemene | END IF |
| 586 | 1 | equemene | ELSE |
| 587 | 1 | equemene | * |
| 588 | 1 | equemene | * Interpolation using THREE most relevant poles |
| 589 | 1 | equemene | * |
| 590 | 1 | equemene | DTIIM = WORK( IIM1 )*DELTA( IIM1 ) |
| 591 | 1 | equemene | DTIIP = WORK( IIP1 )*DELTA( IIP1 ) |
| 592 | 1 | equemene | TEMP = RHOINV + PSI + PHI |
| 593 | 1 | equemene | IF( ORGATI ) THEN |
| 594 | 1 | equemene | TEMP1 = Z( IIM1 ) / DTIIM |
| 595 | 1 | equemene | TEMP1 = TEMP1*TEMP1 |
| 596 | 1 | equemene | C = ( TEMP - DTIIP*( DPSI+DPHI ) ) - |
| 597 | 1 | equemene | $ ( D( IIM1 )-D( IIP1 ) )*( D( IIM1 )+D( IIP1 ) )*TEMP1 |
| 598 | 1 | equemene | ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) |
| 599 | 1 | equemene | IF( DPSI.LT.TEMP1 ) THEN |
| 600 | 1 | equemene | ZZ( 3 ) = DTIIP*DTIIP*DPHI |
| 601 | 1 | equemene | ELSE |
| 602 | 1 | equemene | ZZ( 3 ) = DTIIP*DTIIP*( ( DPSI-TEMP1 )+DPHI ) |
| 603 | 1 | equemene | END IF |
| 604 | 1 | equemene | ELSE |
| 605 | 1 | equemene | TEMP1 = Z( IIP1 ) / DTIIP |
| 606 | 1 | equemene | TEMP1 = TEMP1*TEMP1 |
| 607 | 1 | equemene | C = ( TEMP - DTIIM*( DPSI+DPHI ) ) - |
| 608 | 1 | equemene | $ ( D( IIP1 )-D( IIM1 ) )*( D( IIM1 )+D( IIP1 ) )*TEMP1 |
| 609 | 1 | equemene | IF( DPHI.LT.TEMP1 ) THEN |
| 610 | 1 | equemene | ZZ( 1 ) = DTIIM*DTIIM*DPSI |
| 611 | 1 | equemene | ELSE |
| 612 | 1 | equemene | ZZ( 1 ) = DTIIM*DTIIM*( DPSI+( DPHI-TEMP1 ) ) |
| 613 | 1 | equemene | END IF |
| 614 | 1 | equemene | ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) |
| 615 | 1 | equemene | END IF |
| 616 | 1 | equemene | ZZ( 2 ) = Z( II )*Z( II ) |
| 617 | 1 | equemene | DD( 1 ) = DTIIM |
| 618 | 1 | equemene | DD( 2 ) = DELTA( II )*WORK( II ) |
| 619 | 1 | equemene | DD( 3 ) = DTIIP |
| 620 | 1 | equemene | CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO ) |
| 621 | 1 | equemene | IF( INFO.NE.0 ) |
| 622 | 1 | equemene | $ GO TO 240 |
| 623 | 1 | equemene | END IF |
| 624 | 1 | equemene | * |
| 625 | 1 | equemene | * Note, eta should be positive if w is negative, and |
| 626 | 1 | equemene | * eta should be negative otherwise. However, |
| 627 | 1 | equemene | * if for some reason caused by roundoff, eta*w > 0, |
| 628 | 1 | equemene | * we simply use one Newton step instead. This way |
| 629 | 1 | equemene | * will guarantee eta*w < 0. |
| 630 | 1 | equemene | * |
| 631 | 1 | equemene | IF( W*ETA.GE.ZERO ) |
| 632 | 1 | equemene | $ ETA = -W / DW |
| 633 | 1 | equemene | IF( ORGATI ) THEN |
| 634 | 1 | equemene | TEMP1 = WORK( I )*DELTA( I ) |
| 635 | 1 | equemene | TEMP = ETA - TEMP1 |
| 636 | 1 | equemene | ELSE |
| 637 | 1 | equemene | TEMP1 = WORK( IP1 )*DELTA( IP1 ) |
| 638 | 1 | equemene | TEMP = ETA - TEMP1 |
| 639 | 1 | equemene | END IF |
| 640 | 1 | equemene | IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN |
| 641 | 1 | equemene | IF( W.LT.ZERO ) THEN |
| 642 | 1 | equemene | ETA = ( SG2UB-TAU ) / TWO |
| 643 | 1 | equemene | ELSE |
| 644 | 1 | equemene | ETA = ( SG2LB-TAU ) / TWO |
| 645 | 1 | equemene | END IF |
| 646 | 1 | equemene | END IF |
| 647 | 1 | equemene | * |
| 648 | 1 | equemene | TAU = TAU + ETA |
| 649 | 1 | equemene | ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) ) |
| 650 | 1 | equemene | * |
| 651 | 1 | equemene | PREW = W |
| 652 | 1 | equemene | * |
| 653 | 1 | equemene | SIGMA = SIGMA + ETA |
| 654 | 1 | equemene | DO 170 J = 1, N |
| 655 | 1 | equemene | WORK( J ) = WORK( J ) + ETA |
| 656 | 1 | equemene | DELTA( J ) = DELTA( J ) - ETA |
| 657 | 1 | equemene | 170 CONTINUE |
| 658 | 1 | equemene | * |
| 659 | 1 | equemene | * Evaluate PSI and the derivative DPSI |
| 660 | 1 | equemene | * |
| 661 | 1 | equemene | DPSI = ZERO |
| 662 | 1 | equemene | PSI = ZERO |
| 663 | 1 | equemene | ERRETM = ZERO |
| 664 | 1 | equemene | DO 180 J = 1, IIM1 |
| 665 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 666 | 1 | equemene | PSI = PSI + Z( J )*TEMP |
| 667 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 668 | 1 | equemene | ERRETM = ERRETM + PSI |
| 669 | 1 | equemene | 180 CONTINUE |
| 670 | 1 | equemene | ERRETM = ABS( ERRETM ) |
| 671 | 1 | equemene | * |
| 672 | 1 | equemene | * Evaluate PHI and the derivative DPHI |
| 673 | 1 | equemene | * |
| 674 | 1 | equemene | DPHI = ZERO |
| 675 | 1 | equemene | PHI = ZERO |
| 676 | 1 | equemene | DO 190 J = N, IIP1, -1 |
| 677 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 678 | 1 | equemene | PHI = PHI + Z( J )*TEMP |
| 679 | 1 | equemene | DPHI = DPHI + TEMP*TEMP |
| 680 | 1 | equemene | ERRETM = ERRETM + PHI |
| 681 | 1 | equemene | 190 CONTINUE |
| 682 | 1 | equemene | * |
| 683 | 1 | equemene | TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) |
| 684 | 1 | equemene | DW = DPSI + DPHI + TEMP*TEMP |
| 685 | 1 | equemene | TEMP = Z( II )*TEMP |
| 686 | 1 | equemene | W = RHOINV + PHI + PSI + TEMP |
| 687 | 1 | equemene | ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + |
| 688 | 1 | equemene | $ THREE*ABS( TEMP ) + ABS( TAU )*DW |
| 689 | 1 | equemene | * |
| 690 | 1 | equemene | IF( W.LE.ZERO ) THEN |
| 691 | 1 | equemene | SG2LB = MAX( SG2LB, TAU ) |
| 692 | 1 | equemene | ELSE |
| 693 | 1 | equemene | SG2UB = MIN( SG2UB, TAU ) |
| 694 | 1 | equemene | END IF |
| 695 | 1 | equemene | * |
| 696 | 1 | equemene | SWTCH = .FALSE. |
| 697 | 1 | equemene | IF( ORGATI ) THEN |
| 698 | 1 | equemene | IF( -W.GT.ABS( PREW ) / TEN ) |
| 699 | 1 | equemene | $ SWTCH = .TRUE. |
| 700 | 1 | equemene | ELSE |
| 701 | 1 | equemene | IF( W.GT.ABS( PREW ) / TEN ) |
| 702 | 1 | equemene | $ SWTCH = .TRUE. |
| 703 | 1 | equemene | END IF |
| 704 | 1 | equemene | * |
| 705 | 1 | equemene | * Main loop to update the values of the array DELTA and WORK |
| 706 | 1 | equemene | * |
| 707 | 1 | equemene | ITER = NITER + 1 |
| 708 | 1 | equemene | * |
| 709 | 1 | equemene | DO 230 NITER = ITER, MAXIT |
| 710 | 1 | equemene | * |
| 711 | 1 | equemene | * Test for convergence |
| 712 | 1 | equemene | * |
| 713 | 1 | equemene | IF( ABS( W ).LE.EPS*ERRETM ) THEN |
| 714 | 1 | equemene | GO TO 240 |
| 715 | 1 | equemene | END IF |
| 716 | 1 | equemene | * |
| 717 | 1 | equemene | * Calculate the new step |
| 718 | 1 | equemene | * |
| 719 | 1 | equemene | IF( .NOT.SWTCH3 ) THEN |
| 720 | 1 | equemene | DTIPSQ = WORK( IP1 )*DELTA( IP1 ) |
| 721 | 1 | equemene | DTISQ = WORK( I )*DELTA( I ) |
| 722 | 1 | equemene | IF( .NOT.SWTCH ) THEN |
| 723 | 1 | equemene | IF( ORGATI ) THEN |
| 724 | 1 | equemene | C = W - DTIPSQ*DW + DELSQ*( Z( I ) / DTISQ )**2 |
| 725 | 1 | equemene | ELSE |
| 726 | 1 | equemene | C = W - DTISQ*DW - DELSQ*( Z( IP1 ) / DTIPSQ )**2 |
| 727 | 1 | equemene | END IF |
| 728 | 1 | equemene | ELSE |
| 729 | 1 | equemene | TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) |
| 730 | 1 | equemene | IF( ORGATI ) THEN |
| 731 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 732 | 1 | equemene | ELSE |
| 733 | 1 | equemene | DPHI = DPHI + TEMP*TEMP |
| 734 | 1 | equemene | END IF |
| 735 | 1 | equemene | C = W - DTISQ*DPSI - DTIPSQ*DPHI |
| 736 | 1 | equemene | END IF |
| 737 | 1 | equemene | A = ( DTIPSQ+DTISQ )*W - DTIPSQ*DTISQ*DW |
| 738 | 1 | equemene | B = DTIPSQ*DTISQ*W |
| 739 | 1 | equemene | IF( C.EQ.ZERO ) THEN |
| 740 | 1 | equemene | IF( A.EQ.ZERO ) THEN |
| 741 | 1 | equemene | IF( .NOT.SWTCH ) THEN |
| 742 | 1 | equemene | IF( ORGATI ) THEN |
| 743 | 1 | equemene | A = Z( I )*Z( I ) + DTIPSQ*DTIPSQ* |
| 744 | 1 | equemene | $ ( DPSI+DPHI ) |
| 745 | 1 | equemene | ELSE |
| 746 | 1 | equemene | A = Z( IP1 )*Z( IP1 ) + |
| 747 | 1 | equemene | $ DTISQ*DTISQ*( DPSI+DPHI ) |
| 748 | 1 | equemene | END IF |
| 749 | 1 | equemene | ELSE |
| 750 | 1 | equemene | A = DTISQ*DTISQ*DPSI + DTIPSQ*DTIPSQ*DPHI |
| 751 | 1 | equemene | END IF |
| 752 | 1 | equemene | END IF |
| 753 | 1 | equemene | ETA = B / A |
| 754 | 1 | equemene | ELSE IF( A.LE.ZERO ) THEN |
| 755 | 1 | equemene | ETA = ( A-SQRT( ABS( A*A-FOUR*B*C ) ) ) / ( TWO*C ) |
| 756 | 1 | equemene | ELSE |
| 757 | 1 | equemene | ETA = TWO*B / ( A+SQRT( ABS( A*A-FOUR*B*C ) ) ) |
| 758 | 1 | equemene | END IF |
| 759 | 1 | equemene | ELSE |
| 760 | 1 | equemene | * |
| 761 | 1 | equemene | * Interpolation using THREE most relevant poles |
| 762 | 1 | equemene | * |
| 763 | 1 | equemene | DTIIM = WORK( IIM1 )*DELTA( IIM1 ) |
| 764 | 1 | equemene | DTIIP = WORK( IIP1 )*DELTA( IIP1 ) |
| 765 | 1 | equemene | TEMP = RHOINV + PSI + PHI |
| 766 | 1 | equemene | IF( SWTCH ) THEN |
| 767 | 1 | equemene | C = TEMP - DTIIM*DPSI - DTIIP*DPHI |
| 768 | 1 | equemene | ZZ( 1 ) = DTIIM*DTIIM*DPSI |
| 769 | 1 | equemene | ZZ( 3 ) = DTIIP*DTIIP*DPHI |
| 770 | 1 | equemene | ELSE |
| 771 | 1 | equemene | IF( ORGATI ) THEN |
| 772 | 1 | equemene | TEMP1 = Z( IIM1 ) / DTIIM |
| 773 | 1 | equemene | TEMP1 = TEMP1*TEMP1 |
| 774 | 1 | equemene | TEMP2 = ( D( IIM1 )-D( IIP1 ) )* |
| 775 | 1 | equemene | $ ( D( IIM1 )+D( IIP1 ) )*TEMP1 |
| 776 | 1 | equemene | C = TEMP - DTIIP*( DPSI+DPHI ) - TEMP2 |
| 777 | 1 | equemene | ZZ( 1 ) = Z( IIM1 )*Z( IIM1 ) |
| 778 | 1 | equemene | IF( DPSI.LT.TEMP1 ) THEN |
| 779 | 1 | equemene | ZZ( 3 ) = DTIIP*DTIIP*DPHI |
| 780 | 1 | equemene | ELSE |
| 781 | 1 | equemene | ZZ( 3 ) = DTIIP*DTIIP*( ( DPSI-TEMP1 )+DPHI ) |
| 782 | 1 | equemene | END IF |
| 783 | 1 | equemene | ELSE |
| 784 | 1 | equemene | TEMP1 = Z( IIP1 ) / DTIIP |
| 785 | 1 | equemene | TEMP1 = TEMP1*TEMP1 |
| 786 | 1 | equemene | TEMP2 = ( D( IIP1 )-D( IIM1 ) )* |
| 787 | 1 | equemene | $ ( D( IIM1 )+D( IIP1 ) )*TEMP1 |
| 788 | 1 | equemene | C = TEMP - DTIIM*( DPSI+DPHI ) - TEMP2 |
| 789 | 1 | equemene | IF( DPHI.LT.TEMP1 ) THEN |
| 790 | 1 | equemene | ZZ( 1 ) = DTIIM*DTIIM*DPSI |
| 791 | 1 | equemene | ELSE |
| 792 | 1 | equemene | ZZ( 1 ) = DTIIM*DTIIM*( DPSI+( DPHI-TEMP1 ) ) |
| 793 | 1 | equemene | END IF |
| 794 | 1 | equemene | ZZ( 3 ) = Z( IIP1 )*Z( IIP1 ) |
| 795 | 1 | equemene | END IF |
| 796 | 1 | equemene | END IF |
| 797 | 1 | equemene | DD( 1 ) = DTIIM |
| 798 | 1 | equemene | DD( 2 ) = DELTA( II )*WORK( II ) |
| 799 | 1 | equemene | DD( 3 ) = DTIIP |
| 800 | 1 | equemene | CALL DLAED6( NITER, ORGATI, C, DD, ZZ, W, ETA, INFO ) |
| 801 | 1 | equemene | IF( INFO.NE.0 ) |
| 802 | 1 | equemene | $ GO TO 240 |
| 803 | 1 | equemene | END IF |
| 804 | 1 | equemene | * |
| 805 | 1 | equemene | * Note, eta should be positive if w is negative, and |
| 806 | 1 | equemene | * eta should be negative otherwise. However, |
| 807 | 1 | equemene | * if for some reason caused by roundoff, eta*w > 0, |
| 808 | 1 | equemene | * we simply use one Newton step instead. This way |
| 809 | 1 | equemene | * will guarantee eta*w < 0. |
| 810 | 1 | equemene | * |
| 811 | 1 | equemene | IF( W*ETA.GE.ZERO ) |
| 812 | 1 | equemene | $ ETA = -W / DW |
| 813 | 1 | equemene | IF( ORGATI ) THEN |
| 814 | 1 | equemene | TEMP1 = WORK( I )*DELTA( I ) |
| 815 | 1 | equemene | TEMP = ETA - TEMP1 |
| 816 | 1 | equemene | ELSE |
| 817 | 1 | equemene | TEMP1 = WORK( IP1 )*DELTA( IP1 ) |
| 818 | 1 | equemene | TEMP = ETA - TEMP1 |
| 819 | 1 | equemene | END IF |
| 820 | 1 | equemene | IF( TEMP.GT.SG2UB .OR. TEMP.LT.SG2LB ) THEN |
| 821 | 1 | equemene | IF( W.LT.ZERO ) THEN |
| 822 | 1 | equemene | ETA = ( SG2UB-TAU ) / TWO |
| 823 | 1 | equemene | ELSE |
| 824 | 1 | equemene | ETA = ( SG2LB-TAU ) / TWO |
| 825 | 1 | equemene | END IF |
| 826 | 1 | equemene | END IF |
| 827 | 1 | equemene | * |
| 828 | 1 | equemene | TAU = TAU + ETA |
| 829 | 1 | equemene | ETA = ETA / ( SIGMA+SQRT( SIGMA*SIGMA+ETA ) ) |
| 830 | 1 | equemene | * |
| 831 | 1 | equemene | SIGMA = SIGMA + ETA |
| 832 | 1 | equemene | DO 200 J = 1, N |
| 833 | 1 | equemene | WORK( J ) = WORK( J ) + ETA |
| 834 | 1 | equemene | DELTA( J ) = DELTA( J ) - ETA |
| 835 | 1 | equemene | 200 CONTINUE |
| 836 | 1 | equemene | * |
| 837 | 1 | equemene | PREW = W |
| 838 | 1 | equemene | * |
| 839 | 1 | equemene | * Evaluate PSI and the derivative DPSI |
| 840 | 1 | equemene | * |
| 841 | 1 | equemene | DPSI = ZERO |
| 842 | 1 | equemene | PSI = ZERO |
| 843 | 1 | equemene | ERRETM = ZERO |
| 844 | 1 | equemene | DO 210 J = 1, IIM1 |
| 845 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 846 | 1 | equemene | PSI = PSI + Z( J )*TEMP |
| 847 | 1 | equemene | DPSI = DPSI + TEMP*TEMP |
| 848 | 1 | equemene | ERRETM = ERRETM + PSI |
| 849 | 1 | equemene | 210 CONTINUE |
| 850 | 1 | equemene | ERRETM = ABS( ERRETM ) |
| 851 | 1 | equemene | * |
| 852 | 1 | equemene | * Evaluate PHI and the derivative DPHI |
| 853 | 1 | equemene | * |
| 854 | 1 | equemene | DPHI = ZERO |
| 855 | 1 | equemene | PHI = ZERO |
| 856 | 1 | equemene | DO 220 J = N, IIP1, -1 |
| 857 | 1 | equemene | TEMP = Z( J ) / ( WORK( J )*DELTA( J ) ) |
| 858 | 1 | equemene | PHI = PHI + Z( J )*TEMP |
| 859 | 1 | equemene | DPHI = DPHI + TEMP*TEMP |
| 860 | 1 | equemene | ERRETM = ERRETM + PHI |
| 861 | 1 | equemene | 220 CONTINUE |
| 862 | 1 | equemene | * |
| 863 | 1 | equemene | TEMP = Z( II ) / ( WORK( II )*DELTA( II ) ) |
| 864 | 1 | equemene | DW = DPSI + DPHI + TEMP*TEMP |
| 865 | 1 | equemene | TEMP = Z( II )*TEMP |
| 866 | 1 | equemene | W = RHOINV + PHI + PSI + TEMP |
| 867 | 1 | equemene | ERRETM = EIGHT*( PHI-PSI ) + ERRETM + TWO*RHOINV + |
| 868 | 1 | equemene | $ THREE*ABS( TEMP ) + ABS( TAU )*DW |
| 869 | 1 | equemene | IF( W*PREW.GT.ZERO .AND. ABS( W ).GT.ABS( PREW ) / TEN ) |
| 870 | 1 | equemene | $ SWTCH = .NOT.SWTCH |
| 871 | 1 | equemene | * |
| 872 | 1 | equemene | IF( W.LE.ZERO ) THEN |
| 873 | 1 | equemene | SG2LB = MAX( SG2LB, TAU ) |
| 874 | 1 | equemene | ELSE |
| 875 | 1 | equemene | SG2UB = MIN( SG2UB, TAU ) |
| 876 | 1 | equemene | END IF |
| 877 | 1 | equemene | * |
| 878 | 1 | equemene | 230 CONTINUE |
| 879 | 1 | equemene | * |
| 880 | 1 | equemene | * Return with INFO = 1, NITER = MAXIT and not converged |
| 881 | 1 | equemene | * |
| 882 | 1 | equemene | INFO = 1 |
| 883 | 1 | equemene | * |
| 884 | 1 | equemene | END IF |
| 885 | 1 | equemene | * |
| 886 | 1 | equemene | 240 CONTINUE |
| 887 | 1 | equemene | RETURN |
| 888 | 1 | equemene | * |
| 889 | 1 | equemene | * End of DLASD4 |
| 890 | 1 | equemene | * |
| 891 | 1 | equemene | END |