D2 match with wolfram alpha

tests/mpmath_input_arguments.py

@@ -2,20 +2,20 @@ import mpmath as mp
 import numpy as np
 complex_arguments = [
     # // x, [Re(m), Im(m)], Qext, Qsca, test_name
+    [10000, [1.33,-1e-5], 2.004089, 1.723857, 'f'],
+    [10000, [1.5, -1],    2.004368, 1.236574, 'j'],
+    [10000, [10,  -10],   2.005914, 1.795393, 'm'],
+    [80, [1.05,  1],   0, 0, 'Yang'],
     [0.099, [0.75,0], 7.417859e-06, 7.417859e-06, 'a'],
     [0.101, [0.75,0], 8.033538e-06, 8.033538e-06, 'b'],
     [10,    [0.75,0],     2.232265, 2.232265, 'c'],
     [1000,  [0.75,0],     1.997908, 1.997908, 'd'],
     [100,   [1.33,-1e-5], 2.101321, 2.096594, 'e'],
-    [10000, [1.33,-1e-5], 2.004089, 1.723857, 'f'],
     [0.055, [1.5, -1],    0.101491, 1.131687e-05, 'g'],
     [0.056, [1.5, -1],   0.1033467, 1.216311e-05, 'h'],
     [100,   [1.5, -1],    2.097502, 1.283697, 'i'],
-    [10000, [1.5, -1],    2.004368, 1.236574, 'j'],
     [1,     [10,  -10],   2.532993, 2.049405, 'k'],
     [100,   [10,  -10,],  2.071124, 1.836785, 'l'],
-    [10000, [10,  -10],   2.005914, 1.795393, 'm'],
-    [80, [1.05,  1],   0, 0, 'Yang'],
     [1, [mp.pi,  1],   0, 0, 'pi'],
     [1, [mp.pi,  -1],   0, 0, 'pi'],
     [1, [mp.pi,  mp.pi],   0, 0, 'pi'],

tests/mpmath_riccati_bessel.py

@@ -8,10 +8,23 @@ def LeRu_cutoff(z):
     return int(x + 11 * x**(1/3) + 1)
 
 
+# Wu, Wang, Radio Science, Volume 26, Number 6, Pages 1393-1401, November-December 1991,
+# after eq 13f.
 # Riccati-Bessel z*j_n(z)
 def psi(n,z):
     return mp.sqrt( (mp.pi * z)/2 ) * mp.autoprec(mp.besselj)(n+1/2,z)
+# Riccati-Bessel -z*y_n(z)
+def xi(n,z):
+    return -mp.sqrt( (mp.pi * z)/2 ) * mp.autoprec(mp.bessely)(n+1/2,z)
+# Riccati-Bessel psi - i* xi
+def ksi(n,z):
+    return psi(n,z) - 1.j * xi(n,z)
 
+def psi_div_ksi(n,z):
+    return psi(n,z)/ksi(n,z)
+
+def psi_div_xi(n,z):
+    return psi(n,z)/xi(n,z)
 
 # to compare r(n,z) with Wolfram Alpha
 # n=49, z=1.3-2.1i,  SphericalBesselJ[n-1,z]/SphericalBesselJ[n,z]
@@ -21,5 +34,18 @@ def r(n,z):
     return mp.cos(z)/mp.sin(z)
 
 
+def D(n, z, f):
+    return f(n-1,z)/f(n,z) - n/z
+
 def D1(n,z):
-    return r(n,z) - n/z
+    if n == 0: return mp.cos(z)/mp.sin(z)
+    return D(n, z, psi)
+
+# Wolfram Alpha example D2(10, 10-10j): SphericalBesselY[9, 10-10i]/SphericalBesselY[10,10-10i]-10/(10-10i)
+def D2(n,z):
+    if n == 0: return -mp.sin(z)/mp.cos(z)
+    return D(n, z, xi)
+
+def D3(n,z):
+    if n == 0: return 1j
+    return D(n, z, ksi)

tests/mpmath_special_functions_test_generator.py

@@ -15,7 +15,6 @@ class TestData:
 
     def cpp_parse(self, list_to_parse):
         self.comment = list_to_parse[0]
-        print(self.comment)
         if self.comment[:2] != '//': raise ValueError('Not a comment')
         self.typeline = list_to_parse[1]
         if 'std::vector' not in self.typeline: raise ValueError('Unexpected C++ container')
@@ -112,7 +111,7 @@ class UpdateSpecialFunctionsEvaluations:
         return z_str
 
     def get_test_data(self, Du_test, output_dps, max_num_elements_of_n_list, func, funcname):
-        output_list = ['// complex(z), n, complex(D1(n,z)), abs_err_real, abs_err_imag',
+        output_list = ['// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag',
         'std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >',
         str(funcname)+'_test_' + str(output_dps) + 'digits','= {']
         for z_record in Du_test:
@@ -122,7 +121,9 @@ class UpdateSpecialFunctionsEvaluations:
             mp.mp.dps = 20
             z = mp.mpf(x) * mp.mpc(mr, mi)
             n_list = self.get_n_list(z, max_num_elements_of_n_list)
+            if z_record[4] == 'Yang': n_list = [0,1,30,50,60,70,75,80,85,90,99,116,130]
             print(z, n_list)
+            failed_evaluations = 0
             for n in n_list:
                 mp.mp.dps = 20
                 old_z_string = self.get_test_data_nlist(z_record, output_dps, n, func)
@@ -139,7 +140,9 @@ class UpdateSpecialFunctionsEvaluations:
                 if new_z_string != '':
                     output_list.append(new_z_string)
                 else:
-                    break
+                    failed_evaluations += 1
+                #     break
+            print("\nFailed evaluations ", failed_evaluations, ' of ', len(n_list))
         output_list.append('};')
         return output_list
 
@@ -156,8 +159,12 @@ def main():
     sf_evals = UpdateSpecialFunctionsEvaluations(filename='test_spec_functions_data.hpp',
                                                  complex_arguments=mia.complex_arguments,
                                                  output_dps=16, max_num_elements_of_nlist=51)
-                                                 # output_dps=3, max_num_elements_of_nlist=3)
+                                                 # output_dps=5, max_num_elements_of_nlist=3)
     # sf_evals.run_test(mrb.D1, 'D1')
+    sf_evals.run_test(mrb.D2, 'D2')
+    # sf_evals.run_test(mrb.D3, 'D3')
+    # sf_evals.run_test(mrb.psi_div_ksi, 'psi_div_ksi')
+    # sf_evals.run_test(mrb.psi_div_xi, 'psi_div_xi')
     with open(sf_evals.filename, 'w') as out_file:
         out_file.write(sf_evals.get_file_content())
 

tests/test_spec_functions_data.hpp

@@ -565,3 +565,532 @@ D1_test_16digits
 {{3.141592653589793,0.0},18,{5.966831036716779,0.0},6.0e-16,0.0},
 {{3.141592653589793,0.0},20,{6.611070983143533,0.0},6.6e-16,0.0},
 };
+
+// complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
+std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
+D2_test_16digits
+= {
+{{0.07425,0.0},0,{-0.07438674986902373,0.0},7.4e-18,0.0},
+{{0.07425,0.0},1,{-13.39417131419206,0.0},1.3e-15,0.0},
+{{0.07425,0.0},2,{-26.91123162027382,0.0},2.7e-15,0.0},
+{{0.07425,0.0},3,{-40.3891849341013,0.0},4.0e-15,0.0},
+{{0.07425,0.0},4,{-53.86144505752241,0.0},5.4e-15,0.0},
+{{0.07575,0.0},0,{-0.07589521939842851,0.0},7.6e-18,0.0},
+{{0.07575,0.0},1,{-13.12600313416894,0.0},1.3e-15,0.0},
+{{0.07575,0.0},2,{-26.37734215323807,0.0},2.6e-15,0.0},
+{{0.07575,0.0},3,{-39.58880458732769,0.0},4.0e-15,0.0},
+{{0.07575,0.0},4,{-52.79445732439479,0.0},5.3e-15,0.0},
+{{7.5,0.0},0,{-2.706013866772691,0.0},2.7e-16,0.0},
+{{7.5,0.0},1,{0.2188602976402436,0.0},2.2e-17,0.0},
+{{7.5,0.0},2,{20.65104828146692,0.0},2.1e-15,0.0},
+{{7.5,0.0},3,{-0.4493801597873413,0.0},4.5e-17,0.0},
+{{7.5,0.0},4,{0.4842572533435941,0.0},4.8e-17,0.0},
+{{7.5,0.0},5,{4.81550654897139,0.0},4.8e-16,0.0},
+{{7.5,0.0},6,{-1.049034583259778,0.0},1.0e-16,0.0},
+{{7.5,0.0},7,{-0.4288861055358842,0.0},4.3e-17,0.0},
+{{7.5,0.0},8,{-0.3980175767871659,0.0},4.0e-17,0.0},
+{{7.5,0.0},9,{-0.5742246552691164,0.0},5.7e-17,0.0},
+{{7.5,0.0},10,{-0.809102874298828,0.0},8.1e-17,0.0},
+{{7.5,0.0},11,{-1.027254862439886,0.0},1.0e-16,0.0},
+{{7.5,0.0},12,{-1.219374574466933,0.0},1.2e-16,0.0},
+{{7.5,0.0},13,{-1.39466116147432,0.0},1.4e-16,0.0},
+{{7.5,0.0},14,{-1.560043091026306,0.0},1.6e-16,0.0},
+{{7.5,0.0},16,{-1.873757439540259,0.0},1.9e-16,0.0},
+{{7.5,0.0},17,{-2.025145514642434,0.0},2.0e-16,0.0},
+{{7.5,0.0},18,{-2.174018730753354,0.0},2.2e-16,0.0},
+{{7.5,0.0},19,{-2.320899679256512,0.0},2.3e-16,0.0},
+{{7.5,0.0},21,{-2.610108605596247,0.0},2.6e-16,0.0},
+{{7.5,0.0},22,{-2.752939994498599,0.0},2.8e-16,0.0},
+{{7.5,0.0},24,{-3.035926615655057,0.0},3.0e-16,0.0},
+{{7.5,0.0},26,{-3.316132176384959,0.0},3.3e-16,0.0},
+{{7.5,0.0},27,{-3.455410513492717,0.0},3.5e-16,0.0},
+{{7.5,0.0},30,{-3.870677968225079,0.0},3.9e-16,0.0},
+{{750.0,0.0},0,{1.117079400838733,0.0},1.1e-16,0.0},
+{{750.0,0.0},1,{-0.8975946145725433,0.0},9.0e-17,0.0},
+{{750.0,0.0},2,{1.108121968632076,0.0},1.1e-16,0.0},
+{{750.0,0.0},3,{-0.9096970410967588,0.0},9.1e-17,0.0},
+{{750.0,0.0},4,{1.087526562845337,0.0},1.1e-16,0.0},
+{{750.0,0.0},5,{-0.9318559567267879,0.0},9.3e-17,0.0},
+{{750.0,0.0},6,{1.055992830861736,0.0},1.1e-16,0.0},
+{{750.0,0.0},7,{-0.9647538902206642,0.0},9.6e-17,0.0},
+{{750.0,0.0},9,{-1.009474246275747,0.0},1.0e-16,0.0},
+{{750.0,0.0},10,{0.9643676731279237,0.0},9.6e-17,0.0},
+{{750.0,0.0},11,{-1.067629644695052,0.0},1.1e-16,0.0},
+{{750.0,0.0},13,{-1.141571574212259,0.0},1.1e-16,0.0},
+{{750.0,0.0},15,{-1.234734314089206,0.0},1.2e-16,0.0},
+{{750.0,0.0},18,{0.7026309682530627,0.0},7.0e-17,0.0},
+{{750.0,0.0},20,{0.6275884453721258,0.0},6.3e-17,0.0},
+{{750.0,0.0},23,{-1.95499529719246,0.0},2.0e-16,0.0},
+{{750.0,0.0},27,{-2.856016621139734,0.0},2.9e-16,0.0},
+{{750.0,0.0},31,{-5.515179542724612,0.0},5.5e-16,0.0},
+{{750.0,0.0},35,{-2046.667830368851,0.0},2.0e-13,0.0},
+{{750.0,0.0},41,{3.142443680429311,0.0},3.1e-16,0.0},
+{{750.0,0.0},47,{1.275705385420439,0.0},1.3e-16,0.0},
+{{750.0,0.0},54,{-2.171423411849925,0.0},2.2e-16,0.0},
+{{750.0,0.0},62,{5.070303280958446,0.0},5.1e-16,0.0},
+{{750.0,0.0},71,{-1.547407386670151,0.0},1.5e-16,0.0},
+{{750.0,0.0},81,{2.057198576589978,0.0},2.1e-16,0.0},
+{{750.0,0.0},93,{-0.2880574210963995,0.0},2.9e-17,0.0},
+{{750.0,0.0},107,{1.467167039386753,0.0},1.5e-16,0.0},
+{{750.0,0.0},123,{-13.25668132285312,0.0},1.3e-15,0.0},
+{{750.0,0.0},141,{-51.66788150986426,0.0},5.2e-15,0.0},
+{{750.0,0.0},162,{-2.044123043949385,0.0},2.0e-16,0.0},
+{{750.0,0.0},186,{-0.5017806375070012,0.0},5.0e-17,0.0},
+{{750.0,0.0},214,{4.680543422413898,0.0},4.7e-16,0.0},
+{{750.0,0.0},246,{0.9652329906986826,0.0},9.7e-17,0.0},
+{{750.0,0.0},282,{0.3764839152874788,0.0},3.8e-17,0.0},
+{{750.0,0.0},324,{-5.441038845652591,0.0},5.4e-16,0.0},
+{{750.0,0.0},372,{0.5017189777039316,0.0},5.0e-17,0.0},
+{{750.0,0.0},427,{-0.5396391858059278,0.0},5.4e-17,0.0},
+{{750.0,0.0},490,{0.2475300359343486,0.0},2.5e-17,0.0},
+{{750.0,0.0},562,{0.6550877387674529,0.0},6.6e-17,0.0},
+{{750.0,0.0},645,{-0.0647479220258492,0.0},6.5e-18,0.0},
+{{750.0,0.0},740,{0.9500952443721748,0.0},9.5e-17,0.0},
+{{750.0,0.0},850,{-0.5317183378262854,0.0},5.3e-17,0.0},
+{{133.0,-0.001},0,{-1.755932485461304,0.004083310122507825},1.8e-16,4.1e-19},
+{{133.0,-0.001},1,{0.5595479819348692,0.001312980852946314},5.6e-17,1.3e-19},
+{{133.0,-0.001},2,{-1.85153917185983,0.004427871815312255},1.9e-16,4.4e-19},
+{{133.0,-0.001},3,{0.5110313502646276,0.001260474562555223},5.1e-17,1.3e-19},
+{{133.0,-0.001},4,{-2.109252486188721,0.005447837827720917},2.1e-16,5.4e-19},
+{{133.0,-0.001},5,{0.4282025099144422,0.001181661243690889},4.3e-17,1.2e-19},
+{{133.0,-0.001},6,{-2.655442472579592,0.00804905444898751},2.7e-16,8.0e-19},
+{{133.0,-0.001},7,{0.316631280080747,0.001097089303706201},3.2e-17,1.1e-19},
+{{133.0,-0.001},8,{-3.959004842334986,0.01666990476526257},4.0e-16,1.7e-18},
+{{133.0,-0.001},9,{0.1806704887948465,0.001027553610539269},1.8e-17,1.0e-19},
+{{133.0,-0.001},10,{-9.554533249350271,0.09229128245066224},9.6e-16,9.2e-18},
+{{133.0,-0.001},11,{0.02104786595968763,0.0009929804198924497},2.1e-18,9.9e-20},
+{{133.0,-0.001},13,{-0.1678332578687873,0.00101787881523943},1.7e-17,1.0e-19},
+{{133.0,-0.001},14,{3.556396506011055,0.01363625230438085},3.6e-16,1.4e-18},
+{{133.0,-0.001},16,{1.790016651664875,0.00418879487195259},1.8e-16,4.2e-19},
+{{133.0,-0.001},18,{1.021038366775945,0.002023186744680601},1.0e-16,2.0e-19},
+{{133.0,-0.001},20,{0.5479729709732455,0.001276530775240961},5.5e-17,1.3e-19},
+{{133.0,-0.001},22,{0.1809795706420653,0.001004147964731335},1.8e-17,1.0e-19},
+{{133.0,-0.001},24,{-0.1724263550949475,0.000995811171991787},1.7e-17,1.0e-19},
+{{133.0,-0.001},27,{1.021452430742276,0.002000628091838396},1.0e-16,2.0e-19},
+{{133.0,-0.001},30,{-6.547396546792233,0.04381769113586676},6.5e-16,4.4e-18},
+{{133.0,-0.001},34,{0.8656406474529488,0.001682061020627086},8.7e-17,1.7e-19},
+{{133.0,-0.001},38,{-0.3838684285342646,0.001063573921879943},3.8e-17,1.1e-19},
+{{133.0,-0.001},42,{19.71892539138212,0.3898854651258534},2.0e-15,3.9e-17},
+{{133.0,-0.001},47,{4.536308169130143,0.02145099010357844},4.5e-16,2.1e-18},
+{{133.0,-0.001},52,{1.466938589766846,0.002996111386699881},1.5e-16,3.0e-19},
+{{133.0,-0.001},58,{485.6616787894604,618.8805818920891},4.9e-14,6.2e-14},
+{{133.0,-0.001},65,{-0.2272687651498732,0.0008091273274344002},2.3e-17,8.1e-20},
+{{133.0,-0.001},72,{0.622303863806427,0.001090128451858948},6.2e-17,1.1e-19},
+{{133.0,-0.001},80,{-1.656082363658833,0.003376287990811771},1.7e-16,3.4e-19},
+{{133.0,-0.001},89,{0.3916329094110811,0.0007005525248592523},3.9e-17,7.0e-20},
+{{133.0,-0.001},99,{-1.421092555792892,0.002459838815433856},1.4e-16,2.5e-19},
+{{133.0,-0.001},111,{0.2415850593901129,0.0003555536690688075},2.4e-17,3.6e-20},
+{{133.0,-0.001},123,{-0.02936353008964981,0.0001386314460729032},2.9e-18,1.4e-20},
+{{133.0,-0.001},137,{-0.2015744636220535,-2.816755428233205e-5},2.0e-17,2.8e-21},
+{{133.0,-0.001},153,{-0.5603119660277999,-1.806474698095854e-5},5.6e-17,1.8e-21},
+{{133.0,-0.001},170,{-0.7923542900597165,-1.556887877560696e-5},7.9e-17,1.6e-21},
+{{133.0,-0.001},190,{-1.018068108577178,-1.509479127100921e-5},1.0e-16,1.5e-21},
+{{13300.0,-0.1},0,{4.614747555432858,6.903177205927318},4.6e-16,6.9e-16},
+{{13300.0,-0.1},1,{-0.06700391181106944,0.1001199654937619},6.7e-18,1.0e-17},
+{{13300.0,-0.1},2,{4.620439133200172,6.888811904783909},4.6e-16,6.9e-16},
+{{13300.0,-0.1},3,{-0.06737777840760444,0.1001250179841278},6.7e-18,1.0e-17},
+{{13300.0,-0.1},4,{4.633500440086391,6.855341200224173},4.6e-16,6.9e-16},
+{{13300.0,-0.1},5,{-0.06805078507601441,0.1001341840454214},6.8e-18,1.0e-17},
+{{13300.0,-0.1},6,{4.653411812962385,6.802886700800537},4.7e-16,6.8e-16},
+{{13300.0,-0.1},8,{4.67937396079206,6.731654983192257},4.7e-16,6.7e-16},
+{{13300.0,-0.1},10,{4.710331246539195,6.641956515928427},4.7e-16,6.6e-16},
+{{13300.0,-0.1},12,{4.745003601522665,6.534228448806732},4.7e-16,6.5e-16},
+{{13300.0,-0.1},15,{-0.07590717256243298,0.1002479325549111},7.6e-18,1.0e-17},
+{{13300.0,-0.1},18,{4.856045166555225,6.109630111782805},4.9e-16,6.1e-16},
+{{13300.0,-0.1},22,{4.919273005297511,5.752106274215477},4.9e-16,5.8e-16},
+{{13300.0,-0.1},27,{-0.09525261713282836,0.1005810209670254},9.5e-18,1.0e-17},
+{{13300.0,-0.1},32,{4.952248503162073,4.686287618645416},5.0e-16,4.7e-16},
+{{13300.0,-0.1},40,{4.797687411598633,3.78137609812792},4.8e-16,3.8e-16},
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