0200 BAC-220 STANDARD VERSION 2/1/62 0200 COMMENT FIRST EXAMPLE PROGRAM FROM BALGOL MANUAL, MARCH 1963. 0200 J.G. HERRIOT, OF STANFORD UNIVERSITY, HAS WRITTEN THE FOLLOWING 0200 PROGRAM TO DETERMINE AN APROXIMATION OF HARMONIC-BOUNDARY VALUES, 0200 USING ORTHONORMAL FUNCTIONS$ 0200 0200 COMMENT THIS PROGRAM FIRST CONSTRUCTS A SET OF ORTHONORMAL FUNCTIONS 0200 AND THEN USES THEM TO FIND AN APPROXIMATION TO THE SOLUTION OF A 0200 HARMONIC BOUNDARY-VALUE PROBLEM$ 0200 0200 COMMENT WE FIRST CONSTRUCT THE ORTHONORMAL FUNCTIONS$ 0200 0200 INTEGER I, J, K, L, M, N, NU, TH$ 0200 ARRAY R(29), HFN(29), DSUM(24), HFCN(5), HFCEN(6), 0200 FA(25,25), A(25,25), B(25,25), HA(47), HAA(24)$ 0200 INPUT DATA (FOR I=(1,1,29)$ R(I)), DIMEN(N)$ 0228 OUTPUT FRESULTS (FOR I=(1,1,N)$ FOR J=(1,1,N)$ FA(I,J)), 0267 ARESULTS (FOR I=(1,1,N)$ FOR J=(1,1,N)$ A(I,J)), 0306 BRESULTS (FOR I=(1,1,N)$ FOR J=(1,1,N)$ B(I,J)), 0345 COEFFS (FOR NU=(4,4,N-1)$ HA(2NU-1)), 0372 HFNRES (FOR K=(1,1,29)$ HFN(K)), 0393 CRES(CONST), HFCNRES (TH, FOR K=(1,1,5)$ HFCN(K)), 0424 HFCENRES(TH, FOR K=(1,1,6)$ HFCEN(K))$ 0448 FORMAT VECTOR (B8,6F16.8,W0), 0448 FTITLE (B48,*FRESULTS,FA(I,J)*,W3,W2), 0448 BTITLE (B48,*BRESULTS,B(I,J)*,W3,W2), 0448 ATITLE (B48,*ARESULTS,A(I,J)*,W3,W2), 0448 COEFTITLE (B30,*HA(8NU-1)*,W2), 0448 BDYVALUES (B42,*PRELIMINARY BOUNDARY VALUES*,W3,W2), 0448 CBDYVALUES (B43,*CORRECTED BOUNDARY VALUES*,W2), 0448 CONTITLE (B50,*CONSTANT*,W2), 0448 TABLE (B8,I2,B6,6F16.8,W0), 0448 TABLEHEAD (B40, *THE VALUES OF H(RHO,TH) IN B*, W3,W2), 0448 TABLELINE (B13,*RHO*,B6,*0.5*,B13,*1.0*,B13,*1.5*,B13, 0448 *2.0*,B13,*2.5*,B13,*3.0*,W0), 0448 TABLETH (B8,*TH*,W0)$ 0542 START.. 0542 READ ($$ DATA)$ 0546 RDIM.. 0546 READ ($$ DIMEN)$ 0550 FOR I = (1,1,N)$ 0561 FOR J = (I,4,N)$ 0573 BEGIN 0577 L = I-J$ K = I+J$ 0580 SUM = R(1)*K + 1.5R(18)*K.COS(0.59341195.L) 0595 + 0.5.R(29)*K.COS(0.78539816.L)$ 0615 FOR M = (2,1,17)$ 0626 SUM = SUM + 2.0.R(M)*K.COS((M-1).0.034906585.L)$ 0650 FOR M = (19,1,28)$ 0661 SUM = SUM + R(M)*K.COS((0.59341195 + (M-18).0.017453293).L)$ 0685 FA(I,J) = (8.0/K).0.017453293.SUM 0701 END$ 0703 WRITE ($$ FTITLE)$ 0707 WRITE ($$ FRESULTS, VECTOR)$ 0715 FOR J = (1,1,N)$ 0726 B(1,J) = FA(1,J)$ 0731 FOR I = (2,1,N)$ 0742 BEGIN 0743 FOR J = (1,1,I-1)$ 0757 B(I,J) = -B(J,I)/B(J,J)$ 0781 FOR J = (I,1,N)$ 0792 BEGIN 0793 B(I,J) = FA(I,J)$ 0807 FOR K = (1,1,I-1)$ 0821 B(I,J) = B(I,J) + B(I,K).B(K,J) 0851 END$ 0852 FOR J = (1,1,I-1)$ 0866 B(I,J) = B(I,J).SQRT(B(J,J)/B(I,I)) 0892 END$ 0900 FOR I = (1,1,N)$ 0911 B(I,I) = 1.0/(SQRT(B(I,I)).I)$ 0938 WRITE ($$ BTITLE)$ 0942 WRITE ($$ BRESULTS, VECTOR)$ 0950 FOR I = (1,1,N)$ 0961 FOR J = (1,1,N)$ 0973 A(I,J) = 0$ 0983 A(1,1) = B(1,1)$ 0985 FOR I = (2,1,N)$ 0996 BEGIN 0997 FOR J= (1,1,I-1)$ 1011 BEGIN 1012 A(I,J) = 0$ 1019 FOR K = (J,1,I-1)$ 1033 A(I,J) = A(I,J) + B(I,K).A(K,J) 1063 END$ 1064 A(I,I) = B(I,I) 1078 END$ 1079 WRITE ($$ ATITLE)$ 1083 WRITE ($$ ARESULTS, VECTOR)$ 1083 1091 COMMENT NOW CONSTRUCT THE APROXIMATION TO THE SOLUTION$ 1091 1091 FOR J = (4,4,N-1)$ 1105 BEGIN 1105 DSUM(J) = 0$ 1108 FOR M = (1,1,17)$ 1119 DSUM(J) = DSUM(J) + (R(M)*2 + R(M+1)*2). 1119 (R(M+1)*J.SIN(M.0.034906585.J) 1142 - R(M)*J.SIN((M-1).0.034906585.J))$ 1173 FOR M = (18,1,28)$ 1184 DSUM(J) = DSUM(J) + (R(M)*2 + R(M+1)*2.(R(M+1)*J. 1199 SIN((0.59341195 + (M-17).0.017453293).J) 1208 - R(M)*J.SIN((0.59341195 1220 + (M-18).0.017453293).J))) 1235 END$ 1242 FOR NU = (4,4,N-1)$ 1256 BEGIN 1256 HA(2NU-1) = 0$ 1262 FOR J = (4,4,NU)$ 1273 HA(2NU-1) = HA(2NU-1) + A(NU,J).DSUM(J)$ 1294 HA(2NU-1) = 4.0.HA(2NU-1) 1305 END$ 1306 WRITE ($$ COEFTITLE)$ 1310 WRITE ($$ COEFFS, VECTOR)$ 1318 FOR J = (4,4,N-1)$ 1332 BEGIN 1332 HAA(J) = 0$ 1335 FOR NU = (J,4,N-1)$ 1349 HAA(J) = HAA(J) + HA(2NU-1).A(NU,J) 1366 END$ 1367 FOR M = (1,1,18)$ 1378 BEGIN 1378 HFN(M) = 0$ 1381 FOR J = (4,4,N-1)$ 1395 HFN(M) = HFN(M) + HAA(J).R(M)*J.COS((M-1).0.034906585.J) 1414 END$ 1422 FOR M = (19,1,29)$ 1433 BEGIN 1433 HFN(M) = 0$ 1436 FOR J = (4,4,N-1)$ 1450 HFN(M) = HFN(M) + HAA(J).R(M)*J. 1461 COS((0.59341195 + (M-18).0.017453293).J) 1470 END$ 1478 WRITE ($$ BDYVALUES)$ 1482 WRITE ($$ HFNRES, VECTOR)$ 1490 AVT = 0$ 1491 FOR M = (1,1,29)$ 1502 AVT = AVT + R(M)*2 - HFN(M)$ 1510 CONST = AVT/29.0$ 1514 WRITE ($$ CONTITLE)$ 1518 WRITE ($$ CRES, VECTOR)$ 1526 FOR M = (1,1,29)$ 1537 HFN(M) = CONST + HFN(M)$ 1543 WRITE ($$ CBDYVALUES)$ 1547 WRITE ($$ HFNRES, VECTOR)$ 1555 FOR I = (1,1,5)$ 1566 BEGIN 1569 TH = 5.(I-1)$ 1571 FOR J = (1,1,5)$ 1582 BEGIN 1582 HFCN(J) = CONST$ 1586 FOR M = (4,4,N-1)$ 1600 HFCN(J) = HFCN(J) + HAA(M).(0.5.J)*M.COS((I-1).0.087266463.M) 1621 END$ 1629 WRITE ($$ TABLEHEAD)$ 1633 WRITE ($$ TABLELINE)$ 1637 WRITE ($$ TABLETH)$ 1641 WRITE ($$ HFCNRES, TABLE) 1645 END$ 1650 FOR I = (6,1,10)$ 1661 BEGIN 1664 TH = 5.(I-1)$ 1666 FOR J = (1,1,6)$ 1677 BEGIN 1677 HFCEN(J) = CONST$ 1681 FOR M = (4,4,N-1)$ 1695 HFCEN(J) = HFCEN(J) + HAA(M).(0.5.J)*M. 1708 COS((I-1).0.087266463.M) 1716 END$ 1724 WRITE ($$ HFCNRES, TABLE) 1728 END$ 1733 STOP 1234$ 1735 GO TO RDIM$ 1736 FINISH$ COMPILED PROGRAM ENDS AT 1737 PROGRAM VARIABLES BEGIN AT 2308 FRESULTS,FA(I,J) .46363974, 00 .00000000, 00 .00000000, 00 .00000000, 00 .23764092,-01 .00000000, 00 .00000000, 00 .00000000, 00 -.71568320,-02 .00000000, 00 .00000000, 00 .10859771, 00 .00000000, 00 .00000000, 00 .00000000, 00 .11793550,-01 .00000000, 00 .00000000, 00 .00000000, 00 -.46675562,-02 .00000000, 00 .00000000, 00 .45596608,-01 .00000000, 00 .00000000, 00 .00000000, 00 .66280897,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .23645567,-01 .00000000, 00 .00000000, 00 .00000000, 00 .40349229,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .13723588,-01 .00000000, 00 .00000000, 00 .00000000, 00 .25944880,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .85504589,-02 .00000000, 00 .00000000, 00 .00000000, 00 .17352779,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .55925944,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .37885968,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .26349488,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .18701734,-02 BRESULTS,B(I,J) .14686208, 01 .00000000, 00 .00000000, 00 .00000000, 00 .23764092,-01 .00000000, 00 .00000000, 00 .00000000, 00 -.71568320,-02 .00000000, 00 .00000000, 00 .15172588, 01 .00000000, 00 .00000000, 00 .00000000, 00 .11793550,-01 .00000000, 00 .00000000, 00 .00000000, 00 -.46675562,-02 .00000000, 00 .00000000, 00 .15610344, 01 .00000000, 00 .00000000, 00 .00000000, 00 .66280897,-02 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .16257926, 01 .00000000, 00 .00000000, 00 .00000000, 00 .40349229,-02 .00000000, 00 .00000000, 00 -.31208976, 00 .00000000, 00 .00000000, 00 .00000000, 00 .17884576, 01 .00000000, 00 .00000000, 00 .00000000, 00 .29613151,-02 .00000000, 00 .00000000, 00 -.41973579, 00 .00000000, 00 .00000000, 00 .00000000, 00 .19547472, 01 .00000000, 00 .00000000, 00 .00000000, 00 .22421675,-02 .00000000, 00 .00000000, 00 -.45621891, 00 .00000000, 00 .00000000, 00 .00000000, 00 .20996803, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.47127521, 00 .00000000, 00 .00000000, 00 .00000000, 00 .22450409, 01 .00000000, 00 .00000000, 00 .24615528, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.62017172, 00 .00000000, 00 .00000000, 00 .00000000, 00 .26021732, 01 .00000000, 00 .00000000, 00 .45290390, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.84088526, 00 .00000000, 00 .00000000, 00 .00000000, 00 .31976200, 01 ARESULTS,A(I,J) .14686208, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .15172588, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .15610344, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .16257926, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.45834151, 00 .00000000, 00 .00000000, 00 .00000000, 00 .17884576, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.63684782, 00 .00000000, 00 .00000000, 00 .00000000, 00 .19547472, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.71217341, 00 .00000000, 00 .00000000, 00 .00000000, 00 .20996803, 01 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.76619574, 00 .00000000, 00 .00000000, 00 .00000000, 00 .22450409, 01 .00000000, 00 .00000000, 00 .64575920, 00 .00000000, 00 .00000000, 00 .00000000, 00 -.11091508, 01 .00000000, 00 .00000000, 00 .00000000, 00 .26021732, 01 .00000000, 00 .00000000, 00 .12226884, 01 .00000000, 00 .00000000, 00 .00000000, 00 -.16437181, 01 .00000000, 00 .00000000, 00 .00000000, 00 .31976200, 01 HA(8NU-1) .50545968, 01 .42274676, 01 PRELIMINARY BOUNDARY VALUES .49796075,-03 .79116856,-02 .39293002,-01 .12059664, 00 .28013582, 00 .52195922, 00 .74267199, 00 .54385334, 00 -.10833437, 01 .15377222,-03 .12638536,-03 .35622222,-04 -.14939203,-03 -.46393697,-03 -.94592537,-03 -.16334448,-02 -.25616609,-02 -.37591899,-02 -.49674793,-02 -.64370032,-02 -.81955279,-02 -.10268522,-01 -.12678082,-01 -.15441807,-01 -.18571693,-01 -.22073044,-01 -.25943471,-01 -.30172002,-01 -.34738328,-01 CONSTANT .93176158,-01 CORRECTED BOUNDARY VALUES .93674119,-01 .10108784, 00 .13246916, 00 .21377280, 00 .37331198, 00 .61513538, 00 .83584815, 00 .63702950, 00 -.99016754, 00 .93329930,-01 .93302543,-01 .93211780,-01 .93026766,-01 .92712221,-01 .92230233,-01 .91542713,-01 .90614497,-01 .89416968,-01 .88208679,-01 .86739155,-01 .84980630,-01 .82907636,-01 .80498076,-01 .77734351,-01 .74604465,-01 .71103114,-01 .67232687,-01 .63004156,-01 .58437830,-01 THE VALUES OF H(RHO,TH) IN B RHO 0.5 1.0 1.5 2.0 2.5 3.0 TH 0 .44141589, 00 .14562672, 02 .26853741, 03 .25094061, 04 .14676440, 05 THE VALUES OF H(RHO,TH) IN B RHO 0.5 1.0 1.5 2.0 2.5 3.0 TH 5 .41397671, 00 .12041988, 02 .21011008, 03 .19361708, 04 .11276597, 05 THE VALUES OF H(RHO,TH) IN B RHO 0.5 1.0 1.5 2.0 2.5 3.0 TH 10 .33798103, 00 .55551163, 01 .61639051, 02 .48302017, 03 .26638223, 04 THE VALUES OF H(RHO,TH) IN B RHO 0.5 1.0 1.5 2.0 2.5 3.0 TH 15 .23022242, 00 -.21629137, 01 -.10892449, 03 -.11749048, 04 -.71436015, 04 THE VALUES OF H(RHO,TH) IN B RHO 0.5 1.0 1.5 2.0 2.5 3.0 TH 20 .11237182, 00 -.79607594, 01 -.22410075, 03 -.22692027, 04 -.13574641, 05 25 .11237182, 00 -.79607594, 01 -.22410075, 03 -.22692027, 04 -.13574641, 05 30 .11237182, 00 -.79607594, 01 -.22410075, 03 -.22692027, 04 -.13574641, 05 35 .11237182, 00 -.79607594, 01 -.22410075, 03 -.22692027, 04 -.13574641, 05 40 .11237182, 00 -.79607594, 01 -.22410075, 03 -.22692027, 04 -.13574641, 05 45 .11237182, 00 -.79607594, 01 -.22410075, 03 -.22692027, 04 -.13574641, 05