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annotate liboctave/cruft/slatec-fn/psifn.f @ 20161:65e22ba879f0

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psi: add support to compute the polygamma function (kth-derivative). * libinterp/corefcn/psi.cc: previously, only the digamma function, k == 0, was being computed. Add support for polygamma function, add tests, and improve documentation. * liboctave/cruft/slatec-fn/dpsifn.f, liboctave/cruft/slatec-fn/psifn.f: the two functions that actually compute the the polygamma functions, copied verbatim from SLATEC, and under public domain. * liboctave/cruft/slatec-fn/module.mk: add dpsifn.f and psifn.f to the build system. * liboctave/numeric/lo-specfun.cc: add new signature for function psi to compute polygamma function that wraps the Fortran DPSIFN and PSIFN functions. * liboctave/numeric/lo-specfun.h: declare new function and document all psi() with doxygen.
author Carnë Draug <carandraug@octave.org>
date Sun, 03 May 2015 22:52:07 +0100
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20161
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1 *DECK PSIFN
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2 SUBROUTINE PSIFN (X, N, KODE, M, ANS, NZ, IERR)
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3 C***BEGIN PROLOGUE PSIFN
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4 C***PURPOSE Compute derivatives of the Psi function.
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5 C***LIBRARY SLATEC
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6 C***CATEGORY C7C
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7 C***TYPE SINGLE PRECISION (PSIFN-S, DPSIFN-D)
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8 C***KEYWORDS DERIVATIVES OF THE GAMMA FUNCTION, POLYGAMMA FUNCTION,
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9 C PSI FUNCTION
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10 C***AUTHOR Amos, D. E., (SNLA)
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11 C***DESCRIPTION
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12 C
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13 C The following definitions are used in PSIFN:
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14 C
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15 C Definition 1
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16 C PSI(X) = d/dx (ln(GAMMA(X)), the first derivative of
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17 C the LOG GAMMA function.
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18 C Definition 2
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19 C K K
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20 C PSI(K,X) = d /dx (PSI(X)), the K-th derivative of PSI(X).
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21 C ___________________________________________________________________
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22 C PSIFN computes a sequence of SCALED derivatives of
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23 C the PSI function; i.e. for fixed X and M it computes
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24 C the M-member sequence
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25 C
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26 C ((-1)**(K+1)/GAMMA(K+1))*PSI(K,X)
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27 C for K = N,...,N+M-1
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28 C
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29 C where PSI(K,X) is as defined above. For KODE=1, PSIFN returns
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30 C the scaled derivatives as described. KODE=2 is operative only
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31 C when K=0 and in that case PSIFN returns -PSI(X) + LN(X). That
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32 C is, the logarithmic behavior for large X is removed when KODE=1
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33 C and K=0. When sums or differences of PSI functions are computed
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34 C the logarithmic terms can be combined analytically and computed
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35 C separately to help retain significant digits.
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36 C
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37 C Note that CALL PSIFN(X,0,1,1,ANS) results in
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38 C ANS = -PSI(X)
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39 C
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40 C Input
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41 C X - Argument, X .gt. 0.0E0
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42 C N - First member of the sequence, 0 .le. N .le. 100
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43 C N=0 gives ANS(1) = -PSI(X) for KODE=1
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44 C -PSI(X)+LN(X) for KODE=2
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45 C KODE - Selection parameter
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46 C KODE=1 returns scaled derivatives of the PSI
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47 C function.
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48 C KODE=2 returns scaled derivatives of the PSI
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49 C function EXCEPT when N=0. In this case,
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50 C ANS(1) = -PSI(X) + LN(X) is returned.
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51 C M - Number of members of the sequence, M .ge. 1
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52 C
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53 C Output
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54 C ANS - A vector of length at least M whose first M
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55 C components contain the sequence of derivatives
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56 C scaled according to KODE.
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57 C NZ - Underflow flag
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58 C NZ.eq.0, A normal return
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59 C NZ.ne.0, Underflow, last NZ components of ANS are
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60 C set to zero, ANS(M-K+1)=0.0, K=1,...,NZ
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61 C IERR - Error flag
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62 C IERR=0, A normal return, computation completed
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63 C IERR=1, Input error, no computation
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64 C IERR=2, Overflow, X too small or N+M-1 too
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65 C large or both
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66 C IERR=3, Error, N too large. Dimensioned
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67 C array TRMR(NMAX) is not large enough for N
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68 C
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69 C The nominal computational accuracy is the maximum of unit
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70 C roundoff (=R1MACH(4)) and 1.0E-18 since critical constants
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71 C are given to only 18 digits.
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72 C
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73 C DPSIFN is the Double Precision version of PSIFN.
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74 C
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75 C *Long Description:
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76 C
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77 C The basic method of evaluation is the asymptotic expansion
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78 C for large X.ge.XMIN followed by backward recursion on a two
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79 C term recursion relation
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80 C
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81 C W(X+1) + X**(-N-1) = W(X).
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82 C
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83 C This is supplemented by a series
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84 C
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85 C SUM( (X+K)**(-N-1) , K=0,1,2,... )
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86 C
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87 C which converges rapidly for large N. Both XMIN and the
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88 C number of terms of the series are calculated from the unit
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89 C roundoff of the machine environment.
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90 C
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91 C***REFERENCES Handbook of Mathematical Functions, National Bureau
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92 C of Standards Applied Mathematics Series 55, edited
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93 C by M. Abramowitz and I. A. Stegun, equations 6.3.5,
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94 C 6.3.18, 6.4.6, 6.4.9 and 6.4.10, pp.258-260, 1964.
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95 C D. E. Amos, A portable Fortran subroutine for
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96 C derivatives of the Psi function, Algorithm 610, ACM
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97 C Transactions on Mathematical Software 9, 4 (1983),
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98 C pp. 494-502.
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99 C***ROUTINES CALLED I1MACH, R1MACH
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100 C***REVISION HISTORY (YYMMDD)
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101 C 820601 DATE WRITTEN
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102 C 890531 Changed all specific intrinsics to generic. (WRB)
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103 C 890531 REVISION DATE from Version 3.2
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104 C 891214 Prologue converted to Version 4.0 format. (BAB)
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105 C 920501 Reformatted the REFERENCES section. (WRB)
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106 C***END PROLOGUE PSIFN
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107 INTEGER I, IERR, J, K, KODE, M, MM, MX, N, NMAX, NN, NP, NX, NZ
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108 INTEGER I1MACH
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109 REAL ANS, ARG, B, DEN, ELIM, EPS, FLN, FN, FNP, FNS, FX, RLN,
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110 * RXSQ, R1M4, R1M5, S, SLOPE, T, TA, TK, TOL, TOLS, TRM, TRMR,
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111 * TSS, TST, TT, T1, T2, WDTOL, X, XDMLN, XDMY, XINC, XLN, XM,
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112 * XMIN, XQ, YINT
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113 REAL R1MACH
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114 DIMENSION B(22), TRM(22), TRMR(100), ANS(*)
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115 SAVE NMAX, B
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
116 DATA NMAX /100/
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
117 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
118 C BERNOULLI NUMBERS
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
119 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
120 DATA B(1), B(2), B(3), B(4), B(5), B(6), B(7), B(8), B(9), B(10),
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
121 * B(11), B(12), B(13), B(14), B(15), B(16), B(17), B(18), B(19),
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
122 * B(20), B(21), B(22) /1.00000000000000000E+00,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
123 * -5.00000000000000000E-01,1.66666666666666667E-01,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
124 * -3.33333333333333333E-02,2.38095238095238095E-02,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
125 * -3.33333333333333333E-02,7.57575757575757576E-02,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
126 * -2.53113553113553114E-01,1.16666666666666667E+00,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
127 * -7.09215686274509804E+00,5.49711779448621554E+01,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
128 * -5.29124242424242424E+02,6.19212318840579710E+03,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
129 * -8.65802531135531136E+04,1.42551716666666667E+06,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
130 * -2.72982310678160920E+07,6.01580873900642368E+08,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
131 * -1.51163157670921569E+10,4.29614643061166667E+11,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
132 * -1.37116552050883328E+13,4.88332318973593167E+14,
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
133 * -1.92965793419400681E+16/
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
134 C
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
135 C***FIRST EXECUTABLE STATEMENT PSIFN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
136 IERR = 0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
137 NZ=0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
138 IF (X.LE.0.0E0) IERR=1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
139 IF (N.LT.0) IERR=1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
140 IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
141 IF (M.LT.1) IERR=1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
142 IF (IERR.NE.0) RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
143 MM=M
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
144 NX = MIN(-I1MACH(12),I1MACH(13))
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
145 R1M5 = R1MACH(5)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
146 R1M4 = R1MACH(4)*0.5E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
147 WDTOL = MAX(R1M4,0.5E-18)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
148 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
149 C ELIM = APPROXIMATE EXPONENTIAL OVER AND UNDERFLOW LIMIT
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
150 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
151 ELIM = 2.302E0*(NX*R1M5-3.0E0)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
152 XLN = LOG(X)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
153 41 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
154 NN = N + MM - 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
155 FN = NN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
156 FNP = FN + 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
157 T = FNP*XLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
158 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
159 C OVERFLOW AND UNDERFLOW TEST FOR SMALL AND LARGE X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
160 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
161 IF (ABS(T).GT.ELIM) GO TO 290
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
162 IF (X.LT.WDTOL) GO TO 260
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
163 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
164 C COMPUTE XMIN AND THE NUMBER OF TERMS OF THE SERIES, FLN+1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
165 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
166 RLN = R1M5*I1MACH(11)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
167 RLN = MIN(RLN,18.06E0)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
168 FLN = MAX(RLN,3.0E0) - 3.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
169 YINT = 3.50E0 + 0.40E0*FLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
170 SLOPE = 0.21E0 + FLN*(0.0006038E0*FLN+0.008677E0)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
171 XM = YINT + SLOPE*FN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
172 MX = INT(XM) + 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
173 XMIN = MX
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
174 IF (N.EQ.0) GO TO 50
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
175 XM = -2.302E0*RLN - MIN(0.0E0,XLN)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
176 FNS = N
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
177 ARG = XM/FNS
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
178 ARG = MIN(0.0E0,ARG)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
179 EPS = EXP(ARG)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
180 XM = 1.0E0 - EPS
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
181 IF (ABS(ARG).LT.1.0E-3) XM = -ARG
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
182 FLN = X*XM/EPS
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
183 XM = XMIN - X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
184 IF (XM.GT.7.0E0 .AND. FLN.LT.15.0E0) GO TO 200
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
185 50 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
186 XDMY = X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
187 XDMLN = XLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
188 XINC = 0.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
189 IF (X.GE.XMIN) GO TO 60
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
190 NX = INT(X)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
191 XINC = XMIN - NX
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
192 XDMY = X + XINC
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
193 XDMLN = LOG(XDMY)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
194 60 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
195 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
196 C GENERATE W(N+MM-1,X) BY THE ASYMPTOTIC EXPANSION
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
197 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
198 T = FN*XDMLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
199 T1 = XDMLN + XDMLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
200 T2 = T + XDMLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
201 TK = MAX(ABS(T),ABS(T1),ABS(T2))
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
202 IF (TK.GT.ELIM) GO TO 380
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
203 TSS = EXP(-T)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
204 TT = 0.5E0/XDMY
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
205 T1 = TT
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
206 TST = WDTOL*TT
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
207 IF (NN.NE.0) T1 = TT + 1.0E0/FN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
208 RXSQ = 1.0E0/(XDMY*XDMY)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
209 TA = 0.5E0*RXSQ
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
210 T = FNP*TA
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
211 S = T*B(3)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
212 IF (ABS(S).LT.TST) GO TO 80
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
213 TK = 2.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
214 DO 70 K=4,22
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
215 T = T*((TK+FN+1.0E0)/(TK+1.0E0))*((TK+FN)/(TK+2.0E0))*RXSQ
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
216 TRM(K) = T*B(K)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
217 IF (ABS(TRM(K)).LT.TST) GO TO 80
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
218 S = S + TRM(K)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
219 TK = TK + 2.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
220 70 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
221 80 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
222 S = (S+T1)*TSS
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
223 IF (XINC.EQ.0.0E0) GO TO 100
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
224 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
225 C BACKWARD RECUR FROM XDMY TO X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
226 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
227 NX = INT(XINC)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
228 NP = NN + 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
229 IF (NX.GT.NMAX) GO TO 390
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
230 IF (NN.EQ.0) GO TO 160
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
231 XM = XINC - 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
232 FX = X + XM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
233 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
234 C THIS LOOP SHOULD NOT BE CHANGED. FX IS ACCURATE WHEN X IS SMALL
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
235 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
236 DO 90 I=1,NX
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
237 TRMR(I) = FX**(-NP)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
238 S = S + TRMR(I)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
239 XM = XM - 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
240 FX = X + XM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
241 90 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
242 100 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
243 ANS(MM) = S
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
244 IF (FN.EQ.0.0E0) GO TO 180
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
245 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
246 C GENERATE LOWER DERIVATIVES, J.LT.N+MM-1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
247 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
248 IF (MM.EQ.1) RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
249 DO 150 J=2,MM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
250 FNP = FN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
251 FN = FN - 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
252 TSS = TSS*XDMY
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
253 T1 = TT
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
254 IF (FN.NE.0.0E0) T1 = TT + 1.0E0/FN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
255 T = FNP*TA
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
256 S = T*B(3)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
257 IF (ABS(S).LT.TST) GO TO 120
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
258 TK = 3.0E0 + FNP
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
259 DO 110 K=4,22
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
260 TRM(K) = TRM(K)*FNP/TK
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
261 IF (ABS(TRM(K)).LT.TST) GO TO 120
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
262 S = S + TRM(K)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
263 TK = TK + 2.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
264 110 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
265 120 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
266 S = (S+T1)*TSS
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
267 IF (XINC.EQ.0.0E0) GO TO 140
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
268 IF (FN.EQ.0.0E0) GO TO 160
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
269 XM = XINC - 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
270 FX = X + XM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
271 DO 130 I=1,NX
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
272 TRMR(I) = TRMR(I)*FX
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
273 S = S + TRMR(I)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
274 XM = XM - 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
275 FX = X + XM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
276 130 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
277 140 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
278 MX = MM - J + 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
279 ANS(MX) = S
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
280 IF (FN.EQ.0.0E0) GO TO 180
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
281 150 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
282 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
283 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
284 C RECURSION FOR N = 0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
285 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
286 160 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
287 DO 170 I=1,NX
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
288 S = S + 1.0E0/(X+NX-I)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
289 170 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
290 180 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
291 IF (KODE.EQ.2) GO TO 190
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
292 ANS(1) = S - XDMLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
293 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
294 190 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
295 IF (XDMY.EQ.X) RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
296 XQ = XDMY/X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
297 ANS(1) = S - LOG(XQ)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
298 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
299 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
300 C COMPUTE BY SERIES (X+K)**(-(N+1)) , K=0,1,2,...
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
301 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
302 200 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
303 NN = INT(FLN) + 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
304 NP = N + 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
305 T1 = (FNS+1.0E0)*XLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
306 T = EXP(-T1)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
307 S = T
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
308 DEN = X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
309 DO 210 I=1,NN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
310 DEN = DEN + 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
311 TRM(I) = DEN**(-NP)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
312 S = S + TRM(I)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
313 210 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
314 ANS(1) = S
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
315 IF (N.NE.0) GO TO 220
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
316 IF (KODE.EQ.2) ANS(1) = S + XLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
317 220 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
318 IF (MM.EQ.1) RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
319 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
320 C GENERATE HIGHER DERIVATIVES, J.GT.N
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
321 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
322 TOL = WDTOL/5.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
323 DO 250 J=2,MM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
324 T = T/X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
325 S = T
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
326 TOLS = T*TOL
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
327 DEN = X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
328 DO 230 I=1,NN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
329 DEN = DEN + 1.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
330 TRM(I) = TRM(I)/DEN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
331 S = S + TRM(I)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
332 IF (TRM(I).LT.TOLS) GO TO 240
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
333 230 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
334 240 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
335 ANS(J) = S
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
336 250 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
337 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
338 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
339 C SMALL X.LT.UNIT ROUND OFF
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
340 C-----------------------------------------------------------------------
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
341 260 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
342 ANS(1) = X**(-N-1)
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
343 IF (MM.EQ.1) GO TO 280
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
344 K = 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
345 DO 270 I=2,MM
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
346 ANS(K+1) = ANS(K)/X
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
347 K = K + 1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
348 270 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
349 280 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
350 IF (N.NE.0) RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
351 IF (KODE.EQ.2) ANS(1) = ANS(1) + XLN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
352 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
353 290 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
354 IF (T.GT.0.0E0) GO TO 380
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
355 NZ=0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
356 IERR=2
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
357 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
358 380 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
359 NZ=NZ+1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
360 ANS(MM)=0.0E0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
361 MM=MM-1
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
362 IF(MM.EQ.0) RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
363 GO TO 41
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
364 390 CONTINUE
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
365 IERR=3
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
366 NZ=0
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
367 RETURN
65e22ba879f0 psi: add support to compute the polygamma function (kth-derivative).
Carnë Draug <carandraug@octave.org>
parents:
diff changeset
368 END