annotate libcruft/amos/cseri.f @ 12312:b10ea6efdc58 release-3-4-x ss-3-3-91

version is now 3.3.91
author John W. Eaton <jwe@octave.org>
date Mon, 31 Jan 2011 08:36:58 -0500
parents 82be108cc558
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
7789
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1 SUBROUTINE CSERI(Z, FNU, KODE, N, Y, NZ, TOL, ELIM, ALIM)
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2 C***BEGIN PROLOGUE CSERI
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3 C***REFER TO CBESI,CBESK
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4 C
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5 C CSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY
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6 C MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE
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7 C REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN.
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8 C NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO
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9 C DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE
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10 C CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE
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11 C COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ).
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12 C
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13 C***ROUTINES CALLED CUCHK,GAMLN,R1MACH
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14 C***END PROLOGUE CSERI
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15 COMPLEX AK1, CK, COEF, CONE, CRSC, CZ, CZERO, HZ, RZ, S1, S2, W,
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16 * Y, Z
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17 REAL AA, ACZ, AK, ALIM, ARM, ASCLE, ATOL, AZ, DFNU, ELIM, FNU,
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18 * FNUP, RAK1, RS, RTR1, S, SS, TOL, X, GAMLN, R1MACH
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19 INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NW, NZ
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20 DIMENSION Y(N), W(2)
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21 DATA CZERO, CONE / (0.0E0,0.0E0), (1.0E0,0.0E0) /
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22 C
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23 NZ = 0
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24 AZ = CABS(Z)
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25 IF (AZ.EQ.0.0E0) GO TO 150
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26 X = REAL(Z)
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27 ARM = 1.0E+3*R1MACH(1)
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28 RTR1 = SQRT(ARM)
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29 CRSC = CMPLX(1.0E0,0.0E0)
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30 IFLAG = 0
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31 IF (AZ.LT.ARM) GO TO 140
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32 HZ = Z*CMPLX(0.5E0,0.0E0)
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33 CZ = CZERO
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34 IF (AZ.GT.RTR1) CZ = HZ*HZ
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35 ACZ = CABS(CZ)
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36 NN = N
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37 CK = CLOG(HZ)
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38 10 CONTINUE
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39 DFNU = FNU + FLOAT(NN-1)
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40 FNUP = DFNU + 1.0E0
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41 C-----------------------------------------------------------------------
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42 C UNDERFLOW TEST
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43 C-----------------------------------------------------------------------
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44 AK1 = CK*CMPLX(DFNU,0.0E0)
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45 AK = GAMLN(FNUP,IDUM)
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46 AK1 = AK1 - CMPLX(AK,0.0E0)
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47 IF (KODE.EQ.2) AK1 = AK1 - CMPLX(X,0.0E0)
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48 RAK1 = REAL(AK1)
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49 IF (RAK1.GT.(-ELIM)) GO TO 30
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50 20 CONTINUE
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51 NZ = NZ + 1
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52 Y(NN) = CZERO
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53 IF (ACZ.GT.DFNU) GO TO 170
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54 NN = NN - 1
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55 IF (NN.EQ.0) RETURN
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56 GO TO 10
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57 30 CONTINUE
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58 IF (RAK1.GT.(-ALIM)) GO TO 40
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59 IFLAG = 1
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60 SS = 1.0E0/TOL
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61 CRSC = CMPLX(TOL,0.0E0)
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62 ASCLE = ARM*SS
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63 40 CONTINUE
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64 AK = AIMAG(AK1)
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65 AA = EXP(RAK1)
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66 IF (IFLAG.EQ.1) AA = AA*SS
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67 COEF = CMPLX(AA,0.0E0)*CMPLX(COS(AK),SIN(AK))
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68 ATOL = TOL*ACZ/FNUP
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69 IL = MIN0(2,NN)
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70 DO 80 I=1,IL
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71 DFNU = FNU + FLOAT(NN-I)
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72 FNUP = DFNU + 1.0E0
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73 S1 = CONE
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74 IF (ACZ.LT.TOL*FNUP) GO TO 60
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75 AK1 = CONE
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76 AK = FNUP + 2.0E0
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77 S = FNUP
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78 AA = 2.0E0
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79 50 CONTINUE
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80 RS = 1.0E0/S
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81 AK1 = AK1*CZ*CMPLX(RS,0.0E0)
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82 S1 = S1 + AK1
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83 S = S + AK
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84 AK = AK + 2.0E0
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85 AA = AA*ACZ*RS
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86 IF (AA.GT.ATOL) GO TO 50
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87 60 CONTINUE
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88 M = NN - I + 1
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89 S2 = S1*COEF
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90 W(I) = S2
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91 IF (IFLAG.EQ.0) GO TO 70
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92 CALL CUCHK(S2, NW, ASCLE, TOL)
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93 IF (NW.NE.0) GO TO 20
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94 70 CONTINUE
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95 Y(M) = S2*CRSC
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96 IF (I.NE.IL) COEF = COEF*CMPLX(DFNU,0.0E0)/HZ
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97 80 CONTINUE
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98 IF (NN.LE.2) RETURN
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99 K = NN - 2
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100 AK = FLOAT(K)
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101 RZ = (CONE+CONE)/Z
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102 IF (IFLAG.EQ.1) GO TO 110
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103 IB = 3
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104 90 CONTINUE
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105 DO 100 I=IB,NN
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106 Y(K) = CMPLX(AK+FNU,0.0E0)*RZ*Y(K+1) + Y(K+2)
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107 AK = AK - 1.0E0
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108 K = K - 1
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109 100 CONTINUE
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110 RETURN
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111 C-----------------------------------------------------------------------
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112 C RECUR BACKWARD WITH SCALED VALUES
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113 C-----------------------------------------------------------------------
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114 110 CONTINUE
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115 C-----------------------------------------------------------------------
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116 C EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE
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117 C UNDERFLOW LIMIT = ASCLE = R1MACH(1)*CSCL*1.0E+3
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118 C-----------------------------------------------------------------------
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119 S1 = W(1)
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120 S2 = W(2)
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121 DO 120 L=3,NN
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122 CK = S2
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123 S2 = S1 + CMPLX(AK+FNU,0.0E0)*RZ*S2
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124 S1 = CK
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125 CK = S2*CRSC
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126 Y(K) = CK
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127 AK = AK - 1.0E0
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128 K = K - 1
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129 IF (CABS(CK).GT.ASCLE) GO TO 130
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130 120 CONTINUE
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131 RETURN
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132 130 CONTINUE
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133 IB = L + 1
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134 IF (IB.GT.NN) RETURN
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135 GO TO 90
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136 140 CONTINUE
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137 NZ = N
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138 IF (FNU.EQ.0.0E0) NZ = NZ - 1
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139 150 CONTINUE
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140 Y(1) = CZERO
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141 IF (FNU.EQ.0.0E0) Y(1) = CONE
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142 IF (N.EQ.1) RETURN
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143 DO 160 I=2,N
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144 Y(I) = CZERO
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145 160 CONTINUE
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146 RETURN
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147 C-----------------------------------------------------------------------
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148 C RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE
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149 C THE CALCULATION IN CBINU WITH N=N-IABS(NZ)
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150 C-----------------------------------------------------------------------
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151 170 CONTINUE
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152 NZ = -NZ
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153 RETURN
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154 END