1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557
|
*=======================================================================
* Copyright (C) 1999,2001,2002,2003
* Associated Universities, Inc. Washington DC, USA.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Library General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Library General Public License for more details.
*
* You should have received a copy of the GNU Library General Public
* License along with this library; if not, write to the Free
* Software Foundation, Inc., 675 Massachusetts Ave, Cambridge,
* MA 02139, USA.
*
* Correspondence concerning AIPS++ should be addressed as follows:
* Internet email: aips2-request@nrao.edu.
* Postal address: AIPS++ Project Office
* National Radio Astronomy Observatory
* 520 Edgemont Road
* Charlottesville, VA 22903-2475 USA
*
* $Id$
*-------------------------------------------------------------------------
C
C Routines for polynomial and spline fitting, using the global
C baseline data to get antenna based coefficients
C Written by R.Lucas for IRAM gildas.
C
SUBROUTINE POLYANT(IY, M, NBAS, IANT, JANT, IREF,
$ KPLUS1, NANT, X, Y, W,
$ WK1, WK2, WK3, SS, C)
C------------------------------------------------------------------------
C polyant computes a weighted least-squares polynimial approximation
C to the antenna amplitudes or phases
c for an arbitrary set of baseline data points.
c parameters:
C iy I Input 1 for log(amplitude), 2 for phase
c m I Input the number of data points for each baseline
c nbas I Input the number of baselines
c iant(nbas) I Input start antenna for each baseline
c jant(nbas) I Input end antenna for each baseline
c iref i Input Reference antenna for phases
c kplus1 I Input degree of polynomials + 1
c nant I Input the number of antennas
c x(m) R8 Input the data abscissae
c y(m,nbas) R8 Input the data values
c w(m,mbas) R8 Input weights
c wk1(kplus1) R8 Output work space
c wk2(kplus1**2*nant**2)
c R8 Output work space
c wk3(kplus1*nant)
c R8 Output work space
c ss(nbas) R8 Output rms of fit for each baseline
c c(nant,kplus1) R8 Output the polynomial coefficients
c
C------------------------------------------------------------------------
* Dummy
INTEGER M, KPLUS1, NANT, NBAS, IANT(NBAS), JANT(NBAS), IY, IREF
REAL*8 C(NANT,KPLUS1), W(M,NBAS),
$WK2(KPLUS1*NANT,KPLUS1*NANT), WK3(KPLUS1*NANT),
$WK1(KPLUS1), X(M), Y(M,NBAS), SS(NBAS), NORM, TOL
LOGICAL ERROR
*
PARAMETER (TOL=1D-14)
c-------------------------------------------------------
* PI is defined with more digits than necessary to avoid losing
* the last few bits in the decimal to binary conversion
REAL*8 PI
PARAMETER (PI=3.14159265358979323846D0)
REAL*4 PIS
PARAMETER (PIS=3.141592653)
* Relative precision of REAL*4
REAL*4 EPSR4
PARAMETER (EPSR4=1E-7)
REAL*4 MAXR4
PARAMETER (MAXR4=1E38)
* Maximum acceptable integer
INTEGER MAX_INTEG
PARAMETER (MAX_INTEG=2147483647)
C-------------------------------------------------
* Local
INTEGER ZANT, I, IA, IB, NANTM1, J,
$JA, IC, IL, KN, KP, K, L, ITER, INFO
REAL*8 WI, XI, WN, WW, WWW, TEST, YI, XCAP, X1, XN, D, WSS(4000)
C------------------------------------------------------------------------
C Code
c
c Check that the weights are positive.
c
ERROR=.FALSE.
DO I=1,M
DO IB = 1, NBAS
IF (W(I,IB).LT.0.0D0) THEN
C CALL MESSAGE(6,4,'POLYANT','Weights not positive')
write(*,*)'POLYANT: Weights not positive'
ERROR = .TRUE.
RETURN
ENDIF
ENDDO
ENDDO
X1 = X(1)
XN = X(M)
D = XN-X1
c
* Amplitude case is simple...
c
IF (IY.EQ.1) THEN
DO I=1,NANT*KPLUS1
DO L=1,NANT*KPLUS1
WK2(L,I) = 0.0D0
ENDDO
WK3(I) = 0.0D0
ENDDO
DO I=1, M
XI = X(I)
XCAP = ((XI-X1)-(XN-XI))/D
* compute the chebychev polynomials at point xi.
CALL CHEB (KPLUS1, XCAP, WK1, ERROR)
IF (ERROR) GOTO 999
*
c store the upper-triangular part of the normal equations in wk2
c and the right-hand side in wk3.
c
DO K=1, KPLUS1
WN = WK1(K)
IL = (K-1)*NANT
DO KP = 1, KPLUS1
WW = WN*WK1(KP)
IC = (KP-1)*NANT
DO IB=1,NBAS
WI = W(I,IB)
IF (WI.GT.0) THEN
IA = IANT(IB)
JA = JANT(IB)
WWW = WI*WW
WK2(IL+IA,IC+IA) = WK2(IL+IA,IC+IA)+WWW
WK2(IL+IA,IC+JA) = WK2(IL+IA,IC+JA)+WWW
WK2(IL+JA,IC+IA) = WK2(IL+JA,IC+IA)+WWW
WK2(IL+JA,IC+JA) = WK2(IL+JA,IC+JA)+WWW
ENDIF
ENDDO
ENDDO
DO IB=1, NBAS
IA = IANT(IB)
JA = JANT(IB)
WI = W(I,IB)*WN*Y(I,IB)
* wi = w(i,ib)*wn*xcap*(ja+ia) !**!
WK3(IL+IA) = WK3(IL+IA) + WI
WK3(IL+JA) = WK3(IL+JA) + WI
ENDDO
ENDDO
ENDDO
C
C Solve the system of normal equations by first computing the Cholesky
c factorization
*
CALL MTH_DPOTRF ('POLYANT',
$ 'U',KPLUS1*NANT,WK2,KPLUS1*NANT,INFO)
IF (ERROR) GOTO 999
CALL MTH_DPOTRS ('POLYANT',
$ 'U',KPLUS1*NANT,1,WK2,KPLUS1*NANT,
$ WK3,KPLUS1*NANT,INFO)
IF (ERROR) GOTO 999
DO J=1,KPLUS1
DO I=1,NANT
C(I,J) = WK3(I+(J-1)*NANT)
ENDDO
ENDDO
*
* Phase is more complicated ...
ELSEIF (IY.EQ.2) THEN
NANTM1 = NANT-1
DO I=1,NANT
DO J=1,KPLUS1
C(I,J) = 0.0D0
ENDDO
ENDDO
*
* start iterating
NORM = 1E10
ITER = 0
DO WHILE (NORM.GT.TOL .AND. ITER.LT.100)
ITER = ITER + 1
DO I=1,NANTM1*KPLUS1
DO L=1,NANTM1*KPLUS1
WK2(L,I) = 0.0D0
ENDDO
WK3(I) = 0.0D0
ENDDO
DO I=1, M
XI = X(I)
XCAP = ((XI-X1)-(XN-XI))/D
* compute the chebychev polynomials at point xi.
CALL CHEB (KPLUS1, XCAP, WK1, ERROR)
IF (ERROR) GOTO 999
*
DO K=1, KPLUS1
WN = WK1(K)
IL = (K-1)*NANTM1
DO KP = 1, KPLUS1
WW = WN*WK1(KP)
IC = (KP-1)*NANTM1
DO IB=1,NBAS
WI = W(I,IB)
IF (WI.GT.0) THEN
IA = ZANT(IANT(IB),IREF)
JA = ZANT(JANT(IB),IREF)
WWW = WI*WW
IF (IA.NE.0) THEN
WK2(IL+IA,IC+IA) = WK2(IL+IA,IC+IA)+WWW
ENDIF
IF (JA.NE.0) THEN
WK2(IL+JA,IC+JA) = WK2(IL+JA,IC+JA)+WWW
ENDIF
IF (IA.NE.0 .AND. JA.NE.0) THEN
WK2(IL+JA,IC+IA) = WK2(IL+JA,IC+IA)-WWW
WK2(IL+IA,IC+JA) = WK2(IL+IA,IC+JA)-WWW
ENDIF
ENDIF
ENDDO
ENDDO
DO IB=1, NBAS
IF (W(I,IB).GT.0) THEN
YI = Y(I,IB)
IA = IANT(IB)
JA = JANT(IB)
DO KP=1, KPLUS1
YI = YI+(C(IA,KP)-C(JA,KP))*WK1(KP)
ENDDO
* yi = xcap*(ja-ia) !**!
ELSE
YI = 0
ENDIF
* if (norm.lt.1e9) then
YI = SIN(YI)
* endif
IA = ZANT(IANT(IB),IREF)
JA = ZANT(JANT(IB),IREF)
WI = W(I,IB)*WN*YI
IF (IA.NE.0) THEN
WK3(IA+IL) = WK3(IA+IL) - WI
ENDIF
IF (JA.NE.0) THEN
WK3(JA+IL) = WK3(JA+IL) + WI
ENDIF
ENDDO
ENDDO
ENDDO
C Solve the system of normal equations by first computing the Cholesky
c factorization
CALL MTH_DPOTRF('POLYANT',
$ 'U',KPLUS1*NANTM1,WK2,KPLUS1*NANT,INFO)
IF (ERROR) GOTO 999
CALL MTH_DPOTRS ('POLYANT',
$ 'U',KPLUS1*NANTM1,1,WK2,KPLUS1*NANT,
$ WK3,KPLUS1*NANTM1,INFO)
IF (ERROR) GOTO 999
*
* Add the result to c:
NORM = 0
DO J=1,KPLUS1
DO IA=1,NANT
I = ZANT(IA,IREF)
IF (I.NE.0) THEN
WW = WK3(I+(J-1)*NANTM1)
C(IA,J) = C(IA,J)+WW
NORM = NORM+WW**2
ENDIF
ENDDO
ENDDO
ENDDO
ENDIF
c
c loop over data points to get rms
DO IB=1, NBAS
SS(IB) = 0
WSS(IB) = 0
ENDDO
DO I = 1, M
XI = X(I)
XCAP = ((XI-X1)-(XN-XI))/D
CALL CHEB (KPLUS1, XCAP, WK1, ERROR)
IF (ERROR) GOTO 999
DO IB=1,NBAS
IF (W(I,IB).GT.0) THEN
IA = IANT(IB)
JA = JANT(IB)
TEST = 0
DO KN = 1, KPLUS1
WN = WK1(KN)
IF (IY.EQ.1) THEN
TEST = TEST+(C(IA,KN)+C(JA,KN))*WN
ELSE
TEST = TEST+(-C(IA,KN)+C(JA,KN))*WN
ENDIF
ENDDO
TEST = Y(I,IB)-TEST
IF (IY.EQ.2) TEST = MOD(TEST+11*PI,2*PI)-PI
SS(IB) = SS(IB)+W(I,IB)*TEST**2
WSS(IB) = WSS(IB)+W(I,IB)
ENDIF
ENDDO
ENDDO
DO IB=1, NBAS
IF (WSS(IB).NE.0) THEN
SS(IB) = SQRT(SS(IB)/WSS(IB))
ELSE
SS(IB) = 0
ENDIF
ENDDO
RETURN
999 ERROR = .TRUE.
RETURN
END
*<FF>
SUBROUTINE CHEB(NPLUS1, XCAP, P, ERROR)
C
C Compute nplus1 Che+bishev Polynomials at x = xcap
C
LOGICAL ERROR
INTEGER NPLUS1
REAL*8 XCAP, P(NPLUS1)
*
REAL*8 BK, BKP1, BKP2, DK, ETA, FACTOR
INTEGER N, K
*
c
c eta is the smallest positive number such that
c the computed value of 1.0 + eta exceeds unity.
c with NAG, ETA = X02AAF(1.0D0)
DATA ETA/1.110223024625156D-16/
*
ERROR=.FALSE.
IF (NPLUS1.LT.1) THEN
WRITE(*,*) 'F-CHEB, nplus1.lt.1'
ERROR = .TRUE.
RETURN
ENDIF
IF (DABS(XCAP).GT.1.0D0+4.0D0*ETA) THEN
WRITE(*,*) 'F-CHEB, abs(xcap).gt.1'
ENDIF
P(1) = 0.5D0
IF (NPLUS1.LE.1) RETURN
N = NPLUS1 - 1
K = N + 2
IF (XCAP.LT.-0.5D0) THEN
c
c Gentleman*s modified recurrence.
FACTOR = 2.0D0*(1.0D0+XCAP)
DK = -1.0D0
BK = 0.0D0
DO K=1,N
DK = - DK + FACTOR*BK
BK = DK - BK
P(K+1) = - DK + 0.5D0*FACTOR*BK
ENDDO
ELSEIF (XCAP.LE.0.5D0) THEN
c
c Clenshaw*s original recurrence.
c
FACTOR = 2.0D0*XCAP
BKP1 = 0.0D0
BKP2 = -1.0D0
DO K=1,N
BK = - BKP2 + FACTOR*BKP1
P(K+1) = - BKP1 + 0.5D0*FACTOR*BK
BKP2 = BKP1
BKP1 = BK
ENDDO
ELSE
c
c Reinsch*s modified recurrence.
c
FACTOR = 2.0D0*(1.0D0-XCAP)
DK = 1.0D0
BK = 0.0D0
DO K=1,N
DK = DK - FACTOR*BK
BK = BK + DK
P(K+1) = DK - 0.5D0*FACTOR*BK
ENDDO
ENDIF
P(1) = 0.5D0
RETURN
END
* Linear Algebra: use LAPACK routines
*<FF>
SUBROUTINE MTH_DPOTRF (NAME, UPLO, N, A, LDA, INFO)
CHARACTER*(*) NAME, UPLO
INTEGER INFO, LDA, N
REAL*8 A( LDA, * )
LOGICAL ERROR
*
* Purpose
* =======
*
* DPOTRF computes the Cholesky factorization of a real symmetric
* positive definite matrix A.
*
* The factorization has the form
* A = U**T * U, if UPLO = 'U', or
* A = L * L**T, if UPLO = 'L',
* where U is an upper triangular matrix and L is lower triangular.
*
* This is the block version of the algorithm, calling Level 3 BLAS.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the symmetric matrix A. If UPLO = 'U', the leading
* N-by-N upper triangular part of A contains the upper
* triangular part of the matrix A, and the strictly lower
* triangular part of A is not referenced. If UPLO = 'L', the
* leading N-by-N lower triangular part of A contains the lower
* triangular part of the matrix A, and the strictly upper
* triangular part of A is not referenced.
*
* On exit, if INFO = 0, the factor U or L from the Cholesky
* factorization A = U**T*U or A = L*L**T.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, the leading minor of order i is not
* positive definite, and the factorization could not be
* completed.
*
*
* Call LAPACK routine
CALL DPOTRF (UPLO, N, A, LDA, INFO )
C CALL MTH_FAIL(NAME,'MTH_DPOTRF',INFO,ERROR)
END
SUBROUTINE MTH_DPOTRS (NAME,
$UPLO, N, NRHS, A, LDA, B, LDB, INFO )
CHARACTER*(*) UPLO, NAME
INTEGER INFO, LDA, LDB, N, NRHS
REAL*8 A( LDA, * ), B( LDB, * )
LOGICAL ERROR
*
* Purpose
* =======
*
* DPOTRS solves a system of linear equations A*X = B with a symmetric
* positive definite matrix A using the Cholesky factorization
* A = U**T*U or A = L*L**T computed by DPOTRF.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* A (input) DOUBLE PRECISION array, dimension (LDA,N)
* The triangular factor U or L from the Cholesky factorization
* A = U**T*U or A = L*L**T, as computed by DPOTRF.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the right hand side matrix B.
* On exit, the solution matrix X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Call LAPACK routine
CALL DPOTRS (UPLO, N, NRHS, A, LDA, B, LDB, INFO )
C CALL MTH_FAIL(NAME,'MTH_DPOTRF',INFO,ERROR)
END
FUNCTION ZANT(I,R)
INTEGER I, R, ZANT
IF (I.EQ.R) THEN
ZANT = 0
ELSEIF (I.GT.R) THEN
ZANT = I-1
ELSE
ZANT = I
ENDIF
RETURN
END
SUBROUTINE SPLINANT(IY, M, NBAS, IANT, JANT, IREF,
$NCAP7, NANT, X, Y, W,
$K, WK1, WK2, WK3, SS, C)
C------------------------------------------------------------------------
C splinant computes a weighted least-squares approximation
c to an arbitrary set of data points, either amplitude or phase.
c with knots prescribed by the user.
c parameters:
C iy I Input 1 for log(amplitude), 2 for phase
c m I Input the number of data points for each baseline
c nbas I Input the number of baselines
c iant(nbas) I Input start antenna for each baseline
c jant(nbas) I Input end antenna for each baseline
c iref i Input Reference antenna for phases
c ncap7 I Input number of knots for splines (see e02baf)
c nant I Input the number of antennas
c X(m) R8 Input the data abscissae
c Y(m,nbas) R8 Input the data values
c W(m,mbas) R8 Input weights
c k(ncap7) R8 Input knots for the splines (inners + 4 at each end)
c wk1(4,m) R8 Output wk space
c wk2(4*nant,ncap7*nant)
c R8 Output work space
c wk3(ncap7*nant)
c R8 Output work space
c ss(nbas) R8 Output rms of fit for each baseline
c c(nant,ncap7) R8 Output the spline coefficients (ncap3 values)
c
C------------------------------------------------------------------------
* Dummy
INTEGER M, NCAP7, NANT, NBAS, IANT(NBAS), JANT(NBAS), IY, IREF
REAL*8 C(NANT,NCAP7), K(NCAP7), W(M,NBAS), WK1(4,M),
$WK2(4*NANT,NCAP7*NANT), WK3(NCAP7*NANT),
$X(M), Y(M,NBAS), SS(NBAS),
$NORM, TOL
LOGICAL ERROR
PARAMETER (TOL=1E-14)
INTEGER ZANT
c-------------------------------------------------------
REAL*8 PI
PARAMETER (PI=3.14159265358979323846D0)
REAL*4 PIS
PARAMETER (PIS=3.141592653)
* Relative precision of REAL*4
REAL*4 EPSR4
PARAMETER (EPSR4=1E-7)
REAL*4 MAXR4
PARAMETER (MAXR4=1E38)
* Maximum acceptable integer
INTEGER MAX_INTEG
PARAMETER (MAX_INTEG=2147483647)
C-------------------------------------------------
* Local
INTEGER I, IA, IB, JJ, NANTM1, ITER, JA, IBD, ICOL, NBD,
$KN, KP, J, JOLD, L, NCAP3, NCAP, NCAPM1
REAL*8 D4, D5, D6, D7, D8, D9, E2, E3, E4, E5, K1, K2, K3,
$K4, K5, K6, N1, N2, N3, WI, XI, WN, WW, WWW, TEST, YI
C------------------------------------------------------------------------
C Code
c
ERROR=.FALSE.
CALL SPLINE_CHECK(M, NCAP7, X, K, WK1, ERROR)
IF (ERROR) RETURN
c
c Check that the weights are (strictly) positive.
c
DO I=1,M
DO IB = 1, NBAS
IF (W(I,IB).LT.0.0D0) THEN
WRITE(*,*)'SPLINANT','Weights not positive'
ERROR = .TRUE.
RETURN
ENDIF
ENDDO
ENDDO
NCAP = NCAP7 - 7
NCAPM1 = NCAP - 1
NCAP3 = NCAP + 3
NBD = 4*NANT
NANTM1 = NANT-1
c
c First loop on data abscissae to compute the spline values in wk1
c
J = 0
JOLD = 0
DO I = 1, M
c
c for the data point (x(i), y(i,ib)) determine an interval
c k(j + 3) .le. x .lt. k(j + 4) containing x(i). (in the
c case j + 4 .eq. ncap the second equality is relaxed to
c include equality).
c
XI = X(I)
DO WHILE (XI.GE.K(J+4) .AND. J.LE.NCAPM1)
J = J + 1
ENDDO
IF (J.NE.JOLD) THEN
c
c set certain constants relating to the interval
c k(j + 3) .le. x .le. k(j + 4)
c (i.e. the jth non vanishing interval)
c
K1 = K(J+1)
K2 = K(J+2)
K3 = K(J+3)
K4 = K(J+4)
K5 = K(J+5)
K6 = K(J+6)
D4 = 1.0D0/(K4-K1)
D5 = 1.0D0/(K5-K2)
D6 = 1.0D0/(K6-K3)
D7 = 1.0D0/(K4-K2)
D8 = 1.0D0/(K5-K3)
D9 = 1.0D0/(K4-K3)
JOLD = J
ENDIF
c
c compute and store in wk1(l,i) (l = 1, 2, 3, 4) the values
c of the four normalized cubic b-splines which are non-zero at
c x=x(i), i.e. the splines of indexes j, j+1, j+2, j+3.
c
E5 = K5 - XI
E4 = K4 - XI
E3 = XI - K3
E2 = XI - K2
N1 = E4*D9*D7
N2 = E3*D9*D8
N3 = E3*N2*D6
N2 = (E2*N1+E5*N2)*D5
N1 = E4*N1*D4
WK1(4,I) = E3*N3
WK1(3,I) = E2*N2 + (K6-XI)*N3
WK1(2,I) = (XI-K1)*N1 + E5*N2
WK1(1,I) = E4*N1
ENDDO
c
* Amplitude case is simple...
c
IF (IY.EQ.1) THEN
NBD = 4*NANT
DO I=1,NANT*NCAP3
DO L=1,NBD
WK2(L,I) = 0.0D0
ENDDO
WK3(I) = 0.0D0
ENDDO
J = 0
DO I=1, M
XI = X(I)
DO WHILE (XI.GE.K(J+4) .AND. J.LE.NCAPM1)
J = J + 1
ENDDO
*
c store the upper-triangular part of the normal equations in wk2
*
* write(*,*) i,j,(wk1(kn,i),kn=1,4)
DO KN=0, 3
WN = WK1(KN+1,I)
DO KP = KN, 3
ICOL = (J+KP-1)*NANT
IBD = NBD-(KP-KN)*NANT
WW = WN*WK1(KP+1,I)
DO IB=1,NBAS
WI = W(I,IB)
IF (WI.GT.0) THEN
IA = IANT(IB)
JA = JANT(IB)
WWW = WI*WW
WK2(IBD,ICOL+IA) = WK2(IBD,ICOL+IA)+WWW
WK2(IBD,ICOL+JA) = WK2(IBD,ICOL+JA)+WWW
WK2(IBD+IA-JA,ICOL+JA) =
$ WK2(IBD+IA-JA,ICOL+JA) + WWW
IF (KP.GT.KN) THEN
WK2(IBD+JA-IA,ICOL+IA) =
$ WK2(IBD+JA-IA,ICOL+IA) + WWW
ENDIF
ENDIF
ENDDO
ENDDO
DO IB=1, NBAS
IA = IANT(IB)
JA = JANT(IB)
WI = W(I,IB)*WN*Y(I,IB)
JJ = (J+KN-1)*NANT
WK3(IA+JJ) = WK3(IA+JJ) + WI
WK3(JA+JJ) = WK3(JA+JJ) + WI
ENDDO
ENDDO
ENDDO
C
C Solve the system of normal equations by first computing the Cholesky
c factorization
CALL MTH_DPBTRF ('SPLINANT',
$ 'U',NCAP3*NANT,NBD-1,WK2,4*NANT,ERROR)
IF (ERROR) RETURN
CALL MTH_DPBTRS ('SPLINANT',
$ 'U',NCAP3*NANT,NBD-1,1,WK2,4*NANT,
$ WK3,NCAP3*NANT,ERROR)
IF (ERROR) RETURN
DO J=1,NCAP3
DO I=1,NANT
C(I,J) = WK3(I+(J-1)*NANT)
ENDDO
ENDDO
* Phase is more complicated ...
ELSEIF (IY.EQ.2) THEN
NBD = 4*NANTM1
DO I=1,NANT
DO J=1,NCAP3
C(I,J) = 0.0D0
ENDDO
ENDDO
* start iterating
NORM = 1E10
ITER = 0
DO WHILE (NORM.GT.TOL .AND. ITER.LT.100)
ITER = ITER+1
DO I=1,NANTM1*NCAP3
DO L=1,NBD
WK2(L,I) = 0.0D0
ENDDO
WK3(I) = 0.0D0
ENDDO
J = 0
I = 0
XI = X(1)
DO I=1, M
XI = X(I)
DO WHILE (XI.GE.K(J+4) .AND. J.LE.NCAPM1)
J = J + 1
ENDDO
*
c store the upper-triangular part of the normal equations in wk2
*
DO KN=0, 3
WN = WK1(KN+1,I)
DO KP = KN, 3
ICOL = (J+KP-1)*NANTM1
IBD = NBD-(KP-KN)*NANTM1
WW = WN*WK1(KP+1,I)
DO IB=1,NBAS
WI = W(I,IB)
IF (WI.GT.0) THEN
WWW = WI*WW
IA = ZANT(IANT(IB),IREF)
JA = ZANT(JANT(IB),IREF)
IF (IA.NE.0) THEN
WK2(IBD,ICOL+IA) = WK2(IBD,ICOL+IA)+WWW
ENDIF
IF (JA.NE.0) THEN
WK2(IBD,ICOL+JA) = WK2(IBD,ICOL+JA)+WWW
ENDIF
IF (IA.NE.0 .AND. JA.NE.0) THEN
WK2(IBD+IA-JA,ICOL+JA) =
$ WK2(IBD+IA-JA,ICOL+JA) - WWW
IF (KP.GT.KN) THEN
WK2(IBD+JA-IA,ICOL+IA) =
$ WK2(IBD+JA-IA,ICOL+IA) - WWW
ENDIF
ENDIF
ENDIF
ENDDO
ENDDO
ENDDO
DO IB=1, NBAS
IF (W(I,IB).GT.0) THEN
IA = IANT(IB)
JA = JANT(IB)
YI = Y(I,IB)
IF (J.LE.NCAP3) THEN
DO KN = 0, 3
WN = WK1(KN+1,I)
IF (J+KN.LE.NCAP3) THEN
YI = YI+C(IA,J+KN)*WN
YI = YI-C(JA,J+KN)*WN
ENDIF
ENDDO
ELSE
YI = 0
ENDIF
IF (NORM.LT.1E9) THEN
YI = SIN(YI)
ENDIF
IA = ZANT(IANT(IB),IREF)
JA = ZANT(JANT(IB),IREF)
DO KN = 0, 3
WN = WK1(KN+1,I)
WI = W(I,IB)*WN*YI
JJ = (J+KN-1)*NANTM1
IF (IA.NE.0) THEN
WK3(IA+JJ) = WK3(IA+JJ) - WI
ENDIF
IF (JA.NE.0) THEN
WK3(JA+JJ) = WK3(JA+JJ) + WI
ENDIF
ENDDO
ENDIF
ENDDO
ENDDO
C
C Solve the system of normal equations by first computing the Cholesky
c factorization
CALL MTH_DPBTRF ('SPLINANT',
$ 'U',NCAP3*NANTM1,NBD-1,WK2,4*NANT,ERROR)
IF (ERROR) RETURN
CALL MTH_DPBTRS ('SPLINANT',
$ 'U',NCAP3*NANTM1,NBD-1,1,WK2,4*NANT,
$ WK3,NCAP3*NANT,ERROR)
IF (ERROR) RETURN
*
* Add the result to c:
NORM = 0
DO J=1,NCAP3
DO IA=1,NANT
I = ZANT(IA,IREF)
IF (I.NE.0) THEN
WW = WK3(I+(J-1)*NANTM1)
C(IA,J) = C(IA,J)+WW
NORM = NORM+WW**2
ENDIF
ENDDO
ENDDO
ENDDO
ENDIF
c
c loop over data points to get rms
DO I=1, NBAS
SS(I) = 0
WK2(I,1) = 0
ENDDO
J = 0
DO I = 1, M
XI = X(I)
DO WHILE (XI.GE.K(J+4) .AND. J.LE.NCAPM1)
J = J + 1
ENDDO
DO IB=1,NBAS
IF (W(I,IB).GT.0) THEN
IA = IANT(IB)
JA = JANT(IB)
TEST = 0
DO KN = 0, 3
WN = WK1(KN+1,I)
IF (IY.EQ.1) THEN
TEST = TEST+(C(IA,J+KN)+C(JA,J+KN))*WN
ELSE
TEST = TEST+(-C(IA,J+KN)+C(JA,J+KN))*WN
ENDIF
ENDDO
TEST = Y(I,IB)-TEST
TEST = MOD(TEST+11*PI,2*PI)-PI
SS(IB) = SS(IB)+W(I,IB)*TEST**2
WK2(IB,1) = WK2(IB,1)+W(I,IB)
ENDIF
ENDDO
ENDDO
DO IB=1, NBAS
IF (WK2(IB,1).GT.0) THEN
SS(IB) = SQRT(SS(IB)/WK2(IB,1))
ELSE
SS(IB) = 0
ENDIF
ENDDO
*
RETURN
END
*
SUBROUTINE SPLINE_CHECK(M, NCAP7, X, K, WK, ERROR)
C------------------------------------------------------------------------
C splinant computes a weighted least-squares approximation
c to an arbitrary set of data points by a cubic spline
c with knots prescribed by the user.
C------------------------------------------------------------------------
* Dummy
INTEGER M, NCAP7
REAL*8 K(NCAP7), WK(M), X(M)
LOGICAL ERROR
* Local
INTEGER I, J, L, NCAP3, NCAP, NCAPM1, R
REAL*8 K0, K4
C------------------------------------------------------------------------
C Code
c
c check that the values of m and ncap7 are reasonable
IF (NCAP7.LT.8 .OR. M.LT.NCAP7-4) GO TO 991
NCAP = NCAP7 - 7
NCAPM1 = NCAP - 1
NCAP3 = NCAP + 3
c
c In order to define the full b-spline basis, augment the
c prescribed interior knots by knots of multiplicity four
c at each end of the data range.
c
DO J=1,4
I = NCAP3 + J
K(J) = X(1)
K(I) = X(M)
ENDDO
c
c test the validity of the data.
c
c check that the knots are ordered and are interior
c to the data interval.
c
IF (K(5).LE.X(1) .OR. K(NCAP3).GE.X(M)) THEN
WRITE(*,*)'SPLINE_CHECK',' Knots outside range'
ERROR = .TRUE.
RETURN
ELSE
DO J=4,NCAP3
IF (K(J).GT.K(J+1)) THEN
WRITE(*,*)'SPLINE_CHECK','Knots non increasing'
ERROR = .TRUE.
RETURN
ENDIF
ENDDO
ENDIF
c
c check that the data abscissae are ordered, then form the
c array wk from the array x. the array wk contains
c the set of distinct data abscissae.
c
WK(1) = X(1)
J = 2
DO I=2,M
IF (X(I).LT.WK(J-1)) THEN
write(*,*)'SPLINE_CHECK',
$ 'Data abscissae not ordered'
ERROR = .TRUE.
RETURN
ELSEIF (X(I).GT.WK(J-1)) THEN
WK(J) = X(I)
J = J + 1
ENDIF
ENDDO
R = J - 1
c
c check that there are sufficient distinct data abscissae for
c the prescribed number of knots.
c
IF (R.LT.NCAP3) GOTO 991
c
c check the first s and the last s Schoenberg-Whitney
c conditions ( s = min(ncap - 1, 4) ).
c
DO J=1,4
IF (J.GE.NCAP) RETURN
I = NCAP3 - J + 1
L = R - J + 1
IF (WK(J).GE.K(J+4) .OR. K(I).GE.WK(L)) GOTO 991
ENDDO
c
c check all the remaining schoenberg-whitney conditions.
c
IF (NCAP.GT.5) THEN
R = R - 4
I = 3
DO J= 5, NCAPM1
K0 = K(J+4)
K4 = K(J)
DO WHILE (WK(I).LE.K4)
I = I + 1
ENDDO
IF (I.GT.R .OR. WK(I).GE.K0) GOTO 991
ENDDO
ENDIF
RETURN
991 WRITE(*,*)'SPLINE_CHECK',
$'Too many knots'
WRITE(*,*) 'abscissae: ',(WK(I),I=1,R)
WRITE(*,*) 'knots: ',(K(I),I=1,NCAP7)
ERROR = .TRUE.
RETURN
END
SUBROUTINE MTH_DPBTRF (NAME, UPLO, N, KD, AB, LDAB, ERROR)
CHARACTER*(*) UPLO, NAME
INTEGER INFO, KD, LDAB, N
REAL*8 AB( LDAB, * )
LOGICAL ERROR
*
* Purpose
* =======
*
* DPBTRF computes the Cholesky factorization of a real symmetric
* positive definite band matrix A.
*
* The factorization has the form
* A = U**T * U, if UPLO = 'U', or
* A = L * L**T, if UPLO = 'L',
* where U is an upper triangular matrix and L is lower triangular.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*
* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
* On entry, the upper or lower triangle of the symmetric band
* matrix A, stored in the first KD+1 rows of the array. The
* j-th column of A is stored in the j-th column of the array AB
* as follows:
* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*
* On exit, if INFO = 0, the triangular factor U or L from the
* Cholesky factorization A = U**T*U or A = L*L**T of the band
* matrix A, in the same storage format as A.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD+1.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, the leading minor of order i is not
* positive definite, and the factorization could not be
* completed.
*
* Further Details
* ===============
*
* The band storage scheme is illustrated by the following example, when
* N = 6, KD = 2, and UPLO = 'U':
*
* On entry: On exit:
*
* * * a13 a24 a35 a46 * * u13 u24 u35 u46
* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
*
* Similarly, if UPLO = 'L' the format of A is as follows:
*
* On entry: On exit:
*
* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
* a31 a42 a53 a64 * * l31 l42 l53 l64 * *
*
* Array elements marked * are not used by the routine.
*
* Call LAPACK routine
CALL DPBTRF (UPLO, N, KD, AB, LDAB, INFO )
if(INFO .lt. 0) then
write(*,*) 'DPBTRF NOT SUCCESSFUL; INFO', INFO
endif
if(INFO .gt. 0) then
write(*,*) 'DPBTRF ;problem leading minor ', INFO
endif
C CALL MTH_FAIL(NAME,'MTH_DPBTRF',INFO,ERROR)
END
SUBROUTINE MTH_DPBTRS (NAME,
$UPLO, N, KD, NRHS, AB, LDAB, B, LDB, ERROR)
CHARACTER*(*) UPLO, NAME
INTEGER INFO, KD, LDAB, LDB, N, NRHS
REAL*8 AB( LDAB, * ), B( LDB, * )
LOGICAL ERROR
*
* Purpose
* =======
*
* DPBTRS solves a system of linear equations A*X = B with a symmetric
* positive definite band matrix A using the Cholesky factorization
* A = U**T*U or A = L*L**T computed by DPBTRF.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangular factor stored in AB;
* = 'L': Lower triangular factor stored in AB.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
* The triangular factor U or L from the Cholesky factorization
* A = U**T*U or A = L*L**T of the band matrix A, stored in the
* first KD+1 rows of the array. The j-th column of U or L is
* stored in the j-th column of the array AB as follows:
* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD+1.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the right hand side matrix B.
* On exit, the solution matrix X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Call LAPACK routine
CALL DPBTRS (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
C CALL MTH_FAIL(NAME,'MTH_DPBTRS',INFO,ERROR)
if (INFO .lt. 0) then
write(*,*) 'DPBTRS NOT SUCCESSFUL; INFO', INFO
endif
END
SUBROUTINE GETBSPL(NCAP7, K, C, X, S, IFAIL)
*
* Evaluates a cubic spline from its B-spline representation.
*
* Uses DE BOOR*s method of convex combinations.
*
INTEGER NCAP7, IFAIL, J, J1, L
REAL*8 K(NCAP7), C(NCAP7), X, S, C1, C2, C3, E2, E3, E4,
$E5,K1, K2, K3, K4, K5, K6
*
* Check enough data
IF (NCAP7.LT.8) THEN
IFAIL = 2
RETURN
ENDIF
* Check in boundary
IF (X.LT.K(4) .OR. X.GT.K(NCAP7-3)) THEN
IFAIL = 1
S = 0.0D0
RETURN
ENDIF
*
* Determine J such that K(J + 3) .LE. X .LE. K(J + 4).
J1 = 0
J = NCAP7 - 7
DO WHILE (J-J1.GT.1)
L = (J1+J)/2
IF (X.GE.K(L+4)) THEN
J1 = L
ELSE
J = L
ENDIF
ENDDO
*
* Use the method of convex combinations to compute S(X).
K1 = K(J+1)
K2 = K(J+2)
K3 = K(J+3)
K4 = K(J+4)
K5 = K(J+5)
K6 = K(J+6)
E2 = X - K2
E3 = X - K3
E4 = K4 - X
E5 = K5 - X
C2 = C(J+1)
C3 = C(J+2)
C1 = ((X-K1)*C2+E4*C(J))/(K4-K1)
C2 = (E2*C3+E5*C2)/(K5-K2)
C3 = (E3*C(J+3)+(K6-X)*C3)/(K6-K3)
C1 = (E2*C2+E4*C1)/(K4-K2)
C2 = (E3*C3+E5*C2)/(K5-K3)
S = (E3*C2+E4*C1)/(K4-K3)
IFAIL = 0
END
SUBROUTINE AMPLIANT(ANT1,ANT2,NANT,NBAS,BD,WBD,AD,WAD,ERROR,
$WK2,WK3)
INTEGER ERROR
INTEGER NANT, NBAS
INTEGER ANT1(NBAS), ANT2(NBAS)
REAL*8 BD(NBAS), WBD(NBAS), AD(NANT), WAD(NANT), WB, YI, WW
REAL*8 WK2(NANT, NANT), WK3(NBAS)
INTEGER IB, IA, JA, NANTM1
NANTM1=NANT-1
*
DO IA=1, NANT
DO JA=1, NANT
WK2(IA,JA) = 0
ENDDO
WK3(IA) = 0
AD(IA) = 0
ENDDO
DO IB = 1, NBAS
WB = WBD(IB)
IF (WB.GT.0) THEN
IA = ANT1(IB)
JA = ANT2(IB)
YI = BD(IB) - (AD(JA)+AD(IA))
WK3(IA) = WK3(IA) + WB*YI
WK3(JA) = WK3(JA) + WB*YI
WK2(IA,IA) = WK2(IA,IA) + WB
WK2(JA,JA) = WK2(JA,JA) + WB
WK2(IA,JA) = WK2(IA,JA) + WB
WK2(JA,IA) = WK2(JA,IA) + WB
ENDIF
ENDDO
CALL MTH_DPOTRF ('AMPLI_ANT','U',NANT,WK2,NANT,ERROR)
IF (ERROR.GT.0 .OR. ERROR.LT.0)THEN
WRITE(*,*)'AMPLIANT: DPOTRF RETURNS ', ERROR
ENDIF
CALL MTH_DPOTRS ('AMPLI_ANT',
$'U',NANT,1,WK2,NANT,WK3,NANT,ERROR)
IF (ERROR.GT.0 .OR. ERROR.LT.0) THEN
WRITE(*,*)'AMPLIANT: DPOTRF RETURNS ', ERROR
ENDIF
* Add the result to ad:
DO IA=1,NANT
WW = WK3(IA)
AD(IA) = AD(IA) + WW
ENDDO
RETURN
END
SUBROUTINE PHASEANT(ANT1,ANT2,NANT,NBAS,BD,WBD,AD,WAD,ERROR, WK2,
$ WK3)
INTEGER ERROR
INTEGER NANT, NBAS
INTEGER ANT1(NBAS), ANT2(NBAS)
REAL*8 BD(NBAS), WBD(NBAS), AD(NANT), WAD(NANT), WB, YI, WW
REAL*8 WK2(NANT, NANT), WK3(NBAS), NORM
INTEGER IB, IA, IR, NANTM1, JA, I, ZANT
*
NORM = 1E10
NANTM1 = NANT - 1
IR = 1
DO IA=1, NANT
AD(IA) = 0
ENDDO
DO WHILE (NORM.GT.1E-10)
DO IA=1, NANT
DO JA=1, NANT
WK2(IA,JA) = 0
ENDDO
WK3(IA) = 0
ENDDO
DO IB = 1, NBAS
WB = WBD(IB)
IF (WB.GT.0) THEN
IA = ANT1(IB)
JA = ANT2(IB)
YI = SIN(BD(IB) - (AD(JA)-AD(IA)))
IA = ZANT(IA,IR)
JA = ZANT(JA,IR)
IF (IA.NE.0) THEN
WK2(IA,IA) = WK2(IA,IA) + WB
WK3(IA) = WK3(IA) - WB*YI
ENDIF
IF (JA.NE.0) THEN
WK2(JA,JA) = WK2(JA,JA) + WB
WK3(JA) = WK3(JA) + WB*YI
ENDIF
IF (IA.NE.0 .AND. JA.NE.0) THEN
WK2(IA,JA) = WK2(IA,JA) - WB
WK2(JA,IA) = WK2(JA,IA) - WB
ENDIF
ENDIF
ENDDO
CALL MTH_DPOTRF ('PHASE_ANT','U',NANTM1,WK2,NANT,ERROR)
IF (ERROR .NE. 0) THEN
WRITE(*,*) 'PHASEANT ERROR IN DPOTRF ',ERROR
ENDIF
CALL MTH_DPOTRS ('PHASE_ANT',
$ 'U',NANTM1,1,WK2,NANT,WK3,NANTM1,ERROR)
IF (ERROR .NE. 0) THEN
WRITE(*,*) 'PHASEANT ERROR IN DPOTRS ',ERROR
ENDIF
* Add the result to ad:
NORM = 0
DO IA=1,NANT
I = ZANT(IA,IR)
IF (I.NE.0) THEN
WW = WK3(I)
AD(IA) = AD(IA) + WW
NORM = NORM + WW**2
ENDIF
ENDDO
ENDDO
RETURN
END
SUBROUTINE ANTGAIN (Z,W, IANT, JANT, ZANT,WANT, NANT, NBAS,
$ REF_ANT)
C------------------------------------------------------------------------
C CLIC
C Derive antenna "gains" from baseline visibilities
C Arguments:
C Z(NBAS) COMPLEX Visibility
C W(NBAS) REAL Weight
C IANT(NBAS) INTEGER antenna1 for baseline
C JANT(NBAS) INTEGER antenna2 for baseline
C ZANT(NANT) COMPLEX Complex antenna gain
C WANT(NANT) REAL Weight
C NANT INTEGER number of antennas
C NBAS INTEGER number of baselines
C REF_ANT INTEGER reference antenna
C------------------------------------------------------------------------
* Dummy variables:
REAL*4 W(2016), WANT(64)
COMPLEX Z(2016), ZANT(64), CMPL2
INTEGER REF_ANT, IANT(2016), JANT(2016)
* Local variables:
REAL*4 PHA(64), AMP(64), AA, FAZ, WA, ADD, AJI, AKI, AJK,
$PHA0(64), C(2016)
INTEGER IB, IA, J_I, K_I, J_K, JA, KA, BASE, IREF, ITRY, I
LOGICAL RETRO, REFOK
PARAMETER (RETRO=.FALSE.)
*------------------------------------------------------------------------
* Code:
*
* Solve for phases, using retroprojection algorithm:
*
REFOK = .FALSE.
IREF = REF_ANT
ITRY = 1
DO WHILE (.NOT.REFOK .AND. ITRY.LE.NANT)
DO IA=1, NANT
IF (IA.LT.IREF) THEN
IB = BASE(IA,IREF)
REFOK = REFOK .OR. W(IB).GT.0
ELSEIF (IA.GT.IREF) THEN
IB = BASE(IREF,IA)
REFOK = REFOK .OR. W(IB).GT.0
ENDIF
ENDDO
IF (.NOT.REFOK) THEN
ITRY = ITRY+1
IREF = MOD(IREF,NANT)+1
ENDIF
ENDDO
IF (.NOT.REFOK) THEN
DO I=1, NANT
PHA(I) = 0
ENDDO
ELSE
*
*
PHA0(IREF) = 0.
DO IA=1, NANT
IF (IA.LT.IREF) THEN
IB = BASE(IA,IREF)
IF (W(IB).GT.0) PHA0(IA) = -FAZ(Z(IB))
ELSEIF (IA.GT.IREF) THEN
IB = BASE(IREF,IA)
IF (W(IB).GT.0) PHA0(IA) = FAZ(Z(IB))
ENDIF
ENDDO
DO IA = 1, NANT
ADD = 0
DO JA = 1, NANT
IF (JA.LT.IA) THEN
IB = BASE(JA,IA)
IF (W(IB).GT.0) THEN
ADD = ADD + FAZ(Z(IB)) - PHA0(IA) + PHA0(JA)
ENDIF
ELSEIF (JA.GT.IA) THEN
IB = BASE(IA,JA)
IF (W(IB).GT.0) THEN
ADD = ADD - FAZ(Z(IB)) - PHA0(IA) + PHA0(JA)
ENDIF
ENDIF
ENDDO
ADD = MOD(ADD+31D0*PI,2D0*PI)-PI
PHA(IA) = PHA0(IA)+ADD/NANT
ENDDO
ENDIF
*
* solve for amplitudes, using retroprojection algorithm:
c (to be checked again)
* note:
* to compute this way the weights must be provided by antenna,
* not by baseline. (RL 2002-02-27)
IF (RETRO) THEN
DO IA = 1, NANT
WANT(IA) = 0
AMP(IA) = 0
DO IB=1, NBAS
IF (W(IB).GT.0) THEN
IF (IANT(IB).EQ.IA .OR. JANT(IB).EQ.IA) THEN
AMP(IA) = AMP(IA)+LOG(ABS(Z(IB)))*WA
WANT(IA) = WANT(IA)+WA
ELSE
AMP(IA) = AMP(IA)-LOG(ABS(Z(IB)))*WA/(NANT-2)
WANT(IA) = WANT(IA)-WA/(NANT-2)
ENDIF
ENDIF
ENDDO
IF (WANT(IA).GT.0) THEN
AMP(IA) = AMP(IA)/WANT(IA)
ELSE
AMP(IA) = 0.
ENDIF
IF (R_NANT.GT.1) THEN
AMP(IA) = AMP(IA)/(NANT-1)
WANT(IA) = WANT(IA)/(NANT-1)
ENDIF
ZANT(IA) = EXP(CMPLX(AMP(IA),PHA(IA)))
c if (want(ia).gt.0) WANT(IA) = EXP(WANT(IA))
ENDDO
ELSE
*
* Solve for amplitudes
DO IA = 1, NANT
WANT(IA) = 0
AMP(IA) = 0
IF (NANT.GT.2) THEN
DO JA = 1, NANT
IF (JA.NE.IA .AND. JA.LT.NANT) THEN
DO KA = JA+1, NANT
IF (KA.NE.IA) THEN
J_I = BASE(MIN(JA,IA),MAX(JA,IA))
K_I = BASE(MIN(KA,IA),MAX(KA,IA))
J_K = BASE(JA,KA)
IF (Z(J_K).NE.0 .AND. Z(J_I).NE.0 .AND.
$ Z(K_I).NE.0 .AND. W(J_K).NE.0 .AND.
$ W(J_I).NE.0 .AND. W(K_I).NE.0) THEN
AJI = ABS(Z(J_I))
AKI = ABS(Z(K_I))
AJK = ABS(Z(J_K))
IF (AJI.LT.1E15 .AND. AKI.LT.1E15
$ .AND. AJK.LT.1E15) THEN
AA = AJI*AKI/AJK
WA = 1./W(J_I)/ABS(Z(J_I))**2
$ +1./W(K_I)/ABS(Z(K_I))**2
$ +1./W(J_K)/ABS(Z(J_K))**2
WA = 1/AA**2/WA
AMP(IA) = AMP(IA) + AA*WA
WANT(IA) = WANT(IA) + WA
ENDIF
ENDIF
ENDIF
ENDDO
ENDIF
ENDDO
IF (WANT(IA).NE.0) AMP(IA) = AMP(IA) / WANT(IA)
ENDIF
*
* if previous algorithm did not work, take first valid baseline
* containing IA. This will work if there is only one operational baseline ...
IF (WANT(IA).LE.0) THEN
DO IB=1, NBAS
IF (W(IB).GT.0) THEN
AMP(IA) = ABS(Z(IB))
WANT(IA) = W(IB)
ENDIF
ENDDO
ENDIF
ZANT(IA) = AMP(IA) * EXP(CMPLX(0.,PHA(IA)))
c
c ZANT(IA) =CMPL2(AMP(IA), PHA(IA))
c if (amp(ia).GT.BLANK4-D_BLANK4) want(ia) = 0
ENDDO
ENDIF
RETURN
END
FUNCTION BASE(I,J)
C----------------------------------------------------------------------
C Returns the number of baseline I,J (not oriented)
C----------------------------------------------------------------------
* Global variables:
* Dummy variables:
INTEGER BASE,I,J
* Local variables:
*------------------------------------------------------------------------
* Code:
IF (I.LT.J) THEN
BASE = (J-1)*(J-2)/2 + I
ELSE
BASE = (I-1)*(I-2)/2 + J
ENDIF
END
FUNCTION FAZ(Z)
C------------------------------------------------------------------------
C Compute the phase of a complex number Z
C------------------------------------------------------------------------
* Dummy variables:
COMPLEX Z
REAL FAZ
COMPLEX BLANKC
PARAMETER (BLANKC=(1.23456E34,1.23456E34))
REAL*4 BLANK4
PARAMETER (BLANK4=1.23456E34)
*------------------------------------------------------------------------
* Code:
IF (Z.NE.0 .AND. Z.NE.BLANKC) THEN
FAZ = ATAN2(AIMAG(Z),REAL(Z))
ELSE
FAZ = BLANK4
ENDIF
RETURN
END
|