Révision 162 pobysoPythonSage/src/pobyso.py
| pobyso.py (revision 162) | ||
|---|---|---|
| 99 | 99 |
""" |
| 100 | 100 |
Return a Sollya range from to 2 RealField Sage elements. |
| 101 | 101 |
The Sollya range element has a sufficient precision to hold all |
| 102 |
the digits of the Sage bounds. |
|
| 102 |
the digits of the widest of the Sage bounds.
|
|
| 103 | 103 |
""" |
| 104 | 104 |
# Sanity check. |
| 105 | 105 |
if rnLowerBoundSa > rnUpperBoundSa: |
| ... | ... | |
| 113 | 113 |
else: |
| 114 | 114 |
maxPrecSa = precisionSa |
| 115 | 115 |
# From Sage to Sollya bounds. |
| 116 |
lowerBoundSo = sollya_lib_constant(get_rn_value(rnLowerBoundSa), |
|
| 116 |
# lowerBoundSo = sollya_lib_constant(get_rn_value(rnLowerBoundSa), |
|
| 117 |
# maxPrecSa) |
|
| 118 |
lowerBoundSo = pobyso_constant_sa_so(rnLowerBoundSa, |
|
| 119 |
maxPrecSa) |
|
| 120 |
upperBoundSo = pobyso_constant_sa_so(rnUpperBoundSa, |
|
| 117 | 121 |
maxPrecSa) |
| 118 |
upperBoundSo = sollya_lib_constant(get_rn_value(rnUpperBoundSa), |
|
| 119 |
maxPrecSa) |
|
| 122 |
|
|
| 120 | 123 |
# From Sollya bounds to range. |
| 121 | 124 |
rangeSo = sollya_lib_range(lowerBoundSo, upperBoundSo) |
| 122 | 125 |
# Back to original precision. |
| ... | ... | |
| 798 | 801 |
else: |
| 799 | 802 |
degreeBoundSo = None |
| 800 | 803 |
guessedDegreeSa = pobyso_guess_degree_so_sa(functionSo, |
| 801 |
rangeSo, |
|
| 802 |
approxErrorSo, |
|
| 803 |
weightSo, |
|
| 804 |
degreeBoundSo) |
|
| 804 |
rangeSo,
|
|
| 805 |
approxErrorSo,
|
|
| 806 |
weightSo,
|
|
| 807 |
degreeBoundSo)
|
|
| 805 | 808 |
sollya_lib_clear_obj(functionSo) |
| 806 | 809 |
sollya_lib_clear_obj(rangeSo) |
| 807 | 810 |
sollya_lib_clear_obj(approxErrorSo) |
| ... | ... | |
| 831 | 834 |
if neededPrecisionSa > currentPrecSa: |
| 832 | 835 |
currentPrecSo = pobyso_get_prec_so() |
| 833 | 836 |
pobyso_set_prec_sa_so(neededPrecisionSa) |
| 837 |
print "Guessing degree..." |
|
| 834 | 838 |
# weightSo and degreeBoundsSo are optional arguments. |
| 839 |
# As declared, sollya_lib_guessdegree must take 5 arguments. |
|
| 835 | 840 |
if weightSo is None: |
| 836 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, None) |
|
| 841 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, |
|
| 842 |
0, 0, None) |
|
| 837 | 843 |
elif degreeBoundSo is None: |
| 838 | 844 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, \ |
| 839 |
errorSo, weightSo, None) |
|
| 845 |
errorSo, weightSo, 0, None)
|
|
| 840 | 846 |
else: |
| 841 | 847 |
degreeRangeSo = sollya_lib_guessdegree(functionSo, rangeSo, errorSo, \ |
| 842 | 848 |
weightSo, degreeBoundSo, None) |
| 849 |
print "Degree guess done." |
|
| 843 | 850 |
# Restore internal precision, if applicable. |
| 844 | 851 |
if neededPrecisionSa > currentPrecSa: |
| 845 | 852 |
pobyso_set_prec_so_so(currentPrecSo) |
| ... | ... | |
| 1117 | 1124 |
return resultSo |
| 1118 | 1125 |
# End pobyso_supnorm_so_so |
| 1119 | 1126 |
|
| 1120 |
def pobyso_taylor_expansion_with_change_var_so_so(functionSo, degreeSo, \ |
|
| 1121 |
rangeSo, \ |
|
| 1122 |
errorTypeSo=None, \ |
|
| 1123 |
sollyaPrecSo=None): |
|
| 1127 |
def pobyso_taylor_expansion_no_change_var_so_so(functionSo, |
|
| 1128 |
degreeSo, |
|
| 1129 |
rangeSo, |
|
| 1130 |
errorTypeSo=None, |
|
| 1131 |
sollyaPrecSo=None): |
|
| 1124 | 1132 |
""" |
| 1125 |
Compute the Taylor expansion with the variable change |
|
| 1126 |
x -> (x-intervalCenter) included.
|
|
| 1133 |
Compute the Taylor expansion without the variable change
|
|
| 1134 |
x -> x-intervalCenter.
|
|
| 1127 | 1135 |
""" |
| 1128 | 1136 |
# No global change of the working precision. |
| 1129 | 1137 |
if not sollyaPrecSo is None: |
| 1130 | 1138 |
initialPrecSo = sollya_lib_get_prec(None) |
| 1131 | 1139 |
sollya_lib_set_prec(sollyaPrecSo) |
| 1132 |
# |
|
| 1133 | 1140 |
# Error type stuff: default to absolute. |
| 1134 | 1141 |
if errorTypeSo is None: |
| 1135 | 1142 |
errorTypeIsNone = True |
| 1136 | 1143 |
errorTypeSo = sollya_lib_absolute(None) |
| 1137 | 1144 |
else: |
| 1138 | 1145 |
errorTypeIsNone = False |
| 1139 |
intervalCenterSo = sollya_lib_mid(rangeSo) |
|
| 1140 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, \
|
|
| 1141 |
intervalCenterSo, \
|
|
| 1146 |
intervalCenterSo = sollya_lib_mid(rangeSo, None)
|
|
| 1147 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, |
|
| 1148 |
intervalCenterSo, |
|
| 1142 | 1149 |
rangeSo, errorTypeSo, None) |
| 1143 | 1150 |
# taylorFormListSaSo is a Python list of Sollya objects references that |
| 1144 | 1151 |
# are copies of the elements of taylorFormSo. |
| 1145 | 1152 |
# pobyso_get_list_elements_so_so clears taylorFormSo. |
| 1146 |
(taylorFormListSo, numElements, isEndElliptic) = \
|
|
| 1153 |
(taylorFormListSaSo, numElementsSa, isEndEllipticSa) = \
|
|
| 1147 | 1154 |
pobyso_get_list_elements_so_so(taylorFormSo) |
| 1148 |
polySo = taylorFormListSo[0] |
|
| 1149 |
errorRangeSo = taylorFormListSo[2] |
|
| 1155 |
polySo = sollya_lib_copy_obj(taylorFormListSaSo[0]) |
|
| 1156 |
#print "Num elements:", numElementsSa |
|
| 1157 |
sollya_lib_clear_obj(taylorFormSo) |
|
| 1158 |
#polySo = taylorFormListSaSo[0] |
|
| 1159 |
#errorRangeSo = sollya_lib_copy_obj(taylorFormListSaSo[2]) |
|
| 1160 |
errorRangeSo = taylorFormListSaSo[2] |
|
| 1161 |
# No copy_obj needed here: a new object is created. |
|
| 1150 | 1162 |
maxErrorSo = sollya_lib_sup(errorRangeSo) |
| 1151 |
changeVarExpSo = sollya_lib_build_function_sub(\ |
|
| 1152 |
sollya_lib_build_function_free_variable(),\ |
|
| 1153 |
sollya_lib_copy_obj(intervalCenterSo)) |
|
| 1154 |
polyVarChangedSo = sollya_lib_evaluate(polySo, changeVarExpSo) |
|
| 1155 |
sollya_lib_clear_obj(changeVarExpSo) |
|
| 1156 | 1163 |
# If changed, reset the Sollya working precision. |
| 1157 | 1164 |
if not sollyaPrecSo is None: |
| 1158 | 1165 |
sollya_lib_set_prec(initialPrecSo) |
| 1159 | 1166 |
sollya_lib_clear_obj(initialPrecSo) |
| 1160 | 1167 |
if errorTypeIsNone: |
| 1161 | 1168 |
sollya_lib_clear_obj(errorTypeSo) |
| 1162 |
sollya_lib_clear_obj(taylorFormSo) |
|
| 1163 |
# Do not clear maxErrorSo. |
|
| 1164 |
return((polyVarChangedSo, intervalCenterSo, maxErrorSo)) |
|
| 1165 |
# end pobyso_taylor_expansion_with_change_var_so_so |
|
| 1169 |
pobyso_clear_taylorform_sa_so(taylorFormListSaSo) |
|
| 1170 |
return((polySo, intervalCenterSo, maxErrorSo)) |
|
| 1171 |
# end pobyso_taylor_expansion_no_change_var_so_so |
|
| 1166 | 1172 |
|
| 1167 |
def pobyso_taylor_expansion_no_change_var_so_so(functionSo, degreeSo, rangeSo, |
|
| 1168 |
errorTypeSo=None, |
|
| 1169 |
sollyaPrecSo=None): |
|
| 1173 |
def pobyso_taylor_expansion_with_change_var_so_so(functionSo, degreeSo, \ |
|
| 1174 |
rangeSo, \ |
|
| 1175 |
errorTypeSo=None, \ |
|
| 1176 |
sollyaPrecSo=None): |
|
| 1170 | 1177 |
""" |
| 1171 |
Compute the Taylor expansion without the variable change
|
|
| 1172 |
x -> x-intervalCenter.
|
|
| 1178 |
Compute the Taylor expansion with the variable change |
|
| 1179 |
x -> (x-intervalCenter) included.
|
|
| 1173 | 1180 |
""" |
| 1174 | 1181 |
# No global change of the working precision. |
| 1175 | 1182 |
if not sollyaPrecSo is None: |
| 1176 | 1183 |
initialPrecSo = sollya_lib_get_prec(None) |
| 1177 | 1184 |
sollya_lib_set_prec(sollyaPrecSo) |
| 1185 |
# |
|
| 1178 | 1186 |
# Error type stuff: default to absolute. |
| 1179 | 1187 |
if errorTypeSo is None: |
| 1180 | 1188 |
errorTypeIsNone = True |
| 1181 | 1189 |
errorTypeSo = sollya_lib_absolute(None) |
| 1182 | 1190 |
else: |
| 1183 | 1191 |
errorTypeIsNone = False |
| 1184 |
intervalCenterSo = sollya_lib_mid(rangeSo, None)
|
|
| 1185 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, |
|
| 1186 |
intervalCenterSo, |
|
| 1192 |
intervalCenterSo = sollya_lib_mid(rangeSo) |
|
| 1193 |
taylorFormSo = sollya_lib_taylorform(functionSo, degreeSo, \
|
|
| 1194 |
intervalCenterSo, \
|
|
| 1187 | 1195 |
rangeSo, errorTypeSo, None) |
| 1188 | 1196 |
# taylorFormListSaSo is a Python list of Sollya objects references that |
| 1189 | 1197 |
# are copies of the elements of taylorFormSo. |
| 1190 | 1198 |
# pobyso_get_list_elements_so_so clears taylorFormSo. |
| 1191 |
(taylorFormListSaSo, numElementsSa, isEndEllipticSa) = \
|
|
| 1199 |
(taylorFormListSo, numElements, isEndElliptic) = \
|
|
| 1192 | 1200 |
pobyso_get_list_elements_so_so(taylorFormSo) |
| 1193 |
polySo = sollya_lib_copy_obj(taylorFormListSaSo[0]) |
|
| 1194 |
#print "Num elements:", numElementsSa |
|
| 1195 |
sollya_lib_clear_obj(taylorFormSo) |
|
| 1196 |
#polySo = taylorFormListSaSo[0] |
|
| 1197 |
#errorRangeSo = sollya_lib_copy_obj(taylorFormListSaSo[2]) |
|
| 1198 |
errorRangeSo = taylorFormListSaSo[2] |
|
| 1199 |
# No copy_obj needed here: a new object is created. |
|
| 1201 |
polySo = taylorFormListSo[0] |
|
| 1202 |
errorRangeSo = taylorFormListSo[2] |
|
| 1200 | 1203 |
maxErrorSo = sollya_lib_sup(errorRangeSo) |
| 1204 |
changeVarExpSo = sollya_lib_build_function_sub(\ |
|
| 1205 |
sollya_lib_build_function_free_variable(),\ |
|
| 1206 |
sollya_lib_copy_obj(intervalCenterSo)) |
|
| 1207 |
polyVarChangedSo = sollya_lib_evaluate(polySo, changeVarExpSo) |
|
| 1208 |
sollya_lib_clear_obj(changeVarExpSo) |
|
| 1201 | 1209 |
# If changed, reset the Sollya working precision. |
| 1202 | 1210 |
if not sollyaPrecSo is None: |
| 1203 | 1211 |
sollya_lib_set_prec(initialPrecSo) |
| 1204 | 1212 |
sollya_lib_clear_obj(initialPrecSo) |
| 1205 | 1213 |
if errorTypeIsNone: |
| 1206 | 1214 |
sollya_lib_clear_obj(errorTypeSo) |
| 1207 |
pobyso_clear_taylorform_sa_so(taylorFormListSaSo) |
|
| 1208 |
return((polySo, intervalCenterSo, maxErrorSo)) |
|
| 1209 |
# end pobyso_taylor_expansion_no_change_var_so_so |
|
| 1215 |
sollya_lib_clear_obj(taylorFormSo) |
|
| 1216 |
# Do not clear maxErrorSo. |
|
| 1217 |
return((polyVarChangedSo, intervalCenterSo, maxErrorSo)) |
|
| 1218 |
# end pobyso_taylor_expansion_with_change_var_so_so |
|
| 1210 | 1219 |
|
| 1211 | 1220 |
def pobyso_taylor(function, degree, point): |
| 1212 | 1221 |
""" Legacy function. See pobysoTaylor_so_so. """ |
Formats disponibles : Unified diff